{
  "openapi": "3.1.0",
  "info": {
    "title": "Easing Wizard API",
    "description": "API for generating CSS easing curves of types like Bézier, Spring, Bounce, Wiggle, and Overshoot.",
    "version": "1.0.0",
    "contact": {
      "name": "Matthias Martin",
      "url": "https://x.com/RoyDigerhund"
    }
  },
  "servers": [
    {
      "url": "https://api.easingwizard.com/v1"
    }
  ],
  "tags": [
    {
      "name": "Curves",
      "description": "Endpoints for managing easing curves"
    },
    {
      "name": "Health",
      "description": "Health check endpoint"
    }
  ],
  "paths": {
    "/presets": {
      "get": {
        "operationId": "getPresets",
        "summary": "Get Preset Easing Curves",
        "description": "Retrieve available preset easing curves, optionally filtered by type.",
        "tags": [
          "Curves"
        ],
        "parameters": [
          {
            "in": "query",
            "name": "type",
            "schema": {
              "title": "Easing Type",
              "description": "Type of easing function",
              "example": "BEZIER",
              "type": "string",
              "enum": [
                "BEZIER",
                "SPRING",
                "BOUNCE",
                "WIGGLE",
                "OVERSHOOT"
              ]
            }
          }
        ],
        "responses": {
          "200": {
            "description": "200 OK",
            "content": {
              "application/json": {
                "schema": {
                  "title": "Presets Response",
                  "description": "Collection of preset easing curves",
                  "type": "object",
                  "properties": {
                    "version": {
                      "description": "Version hash of the presets data",
                      "example": "a1b2c3d4",
                      "type": "string"
                    },
                    "presets": {
                      "description": "Array of all easing presets",
                      "type": "array",
                      "items": {
                        "title": "Easing Presets",
                        "description": "Easing preset configuration",
                        "anyOf": [
                          {
                            "type": "object",
                            "properties": {
                              "id": {
                                "description": "The ID of the easing curve",
                                "example": "0a1b2c3xy",
                                "type": "string"
                              },
                              "type": {
                                "description": "Bézier easing type",
                                "type": "string",
                                "const": "BEZIER"
                              },
                              "style": {
                                "description": "Bézier easing style",
                                "example": "IN_OUT",
                                "type": "string",
                                "enum": [
                                  "IN",
                                  "OUT",
                                  "IN_OUT",
                                  "OUT_IN"
                                ]
                              },
                              "curve": {
                                "description": "Bézier curve variant",
                                "example": "CUBIC",
                                "type": "string",
                                "enum": [
                                  "SINE",
                                  "QUAD",
                                  "CUBIC",
                                  "QUART",
                                  "QUINT",
                                  "EXPO",
                                  "CIRC",
                                  "BACK",
                                  "JUMP",
                                  "ANTICIPATE"
                                ]
                              },
                              "params": {
                                "title": "Bézier Curve Parameters",
                                "description": "Parameters for a cubic Bézier curve",
                                "type": "object",
                                "properties": {
                                  "x1": {
                                    "description": "First control point X coordinate (0-1)",
                                    "example": 0.25,
                                    "type": "number",
                                    "minimum": 0,
                                    "maximum": 1
                                  },
                                  "y1": {
                                    "description": "First control point Y coordinate (-1 to 2)",
                                    "example": 0.1,
                                    "type": "number",
                                    "minimum": -1,
                                    "maximum": 2
                                  },
                                  "x2": {
                                    "description": "Second control point X coordinate (0-1)",
                                    "example": 0.75,
                                    "type": "number",
                                    "minimum": 0,
                                    "maximum": 1
                                  },
                                  "y2": {
                                    "description": "Second control point Y coordinate (-1 to 2)",
                                    "example": 0.9,
                                    "type": "number",
                                    "minimum": -1,
                                    "maximum": 2
                                  }
                                },
                                "required": [
                                  "x1",
                                  "y1",
                                  "x2",
                                  "y2"
                                ],
                                "additionalProperties": false
                              },
                              "output": {
                                "title": "Bézier Easing Output",
                                "description": "CSS and SVG output for Bézier easing functions",
                                "type": "object",
                                "properties": {
                                  "css": {
                                    "description": "CSS easing function string",
                                    "example": "cubic-bezier(0.66, 0, 0.34, 1)",
                                    "type": "string"
                                  },
                                  "tailwind_css": {
                                    "description": "Tailwind CSS compatible easing function string",
                                    "example": "ease-[cubic-bezier(0.66,0,0.34,1)]",
                                    "type": "string"
                                  },
                                  "svg_path": {
                                    "description": "SVG path for Bézier curves",
                                    "example": "M0,100 C66,100 34,0 100,0",
                                    "type": "string"
                                  }
                                },
                                "required": [
                                  "css",
                                  "tailwind_css",
                                  "svg_path"
                                ],
                                "additionalProperties": false
                              },
                              "links": {
                                "title": "Easing Curve Links Response",
                                "description": "HATEOAS navigation links for the easing curve",
                                "type": "object",
                                "properties": {
                                  "self": {
                                    "description": "Link to this curve resource",
                                    "example": "/curves/abc123def",
                                    "type": "string"
                                  },
                                  "share_url": {
                                    "description": "Shareable URL for this curve",
                                    "example": "https://easingwizard.com/#abc123def",
                                    "type": "string",
                                    "format": "uri"
                                  },
                                  "create": {
                                    "description": "Endpoint to create curves of this type",
                                    "example": "/curves/bezier",
                                    "type": "string"
                                  }
                                },
                                "required": [
                                  "self",
                                  "share_url",
                                  "create"
                                ],
                                "additionalProperties": false
                              }
                            },
                            "required": [
                              "id",
                              "type",
                              "style",
                              "curve",
                              "params",
                              "output",
                              "links"
                            ],
                            "additionalProperties": false
                          },
                          {
                            "type": "object",
                            "properties": {
                              "id": {
                                "description": "The ID of the easing curve",
                                "example": "0a1b2c3xy",
                                "type": "string"
                              },
                              "type": {
                                "description": "Spring easing type",
                                "type": "string",
                                "const": "SPRING"
                              },
                              "curve": {
                                "description": "Spring curve variant",
                                "example": "HEAVY",
                                "type": "string",
                                "enum": [
                                  "HEAVY",
                                  "BOUNCY",
                                  "DROP",
                                  "GLIDE",
                                  "SNAP",
                                  "LAZY",
                                  "ELASTIC"
                                ]
                              },
                              "params": {
                                "title": "Spring Animation Parameters",
                                "description": "Parameters for spring-based easing animations",
                                "type": "object",
                                "properties": {
                                  "mass": {
                                    "description": "Mass (1-5)",
                                    "example": 2.5,
                                    "type": "number",
                                    "minimum": 1,
                                    "maximum": 5
                                  },
                                  "stiffness": {
                                    "description": "Stiffness (0-100)",
                                    "example": 50,
                                    "type": "number",
                                    "minimum": 0,
                                    "maximum": 100
                                  },
                                  "damping": {
                                    "description": "Damping (0-100)",
                                    "example": 50,
                                    "type": "number",
                                    "minimum": 0,
                                    "maximum": 100
                                  },
                                  "accuracy": {
                                    "description": "Accuracy level for the linear easing approximation, HIGH is the best option for most cases.",
                                    "example": "HIGH",
                                    "type": "string",
                                    "enum": [
                                      "LOW",
                                      "MEDIUM",
                                      "HIGH",
                                      "ULTRA"
                                    ]
                                  }
                                },
                                "required": [
                                  "mass",
                                  "stiffness",
                                  "damping",
                                  "accuracy"
                                ],
                                "additionalProperties": false
                              },
                              "output": {
                                "title": "Linear Easing Output",
                                "description": "CSS and SVG output for linear easing functions",
                                "type": "object",
                                "properties": {
                                  "css": {
                                    "description": "CSS easing function string",
                                    "example": "cubic-bezier(0.66, 0, 0.34, 1)",
                                    "type": "string"
                                  },
                                  "tailwind_css": {
                                    "description": "Tailwind CSS compatible easing function string",
                                    "example": "ease-[cubic-bezier(0.66,0,0.34,1)]",
                                    "type": "string"
                                  },
                                  "svg_polyline": {
                                    "description": "SVG polyline for linear easing curves",
                                    "example": "0,75 15.2,39.6 32.8,21.75 50,18.45 100,25",
                                    "type": "string"
                                  },
                                  "suggested_duration_ms": {
                                    "description": "Suggested duration range derived from the curve physics. Shorter durations feel snappier, longer durations let complex motions (bounces, oscillations) breathe.",
                                    "type": "object",
                                    "properties": {
                                      "min": {
                                        "description": "Minimum suggested CSS animation/transition duration in milliseconds",
                                        "example": 300,
                                        "type": "integer",
                                        "exclusiveMinimum": 0,
                                        "maximum": 9007199254740991
                                      },
                                      "max": {
                                        "description": "Maximum suggested CSS animation/transition duration in milliseconds",
                                        "example": 600,
                                        "type": "integer",
                                        "exclusiveMinimum": 0,
                                        "maximum": 9007199254740991
                                      }
                                    },
                                    "required": [
                                      "min",
                                      "max"
                                    ],
                                    "additionalProperties": false
                                  }
                                },
                                "required": [
                                  "css",
                                  "tailwind_css",
                                  "svg_polyline",
                                  "suggested_duration_ms"
                                ],
                                "additionalProperties": false
                              },
                              "links": {
                                "title": "Easing Curve Links Response",
                                "description": "HATEOAS navigation links for the easing curve",
                                "type": "object",
                                "properties": {
                                  "self": {
                                    "description": "Link to this curve resource",
                                    "example": "/curves/abc123def",
                                    "type": "string"
                                  },
                                  "share_url": {
                                    "description": "Shareable URL for this curve",
                                    "example": "https://easingwizard.com/#abc123def",
                                    "type": "string",
                                    "format": "uri"
                                  },
                                  "create": {
                                    "description": "Endpoint to create curves of this type",
                                    "example": "/curves/bezier",
                                    "type": "string"
                                  }
                                },
                                "required": [
                                  "self",
                                  "share_url",
                                  "create"
                                ],
                                "additionalProperties": false
                              }
                            },
                            "required": [
                              "id",
                              "type",
                              "curve",
                              "params",
                              "output",
                              "links"
                            ],
                            "additionalProperties": false
                          },
                          {
                            "type": "object",
                            "properties": {
                              "id": {
                                "description": "The ID of the easing curve",
                                "example": "0a1b2c3xy",
                                "type": "string"
                              },
                              "type": {
                                "description": "Bounce easing type",
                                "type": "string",
                                "const": "BOUNCE"
                              },
                              "curve": {
                                "description": "Bounce curve variant",
                                "example": "FIRM",
                                "type": "string",
                                "enum": [
                                  "FIRM",
                                  "SOFT",
                                  "SHARP",
                                  "SUBTLE",
                                  "PLAYFUL",
                                  "SPRINGY"
                                ]
                              },
                              "params": {
                                "title": "Bounce Animation Parameters",
                                "description": "Parameters for bounce-based easing animations",
                                "type": "object",
                                "properties": {
                                  "bounces": {
                                    "description": "Number of bounces (1-10)",
                                    "example": 3,
                                    "type": "number",
                                    "minimum": 1,
                                    "maximum": 10
                                  },
                                  "mass": {
                                    "default": 1,
                                    "description": "Mass (1-5)",
                                    "example": 2.5,
                                    "type": "number",
                                    "minimum": 1,
                                    "maximum": 5
                                  },
                                  "damping": {
                                    "description": "Damping (0-100)",
                                    "example": 50,
                                    "type": "number",
                                    "minimum": 0,
                                    "maximum": 100
                                  },
                                  "accuracy": {
                                    "description": "Accuracy level for the linear easing approximation, HIGH is the best option for most cases.",
                                    "example": "HIGH",
                                    "type": "string",
                                    "enum": [
                                      "LOW",
                                      "MEDIUM",
                                      "HIGH",
                                      "ULTRA"
                                    ]
                                  }
                                },
                                "required": [
                                  "bounces",
                                  "mass",
                                  "damping",
                                  "accuracy"
                                ],
                                "additionalProperties": false
                              },
                              "output": {
                                "title": "Linear Easing Output",
                                "description": "CSS and SVG output for linear easing functions",
                                "type": "object",
                                "properties": {
                                  "css": {
                                    "description": "CSS easing function string",
                                    "example": "cubic-bezier(0.66, 0, 0.34, 1)",
                                    "type": "string"
                                  },
                                  "tailwind_css": {
                                    "description": "Tailwind CSS compatible easing function string",
                                    "example": "ease-[cubic-bezier(0.66,0,0.34,1)]",
                                    "type": "string"
                                  },
                                  "svg_polyline": {
                                    "description": "SVG polyline for linear easing curves",
                                    "example": "0,75 15.2,39.6 32.8,21.75 50,18.45 100,25",
                                    "type": "string"
                                  },
                                  "suggested_duration_ms": {
                                    "description": "Suggested duration range derived from the curve physics. Shorter durations feel snappier, longer durations let complex motions (bounces, oscillations) breathe.",
                                    "type": "object",
                                    "properties": {
                                      "min": {
                                        "description": "Minimum suggested CSS animation/transition duration in milliseconds",
                                        "example": 300,
                                        "type": "integer",
                                        "exclusiveMinimum": 0,
                                        "maximum": 9007199254740991
                                      },
                                      "max": {
                                        "description": "Maximum suggested CSS animation/transition duration in milliseconds",
                                        "example": 600,
                                        "type": "integer",
                                        "exclusiveMinimum": 0,
                                        "maximum": 9007199254740991
                                      }
                                    },
                                    "required": [
                                      "min",
                                      "max"
                                    ],
                                    "additionalProperties": false
                                  }
                                },
                                "required": [
                                  "css",
                                  "tailwind_css",
                                  "svg_polyline",
                                  "suggested_duration_ms"
                                ],
                                "additionalProperties": false
                              },
                              "links": {
                                "title": "Easing Curve Links Response",
                                "description": "HATEOAS navigation links for the easing curve",
                                "type": "object",
                                "properties": {
                                  "self": {
                                    "description": "Link to this curve resource",
                                    "example": "/curves/abc123def",
                                    "type": "string"
                                  },
                                  "share_url": {
                                    "description": "Shareable URL for this curve",
                                    "example": "https://easingwizard.com/#abc123def",
                                    "type": "string",
                                    "format": "uri"
                                  },
                                  "create": {
                                    "description": "Endpoint to create curves of this type",
                                    "example": "/curves/bezier",
                                    "type": "string"
                                  }
                                },
                                "required": [
                                  "self",
                                  "share_url",
                                  "create"
                                ],
                                "additionalProperties": false
                              }
                            },
                            "required": [
                              "id",
                              "type",
                              "curve",
                              "params",
                              "output",
                              "links"
                            ],
                            "additionalProperties": false
                          },
                          {
                            "type": "object",
                            "properties": {
                              "id": {
                                "description": "The ID of the easing curve",
                                "example": "0a1b2c3xy",
                                "type": "string"
                              },
                              "type": {
                                "description": "Wiggle easing type",
                                "type": "string",
                                "const": "WIGGLE"
                              },
                              "curve": {
                                "description": "Wiggle curve variant",
                                "example": "SUBTLE",
                                "type": "string",
                                "enum": [
                                  "SUBTLE",
                                  "ENERGETIC",
                                  "PLAYFUL",
                                  "SHARP",
                                  "SMOOTH",
                                  "INTENSE",
                                  "DYNAMIC"
                                ]
                              },
                              "params": {
                                "title": "Wiggle Animation Parameters",
                                "description": "Parameters for wiggle-based easing animations",
                                "type": "object",
                                "properties": {
                                  "wiggles": {
                                    "description": "Number of wiggle oscillations (1-10)",
                                    "example": 5,
                                    "type": "number",
                                    "minimum": 1,
                                    "maximum": 10
                                  },
                                  "mass": {
                                    "default": 1,
                                    "description": "Mass (1-5)",
                                    "example": 2.5,
                                    "type": "number",
                                    "minimum": 1,
                                    "maximum": 5
                                  },
                                  "damping": {
                                    "description": "Damping (0-100)",
                                    "example": 50,
                                    "type": "number",
                                    "minimum": 0,
                                    "maximum": 100
                                  },
                                  "accuracy": {
                                    "description": "Accuracy level for the linear easing approximation, HIGH is the best option for most cases.",
                                    "example": "HIGH",
                                    "type": "string",
                                    "enum": [
                                      "LOW",
                                      "MEDIUM",
                                      "HIGH",
                                      "ULTRA"
                                    ]
                                  }
                                },
                                "required": [
                                  "wiggles",
                                  "mass",
                                  "damping",
                                  "accuracy"
                                ],
                                "additionalProperties": false
                              },
                              "output": {
                                "title": "Linear Easing Output",
                                "description": "CSS and SVG output for linear easing functions",
                                "type": "object",
                                "properties": {
                                  "css": {
                                    "description": "CSS easing function string",
                                    "example": "cubic-bezier(0.66, 0, 0.34, 1)",
                                    "type": "string"
                                  },
                                  "tailwind_css": {
                                    "description": "Tailwind CSS compatible easing function string",
                                    "example": "ease-[cubic-bezier(0.66,0,0.34,1)]",
                                    "type": "string"
                                  },
                                  "svg_polyline": {
                                    "description": "SVG polyline for linear easing curves",
                                    "example": "0,75 15.2,39.6 32.8,21.75 50,18.45 100,25",
                                    "type": "string"
                                  },
                                  "suggested_duration_ms": {
                                    "description": "Suggested duration range derived from the curve physics. Shorter durations feel snappier, longer durations let complex motions (bounces, oscillations) breathe.",
                                    "type": "object",
                                    "properties": {
                                      "min": {
                                        "description": "Minimum suggested CSS animation/transition duration in milliseconds",
                                        "example": 300,
                                        "type": "integer",
                                        "exclusiveMinimum": 0,
                                        "maximum": 9007199254740991
                                      },
                                      "max": {
                                        "description": "Maximum suggested CSS animation/transition duration in milliseconds",
                                        "example": 600,
                                        "type": "integer",
                                        "exclusiveMinimum": 0,
                                        "maximum": 9007199254740991
                                      }
                                    },
                                    "required": [
                                      "min",
                                      "max"
                                    ],
                                    "additionalProperties": false
                                  }
                                },
                                "required": [
                                  "css",
                                  "tailwind_css",
                                  "svg_polyline",
                                  "suggested_duration_ms"
                                ],
                                "additionalProperties": false
                              },
                              "links": {
                                "title": "Easing Curve Links Response",
                                "description": "HATEOAS navigation links for the easing curve",
                                "type": "object",
                                "properties": {
                                  "self": {
                                    "description": "Link to this curve resource",
                                    "example": "/curves/abc123def",
                                    "type": "string"
                                  },
                                  "share_url": {
                                    "description": "Shareable URL for this curve",
                                    "example": "https://easingwizard.com/#abc123def",
                                    "type": "string",
                                    "format": "uri"
                                  },
                                  "create": {
                                    "description": "Endpoint to create curves of this type",
                                    "example": "/curves/bezier",
                                    "type": "string"
                                  }
                                },
                                "required": [
                                  "self",
                                  "share_url",
                                  "create"
                                ],
                                "additionalProperties": false
                              }
                            },
                            "required": [
                              "id",
                              "type",
                              "curve",
                              "params",
                              "output",
                              "links"
                            ],
                            "additionalProperties": false
                          },
                          {
                            "type": "object",
                            "properties": {
                              "id": {
                                "description": "The ID of the easing curve",
                                "example": "0a1b2c3xy",
                                "type": "string"
                              },
                              "type": {
                                "description": "Overshoot easing type",
                                "type": "string",
                                "const": "OVERSHOOT"
                              },
                              "style": {
                                "description": "Overshoot easing style",
                                "example": "IN",
                                "type": "string",
                                "enum": [
                                  "IN",
                                  "OUT",
                                  "IN_OUT"
                                ]
                              },
                              "curve": {
                                "description": "Overshoot curve variant",
                                "example": "SOFT",
                                "type": "string",
                                "enum": [
                                  "SOFT",
                                  "FIRM",
                                  "SMOOTH",
                                  "DYNAMIC",
                                  "DRAMATIC"
                                ]
                              },
                              "params": {
                                "title": "Overshoot Animation Parameters",
                                "description": "Parameters for overshoot-based easing animations",
                                "type": "object",
                                "properties": {
                                  "style": {
                                    "description": "Style of overshoot animation",
                                    "example": "OUT",
                                    "type": "string",
                                    "enum": [
                                      "IN",
                                      "OUT",
                                      "IN_OUT"
                                    ]
                                  },
                                  "mass": {
                                    "description": "Mass (1-5)",
                                    "example": 2.5,
                                    "type": "number",
                                    "minimum": 1,
                                    "maximum": 5
                                  },
                                  "damping": {
                                    "description": "Damping (0-100)",
                                    "example": 50,
                                    "type": "number",
                                    "minimum": 0,
                                    "maximum": 100
                                  },
                                  "accuracy": {
                                    "description": "Accuracy level for the linear easing approximation, HIGH is the best option for most cases.",
                                    "example": "HIGH",
                                    "type": "string",
                                    "enum": [
                                      "LOW",
                                      "MEDIUM",
                                      "HIGH",
                                      "ULTRA"
                                    ]
                                  }
                                },
                                "required": [
                                  "style",
                                  "mass",
                                  "damping",
                                  "accuracy"
                                ],
                                "additionalProperties": false
                              },
                              "output": {
                                "title": "Linear Easing Output",
                                "description": "CSS and SVG output for linear easing functions",
                                "type": "object",
                                "properties": {
                                  "css": {
                                    "description": "CSS easing function string",
                                    "example": "cubic-bezier(0.66, 0, 0.34, 1)",
                                    "type": "string"
                                  },
                                  "tailwind_css": {
                                    "description": "Tailwind CSS compatible easing function string",
                                    "example": "ease-[cubic-bezier(0.66,0,0.34,1)]",
                                    "type": "string"
                                  },
                                  "svg_polyline": {
                                    "description": "SVG polyline for linear easing curves",
                                    "example": "0,75 15.2,39.6 32.8,21.75 50,18.45 100,25",
                                    "type": "string"
                                  },
                                  "suggested_duration_ms": {
                                    "description": "Suggested duration range derived from the curve physics. Shorter durations feel snappier, longer durations let complex motions (bounces, oscillations) breathe.",
                                    "type": "object",
                                    "properties": {
                                      "min": {
                                        "description": "Minimum suggested CSS animation/transition duration in milliseconds",
                                        "example": 300,
                                        "type": "integer",
                                        "exclusiveMinimum": 0,
                                        "maximum": 9007199254740991
                                      },
                                      "max": {
                                        "description": "Maximum suggested CSS animation/transition duration in milliseconds",
                                        "example": 600,
                                        "type": "integer",
                                        "exclusiveMinimum": 0,
                                        "maximum": 9007199254740991
                                      }
                                    },
                                    "required": [
                                      "min",
                                      "max"
                                    ],
                                    "additionalProperties": false
                                  }
                                },
                                "required": [
                                  "css",
                                  "tailwind_css",
                                  "svg_polyline",
                                  "suggested_duration_ms"
                                ],
                                "additionalProperties": false
                              },
                              "links": {
                                "title": "Easing Curve Links Response",
                                "description": "HATEOAS navigation links for the easing curve",
                                "type": "object",
                                "properties": {
                                  "self": {
                                    "description": "Link to this curve resource",
                                    "example": "/curves/abc123def",
                                    "type": "string"
                                  },
                                  "share_url": {
                                    "description": "Shareable URL for this curve",
                                    "example": "https://easingwizard.com/#abc123def",
                                    "type": "string",
                                    "format": "uri"
                                  },
                                  "create": {
                                    "description": "Endpoint to create curves of this type",
                                    "example": "/curves/bezier",
                                    "type": "string"
                                  }
                                },
                                "required": [
                                  "self",
                                  "share_url",
                                  "create"
                                ],
                                "additionalProperties": false
                              }
                            },
                            "required": [
                              "id",
                              "type",
                              "style",
                              "curve",
                              "params",
                              "output",
                              "links"
                            ],
                            "additionalProperties": false
                          }
                        ]
                      }
                    },
                    "links": {
                      "title": "Presets Links Response",
                      "description": "HATEOAS navigation links",
                      "type": "object",
                      "properties": {
                        "self": {
                          "description": "Link to this presets collection",
                          "example": "/presets",
                          "type": "string"
                        },
                        "filter": {
                          "description": "Template for filtering presets by type",
                          "example": "/presets{?type}",
                          "type": "string"
                        }
                      },
                      "required": [
                        "self",
                        "filter"
                      ],
                      "additionalProperties": false
                    }
                  },
                  "required": [
                    "version",
                    "presets",
                    "links"
                  ],
                  "additionalProperties": false
                }
              }
            }
          },
          "400": {
            "description": "400 Bad Request",
            "content": {
              "application/json": {
                "schema": {
                  "description": "Error response with validation details",
                  "type": "object",
                  "properties": {
                    "errors": {
                      "description": "Array of validation errors",
                      "type": "array",
                      "items": {
                        "type": "object",
                        "properties": {
                          "expected": {
                            "description": "Expected type or value",
                            "example": "number",
                            "type": "string"
                          },
                          "values": {
                            "description": "List of valid values or types",
                            "example": [
                              "BEZIER",
                              "SPRING",
                              "BOUNCE",
                              "WIGGLE",
                              "OVERSHOOT"
                            ],
                            "type": "array",
                            "items": {
                              "type": "string"
                            }
                          },
                          "code": {
                            "description": "Error code",
                            "example": "invalid_type",
                            "type": "string"
                          },
                          "message": {
                            "description": "Human-readable error message",
                            "example": "Expected number, received string",
                            "type": "string"
                          },
                          "path": {
                            "description": "Path to the field that caused the error",
                            "example": [
                              "x1"
                            ],
                            "type": "array",
                            "items": {
                              "anyOf": [
                                {
                                  "type": "string"
                                },
                                {
                                  "type": "number"
                                }
                              ]
                            }
                          }
                        },
                        "required": [
                          "code",
                          "message",
                          "path"
                        ],
                        "additionalProperties": false
                      }
                    }
                  },
                  "required": [
                    "errors"
                  ],
                  "additionalProperties": false
                }
              }
            }
          }
        }
      }
    },
    "/curves/{id}": {
      "get": {
        "operationId": "getCurveById",
        "summary": "Get Easing Curve by ID",
        "description": "Retrieve a specific easing curve by its unique ID.",
        "tags": [
          "Curves"
        ],
        "parameters": [
          {
            "in": "path",
            "name": "id",
            "schema": {
              "description": "The ID of the easing curve",
              "example": "0a1b2c3xy",
              "type": "string"
            },
            "required": true,
            "description": "The ID of the easing curve"
          }
        ],
        "responses": {
          "200": {
            "description": "200 OK",
            "content": {
              "application/json": {
                "schema": {
                  "title": "Easing Curve Response",
                  "description": "Complete easing curve response with metadata and links",
                  "anyOf": [
                    {
                      "title": "Bézier Easing Curve Response",
                      "description": "Bézier easing curve response with specific input and output types",
                      "type": "object",
                      "properties": {
                        "id": {
                          "description": "The ID of the easing curve",
                          "example": "0a1b2c3xy",
                          "type": "string"
                        },
                        "type": {
                          "type": "string",
                          "const": "BEZIER"
                        },
                        "input": {
                          "title": "Bézier Curve Parameters",
                          "description": "Parameters for a cubic Bézier curve",
                          "type": "object",
                          "properties": {
                            "x1": {
                              "description": "First control point X coordinate (0-1)",
                              "example": 0.25,
                              "type": "number",
                              "minimum": 0,
                              "maximum": 1
                            },
                            "y1": {
                              "description": "First control point Y coordinate (-1 to 2)",
                              "example": 0.1,
                              "type": "number",
                              "minimum": -1,
                              "maximum": 2
                            },
                            "x2": {
                              "description": "Second control point X coordinate (0-1)",
                              "example": 0.75,
                              "type": "number",
                              "minimum": 0,
                              "maximum": 1
                            },
                            "y2": {
                              "description": "Second control point Y coordinate (-1 to 2)",
                              "example": 0.9,
                              "type": "number",
                              "minimum": -1,
                              "maximum": 2
                            }
                          },
                          "required": [
                            "x1",
                            "y1",
                            "x2",
                            "y2"
                          ],
                          "additionalProperties": false
                        },
                        "output": {
                          "title": "Bézier Easing Output",
                          "description": "CSS and SVG output for Bézier easing functions",
                          "type": "object",
                          "properties": {
                            "css": {
                              "description": "CSS easing function string",
                              "example": "cubic-bezier(0.66, 0, 0.34, 1)",
                              "type": "string"
                            },
                            "tailwind_css": {
                              "description": "Tailwind CSS compatible easing function string",
                              "example": "ease-[cubic-bezier(0.66,0,0.34,1)]",
                              "type": "string"
                            },
                            "svg_path": {
                              "description": "SVG path for Bézier curves",
                              "example": "M0,100 C66,100 34,0 100,0",
                              "type": "string"
                            }
                          },
                          "required": [
                            "css",
                            "tailwind_css",
                            "svg_path"
                          ],
                          "additionalProperties": false
                        },
                        "links": {
                          "title": "Easing Curve Links Response",
                          "description": "HATEOAS navigation links for the easing curve",
                          "type": "object",
                          "properties": {
                            "self": {
                              "description": "Link to this curve resource",
                              "example": "/curves/abc123def",
                              "type": "string"
                            },
                            "share_url": {
                              "description": "Shareable URL for this curve",
                              "example": "https://easingwizard.com/#abc123def",
                              "type": "string",
                              "format": "uri"
                            },
                            "create": {
                              "description": "Endpoint to create curves of this type",
                              "example": "/curves/bezier",
                              "type": "string"
                            }
                          },
                          "required": [
                            "self",
                            "share_url",
                            "create"
                          ],
                          "additionalProperties": false
                        },
                        "generated_at": {
                          "description": "ISO 8601 timestamp when the curve was generated",
                          "example": "2025-07-03T12:00:00Z",
                          "format": "date-time",
                          "type": "string"
                        }
                      },
                      "required": [
                        "id",
                        "type",
                        "input",
                        "output",
                        "links",
                        "generated_at"
                      ],
                      "additionalProperties": false
                    },
                    {
                      "title": "Spring Easing Curve Response",
                      "description": "Spring easing curve response with specific input and output types",
                      "type": "object",
                      "properties": {
                        "id": {
                          "description": "The ID of the easing curve",
                          "example": "0a1b2c3xy",
                          "type": "string"
                        },
                        "type": {
                          "type": "string",
                          "const": "SPRING"
                        },
                        "input": {
                          "title": "Spring Animation Parameters",
                          "description": "Parameters for spring-based easing animations",
                          "type": "object",
                          "properties": {
                            "mass": {
                              "description": "Mass (1-5)",
                              "example": 2.5,
                              "type": "number",
                              "minimum": 1,
                              "maximum": 5
                            },
                            "stiffness": {
                              "description": "Stiffness (0-100)",
                              "example": 50,
                              "type": "number",
                              "minimum": 0,
                              "maximum": 100
                            },
                            "damping": {
                              "description": "Damping (0-100)",
                              "example": 50,
                              "type": "number",
                              "minimum": 0,
                              "maximum": 100
                            },
                            "accuracy": {
                              "description": "Accuracy level for the linear easing approximation, HIGH is the best option for most cases.",
                              "example": "HIGH",
                              "type": "string",
                              "enum": [
                                "LOW",
                                "MEDIUM",
                                "HIGH",
                                "ULTRA"
                              ]
                            }
                          },
                          "required": [
                            "mass",
                            "stiffness",
                            "damping",
                            "accuracy"
                          ],
                          "additionalProperties": false
                        },
                        "output": {
                          "title": "Linear Easing Output",
                          "description": "CSS and SVG output for linear easing functions",
                          "type": "object",
                          "properties": {
                            "css": {
                              "description": "CSS easing function string",
                              "example": "cubic-bezier(0.66, 0, 0.34, 1)",
                              "type": "string"
                            },
                            "tailwind_css": {
                              "description": "Tailwind CSS compatible easing function string",
                              "example": "ease-[cubic-bezier(0.66,0,0.34,1)]",
                              "type": "string"
                            },
                            "svg_polyline": {
                              "description": "SVG polyline for linear easing curves",
                              "example": "0,75 15.2,39.6 32.8,21.75 50,18.45 100,25",
                              "type": "string"
                            },
                            "suggested_duration_ms": {
                              "description": "Suggested duration range derived from the curve physics. Shorter durations feel snappier, longer durations let complex motions (bounces, oscillations) breathe.",
                              "type": "object",
                              "properties": {
                                "min": {
                                  "description": "Minimum suggested CSS animation/transition duration in milliseconds",
                                  "example": 300,
                                  "type": "integer",
                                  "exclusiveMinimum": 0,
                                  "maximum": 9007199254740991
                                },
                                "max": {
                                  "description": "Maximum suggested CSS animation/transition duration in milliseconds",
                                  "example": 600,
                                  "type": "integer",
                                  "exclusiveMinimum": 0,
                                  "maximum": 9007199254740991
                                }
                              },
                              "required": [
                                "min",
                                "max"
                              ],
                              "additionalProperties": false
                            }
                          },
                          "required": [
                            "css",
                            "tailwind_css",
                            "svg_polyline",
                            "suggested_duration_ms"
                          ],
                          "additionalProperties": false
                        },
                        "links": {
                          "title": "Easing Curve Links Response",
                          "description": "HATEOAS navigation links for the easing curve",
                          "type": "object",
                          "properties": {
                            "self": {
                              "description": "Link to this curve resource",
                              "example": "/curves/abc123def",
                              "type": "string"
                            },
                            "share_url": {
                              "description": "Shareable URL for this curve",
                              "example": "https://easingwizard.com/#abc123def",
                              "type": "string",
                              "format": "uri"
                            },
                            "create": {
                              "description": "Endpoint to create curves of this type",
                              "example": "/curves/bezier",
                              "type": "string"
                            }
                          },
                          "required": [
                            "self",
                            "share_url",
                            "create"
                          ],
                          "additionalProperties": false
                        },
                        "generated_at": {
                          "description": "ISO 8601 timestamp when the curve was generated",
                          "example": "2025-07-03T12:00:00Z",
                          "format": "date-time",
                          "type": "string"
                        }
                      },
                      "required": [
                        "id",
                        "type",
                        "input",
                        "output",
                        "links",
                        "generated_at"
                      ],
                      "additionalProperties": false
                    },
                    {
                      "title": "Bounce Easing Curve Response",
                      "description": "Bounce easing curve response with specific input and output types",
                      "type": "object",
                      "properties": {
                        "id": {
                          "description": "The ID of the easing curve",
                          "example": "0a1b2c3xy",
                          "type": "string"
                        },
                        "type": {
                          "type": "string",
                          "const": "BOUNCE"
                        },
                        "input": {
                          "title": "Bounce Animation Parameters",
                          "description": "Parameters for bounce-based easing animations",
                          "type": "object",
                          "properties": {
                            "bounces": {
                              "description": "Number of bounces (1-10)",
                              "example": 3,
                              "type": "number",
                              "minimum": 1,
                              "maximum": 10
                            },
                            "mass": {
                              "default": 1,
                              "description": "Mass (1-5)",
                              "example": 2.5,
                              "type": "number",
                              "minimum": 1,
                              "maximum": 5
                            },
                            "damping": {
                              "description": "Damping (0-100)",
                              "example": 50,
                              "type": "number",
                              "minimum": 0,
                              "maximum": 100
                            },
                            "accuracy": {
                              "description": "Accuracy level for the linear easing approximation, HIGH is the best option for most cases.",
                              "example": "HIGH",
                              "type": "string",
                              "enum": [
                                "LOW",
                                "MEDIUM",
                                "HIGH",
                                "ULTRA"
                              ]
                            }
                          },
                          "required": [
                            "bounces",
                            "mass",
                            "damping",
                            "accuracy"
                          ],
                          "additionalProperties": false
                        },
                        "output": {
                          "title": "Linear Easing Output",
                          "description": "CSS and SVG output for linear easing functions",
                          "type": "object",
                          "properties": {
                            "css": {
                              "description": "CSS easing function string",
                              "example": "cubic-bezier(0.66, 0, 0.34, 1)",
                              "type": "string"
                            },
                            "tailwind_css": {
                              "description": "Tailwind CSS compatible easing function string",
                              "example": "ease-[cubic-bezier(0.66,0,0.34,1)]",
                              "type": "string"
                            },
                            "svg_polyline": {
                              "description": "SVG polyline for linear easing curves",
                              "example": "0,75 15.2,39.6 32.8,21.75 50,18.45 100,25",
                              "type": "string"
                            },
                            "suggested_duration_ms": {
                              "description": "Suggested duration range derived from the curve physics. Shorter durations feel snappier, longer durations let complex motions (bounces, oscillations) breathe.",
                              "type": "object",
                              "properties": {
                                "min": {
                                  "description": "Minimum suggested CSS animation/transition duration in milliseconds",
                                  "example": 300,
                                  "type": "integer",
                                  "exclusiveMinimum": 0,
                                  "maximum": 9007199254740991
                                },
                                "max": {
                                  "description": "Maximum suggested CSS animation/transition duration in milliseconds",
                                  "example": 600,
                                  "type": "integer",
                                  "exclusiveMinimum": 0,
                                  "maximum": 9007199254740991
                                }
                              },
                              "required": [
                                "min",
                                "max"
                              ],
                              "additionalProperties": false
                            }
                          },
                          "required": [
                            "css",
                            "tailwind_css",
                            "svg_polyline",
                            "suggested_duration_ms"
                          ],
                          "additionalProperties": false
                        },
                        "links": {
                          "title": "Easing Curve Links Response",
                          "description": "HATEOAS navigation links for the easing curve",
                          "type": "object",
                          "properties": {
                            "self": {
                              "description": "Link to this curve resource",
                              "example": "/curves/abc123def",
                              "type": "string"
                            },
                            "share_url": {
                              "description": "Shareable URL for this curve",
                              "example": "https://easingwizard.com/#abc123def",
                              "type": "string",
                              "format": "uri"
                            },
                            "create": {
                              "description": "Endpoint to create curves of this type",
                              "example": "/curves/bezier",
                              "type": "string"
                            }
                          },
                          "required": [
                            "self",
                            "share_url",
                            "create"
                          ],
                          "additionalProperties": false
                        },
                        "generated_at": {
                          "description": "ISO 8601 timestamp when the curve was generated",
                          "example": "2025-07-03T12:00:00Z",
                          "format": "date-time",
                          "type": "string"
                        }
                      },
                      "required": [
                        "id",
                        "type",
                        "input",
                        "output",
                        "links",
                        "generated_at"
                      ],
                      "additionalProperties": false
                    },
                    {
                      "title": "Wiggle Easing Curve Response",
                      "description": "Wiggle easing curve response with specific input and output types",
                      "type": "object",
                      "properties": {
                        "id": {
                          "description": "The ID of the easing curve",
                          "example": "0a1b2c3xy",
                          "type": "string"
                        },
                        "type": {
                          "type": "string",
                          "const": "WIGGLE"
                        },
                        "input": {
                          "title": "Wiggle Animation Parameters",
                          "description": "Parameters for wiggle-based easing animations",
                          "type": "object",
                          "properties": {
                            "wiggles": {
                              "description": "Number of wiggle oscillations (1-10)",
                              "example": 5,
                              "type": "number",
                              "minimum": 1,
                              "maximum": 10
                            },
                            "mass": {
                              "default": 1,
                              "description": "Mass (1-5)",
                              "example": 2.5,
                              "type": "number",
                              "minimum": 1,
                              "maximum": 5
                            },
                            "damping": {
                              "description": "Damping (0-100)",
                              "example": 50,
                              "type": "number",
                              "minimum": 0,
                              "maximum": 100
                            },
                            "accuracy": {
                              "description": "Accuracy level for the linear easing approximation, HIGH is the best option for most cases.",
                              "example": "HIGH",
                              "type": "string",
                              "enum": [
                                "LOW",
                                "MEDIUM",
                                "HIGH",
                                "ULTRA"
                              ]
                            }
                          },
                          "required": [
                            "wiggles",
                            "mass",
                            "damping",
                            "accuracy"
                          ],
                          "additionalProperties": false
                        },
                        "output": {
                          "title": "Linear Easing Output",
                          "description": "CSS and SVG output for linear easing functions",
                          "type": "object",
                          "properties": {
                            "css": {
                              "description": "CSS easing function string",
                              "example": "cubic-bezier(0.66, 0, 0.34, 1)",
                              "type": "string"
                            },
                            "tailwind_css": {
                              "description": "Tailwind CSS compatible easing function string",
                              "example": "ease-[cubic-bezier(0.66,0,0.34,1)]",
                              "type": "string"
                            },
                            "svg_polyline": {
                              "description": "SVG polyline for linear easing curves",
                              "example": "0,75 15.2,39.6 32.8,21.75 50,18.45 100,25",
                              "type": "string"
                            },
                            "suggested_duration_ms": {
                              "description": "Suggested duration range derived from the curve physics. Shorter durations feel snappier, longer durations let complex motions (bounces, oscillations) breathe.",
                              "type": "object",
                              "properties": {
                                "min": {
                                  "description": "Minimum suggested CSS animation/transition duration in milliseconds",
                                  "example": 300,
                                  "type": "integer",
                                  "exclusiveMinimum": 0,
                                  "maximum": 9007199254740991
                                },
                                "max": {
                                  "description": "Maximum suggested CSS animation/transition duration in milliseconds",
                                  "example": 600,
                                  "type": "integer",
                                  "exclusiveMinimum": 0,
                                  "maximum": 9007199254740991
                                }
                              },
                              "required": [
                                "min",
                                "max"
                              ],
                              "additionalProperties": false
                            }
                          },
                          "required": [
                            "css",
                            "tailwind_css",
                            "svg_polyline",
                            "suggested_duration_ms"
                          ],
                          "additionalProperties": false
                        },
                        "links": {
                          "title": "Easing Curve Links Response",
                          "description": "HATEOAS navigation links for the easing curve",
                          "type": "object",
                          "properties": {
                            "self": {
                              "description": "Link to this curve resource",
                              "example": "/curves/abc123def",
                              "type": "string"
                            },
                            "share_url": {
                              "description": "Shareable URL for this curve",
                              "example": "https://easingwizard.com/#abc123def",
                              "type": "string",
                              "format": "uri"
                            },
                            "create": {
                              "description": "Endpoint to create curves of this type",
                              "example": "/curves/bezier",
                              "type": "string"
                            }
                          },
                          "required": [
                            "self",
                            "share_url",
                            "create"
                          ],
                          "additionalProperties": false
                        },
                        "generated_at": {
                          "description": "ISO 8601 timestamp when the curve was generated",
                          "example": "2025-07-03T12:00:00Z",
                          "format": "date-time",
                          "type": "string"
                        }
                      },
                      "required": [
                        "id",
                        "type",
                        "input",
                        "output",
                        "links",
                        "generated_at"
                      ],
                      "additionalProperties": false
                    },
                    {
                      "title": "Overshoot Easing Curve Response",
                      "description": "Overshoot easing curve response with specific input and output types",
                      "type": "object",
                      "properties": {
                        "id": {
                          "description": "The ID of the easing curve",
                          "example": "0a1b2c3xy",
                          "type": "string"
                        },
                        "type": {
                          "type": "string",
                          "const": "OVERSHOOT"
                        },
                        "input": {
                          "title": "Overshoot Animation Parameters",
                          "description": "Parameters for overshoot-based easing animations",
                          "type": "object",
                          "properties": {
                            "style": {
                              "description": "Style of overshoot animation",
                              "example": "OUT",
                              "type": "string",
                              "enum": [
                                "IN",
                                "OUT",
                                "IN_OUT"
                              ]
                            },
                            "mass": {
                              "description": "Mass (1-5)",
                              "example": 2.5,
                              "type": "number",
                              "minimum": 1,
                              "maximum": 5
                            },
                            "damping": {
                              "description": "Damping (0-100)",
                              "example": 50,
                              "type": "number",
                              "minimum": 0,
                              "maximum": 100
                            },
                            "accuracy": {
                              "description": "Accuracy level for the linear easing approximation, HIGH is the best option for most cases.",
                              "example": "HIGH",
                              "type": "string",
                              "enum": [
                                "LOW",
                                "MEDIUM",
                                "HIGH",
                                "ULTRA"
                              ]
                            }
                          },
                          "required": [
                            "style",
                            "mass",
                            "damping",
                            "accuracy"
                          ],
                          "additionalProperties": false
                        },
                        "output": {
                          "title": "Linear Easing Output",
                          "description": "CSS and SVG output for linear easing functions",
                          "type": "object",
                          "properties": {
                            "css": {
                              "description": "CSS easing function string",
                              "example": "cubic-bezier(0.66, 0, 0.34, 1)",
                              "type": "string"
                            },
                            "tailwind_css": {
                              "description": "Tailwind CSS compatible easing function string",
                              "example": "ease-[cubic-bezier(0.66,0,0.34,1)]",
                              "type": "string"
                            },
                            "svg_polyline": {
                              "description": "SVG polyline for linear easing curves",
                              "example": "0,75 15.2,39.6 32.8,21.75 50,18.45 100,25",
                              "type": "string"
                            },
                            "suggested_duration_ms": {
                              "description": "Suggested duration range derived from the curve physics. Shorter durations feel snappier, longer durations let complex motions (bounces, oscillations) breathe.",
                              "type": "object",
                              "properties": {
                                "min": {
                                  "description": "Minimum suggested CSS animation/transition duration in milliseconds",
                                  "example": 300,
                                  "type": "integer",
                                  "exclusiveMinimum": 0,
                                  "maximum": 9007199254740991
                                },
                                "max": {
                                  "description": "Maximum suggested CSS animation/transition duration in milliseconds",
                                  "example": 600,
                                  "type": "integer",
                                  "exclusiveMinimum": 0,
                                  "maximum": 9007199254740991
                                }
                              },
                              "required": [
                                "min",
                                "max"
                              ],
                              "additionalProperties": false
                            }
                          },
                          "required": [
                            "css",
                            "tailwind_css",
                            "svg_polyline",
                            "suggested_duration_ms"
                          ],
                          "additionalProperties": false
                        },
                        "links": {
                          "title": "Easing Curve Links Response",
                          "description": "HATEOAS navigation links for the easing curve",
                          "type": "object",
                          "properties": {
                            "self": {
                              "description": "Link to this curve resource",
                              "example": "/curves/abc123def",
                              "type": "string"
                            },
                            "share_url": {
                              "description": "Shareable URL for this curve",
                              "example": "https://easingwizard.com/#abc123def",
                              "type": "string",
                              "format": "uri"
                            },
                            "create": {
                              "description": "Endpoint to create curves of this type",
                              "example": "/curves/bezier",
                              "type": "string"
                            }
                          },
                          "required": [
                            "self",
                            "share_url",
                            "create"
                          ],
                          "additionalProperties": false
                        },
                        "generated_at": {
                          "description": "ISO 8601 timestamp when the curve was generated",
                          "example": "2025-07-03T12:00:00Z",
                          "format": "date-time",
                          "type": "string"
                        }
                      },
                      "required": [
                        "id",
                        "type",
                        "input",
                        "output",
                        "links",
                        "generated_at"
                      ],
                      "additionalProperties": false
                    }
                  ]
                }
              }
            }
          },
          "400": {
            "description": "400 Bad Request",
            "content": {
              "application/json": {
                "schema": {
                  "description": "Error response with validation details",
                  "type": "object",
                  "properties": {
                    "errors": {
                      "description": "Array of validation errors",
                      "type": "array",
                      "items": {
                        "type": "object",
                        "properties": {
                          "expected": {
                            "description": "Expected type or value",
                            "example": "number",
                            "type": "string"
                          },
                          "values": {
                            "description": "List of valid values or types",
                            "example": [
                              "BEZIER",
                              "SPRING",
                              "BOUNCE",
                              "WIGGLE",
                              "OVERSHOOT"
                            ],
                            "type": "array",
                            "items": {
                              "type": "string"
                            }
                          },
                          "code": {
                            "description": "Error code",
                            "example": "invalid_type",
                            "type": "string"
                          },
                          "message": {
                            "description": "Human-readable error message",
                            "example": "Expected number, received string",
                            "type": "string"
                          },
                          "path": {
                            "description": "Path to the field that caused the error",
                            "example": [
                              "x1"
                            ],
                            "type": "array",
                            "items": {
                              "anyOf": [
                                {
                                  "type": "string"
                                },
                                {
                                  "type": "number"
                                }
                              ]
                            }
                          }
                        },
                        "required": [
                          "code",
                          "message",
                          "path"
                        ],
                        "additionalProperties": false
                      }
                    }
                  },
                  "required": [
                    "errors"
                  ],
                  "additionalProperties": false
                }
              }
            }
          }
        }
      }
    },
    "/curves/bezier": {
      "post": {
        "operationId": "createBezierCurve",
        "summary": "Create Bézier Curve",
        "description": "Generate a CSS easing curve using Bézier control points.",
        "tags": [
          "Curves"
        ],
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "title": "Bézier Curve Parameters",
                "description": "Parameters for a cubic Bézier curve",
                "type": "object",
                "properties": {
                  "x1": {
                    "description": "First control point X coordinate (0-1)",
                    "example": 0.25,
                    "type": "number",
                    "minimum": 0,
                    "maximum": 1
                  },
                  "y1": {
                    "description": "First control point Y coordinate (-1 to 2)",
                    "example": 0.1,
                    "type": "number",
                    "minimum": -1,
                    "maximum": 2
                  },
                  "x2": {
                    "description": "Second control point X coordinate (0-1)",
                    "example": 0.75,
                    "type": "number",
                    "minimum": 0,
                    "maximum": 1
                  },
                  "y2": {
                    "description": "Second control point Y coordinate (-1 to 2)",
                    "example": 0.9,
                    "type": "number",
                    "minimum": -1,
                    "maximum": 2
                  }
                },
                "required": [
                  "x1",
                  "y1",
                  "x2",
                  "y2"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "200 OK",
            "content": {
              "application/json": {
                "schema": {
                  "title": "Bézier Easing Curve Response",
                  "description": "Bézier easing curve response with specific input and output types",
                  "type": "object",
                  "properties": {
                    "id": {
                      "description": "The ID of the easing curve",
                      "example": "0a1b2c3xy",
                      "type": "string"
                    },
                    "type": {
                      "type": "string",
                      "const": "BEZIER"
                    },
                    "input": {
                      "title": "Bézier Curve Parameters",
                      "description": "Parameters for a cubic Bézier curve",
                      "type": "object",
                      "properties": {
                        "x1": {
                          "description": "First control point X coordinate (0-1)",
                          "example": 0.25,
                          "type": "number",
                          "minimum": 0,
                          "maximum": 1
                        },
                        "y1": {
                          "description": "First control point Y coordinate (-1 to 2)",
                          "example": 0.1,
                          "type": "number",
                          "minimum": -1,
                          "maximum": 2
                        },
                        "x2": {
                          "description": "Second control point X coordinate (0-1)",
                          "example": 0.75,
                          "type": "number",
                          "minimum": 0,
                          "maximum": 1
                        },
                        "y2": {
                          "description": "Second control point Y coordinate (-1 to 2)",
                          "example": 0.9,
                          "type": "number",
                          "minimum": -1,
                          "maximum": 2
                        }
                      },
                      "required": [
                        "x1",
                        "y1",
                        "x2",
                        "y2"
                      ],
                      "additionalProperties": false
                    },
                    "output": {
                      "title": "Bézier Easing Output",
                      "description": "CSS and SVG output for Bézier easing functions",
                      "type": "object",
                      "properties": {
                        "css": {
                          "description": "CSS easing function string",
                          "example": "cubic-bezier(0.66, 0, 0.34, 1)",
                          "type": "string"
                        },
                        "tailwind_css": {
                          "description": "Tailwind CSS compatible easing function string",
                          "example": "ease-[cubic-bezier(0.66,0,0.34,1)]",
                          "type": "string"
                        },
                        "svg_path": {
                          "description": "SVG path for Bézier curves",
                          "example": "M0,100 C66,100 34,0 100,0",
                          "type": "string"
                        }
                      },
                      "required": [
                        "css",
                        "tailwind_css",
                        "svg_path"
                      ],
                      "additionalProperties": false
                    },
                    "links": {
                      "title": "Easing Curve Links Response",
                      "description": "HATEOAS navigation links for the easing curve",
                      "type": "object",
                      "properties": {
                        "self": {
                          "description": "Link to this curve resource",
                          "example": "/curves/abc123def",
                          "type": "string"
                        },
                        "share_url": {
                          "description": "Shareable URL for this curve",
                          "example": "https://easingwizard.com/#abc123def",
                          "type": "string",
                          "format": "uri"
                        },
                        "create": {
                          "description": "Endpoint to create curves of this type",
                          "example": "/curves/bezier",
                          "type": "string"
                        }
                      },
                      "required": [
                        "self",
                        "share_url",
                        "create"
                      ],
                      "additionalProperties": false
                    },
                    "generated_at": {
                      "description": "ISO 8601 timestamp when the curve was generated",
                      "example": "2025-07-03T12:00:00Z",
                      "format": "date-time",
                      "type": "string"
                    }
                  },
                  "required": [
                    "id",
                    "type",
                    "input",
                    "output",
                    "links",
                    "generated_at"
                  ],
                  "additionalProperties": false
                }
              }
            }
          },
          "400": {
            "description": "400 Bad Request",
            "content": {
              "application/json": {
                "schema": {
                  "description": "Error response with validation details",
                  "type": "object",
                  "properties": {
                    "errors": {
                      "description": "Array of validation errors",
                      "type": "array",
                      "items": {
                        "type": "object",
                        "properties": {
                          "expected": {
                            "description": "Expected type or value",
                            "example": "number",
                            "type": "string"
                          },
                          "values": {
                            "description": "List of valid values or types",
                            "example": [
                              "BEZIER",
                              "SPRING",
                              "BOUNCE",
                              "WIGGLE",
                              "OVERSHOOT"
                            ],
                            "type": "array",
                            "items": {
                              "type": "string"
                            }
                          },
                          "code": {
                            "description": "Error code",
                            "example": "invalid_type",
                            "type": "string"
                          },
                          "message": {
                            "description": "Human-readable error message",
                            "example": "Expected number, received string",
                            "type": "string"
                          },
                          "path": {
                            "description": "Path to the field that caused the error",
                            "example": [
                              "x1"
                            ],
                            "type": "array",
                            "items": {
                              "anyOf": [
                                {
                                  "type": "string"
                                },
                                {
                                  "type": "number"
                                }
                              ]
                            }
                          }
                        },
                        "required": [
                          "code",
                          "message",
                          "path"
                        ],
                        "additionalProperties": false
                      }
                    }
                  },
                  "required": [
                    "errors"
                  ],
                  "additionalProperties": false
                }
              }
            }
          }
        }
      }
    },
    "/curves/spring": {
      "post": {
        "operationId": "createSpringCurve",
        "summary": "Create Spring Curve",
        "description": "Generate a CSS easing curve with spring motion.",
        "tags": [
          "Curves"
        ],
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "title": "Spring Animation Parameters",
                "description": "Parameters for spring-based easing animations",
                "type": "object",
                "properties": {
                  "mass": {
                    "description": "Mass (1-5)",
                    "example": 2.5,
                    "type": "number",
                    "minimum": 1,
                    "maximum": 5
                  },
                  "stiffness": {
                    "description": "Stiffness (0-100)",
                    "example": 50,
                    "type": "number",
                    "minimum": 0,
                    "maximum": 100
                  },
                  "damping": {
                    "description": "Damping (0-100)",
                    "example": 50,
                    "type": "number",
                    "minimum": 0,
                    "maximum": 100
                  },
                  "accuracy": {
                    "description": "Accuracy level for the linear easing approximation, HIGH is the best option for most cases.",
                    "example": "HIGH",
                    "type": "string",
                    "enum": [
                      "LOW",
                      "MEDIUM",
                      "HIGH",
                      "ULTRA"
                    ]
                  }
                },
                "required": [
                  "mass",
                  "stiffness",
                  "damping",
                  "accuracy"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "200 OK",
            "content": {
              "application/json": {
                "schema": {
                  "title": "Spring Easing Curve Response",
                  "description": "Spring easing curve response with specific input and output types",
                  "type": "object",
                  "properties": {
                    "id": {
                      "description": "The ID of the easing curve",
                      "example": "0a1b2c3xy",
                      "type": "string"
                    },
                    "type": {
                      "type": "string",
                      "const": "SPRING"
                    },
                    "input": {
                      "title": "Spring Animation Parameters",
                      "description": "Parameters for spring-based easing animations",
                      "type": "object",
                      "properties": {
                        "mass": {
                          "description": "Mass (1-5)",
                          "example": 2.5,
                          "type": "number",
                          "minimum": 1,
                          "maximum": 5
                        },
                        "stiffness": {
                          "description": "Stiffness (0-100)",
                          "example": 50,
                          "type": "number",
                          "minimum": 0,
                          "maximum": 100
                        },
                        "damping": {
                          "description": "Damping (0-100)",
                          "example": 50,
                          "type": "number",
                          "minimum": 0,
                          "maximum": 100
                        },
                        "accuracy": {
                          "description": "Accuracy level for the linear easing approximation, HIGH is the best option for most cases.",
                          "example": "HIGH",
                          "type": "string",
                          "enum": [
                            "LOW",
                            "MEDIUM",
                            "HIGH",
                            "ULTRA"
                          ]
                        }
                      },
                      "required": [
                        "mass",
                        "stiffness",
                        "damping",
                        "accuracy"
                      ],
                      "additionalProperties": false
                    },
                    "output": {
                      "title": "Linear Easing Output",
                      "description": "CSS and SVG output for linear easing functions",
                      "type": "object",
                      "properties": {
                        "css": {
                          "description": "CSS easing function string",
                          "example": "cubic-bezier(0.66, 0, 0.34, 1)",
                          "type": "string"
                        },
                        "tailwind_css": {
                          "description": "Tailwind CSS compatible easing function string",
                          "example": "ease-[cubic-bezier(0.66,0,0.34,1)]",
                          "type": "string"
                        },
                        "svg_polyline": {
                          "description": "SVG polyline for linear easing curves",
                          "example": "0,75 15.2,39.6 32.8,21.75 50,18.45 100,25",
                          "type": "string"
                        },
                        "suggested_duration_ms": {
                          "description": "Suggested duration range derived from the curve physics. Shorter durations feel snappier, longer durations let complex motions (bounces, oscillations) breathe.",
                          "type": "object",
                          "properties": {
                            "min": {
                              "description": "Minimum suggested CSS animation/transition duration in milliseconds",
                              "example": 300,
                              "type": "integer",
                              "exclusiveMinimum": 0,
                              "maximum": 9007199254740991
                            },
                            "max": {
                              "description": "Maximum suggested CSS animation/transition duration in milliseconds",
                              "example": 600,
                              "type": "integer",
                              "exclusiveMinimum": 0,
                              "maximum": 9007199254740991
                            }
                          },
                          "required": [
                            "min",
                            "max"
                          ],
                          "additionalProperties": false
                        }
                      },
                      "required": [
                        "css",
                        "tailwind_css",
                        "svg_polyline",
                        "suggested_duration_ms"
                      ],
                      "additionalProperties": false
                    },
                    "links": {
                      "title": "Easing Curve Links Response",
                      "description": "HATEOAS navigation links for the easing curve",
                      "type": "object",
                      "properties": {
                        "self": {
                          "description": "Link to this curve resource",
                          "example": "/curves/abc123def",
                          "type": "string"
                        },
                        "share_url": {
                          "description": "Shareable URL for this curve",
                          "example": "https://easingwizard.com/#abc123def",
                          "type": "string",
                          "format": "uri"
                        },
                        "create": {
                          "description": "Endpoint to create curves of this type",
                          "example": "/curves/bezier",
                          "type": "string"
                        }
                      },
                      "required": [
                        "self",
                        "share_url",
                        "create"
                      ],
                      "additionalProperties": false
                    },
                    "generated_at": {
                      "description": "ISO 8601 timestamp when the curve was generated",
                      "example": "2025-07-03T12:00:00Z",
                      "format": "date-time",
                      "type": "string"
                    }
                  },
                  "required": [
                    "id",
                    "type",
                    "input",
                    "output",
                    "links",
                    "generated_at"
                  ],
                  "additionalProperties": false
                }
              }
            }
          },
          "400": {
            "description": "400 Bad Request",
            "content": {
              "application/json": {
                "schema": {
                  "description": "Error response with validation details",
                  "type": "object",
                  "properties": {
                    "errors": {
                      "description": "Array of validation errors",
                      "type": "array",
                      "items": {
                        "type": "object",
                        "properties": {
                          "expected": {
                            "description": "Expected type or value",
                            "example": "number",
                            "type": "string"
                          },
                          "values": {
                            "description": "List of valid values or types",
                            "example": [
                              "BEZIER",
                              "SPRING",
                              "BOUNCE",
                              "WIGGLE",
                              "OVERSHOOT"
                            ],
                            "type": "array",
                            "items": {
                              "type": "string"
                            }
                          },
                          "code": {
                            "description": "Error code",
                            "example": "invalid_type",
                            "type": "string"
                          },
                          "message": {
                            "description": "Human-readable error message",
                            "example": "Expected number, received string",
                            "type": "string"
                          },
                          "path": {
                            "description": "Path to the field that caused the error",
                            "example": [
                              "x1"
                            ],
                            "type": "array",
                            "items": {
                              "anyOf": [
                                {
                                  "type": "string"
                                },
                                {
                                  "type": "number"
                                }
                              ]
                            }
                          }
                        },
                        "required": [
                          "code",
                          "message",
                          "path"
                        ],
                        "additionalProperties": false
                      }
                    }
                  },
                  "required": [
                    "errors"
                  ],
                  "additionalProperties": false
                }
              }
            }
          }
        }
      }
    },
    "/curves/bounce": {
      "post": {
        "operationId": "createBounceCurve",
        "summary": "Create Bounce Curve",
        "description": "Generate a CSS easing curve with bounce motion.",
        "tags": [
          "Curves"
        ],
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "title": "Bounce Animation Parameters",
                "description": "Parameters for bounce-based easing animations",
                "type": "object",
                "properties": {
                  "bounces": {
                    "description": "Number of bounces (1-10)",
                    "example": 3,
                    "type": "number",
                    "minimum": 1,
                    "maximum": 10
                  },
                  "mass": {
                    "description": "Mass (1-5)",
                    "example": 2.5,
                    "type": "number",
                    "minimum": 1,
                    "maximum": 5
                  },
                  "damping": {
                    "description": "Damping (0-100)",
                    "example": 50,
                    "type": "number",
                    "minimum": 0,
                    "maximum": 100
                  },
                  "accuracy": {
                    "description": "Accuracy level for the linear easing approximation, HIGH is the best option for most cases.",
                    "example": "HIGH",
                    "type": "string",
                    "enum": [
                      "LOW",
                      "MEDIUM",
                      "HIGH",
                      "ULTRA"
                    ]
                  }
                },
                "required": [
                  "bounces",
                  "damping",
                  "accuracy"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "200 OK",
            "content": {
              "application/json": {
                "schema": {
                  "title": "Bounce Easing Curve Response",
                  "description": "Bounce easing curve response with specific input and output types",
                  "type": "object",
                  "properties": {
                    "id": {
                      "description": "The ID of the easing curve",
                      "example": "0a1b2c3xy",
                      "type": "string"
                    },
                    "type": {
                      "type": "string",
                      "const": "BOUNCE"
                    },
                    "input": {
                      "title": "Bounce Animation Parameters",
                      "description": "Parameters for bounce-based easing animations",
                      "type": "object",
                      "properties": {
                        "bounces": {
                          "description": "Number of bounces (1-10)",
                          "example": 3,
                          "type": "number",
                          "minimum": 1,
                          "maximum": 10
                        },
                        "mass": {
                          "default": 1,
                          "description": "Mass (1-5)",
                          "example": 2.5,
                          "type": "number",
                          "minimum": 1,
                          "maximum": 5
                        },
                        "damping": {
                          "description": "Damping (0-100)",
                          "example": 50,
                          "type": "number",
                          "minimum": 0,
                          "maximum": 100
                        },
                        "accuracy": {
                          "description": "Accuracy level for the linear easing approximation, HIGH is the best option for most cases.",
                          "example": "HIGH",
                          "type": "string",
                          "enum": [
                            "LOW",
                            "MEDIUM",
                            "HIGH",
                            "ULTRA"
                          ]
                        }
                      },
                      "required": [
                        "bounces",
                        "mass",
                        "damping",
                        "accuracy"
                      ],
                      "additionalProperties": false
                    },
                    "output": {
                      "title": "Linear Easing Output",
                      "description": "CSS and SVG output for linear easing functions",
                      "type": "object",
                      "properties": {
                        "css": {
                          "description": "CSS easing function string",
                          "example": "cubic-bezier(0.66, 0, 0.34, 1)",
                          "type": "string"
                        },
                        "tailwind_css": {
                          "description": "Tailwind CSS compatible easing function string",
                          "example": "ease-[cubic-bezier(0.66,0,0.34,1)]",
                          "type": "string"
                        },
                        "svg_polyline": {
                          "description": "SVG polyline for linear easing curves",
                          "example": "0,75 15.2,39.6 32.8,21.75 50,18.45 100,25",
                          "type": "string"
                        },
                        "suggested_duration_ms": {
                          "description": "Suggested duration range derived from the curve physics. Shorter durations feel snappier, longer durations let complex motions (bounces, oscillations) breathe.",
                          "type": "object",
                          "properties": {
                            "min": {
                              "description": "Minimum suggested CSS animation/transition duration in milliseconds",
                              "example": 300,
                              "type": "integer",
                              "exclusiveMinimum": 0,
                              "maximum": 9007199254740991
                            },
                            "max": {
                              "description": "Maximum suggested CSS animation/transition duration in milliseconds",
                              "example": 600,
                              "type": "integer",
                              "exclusiveMinimum": 0,
                              "maximum": 9007199254740991
                            }
                          },
                          "required": [
                            "min",
                            "max"
                          ],
                          "additionalProperties": false
                        }
                      },
                      "required": [
                        "css",
                        "tailwind_css",
                        "svg_polyline",
                        "suggested_duration_ms"
                      ],
                      "additionalProperties": false
                    },
                    "links": {
                      "title": "Easing Curve Links Response",
                      "description": "HATEOAS navigation links for the easing curve",
                      "type": "object",
                      "properties": {
                        "self": {
                          "description": "Link to this curve resource",
                          "example": "/curves/abc123def",
                          "type": "string"
                        },
                        "share_url": {
                          "description": "Shareable URL for this curve",
                          "example": "https://easingwizard.com/#abc123def",
                          "type": "string",
                          "format": "uri"
                        },
                        "create": {
                          "description": "Endpoint to create curves of this type",
                          "example": "/curves/bezier",
                          "type": "string"
                        }
                      },
                      "required": [
                        "self",
                        "share_url",
                        "create"
                      ],
                      "additionalProperties": false
                    },
                    "generated_at": {
                      "description": "ISO 8601 timestamp when the curve was generated",
                      "example": "2025-07-03T12:00:00Z",
                      "format": "date-time",
                      "type": "string"
                    }
                  },
                  "required": [
                    "id",
                    "type",
                    "input",
                    "output",
                    "links",
                    "generated_at"
                  ],
                  "additionalProperties": false
                }
              }
            }
          },
          "400": {
            "description": "400 Bad Request",
            "content": {
              "application/json": {
                "schema": {
                  "description": "Error response with validation details",
                  "type": "object",
                  "properties": {
                    "errors": {
                      "description": "Array of validation errors",
                      "type": "array",
                      "items": {
                        "type": "object",
                        "properties": {
                          "expected": {
                            "description": "Expected type or value",
                            "example": "number",
                            "type": "string"
                          },
                          "values": {
                            "description": "List of valid values or types",
                            "example": [
                              "BEZIER",
                              "SPRING",
                              "BOUNCE",
                              "WIGGLE",
                              "OVERSHOOT"
                            ],
                            "type": "array",
                            "items": {
                              "type": "string"
                            }
                          },
                          "code": {
                            "description": "Error code",
                            "example": "invalid_type",
                            "type": "string"
                          },
                          "message": {
                            "description": "Human-readable error message",
                            "example": "Expected number, received string",
                            "type": "string"
                          },
                          "path": {
                            "description": "Path to the field that caused the error",
                            "example": [
                              "x1"
                            ],
                            "type": "array",
                            "items": {
                              "anyOf": [
                                {
                                  "type": "string"
                                },
                                {
                                  "type": "number"
                                }
                              ]
                            }
                          }
                        },
                        "required": [
                          "code",
                          "message",
                          "path"
                        ],
                        "additionalProperties": false
                      }
                    }
                  },
                  "required": [
                    "errors"
                  ],
                  "additionalProperties": false
                }
              }
            }
          }
        }
      }
    },
    "/curves/wiggle": {
      "post": {
        "operationId": "createWiggleCurve",
        "summary": "Create Wiggle Curve",
        "description": "Generate a CSS easing curve with wiggle motion.",
        "tags": [
          "Curves"
        ],
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "title": "Wiggle Animation Parameters",
                "description": "Parameters for wiggle-based easing animations",
                "type": "object",
                "properties": {
                  "wiggles": {
                    "description": "Number of wiggle oscillations (1-10)",
                    "example": 5,
                    "type": "number",
                    "minimum": 1,
                    "maximum": 10
                  },
                  "mass": {
                    "description": "Mass (1-5)",
                    "example": 2.5,
                    "type": "number",
                    "minimum": 1,
                    "maximum": 5
                  },
                  "damping": {
                    "description": "Damping (0-100)",
                    "example": 50,
                    "type": "number",
                    "minimum": 0,
                    "maximum": 100
                  },
                  "accuracy": {
                    "description": "Accuracy level for the linear easing approximation, HIGH is the best option for most cases.",
                    "example": "HIGH",
                    "type": "string",
                    "enum": [
                      "LOW",
                      "MEDIUM",
                      "HIGH",
                      "ULTRA"
                    ]
                  }
                },
                "required": [
                  "wiggles",
                  "damping",
                  "accuracy"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "200 OK",
            "content": {
              "application/json": {
                "schema": {
                  "title": "Wiggle Easing Curve Response",
                  "description": "Wiggle easing curve response with specific input and output types",
                  "type": "object",
                  "properties": {
                    "id": {
                      "description": "The ID of the easing curve",
                      "example": "0a1b2c3xy",
                      "type": "string"
                    },
                    "type": {
                      "type": "string",
                      "const": "WIGGLE"
                    },
                    "input": {
                      "title": "Wiggle Animation Parameters",
                      "description": "Parameters for wiggle-based easing animations",
                      "type": "object",
                      "properties": {
                        "wiggles": {
                          "description": "Number of wiggle oscillations (1-10)",
                          "example": 5,
                          "type": "number",
                          "minimum": 1,
                          "maximum": 10
                        },
                        "mass": {
                          "default": 1,
                          "description": "Mass (1-5)",
                          "example": 2.5,
                          "type": "number",
                          "minimum": 1,
                          "maximum": 5
                        },
                        "damping": {
                          "description": "Damping (0-100)",
                          "example": 50,
                          "type": "number",
                          "minimum": 0,
                          "maximum": 100
                        },
                        "accuracy": {
                          "description": "Accuracy level for the linear easing approximation, HIGH is the best option for most cases.",
                          "example": "HIGH",
                          "type": "string",
                          "enum": [
                            "LOW",
                            "MEDIUM",
                            "HIGH",
                            "ULTRA"
                          ]
                        }
                      },
                      "required": [
                        "wiggles",
                        "mass",
                        "damping",
                        "accuracy"
                      ],
                      "additionalProperties": false
                    },
                    "output": {
                      "title": "Linear Easing Output",
                      "description": "CSS and SVG output for linear easing functions",
                      "type": "object",
                      "properties": {
                        "css": {
                          "description": "CSS easing function string",
                          "example": "cubic-bezier(0.66, 0, 0.34, 1)",
                          "type": "string"
                        },
                        "tailwind_css": {
                          "description": "Tailwind CSS compatible easing function string",
                          "example": "ease-[cubic-bezier(0.66,0,0.34,1)]",
                          "type": "string"
                        },
                        "svg_polyline": {
                          "description": "SVG polyline for linear easing curves",
                          "example": "0,75 15.2,39.6 32.8,21.75 50,18.45 100,25",
                          "type": "string"
                        },
                        "suggested_duration_ms": {
                          "description": "Suggested duration range derived from the curve physics. Shorter durations feel snappier, longer durations let complex motions (bounces, oscillations) breathe.",
                          "type": "object",
                          "properties": {
                            "min": {
                              "description": "Minimum suggested CSS animation/transition duration in milliseconds",
                              "example": 300,
                              "type": "integer",
                              "exclusiveMinimum": 0,
                              "maximum": 9007199254740991
                            },
                            "max": {
                              "description": "Maximum suggested CSS animation/transition duration in milliseconds",
                              "example": 600,
                              "type": "integer",
                              "exclusiveMinimum": 0,
                              "maximum": 9007199254740991
                            }
                          },
                          "required": [
                            "min",
                            "max"
                          ],
                          "additionalProperties": false
                        }
                      },
                      "required": [
                        "css",
                        "tailwind_css",
                        "svg_polyline",
                        "suggested_duration_ms"
                      ],
                      "additionalProperties": false
                    },
                    "links": {
                      "title": "Easing Curve Links Response",
                      "description": "HATEOAS navigation links for the easing curve",
                      "type": "object",
                      "properties": {
                        "self": {
                          "description": "Link to this curve resource",
                          "example": "/curves/abc123def",
                          "type": "string"
                        },
                        "share_url": {
                          "description": "Shareable URL for this curve",
                          "example": "https://easingwizard.com/#abc123def",
                          "type": "string",
                          "format": "uri"
                        },
                        "create": {
                          "description": "Endpoint to create curves of this type",
                          "example": "/curves/bezier",
                          "type": "string"
                        }
                      },
                      "required": [
                        "self",
                        "share_url",
                        "create"
                      ],
                      "additionalProperties": false
                    },
                    "generated_at": {
                      "description": "ISO 8601 timestamp when the curve was generated",
                      "example": "2025-07-03T12:00:00Z",
                      "format": "date-time",
                      "type": "string"
                    }
                  },
                  "required": [
                    "id",
                    "type",
                    "input",
                    "output",
                    "links",
                    "generated_at"
                  ],
                  "additionalProperties": false
                }
              }
            }
          },
          "400": {
            "description": "400 Bad Request",
            "content": {
              "application/json": {
                "schema": {
                  "description": "Error response with validation details",
                  "type": "object",
                  "properties": {
                    "errors": {
                      "description": "Array of validation errors",
                      "type": "array",
                      "items": {
                        "type": "object",
                        "properties": {
                          "expected": {
                            "description": "Expected type or value",
                            "example": "number",
                            "type": "string"
                          },
                          "values": {
                            "description": "List of valid values or types",
                            "example": [
                              "BEZIER",
                              "SPRING",
                              "BOUNCE",
                              "WIGGLE",
                              "OVERSHOOT"
                            ],
                            "type": "array",
                            "items": {
                              "type": "string"
                            }
                          },
                          "code": {
                            "description": "Error code",
                            "example": "invalid_type",
                            "type": "string"
                          },
                          "message": {
                            "description": "Human-readable error message",
                            "example": "Expected number, received string",
                            "type": "string"
                          },
                          "path": {
                            "description": "Path to the field that caused the error",
                            "example": [
                              "x1"
                            ],
                            "type": "array",
                            "items": {
                              "anyOf": [
                                {
                                  "type": "string"
                                },
                                {
                                  "type": "number"
                                }
                              ]
                            }
                          }
                        },
                        "required": [
                          "code",
                          "message",
                          "path"
                        ],
                        "additionalProperties": false
                      }
                    }
                  },
                  "required": [
                    "errors"
                  ],
                  "additionalProperties": false
                }
              }
            }
          }
        }
      }
    },
    "/curves/overshoot": {
      "post": {
        "operationId": "createOvershootCurve",
        "summary": "Create Overshoot Curve",
        "description": "Generate a CSS easing curve with overshoot motion.",
        "tags": [
          "Curves"
        ],
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "title": "Overshoot Animation Parameters",
                "description": "Parameters for overshoot-based easing animations",
                "type": "object",
                "properties": {
                  "style": {
                    "description": "Style of overshoot animation",
                    "example": "OUT",
                    "type": "string",
                    "enum": [
                      "IN",
                      "OUT",
                      "IN_OUT"
                    ]
                  },
                  "mass": {
                    "description": "Mass (1-5)",
                    "example": 2.5,
                    "type": "number",
                    "minimum": 1,
                    "maximum": 5
                  },
                  "damping": {
                    "description": "Damping (0-100)",
                    "example": 50,
                    "type": "number",
                    "minimum": 0,
                    "maximum": 100
                  },
                  "accuracy": {
                    "description": "Accuracy level for the linear easing approximation, HIGH is the best option for most cases.",
                    "example": "HIGH",
                    "type": "string",
                    "enum": [
                      "LOW",
                      "MEDIUM",
                      "HIGH",
                      "ULTRA"
                    ]
                  }
                },
                "required": [
                  "style",
                  "mass",
                  "damping",
                  "accuracy"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "200 OK",
            "content": {
              "application/json": {
                "schema": {
                  "title": "Overshoot Easing Curve Response",
                  "description": "Overshoot easing curve response with specific input and output types",
                  "type": "object",
                  "properties": {
                    "id": {
                      "description": "The ID of the easing curve",
                      "example": "0a1b2c3xy",
                      "type": "string"
                    },
                    "type": {
                      "type": "string",
                      "const": "OVERSHOOT"
                    },
                    "input": {
                      "title": "Overshoot Animation Parameters",
                      "description": "Parameters for overshoot-based easing animations",
                      "type": "object",
                      "properties": {
                        "style": {
                          "description": "Style of overshoot animation",
                          "example": "OUT",
                          "type": "string",
                          "enum": [
                            "IN",
                            "OUT",
                            "IN_OUT"
                          ]
                        },
                        "mass": {
                          "description": "Mass (1-5)",
                          "example": 2.5,
                          "type": "number",
                          "minimum": 1,
                          "maximum": 5
                        },
                        "damping": {
                          "description": "Damping (0-100)",
                          "example": 50,
                          "type": "number",
                          "minimum": 0,
                          "maximum": 100
                        },
                        "accuracy": {
                          "description": "Accuracy level for the linear easing approximation, HIGH is the best option for most cases.",
                          "example": "HIGH",
                          "type": "string",
                          "enum": [
                            "LOW",
                            "MEDIUM",
                            "HIGH",
                            "ULTRA"
                          ]
                        }
                      },
                      "required": [
                        "style",
                        "mass",
                        "damping",
                        "accuracy"
                      ],
                      "additionalProperties": false
                    },
                    "output": {
                      "title": "Linear Easing Output",
                      "description": "CSS and SVG output for linear easing functions",
                      "type": "object",
                      "properties": {
                        "css": {
                          "description": "CSS easing function string",
                          "example": "cubic-bezier(0.66, 0, 0.34, 1)",
                          "type": "string"
                        },
                        "tailwind_css": {
                          "description": "Tailwind CSS compatible easing function string",
                          "example": "ease-[cubic-bezier(0.66,0,0.34,1)]",
                          "type": "string"
                        },
                        "svg_polyline": {
                          "description": "SVG polyline for linear easing curves",
                          "example": "0,75 15.2,39.6 32.8,21.75 50,18.45 100,25",
                          "type": "string"
                        },
                        "suggested_duration_ms": {
                          "description": "Suggested duration range derived from the curve physics. Shorter durations feel snappier, longer durations let complex motions (bounces, oscillations) breathe.",
                          "type": "object",
                          "properties": {
                            "min": {
                              "description": "Minimum suggested CSS animation/transition duration in milliseconds",
                              "example": 300,
                              "type": "integer",
                              "exclusiveMinimum": 0,
                              "maximum": 9007199254740991
                            },
                            "max": {
                              "description": "Maximum suggested CSS animation/transition duration in milliseconds",
                              "example": 600,
                              "type": "integer",
                              "exclusiveMinimum": 0,
                              "maximum": 9007199254740991
                            }
                          },
                          "required": [
                            "min",
                            "max"
                          ],
                          "additionalProperties": false
                        }
                      },
                      "required": [
                        "css",
                        "tailwind_css",
                        "svg_polyline",
                        "suggested_duration_ms"
                      ],
                      "additionalProperties": false
                    },
                    "links": {
                      "title": "Easing Curve Links Response",
                      "description": "HATEOAS navigation links for the easing curve",
                      "type": "object",
                      "properties": {
                        "self": {
                          "description": "Link to this curve resource",
                          "example": "/curves/abc123def",
                          "type": "string"
                        },
                        "share_url": {
                          "description": "Shareable URL for this curve",
                          "example": "https://easingwizard.com/#abc123def",
                          "type": "string",
                          "format": "uri"
                        },
                        "create": {
                          "description": "Endpoint to create curves of this type",
                          "example": "/curves/bezier",
                          "type": "string"
                        }
                      },
                      "required": [
                        "self",
                        "share_url",
                        "create"
                      ],
                      "additionalProperties": false
                    },
                    "generated_at": {
                      "description": "ISO 8601 timestamp when the curve was generated",
                      "example": "2025-07-03T12:00:00Z",
                      "format": "date-time",
                      "type": "string"
                    }
                  },
                  "required": [
                    "id",
                    "type",
                    "input",
                    "output",
                    "links",
                    "generated_at"
                  ],
                  "additionalProperties": false
                }
              }
            }
          },
          "400": {
            "description": "400 Bad Request",
            "content": {
              "application/json": {
                "schema": {
                  "description": "Error response with validation details",
                  "type": "object",
                  "properties": {
                    "errors": {
                      "description": "Array of validation errors",
                      "type": "array",
                      "items": {
                        "type": "object",
                        "properties": {
                          "expected": {
                            "description": "Expected type or value",
                            "example": "number",
                            "type": "string"
                          },
                          "values": {
                            "description": "List of valid values or types",
                            "example": [
                              "BEZIER",
                              "SPRING",
                              "BOUNCE",
                              "WIGGLE",
                              "OVERSHOOT"
                            ],
                            "type": "array",
                            "items": {
                              "type": "string"
                            }
                          },
                          "code": {
                            "description": "Error code",
                            "example": "invalid_type",
                            "type": "string"
                          },
                          "message": {
                            "description": "Human-readable error message",
                            "example": "Expected number, received string",
                            "type": "string"
                          },
                          "path": {
                            "description": "Path to the field that caused the error",
                            "example": [
                              "x1"
                            ],
                            "type": "array",
                            "items": {
                              "anyOf": [
                                {
                                  "type": "string"
                                },
                                {
                                  "type": "number"
                                }
                              ]
                            }
                          }
                        },
                        "required": [
                          "code",
                          "message",
                          "path"
                        ],
                        "additionalProperties": false
                      }
                    }
                  },
                  "required": [
                    "errors"
                  ],
                  "additionalProperties": false
                }
              }
            }
          }
        }
      }
    },
    "/healthz": {
      "get": {
        "servers": [
          {
            "url": "https://api.easingwizard.com"
          }
        ],
        "operationId": "healthCheck",
        "summary": "Health Check",
        "description": "Check the health status of the Easing Wizard API.",
        "tags": [
          "Health"
        ],
        "responses": {
          "200": {
            "description": "200 OK",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "status": {
                      "description": "Health status of the API",
                      "type": "string",
                      "enum": [
                        "ok",
                        "degraded",
                        "error"
                      ]
                    },
                    "timestamp": {
                      "description": "Current timestamp",
                      "type": "string"
                    }
                  },
                  "required": [
                    "status",
                    "timestamp"
                  ],
                  "additionalProperties": false
                }
              }
            }
          }
        }
      }
    }
  }
}