Bezier point/tangent/length API

Evaluate a quadratic or cubic Bezier curve at parameter t with the tangent direction and an arc-length estimate via adaptive sampling. Answers 'what point and tangent lie at t on this Bezier?', 'how long is the curve?'.

Price$0.03per request

MethodPOST

Route/v1/geometry/bezier

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

beziercurvetangentarc-lengthde-casteljaucubicquadratic

API URLhttps://x402.hexl.dev/v1/geometry/bezier

Integration docs

Example request

{
  "controlPoints": [
    [
      0,
      0
    ],
    [
      1,
      2
    ],
    [
      3,
      2
    ],
    [
      4,
      0
    ]
  ],
  "t": 0.5
}

Example response

{
  "point": [
    2,
    1.5
  ],
  "tangent": [
    4.5,
    0
  ],
  "unitTangent": [
    1,
    0
  ],
  "degree": 3,
  "arcLength": 5.268259404,
  "t": 0.5
}

Input schema

{
  "type": "object",
  "required": [
    "controlPoints",
    "t"
  ],
  "properties": {
    "controlPoints": {
      "type": "array",
      "items": {
        "type": "array",
        "items": {
          "type": "number"
        }
      },
      "description": "3 (quadratic) or 4 (cubic) 2D/3D points",
      "examples": [
        [
          [
            0,
            0
          ],
          [
            1,
            2
          ],
          [
            3,
            2
          ],
          [
            4,
            0
          ]
        ]
      ]
    },
    "t": {
      "type": "number",
      "examples": [
        0.5
      ]
    },
    "lengthSamples": {
      "type": "integer",
      "examples": [
        100
      ]
    }
  }
}

Output schema

{
  "type": "object",
  "additionalProperties": true
}