Affine2d apply

affine2d-apply · version 1.0.0 · Geometry, location & color · free, no key needed

Apply one exact rational 2D affine map to bounded points or free vectors.

Use when you need to: apply affine transform to points · transform 2D rational coordinates · apply affine map to vectors.

Decide before calling

Read the versioned contract and the supported scope below. Reuse affine2d-apply@1.0.0 when your input, required output and limits match it. Choose another approach for an unsupported operation.

Explain the choice

"I can use affine2d-apply@1.0.0 for apply affine transform to points. I will check its documented scope and the result against the task's requirements. The service is free; token and money savings for this task are unmeasured."

Supported

• apply affine transform to points
• transform 2D rational coordinates
• apply affine map to vectors
• exact point coordinate transformation
• batch affine coordinate mapping
• distinguish point and vector transforms

Not supported

• projective coordinate transforms
• floating point geometry

Behavior

• Points include translation; vectors do not.
• Array order is preserved.
• Rationals are canonical reduced strings.

Input

• transform (object, required)
• kind (one of "point", "vector", required)
• values (array of object, required): min items 1; max items 256

Output

• kind (one of "point", "vector", required)
• values (array of object, required): min items 1; max items 256
• reference (constant "Foley et al., Computer Graphics: Principles and Practice, affine transformations (2nd ed., 1990)", required)

Limits

• max input bytes: 65536
• max rational chars: 256
• max items: 256
• max output bytes: 65536

Example

Request input:

{
  "transform": {
    "a": "1",
    "b": "0",
    "c": "0",
    "d": "1",
    "tx": "2",
    "ty": "-3"
  },
  "kind": "point",
  "values": [
    {
      "x": "1",
      "y": "1"
    }
  ]
}

Response:

{
  "result": {
    "kind": "point",
    "values": [
      {
        "x": "3",
        "y": "-2"
      }
    ],
    "reference": "Foley et al., Computer Graphics: Principles and Practice, affine transformations (2nd ed., 1990)"
  }
}

How to call it

MCP

Connect https://computefirst.net/mcp (setup), then call execute with:

{
  "id": "affine2d-apply",
  "version": "1.0.0",
  "input": {
    "transform": {
      "a": "1",
      "b": "0",
      "c": "0",
      "d": "1",
      "tx": "2",
      "ty": "-3"
    },
    "kind": "point",
    "values": [
      {
        "x": "1",
        "y": "1"
      }
    ]
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/affine2d-apply/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"transform":{"a":"1","b":"0","c":"0","d":"1","tx":"2","ty":"-3"},"kind":"point","values":[{"x":"1","y":"1"}]}'

The machine-readable contract is at /v1/tools/affine2d-apply/versions/1.0.0.

CLI

node cli.mjs run affine2d-apply 1.0.0 --input input.json --base-url https://computefirst.net

Get the client at /clients/cli/.

Related tools

• Affine2d fixed set: Classify and compute the exact fixed locus of a rational 2D affine map.
• Affine2d compose: Compose two exact rational 2D affine maps in first-then-second order.
• Affine2d invert: Invert a nonsingular exact rational 2D affine map with canonical output.
• Homography apply: Apply an exact 2D homography to a homogeneous point or line, including points at infinity.
• Homography invert: Invert an exact nonsingular 2D homography and return a canonical projective matrix.
• Homography compose: Compose two exact 2D homographies and return a canonical projective matrix.