Affine2d fixed set

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

Classify and compute the exact fixed locus of a rational 2D affine map.

Use when you need to: find fixed points of affine transform · compute affine fixed locus · classify fixed set as point line all or none.

Decide before calling

Read the versioned contract and the supported scope below. Reuse affine2d-fixed-set@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-fixed-set@1.0.0 for find fixed points of affine transform. 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

• find fixed points of affine transform
• compute affine fixed locus
• classify fixed set as point line all or none
• solve exact 2D affine fixed equations
• find invariant points of planar map
• exact rational fixed line

Not supported

• iterated periodic points
• approximate eigenspaces

Behavior

• Solve (M-I)p=-t with exact rank predicates.
• Result is all, none, point, or line.
• A line a*x+b*y=c has first nonzero coefficient 1.

Input

• transform (object, required)

Output

• kind (one of "all", "none", "point", "line", required)
• point (object, optional)
• line (object, optional)
• 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": "0",
    "ty": "0"
  }
}

Response:

{
  "result": {
    "kind": "all",
    "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-fixed-set",
  "version": "1.0.0",
  "input": {
    "transform": {
      "a": "1",
      "b": "0",
      "c": "0",
      "d": "1",
      "tx": "0",
      "ty": "0"
    }
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/affine2d-fixed-set/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"transform":{"a":"1","b":"0","c":"0","d":"1","tx":"0","ty":"0"}}'

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

CLI

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

Get the client at /clients/cli/.

Related tools

• Affine2d invert: Invert a nonsingular exact rational 2D affine map with canonical output.
• Affine2d apply: Apply one exact rational 2D affine map to bounded points or free vectors.
• Affine2d compose: Compose two exact rational 2D affine maps in first-then-second order.
• 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.
• Point in polygon classify: Classifies a rational-coordinate point as inside, outside, or boundary using an exact half-open ray rule.