Homography incidence verify

homography-incidence-verify · version 1.0.0 · Geometry, location & color · free, no key needed

Verify exact point-line incidence before and after a 2D homography with certificates.

Use when you need to: verify projective incidence · check point lies on line after homography · certify homogeneous point line incidence.

Decide before calling

Read the versioned contract and the supported scope below. Reuse homography-incidence-verify@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 homography-incidence-verify@1.0.0 for verify projective incidence. 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

• verify projective incidence
• check point lies on line after homography
• certify homogeneous point line incidence
• exact incidence preservation test
• validate transformed point and line
• produce projective incidence certificate

Not supported

• approximate distance to a line
• polygon topology validation

Behavior

• Canonical rationals are integers or reduced p/q strings with a positive denominator.
• Homogeneous outputs are primitive integer tuples with first nonzero coordinate positive.
• All arithmetic and predicates use exact BigInt cross-products; binary floating point and epsilon comparisons are never used.
• Reference: Hartley & Zisserman, Multiple View Geometry, 2nd ed., Chapter 2.

Input

• matrix (array of array of string, required): min items 3; max items 3; each min items 3; each max items 3; each each min length 1; each each max length 256; each each pattern ^(?:0|-?[1-9][0-9]*)(?:/[1-9][0-9]*)?$
• point (array of string, required): min items 3; max items 3; each min length 1; each max length 256; each pattern ^(?:0|-?[1-9][0-9]*)(?:/[1-9][0-9]*)?$
• line (array of string, required): min items 3; max items 3; each min length 1; each max length 256; each pattern ^(?:0|-?[1-9][0-9]*)(?:/[1-9][0-9]*)?$

Output

• source_incident (boolean, required)
• transformed_incident (boolean, required)
• source_certificate (string, required): min length 1; max length 256; pattern ^(?:0|-?[1-9][0-9]*)(?:/[1-9][0-9]*)?$
• transformed_certificate (string, required): min length 1; max length 256; pattern ^(?:0|-?[1-9][0-9]*)(?:/[1-9][0-9]*)?$
• point (array of string, required): min items 3; max items 3; each min length 1; each max length 256; each pattern ^(?:0|-?[1-9][0-9]*)(?:/[1-9][0-9]*)?$
• line (array of string, required): min items 3; max items 3; each min length 1; each max length 256; each pattern ^(?:0|-?[1-9][0-9]*)(?:/[1-9][0-9]*)?$
• reference (constant "Hartley & Zisserman, Multiple View Geometry, 2nd ed., Chapter 2", required)

Limits

• max input bytes: 8192
• max rational bytes: 256
• max output bytes: 8192
• max tree nodes: 128

Example

Request input:

{
  "matrix": [
    [
      "1",
      "0",
      "0"
    ],
    [
      "0",
      "1",
      "0"
    ],
    [
      "0",
      "0",
      "1"
    ]
  ],
  "point": [
    "1",
    "2",
    "1"
  ],
  "line": [
    "1",
    "0",
    "-1"
  ]
}

Response:

{
  "result": {
    "source_incident": true,
    "transformed_incident": true,
    "source_certificate": "0",
    "transformed_certificate": "0",
    "point": [
      "1",
      "2",
      "1"
    ],
    "line": [
      "1",
      "0",
      "-1"
    ],
    "reference": "Hartley & Zisserman, Multiple View Geometry, 2nd ed., Chapter 2"
  }
}

How to call it

MCP

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

{
  "id": "homography-incidence-verify",
  "version": "1.0.0",
  "input": {
    "matrix": [
      [
        "1",
        "0",
        "0"
      ],
      [
        "0",
        "1",
        "0"
      ],
      [
        "0",
        "0",
        "1"
      ]
    ],
    "point": [
      "1",
      "2",
      "1"
    ],
    "line": [
      "1",
      "0",
      "-1"
    ]
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/homography-incidence-verify/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"matrix":[["1","0","0"],["0","1","0"],["0","0","1"]],"point":["1","2","1"],"line":["1","0","-1"]}'

The machine-readable contract is at /v1/tools/homography-incidence-verify/versions/1.0.0.

CLI

node cli.mjs run homography-incidence-verify 1.0.0 --input input.json --base-url https://computefirst.net

Get the client at /clients/cli/.

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