3D Surface Plotter implementation

Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

Record owner

Guth Instruments

Lifecycle

verified-clean

Evidence ID

t8-029

Effect

Computation or source lookup only

Input and validation requirements

The specification does not define handling for singular expression samples. For f(x,y)=1/(x-y), a normal grid containing x=y produces 1/0. If the plotter forwards Infinity or NaN to the rendering pipeline instead of rejecting the sample and splitting the surface, mesh generation, contouring, shading, or camera bounds can fail.

Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

{
  "inputs": {
    "expression": "f(x,y)=x^2+y^2",
    "x_domain": [
      -1,
      1
    ],
    "y_domain": [
      -1,
      1
    ],
    "sample_x": [
      -1,
      0,
      1
    ],
    "sample_y": [
      -1,
      0,
      1
    ],
    "contour_level": 1
  },
  "expected_outputs": {
    "sampled_z_rows_by_y": [
      [
        2,
        1,
        2
      ],
      [
        1,
        0,
        1
      ],
      [
        2,
        1,
        2
      ]
    ],
    "contour_level_1_reference_points": [
      [
        -1,
        0
      ],
      [
        0,
        -1
      ],
      [
        0,
        1
      ],
      [
        1,
        0
      ]
    ],
    "gradient_at": {
      "x": 1,
      "y": 0,
      "gradient": [
        2,
        0
      ],
      "upward_unit_normal": [
        "-2/sqrt(5)",
        "0",
        "1/sqrt(5)"
      ]
    }
  },
  "reference_data": {
    "surface": "Paraboloid z=x^2+y^2",
    "contour_equation": "x^2+y^2=1",
    "gradient_formula": "(f_x,f_y)=(2x,2y)",
    "normal_formula": "n=(-f_x,-f_y,1)/sqrt(f_x^2+f_y^2+1)"
  },
  "working": "Evaluate each grid point: f(-1,-1)=(-1)^2+(-1)^2=1+1=2; f(0,-1)=0^2+(-1)^2=0+1=1; f(1,-1)=1+1=2. For y=0: f(-1,0)=1+0=1; f(0,0)=0+0=0; f(1,0)=1+0=1. For y=1 the row is again [2,1,2]. The level-1 contour satisfies x^2+y^2=1, whose axis intersections are (-1,0),(0,-1),(0,1),(1,0). At (1,0), (f_x,f_y)=(2,0), so n=(-2,0,1), ||n||=sqrt(4+1)=sqrt(5), giving the stated unit normal."
}

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche8/tranche8-results.json