3D Surface Plotter mechanism

Model scope

The stated grid-sampling approach is mathematically appropriate for approximate surface visualization. Verdict is NEEDS_REVIEW because sampling resolution, contour extraction, gradient-shading behavior, coordinate/trigonometric units, singularity handling, and the required honest approximation label are unspecified.

• Grid sampling of f(x,y) is a standard numerical plotting method, but the specification does not define grid resolution, spacing, interpolation, or adaptive refinement; undersampling can miss narrow features, discontinuities, and extrema.
• Contour projection is claimed but no contour-extraction method, interpolation rule, or contour-level input is specified. A standard implementation would use marching squares or an equivalent method on sampled cells.
• Optional gradient shading is underspecified. For z=f(x,y), the standard upward surface normal is n=(-f_x,-f_y,1), normalized as n/||n||; numerical gradients require a finite-difference scheme and boundary handling.
• The empty honest_label is inadequate for a numerically sampled plotter: it should disclose that surfaces and contours are approximate and may be unreliable near discontinuities, singularities, or undersampled features.

Units and conventions

• x and y are numerical coordinate values with user-defined units; no physical unit metadata is specified.
• z inherits the units implied by f(x,y). For mixed or dimensional expressions, the expression parser must enforce dimensionally valid operations.
• Trigonometric arguments are assumed to be in radians unless the instrument explicitly documents degree input.
• The contour level z=c must use the same z units as the function output.

Inspectable vector

One of 4 source-bound review vectors:

{
  "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."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

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.

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
• BOUNDARY_HAZARD_CATALOG.json