061c0f3333
Co-Authored-By: selune <[email protected]> Co-Authored-By: Claude Sonnet 5.5 <[email protected]>
55 lines
3.6 KiB
Markdown
55 lines
3.6 KiB
Markdown
# Perspective UV differential reference
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The independent L1 helper in #1346 supports the first wood consumer #1345.
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`solidcraft_render::texture_interpolation::PerspectiveUv` accepts three unwrapped
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vertex UVs and positive reciprocal clip-w values. `evaluate` takes the existing
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rasterizer's screen barycentric weights and their x/y derivatives. It returns UV
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and analytic perspective-correct derivatives without changing raster coverage,
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projection, clipping, local mm mapping, instance transforms or resource ownership.
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No pending helper branch, new dependency, file asset or GPU code is required.
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Vertex UV magnitudes are at most one million repeats. Reciprocal-w is finite in
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[1e-12, 1e12]; only a common scale is removed, preserving relative perspective.
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Weights must be finite in [-1e-9, 1+2e-9] and sum to one within 1e-12. The lower
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bound matches the existing raster's near-edge tolerance; the upper bound follows
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from two weights at that lower bound and partition of unity. This admits bounded
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near-edge extrapolation and preserves the exact supplied weights, including small
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negative UV results. It neither clamps weights nor replaces the caller's shared-edge
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top-left decision. Negative near-edge weights can make a perspective denominator
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nonpositive at extreme clip-w ratios; that explicitly refuses. The caller retains
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its existing raw reciprocal-w sum/depth/coverage guards before invoking the helper.
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Each derivative must
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be finite with magnitude at most one million and sum to zero within
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`1e-12 * max(1, largest_component_magnitude)`. No weights or derivatives are
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silently repaired, normalized or clamped. The caller must supply derivatives
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consistent with its projected triangle; admission alone cannot prove that.
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For q=1/w, the interpolation is `UV = sum(b*q*UV_vertex) / sum(b*q)`.
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The helper subtracts the first vertex's UV before forming the numerator, then
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adds it back to the result. This makes a constant large UV offset have exactly
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zero derivatives instead of cancellation artifacts. Derivatives use the quotient
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rule as `(dN - (N/D)*dD)/D`, avoiding a squared tiny denominator. Intermediates
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are f64. Returned UV and derivative magnitudes must remain at most one million,
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finite, or the evaluation refuses. No affine fallback hides unsupported results.
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UVs remain unwrapped: do not repeat-wrap vertices before interpolation. No Y flip
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or normal/tangent interpretation is added. The barycentric derivatives are per
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pixel of the actual shading grid. When starting from final-image-pixel derivatives
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and supersampling Sx by Sy, the caller divides x/y derivatives by Sx/Sy exactly
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once. Already shading-grid derivatives must not be rescaled. This matches #1339's
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LOD boundary without introducing a dependency on that unpublished implementation.
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Caller responsibilities include positive clip-w after near-plane clipping,
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triangle degeneracy/coverage/top-left rules, sample placement and valid derivatives.
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This is a numerical reference, not a new rasterizer, clipping algorithm or proof
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of that caller policy. GPU interpolation/gradient precision requires separate parity
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evidence. Anisotropy, normal filtering, grain-frame inference and a visible texture
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consumer remain separate work. No HDRI or final renderer capability is advertised.
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Version identifier `solidcraft.perspective-uv-differential/1` documents the input,
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partition, precision and refusal policy. Original analytic tests cover affine and
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perspective values/derivatives, reciprocal-w scaling, vertex order, large constant
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offsets, edges, supersampling units and hostile/refused outputs. This invisible
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helper has no useful app screenshot; actual wood still requires PNG, CPU/GPU and
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offline-reopen evidence from the installed consumer.
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