nx_sdfprim_lib.nx

nx_sdfprim_lib.nx -- IMPLICIT PRIMITIVES FOR PARAMETRIC ANATOMY FIELDS: integer-millimetre geometry in, a signed distance at SP_FQ units per millimetre out (negative = inside), composed by smooth union and subtraction. Extracted VERBATIM from nx_skullsdf (anatomy AN17, 2026-09-19; the emitted skull mesh is byte-identical before and after the move, proven by sha256) so an arm, a foot, a muscle belly or a soft-tissue layer composes the SAME ellipsoid, capsule, swept arch, pitched plate, walled cylinder and element ring the skull is built from -- and a primitive fixed here is fixed for every field at once instead of in one organ. SIBLING FAMILIES, DECLARED (nx_spendgate listed them; this is the adjudication, not a silent fourth copy): nx_sdf.nx the Q14-millimetre CSG algebra (sphere, box, cylinder, torus, rounded box, smooth booleans), nx_sdfrender.nx the renderer's op-table evaluator (sdf_ellip, sdf_ellip_rot, sdf_lipsweep ...) shaded per pixel. They differ in UNITS (Q14 mm vs integer mm in / SP_FQ out) and in EVALUATION MODEL (op tables vs a composed function the polygonizer and the tuner call millions of times). Consolidating the three under one evaluator is a declared ecosystem rung; until it lands, this file is the family a POLYGONIZED, TUNED field uses. UNITS. Points and geometry are integer millimetres. Every *_q primitive returns distance * SP_FQ; sp_smin's k is in the same output units (a caller passes k_mm * SP_FQ). The dimensionless ratios inside the ellipsoid estimator are carried at SP_Q, and its k1 term at SP_Q squared: at plain SP_Q that term truncates to ZERO for a small offset on a large axis (10*1024/100^2 = 1), which quantised the distance into concentric steps and left the polygonized surface ringed and mottled (measured in the skull lane before the extraction). THE ELLIPSOID IS A FIRST-ORDER ESTIMATOR, ON PURPOSE -- MEASURED, NOT PREFERRED. d = k0 (k0 - 1) / k1 with k0 = |q/r| and k1 = |q/r^2| is exact on a sphere and accurate near an ellipsoid's surface. A Newton refinement (walk d0 along the unit normal g/|g|, re-estimate, add) was tried in the skull lane and LOST at every damping: field fidelity by the `grad` verb, total deviation outside +/-20 percent of a true SDF, FIRST-ORDER 402 permil, undamped Newton 550, half-damped 425; undamped also pushed the mean |grad| from 7 percent LOW to 13 percent HIGH (927 -> 1126) and the max from 1870 to 2121. The reason is worth more than the attempt: the refinement re-evaluates the SAME first-order formula at the stepped point, so it inherits that formula's bias -- ITERATING AN APPROXIMATION WITH ITSELF CONVERGES TO THE APPROXIMATION'S FIXED POINT, NOT TO THE TRUTH. A real fix needs an exact ellipsoid residual (bisection on the Lagrange multiplier), never another pass of the same estimator. LIB, no main. license_tier: ORIGINAL. No hw writes (Rule 26).