`nx_skullsdf.nx` source

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1// nx_skullsdf.nx -- the skull as a FUSED SHELL WITH OPENINGS, built in the implicit path.
2//
3// ★WHY THIS EXISTS, from two render cycles of evidence rather than preference. nx_skullgen emits the
4// skull as seven LOFTED TUBES. Rendered, that is seven separate objects sharing a bounding box: the
5// nasal bones float clear of the face, the zygomatic arch is a rod passing through nothing, and the
6// braincase is a balloon with a jaw hanging near it. Moving the tubes closer helps a little and cannot
7// fix the class of problem, because A SKULL IS NOT A SET OF TUBES -- it is one continuous fused shell
8// with holes cut in it. Tubes cannot fuse and cannot have holes.
9//
10// ★THE IMPLICIT PATH DOES EXACTLY THOSE TWO THINGS AND WE ALREADY OWN IT: smooth-union joins bones into
11// one surface, subtraction cuts the orbits and the nasal aperture as real openings, and nx_isosurf's
12// surface_nets polygonizes the result into nx_trimesh. The plan reserved SDF for viscera on the grounds
13// that it cannot resolve an eyelash -- true, and irrelevant to bone, whose features are centimetres.
14// ⚠So this does NOT replace the loft path for skin. It claims the skull only.
15//
16//   nx_skullsdf <out.nxmesh> [sex 0-1000] [robust 0-1000] [grid]
17// license_tier: ORIGINAL  expect_exit: 0  No hw writes (Rule 26).
18import "nx_isosurf.nx"
19import "nx_itoa_lib.nx"   // shared MSB-first emitter (zero-alloc)
20import "nx_memfloor.nx"   // mf_admit: refuse an O(G^3) grid that would eat the host (2026-07-30 incident)
21const SS_MAGIC_2026: i64 = 2026
22const SS_MAGIC_1024: i64 = 1024
23const SS_MAGIC_8388608: i64 = 8388608
24const SS_MAGIC_8388607: i64 = 8388607
25const SS_MAGIC_40000: i64 = 40000
26
27const SS_G: i64 = 160             // grid cells per axis
28const SS_EXT: i64 = 120           // world half-extent in MILLIMETRES. A male skull is ~185mm long and
                                // ~145mm broad, so 260mm of grid covers it with no wasted resolution
                                // (the first version sampled 600mm and spent most of the grid on air)
31// ★THE PRIMITIVES ARE AUTHORED IN AN ARBITRARY ~90-UNIT SPACE, NOT MILLIMETRES. Assuming otherwise
32// produced a skull measuring 84x75x93mm against the reference's 151x209x215 -- roughly half scale and
33// wrongly proportioned. This factor maps the authored space onto real millimetres, and the three
34// reference dimensions are named so the gate can check the result against them instead of my eye.
35// Derived from the measurement, not guessed: at 1850 the emitted skull stood 348mm against a 209mm
36// reference, so the factor is 1850 x 209/348. Each correction here is now driven by the bbox the organ
37// prints, which is the whole reason that check exists.
38// ★IDENTITY. The field below is now authored in REAL MILLIMETRES against the reference's measured box,
39// so there is no unit-space to get wrong. The previous arbitrary ~90-unit space needed a fudge factor
40// that could correct overall size but never proportion -- the skull came out 176x256x210 where the
41// reference is 151x209x215: too tall AND too shallow, which no single multiplier can fix.
42const SS_SCALE: i64 = 1000
43const SS_REF_W: i64 = 151         // reference bounding box, mm, measured off BodyParts3D
44const SS_REF_H: i64 = 209
45const SS_REF_D: i64 = 215
46const SS_TOL: i64 = 25            // mm each dimension may differ before the build is called wrong
47const SS_Q: i64 = 1024            // fixed point for the distance functions
48const SS_NQ: i64 = 4096           // the scale surface_nets emits gradient normals in (nx_isosurf.nx:68)
49const SS_ISO: i64 = 0
50const SS_BONE: i64 = 0xe8e0d8
51// ★★SMOOTH-UNION RADIUS -- AND WHY IT IS NOW ZERO. ss_smin subtracts h^2/(4k) from the result, so every
52// chained call pushes the field further negative. Chaining eleven of them means the value at a point
53// depends on how many bones are near it, and the result is NOT a distance field -- gradient magnitude
54// drifts far from 1. surface_nets places each vertex by LINEAR INTERPOLATION along a cell edge, which
55// assumes the field is locally linear in distance; feed it a distorted field and vertices land in
56// inconsistent places, giving a jagged self-intersecting shell that renders as speckle.
57// ★Plain min() is the exact union of two SDFs and cannot distort anything. It is also anatomically
58// right: bones meet at SUTURES, which are sharp, not blended.
59// Restored to a real millimetre blend. At 0 (plain union) the mandible and face floated as separate
60// lumps with visible seams; bones do meet at sutures, but a 6mm blend at 2mm sampling is what makes
61// adjacent masses read as ONE bone rather than a pile of touching balls.
62const SS_K: i64 = 6
63// ***SS_K IS NOW RUNTIME-SETTABLE (argv[7]) SO THE SMOOTH-UNION/DISTANCE-FIDELITY TRADE CAN BE A/B'd
64// WITHOUT A REBUILD. This file already records setting K to ZERO once, for exactly the reason that
65// matters here -- plain min() is the EXACT union of two SDFs and cannot distort anything, whereas every
66// chained ss_smin subtracts h*h/(4k) and pushes the field away from a true distance function. K=0 gives
67// honest distances with visible sutures; K=6 gives one fused shell with a distorted field. Until now that
68// trade was a recompile, so nobody measured it. Default is unchanged, so every existing caller is
69// byte-identical.
70static SS_KSET: i64
71static SS_KVAL: i64
72func ss_k() -> i64 { if SS_KSET == 1 { return SS_KVAL } return SS_K }
73
74func ss_puts(s: *u8) -> i64 { var n: i64=0; while s[n]!=(0 as u8){n=n+1} sys_write(1,s,n); return 0 }
75// MIGRATED to nxi_out (debt 1785563586). The old body mmapped 32 bytes per call and never freed it,
76// across 33 call sites. THIS ORGAN ALREADY IMPORTS nx_memfloor mf_admit after the 2026-07-30
77// incident where it took 27.7GB of 36GB and froze every seat -- the GUARD was added, the CAUSE
78// was not. nxi_out is MSB-first, allocates NOTHING, and emits identical bytes including the sign.
79func ss_pn(v: i64) -> i64 { nxi_out(v); return 0 }
80func ss_atoi(s: *u8) -> i64 {
  var i: i64=0; var n: i64=0; var sg: i64=1
  if s[0]==(45 as u8) { sg=0-1; i=1 }
  while s[i]!=(0 as u8) { let c: i64=s[i] as i64; if c>=48 { if c<=57 { n=n*10+(c-48) } } i=i+1 }
  return n*sg
85}
86func ss_streq(a: *u8, b: *u8) -> i64 {
  var i: i64=0; var go: i64=1; var eq: i64=1
  while go==1 { if a[i]!=b[i] { eq=0; go=0 } else { if a[i]==(0 as u8) { go=0 } else { i=i+1 } } }
  return eq
90}
91func ss_isqrt(v: i64) -> i64 { if v<=0 { return 0 } var x: i64=v; var y: i64=(x+1)/2; while y<x { x=y; y=(x+v/x)/2 } return x }
92func ss_abs(v: i64) -> i64 { if v<0 { return 0-v } return v }
93func ss_min(a: i64, b: i64) -> i64 { if a<b { return a } return b }
94func ss_max(a: i64, b: i64) -> i64 { if a>b { return a } return b }
95
96// ---- primitives. All return a signed distance in world units: negative inside.
97// An ellipsoid's exact SDF has no closed form; the standard cheap bound (scaled radial distance times
98// the smallest semi-axis) is used, which is what every SDF modeller uses and is accurate near the
99// surface -- the only place the polygonizer looks.
100// ★★TRUE ELLIPSOID DISTANCE, not a radial bound. The previous version returned
101// (radial-1) x smallest-semi-axis, which is only correct on a sphere and drifts badly off-axis. Alone
102// that is invisible; SMOOTH-UNIONED a dozen times it produced grid-scale ripples in the field, and
103// surface nets faithfully polygonized the ripples into a lumpy self-intersecting shell that z-fought
104// against itself. ★The error was in the PRIMITIVE and only became visible under COMPOSITION.
105// This is the standard first-order approximation d = k0(k0-1)/k1, exact on a sphere and accurate near
106// the surface of an ellipsoid -- which is the only region the polygonizer samples.
107func ss_ellipsoid(px: i64, py: i64, pz: i64, cx: i64, cy: i64, cz: i64, rx: i64, ry: i64, rz: i64) -> i64 {
  var ax: i64 = rx; var ay: i64 = ry; var az: i64 = rz
  if ax < 1 { ax = 1 }
  if ay < 1 { ay = 1 }
  if az < 1 { az = 1 }
  let qx: i64 = px-cx
  let qy: i64 = py-cy
  let qz: i64 = pz-cz
  // k0 = |q/r|, in SS_Q fixed point
  let n0x: i64 = qx*SS_Q/ax
  let n0y: i64 = qy*SS_Q/ay
  let n0z: i64 = qz*SS_Q/az
  let k0: i64 = ss_isqrt(n0x*n0x + n0y*n0y + n0z*n0z)
  if k0 == 0 { return 0 - ss_min(ss_min(ax,ay),az) }
  // k1 = |q/r^2|, carried at SS_Q SQUARED. ⚠At plain SS_Q this term truncates to ZERO for small
  // offsets on a large axis (10*1024/100^2 = 1), so the distance quantised into concentric steps and
  // the polygonized surface came out ringed and mottled. The extra factor costs nothing and makes the
  // division exact: d = k0(k0-1)/k1 reduces to k0_int*(k0_int-Q)/k1_int with these scalings.
  let n1x: i64 = qx*SS_Q*SS_Q/(ax*ax)
  let n1y: i64 = qy*SS_Q*SS_Q/(ay*ay)
  let n1z: i64 = qz*SS_Q*SS_Q/(az*az)
  var k1: i64 = ss_isqrt(n1x*n1x + n1y*n1y + n1z*n1z)
  if k1 < 1 { k1 = 1 }
  let d0: i64 = k0*(k0-SS_Q)/k1
  // ***ONE NEWTON REFINEMENT STEP. MEASURED MOTIVE, not preference: the `grad` verb reports |grad f|
  // over the near-surface field as mean 927 with 25.6 percent below 800 and 14.6 percent above 1200 --
  // i.e. 40 percent of the field deviates more than 20 percent from a true SDF, which is exactly the
  // 3-6mm tissue-thickness scatter. K=0 showed the SMOOTH UNION is not responsible, so the error is in
  // this function, and this function's own comment already says why: d = k0(k0-1)/k1 is the FIRST-ORDER
  // form, 'exact on a sphere and accurate near the surface of an ellipsoid'. Offsetting an iso-level by
  // 3-11mm deliberately leaves that region, and our primitives are eccentric (81x71x75, 30x13x53,
  // 9x18x12) where first-order error grows fastest.
  // ***THE STEP: the unit normal is g/|g| with g = q/r^2, which we already have as (n1x,n1y,n1z)/k1.
  // Walk d0 along it, re-estimate there, and add. That is Newton on F(x)=|x/r|-1, and on a sphere the
  // second term is exactly zero so this stays EXACT where it already was.
  // ***MEASURED AND REVERTED -- THE NEWTON REFINEMENT LOSES AT EVERY DAMPING TRIED. 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. Plain first-order WINS. Undamped also pushed the mean from
  // 7 percent LOW to 13 percent HIGH (927 -> 1126) and the max from 1870 to 2121.
  // ***THE LIKELY REASON, and it 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 own bias. ITERATING AN
  // APPROXIMATION WITH ITSELF CONVERGES TO THE APPROXIMATION'S FIXED POINT, NOT TO THE TRUTH. A Newton
  // step only refines when the residual and its gradient are evaluated EXACTLY; here both come from the
  // estimator being corrected. A real fix needs an exact ellipsoid residual (bisection on the Lagrange
  // multiplier is the standard one) rather than another pass of the same estimator.
  // Block RETAINED UNUSED behind a constant-false guard (GX-34 emitLimbTube precedent) so the next
  // attempt starts from measured ground rather than re-deriving this.
  if SS_Q < 0 {
  var ux: i64 = n1x*SS_Q/k1
  var uy: i64 = n1y*SS_Q/k1
  var uz: i64 = n1z*SS_Q/k1
  let ex: i64 = qx - d0*ux/SS_Q
  let ey: i64 = qy - d0*uy/SS_Q
  let ez: i64 = qz - d0*uz/SS_Q
  let m0x: i64 = ex*SS_Q/ax
  let m0y: i64 = ey*SS_Q/ay
  let m0z: i64 = ez*SS_Q/az
  let j0: i64 = ss_isqrt(m0x*m0x + m0y*m0y + m0z*m0z)
  if j0 == 0 { return d0 }
  let m1x: i64 = ex*SS_Q*SS_Q/(ax*ax)
  let m1y: i64 = ey*SS_Q*SS_Q/(ay*ay)
  let m1z: i64 = ez*SS_Q*SS_Q/(az*az)
  var j1: i64 = ss_isqrt(m1x*m1x + m1y*m1y + m1z*m1z)
  if j1 < 1 { j1 = 1 }
  // ***DAMPED. THE UNDAMPED STEP OVERSHOT, MEASURED: mean 927 -> 1126 (7 percent LOW became 13 percent
  // HIGH), under_800 256 -> 154 permil which is the improvement it was meant to make, but over_1200
  // 146 -> 396, so TOTAL deviation outside +/-20 percent went 402 -> 550 permil. It corrected the right
  // error in the right direction and went too far -- the textbook behaviour of an undamped Newton step
  // on an approximate, non-convex function. Half-stepping is the standard remedy and costs one shift.
  return d0 + (j0*(j0-SS_Q)/j1)/2
  }
  return d0
179}
180// capsule between two points with radius r -- the right primitive for an ARCH, which is what the
181// zygomatic actually is and what a straight tube could never be
182func ss_capsule(px: i64, py: i64, pz: i64, ax: i64, ay: i64, az: i64, bx: i64, by: i64, bz: i64, r: i64) -> i64 {
  let ex: i64 = bx-ax; let ey: i64 = by-ay; let ez: i64 = bz-az
  let den: i64 = ex*ex + ey*ey + ez*ez
  var t: i64 = 0
  if den > 0 {
      t = ((px-ax)*ex + (py-ay)*ey + (pz-az)*ez) * SS_MAGIC_1024 / den
      if t < 0 { t = 0 }
      if t > SS_MAGIC_1024 { t = SS_MAGIC_1024 }
  }
  let qx: i64 = ax + ex*t/SS_MAGIC_1024
  let qy: i64 = ay + ey*t/SS_MAGIC_1024
  let qz: i64 = az + ez*t/SS_MAGIC_1024
  let dx: i64 = px-qx; let dy: i64 = py-qy; let dz: i64 = pz-qz
  return ss_isqrt(dx*dx + dy*dy + dz*dz) - r
196}
197// ★smooth union: the operation that makes separate bones ONE SURFACE instead of touching objects
198func ss_smin(a: i64, b: i64, k: i64) -> i64 {
  if k <= 0 { return ss_min(a,b) }
  var h: i64 = k - ss_abs(a-b)
  if h < 0 { h = 0 }
  return ss_min(a,b) - h*h/(4*k)
203}
204// subtraction: carve B out of A. This is how an orbit becomes a real OPENING rather than a dent.
205func ss_sub(a: i64, b: i64) -> i64 { return ss_max(a, 0-b) }
206
207// ---- THE SKULL FIELD. Every dimension is a function of the sex/robusticity knobs, as in nx_skullgen;
208// the difference is purely that these compose by union and subtraction instead of standing apart.
209// ★AUTHORED IN MILLIMETRES, in a frame centred on the cranium: +y up, +z forward (toward the face),
210// x lateral. Every figure is a real skull dimension, so the emitted bounding box can be compared
211// directly against the reference's 151 x 209 x 215 instead of through a fudge factor.
212// ★★THE SKULL AS A PARAMETER VECTOR. Hand-placing coordinates got the bounding box to 5mm and left the
213// SHAPE at 8mm mean error, because a person adjusting numbers by eye cannot search twenty dimensions.
214// Exposing the dimensions as data lets the fit metric DRIVE them instead: `tune` runs coordinate
215// descent against the real scanned reference and keeps only changes that lower the measured error.
216const SP_N: i64 = 20
217const P_VW: i64 = 0            // vault half-width
218const P_VH: i64 = 1            // vault half-height
219const P_VD: i64 = 2            // vault half-depth
220const P_VY: i64 = 3            // vault centre y
221const P_VZ: i64 = 4            // vault centre z
222const P_FY: i64 = 5            // frontal centre y
223const P_FZ: i64 = 6            // frontal centre z
224const P_FH: i64 = 7            // frontal half-height
225const P_FD: i64 = 8            // frontal half-depth
226const P_MY: i64 = 9            // maxilla centre y
227const P_MZ: i64 = 10           // maxilla centre z
228const P_MW: i64 = 11           // maxilla half-width
229const P_MH: i64 = 12           // maxilla half-height
230const P_MD: i64 = 13           // maxilla half-depth
231const P_JY: i64 = 14           // mandible chin y
232const P_JZ: i64 = 15           // mandible chin z
233const P_RX: i64 = 16           // ramus x offset
234const P_RY: i64 = 17           // ramus centre y
235const P_OR: i64 = 18           // orbit radius
236const P_OX: i64 = 19           // orbit centre x
237// ★FITTED, NOT TYPED. These are the output of `tune` -- coordinate descent against the 171k-triangle
238// scanned reference, which took the mean surface error from 8.37mm to 5.06mm in one run. Every value
239// here was accepted only because it LOWERED a measured number, which is the opposite of how the
240// previous eight rounds of hand-placed coordinates were chosen.
241func ss_defaults(P: *i64) -> i64 {
  P[P_VW]=81; P[P_VH]=71; P[P_VD]=75; P[P_VY]=24;  P[P_VZ]=0-33
  P[P_FY]=46; P[P_FZ]=15; P[P_FH]=34; P[P_FD]=33
  P[P_MY]=0-45; P[P_MZ]=58; P[P_MW]=30; P[P_MH]=13; P[P_MD]=53
  P[P_JY]=0-78; P[P_JZ]=60; P[P_RX]=57; P[P_RY]=0-46
  P[P_OR]=8; P[P_OX]=30
  return 0
248}
249
250func ss_field_p(px: i64, py: i64, pz: i64, sexf: i64, robust: i64, P: *i64) -> i64 {
  let vw: i64 = P[P_VW] - 3*sexf/1000
  let vh: i64 = P[P_VH] - 2*sexf/1000
  let vd: i64 = P[P_VD] - 2*sexf/1000
  let jaw: i64 = 46 - 5*sexf/1000 + 4*robust/1000
  let brow: i64 = 10 - 3*sexf/1000 + 5*robust/1000
  var d: i64 = ss_ellipsoid(px,py,pz, 0, P[P_VY], P[P_VZ], vw, vh, vd)
  d = ss_smin(d, ss_ellipsoid(px,py,pz, 0, P[P_FY], P[P_FZ], vw*78/100, P[P_FH], P[P_FD]), ss_k())
  d = ss_smin(d, ss_capsule(px,py,pz, 0-52,22,62, 52,22,62, brow), ss_k())
  d = ss_smin(d, ss_ellipsoid(px,py,pz, 0, P[P_MY], P[P_MZ], P[P_MW], P[P_MH], P[P_MD]), ss_k())
  d = ss_smin(d, ss_ellipsoid(px,py,pz, 0, P[P_MY]-18, P[P_MZ]-4, P[P_MW]*86/100, 12, P[P_MD]*85/100), ss_k())
  d = ss_smin(d, ss_capsule(px,py,pz, 0-52,6,52, 0-62,8,0-30, 7), ss_k())
  d = ss_smin(d, ss_capsule(px,py,pz,   52,6,52,   62,8,0-30, 7), ss_k())
  d = ss_smin(d, ss_ellipsoid(px,py,pz, 0, 8, 76, 9, 18, 12), ss_k())
  d = ss_smin(d, ss_ellipsoid(px,py,pz, 0, P[P_JY], P[P_JZ], 26, 18, 22), ss_k())
  d = ss_smin(d, ss_capsule(px,py,pz, 0-22,P[P_JY],P[P_JZ]-4, 0-46,P[P_JY]+10,10, 17), ss_k())
  d = ss_smin(d, ss_capsule(px,py,pz,   22,P[P_JY],P[P_JZ]-4,   46,P[P_JY]+10,10, 17), ss_k())
  d = ss_smin(d, ss_ellipsoid(px,py,pz, 0-P[P_RX], P[P_RY], 0-6, 9, 34, 26), ss_k())
  d = ss_smin(d, ss_ellipsoid(px,py,pz,   P[P_RX], P[P_RY], 0-6, 9, 34, 26), ss_k())
  d = ss_sub(d, ss_capsule(px,py,pz, 0-P[P_OX],18,80, 0-20,12,18, P[P_OR]))
  d = ss_sub(d, ss_capsule(px,py,pz,   P[P_OX],18,80,   20,12,18, P[P_OR]))
  d = ss_sub(d, ss_capsule(px,py,pz,    0,0-8,92,   0,0-2,40, 13))
  return d
273}
274
275// THE DEFAULT PARAMETER VECTOR IS MAPPED ONCE, NOT ONCE PER SAMPLE -- the organ's single largest
276// defect, not a tuning matter. ss_field is the hot path of the whole program: the polygonizer
277// evaluates it at every one of (G+1)^3 grid corners. It used to sys_mmap(SP_N*8) on EVERY call, and
278// sys_mmap is PAGE-GRANULAR -- a 160-byte request costs a whole 4096-byte page, nothing here frees,
279// so THE FIELD LEAKED ONE PAGE PER SAMPLE.
280// MEASURED, and it reproduces the 2026-07-30 incident to the digit: G=224 is 225^3 = 11,390,625
281// samples x 4096 B = 46.6 GB of anonymous pages; the box OOM-killed it at total-vm 33.8 GB /
282// anon-rss 28.0 GB partway through. The grid array at that size is only 91 MB and cv another 90 MB,
283// so 2,966 bytes per cell was never the grid -- it was this line. It is also why G=1500 mapped 27 GB
284// and froze every other seat's builds.
285// THE BANKED DIAGNOSIS -- 'the knob allocates on the RAW argument while computing on a CAPPED one' --
286// WAS WRONG, and the memory arithmetic refutes it: the raw-argument allocation is O(G^3)x8 = 91 MB at
287// G=224, three orders of magnitude short of the observed kill. The cost was per-EVALUATION, not
288// per-cell-of-storage.
289// A static POINTER lazily mapped once is the sanctioned shape here (a static ARRAY in BSS is the
290// banked crash-on-startup hazard, and this is the idiom nx_fluid/nx_genome/nx_ghash already use). The
291// vector is immutable after ss_defaults, so ONE copy is correct for every caller and ss_field stays a
292// pure function of its arguments -- the property the tuner and the polygonizer both rely on.
293static SS_PDEF: i64
294func ss_pdef() -> *i64 {
  if SS_PDEF == 0 {
      SS_PDEF = sys_mmap(SP_N*8) as i64
      ss_defaults(SS_PDEF as *i64)
  }
  return SS_PDEF as *i64
300}
301func ss_field(px: i64, py: i64, pz: i64, sexf: i64, robust: i64) -> i64 {
  // delegates to the parameterised field with the default vector, so every existing caller is
  // unchanged and there is exactly ONE definition of the skull's geometry
  return ss_field_p(px, py, pz, sexf, robust, ss_pdef())
305}
306
307// Evaluate the authored field at a WORLD millimetre point: map the point back into authored space,
308// then scale the returned distance forward again so the field stays a true SDF in world units.
309func ss_field_world(px: i64, py: i64, pz: i64, sexf: i64, robust: i64) -> i64 {
  let d: i64 = ss_field(px*1000/SS_SCALE, py*1000/SS_SCALE, pz*1000/SS_SCALE, sexf, robust)
  return d * SS_SCALE / 1000
312}
313
314// ★★★SKIN AS A TRUE ENVELOPE -- THE ANSWER THE OFFSET FAILURE HANDED US. nx_skinwrap displaced every
315// bone vertex outward along its own normal by the forensic tissue depth, and it LOWERED the binding judge
316// 99 -> 88 against the cadaver skin. The reason was structural, not tuning: AN OFFSET ALONG A NORMAL
317// CANNOT BRIDGE A CAVITY, and a face is largely defined by the cavities its skin bridges -- the orbits,
318// the nasal aperture, the temporal fossa. A per-vertex offset reproduces every opening and pushes its rim
319// outward, so a socket becomes a bulging crater. That is the exact inverse of this lane's banked law that
320// relief modulates a radius and cannot CUT a hole: a normal offset cannot FILL one.
321// ★THE IMPLICIT PATH DOES IT FOR FREE, and that is why this belongs here and not in a new organ. The skull
322// is already a distance FIELD. Subtracting a depth from the distance before polygonizing moves the zero
323// level OUTWARD by that depth, and AN ISO-SURFACE AT DISTANCE d NATURALLY BRIDGES ANY OPENING NARROWER
324// THAN 2d -- which is precisely the eyelid-over-orbit and skin-over-aperture behaviour we want, arising
325// from the representation rather than from a special case.
326// ★DEPTH IS KEYED ON THE FIELD'S OWN AUTHORED STATIONS, not on a per-mille of some bounding box, because
327// the field already places every landmark in millimetres in a frame centred on the cranium. These are the
328// published forensic depths (Rhine/De Greef class) this codebase carries in knowledge/face_tissue.dat.
329// ⚠HONEST v1 LIMIT, declared here rather than discovered later: this varies with HEIGHT only. The temple
330// is 3mm while the cheekbone at nearly the same height is 7, so a height-keyed table cannot express a
331// lateral difference. The nasion dip at 3mm between brow 7 and nasal 6 IS expressible, and it is the one
332// that makes a nose read as a nose.
333static SS_TISSUE: i64
334// ★★★DENSE-ER TISSUE MAP: DEPTH IS A FUNCTION OF (HEIGHT, LATERAL DISTANCE), NOT HEIGHT ALONE.
335// ★WHY, from the 2026 literature rather than from taste: the state of the art in anatomy-guided face
336// generation (Skull-to-Face, arXiv 2403.16207; SCULPTOR skeleton-consistent parametric generator; and the
337// PLOS One automatic forensic reconstruction from DENSE STATISTICS OF SOFT TISSUE THICKNESS) does not use
338// a sparse landmark list -- it fits a DENSE MAP of tissue thickness over the skull surface. Our v1 was a
339// 9-band table keyed on height only, and I declared its limit when I shipped it: the temple is ~3mm while
340// the zygion sits at ~7mm at nearly the SAME HEIGHT, so a 1-D table structurally cannot express either
341// without corrupting the other. Adding the lateral axis is the smallest honest step toward a dense map,
342// and it is the axis that carries the largest published disagreement.
343// ★THE LATERAL STRUCTURE IS REAL ANATOMY, NOT SMOOTHING. Two rows invert with distance from the midline
344// and they are the reason this matters: at the BROW LINE the midline glabella is thick (7) while the
345// TEMPLE is the thinnest soft tissue on the whole head (3); at the JAW the midline chin is 11 but the
346// GONION is thicker still going outward (11) because the MASSETER inserts there. A height-only table gets
347// the temple and the gonion wrong in OPPOSITE directions, which is exactly the kind of error that shows up
348// as a wrong silhouette rather than a wrong number.
349// ⚠STILL NOT A DENSE MAP: this is 9 height bands x 3 lateral bands = 27 cells, against a literature
350// standard of a per-vertex statistical field. It is a strict superset of v1's information, not parity.
351const SS_LAT_MID: i64 = 25     // |x| under this is the midline column
352const SS_LAT_FAR: i64 = 55     // |x| over this is the far-lateral column (temple / zygomatic arch / gonion)
353func ss_tdepth2(y: i64, ax: i64) -> i64 {
  var col: i64 = 0
  if ax >= SS_LAT_MID { col = 1 }
  if ax >= SS_LAT_FAR { col = 2 }
  if y < 0-78 { if col==0 { return 11 } if col==1 { return 10 } return 8 }    // chin / mental
  if y < 0-60 { if col==0 { return 9 }  if col==1 { return 10 } return 11 }   // jaw -- THICKENS outward (masseter)
  if y < 0-38 { if col==0 { return 11 } if col==1 { return 9 }  return 8 }    // lower lip
  if y < 0-30 { if col==0 { return 10 } if col==1 { return 8 }  return 7 }    // upper lip
  if y < 0    { if col==0 { return 7 }  if col==1 { return 7 }  return 6 }    // maxilla / zygion
  if y < 8    { if col==0 { return 6 }  if col==1 { return 7 }  return 6 }    // nasal
  if y < 22   { if col==0 { return 3 }  if col==1 { return 6 }  return 5 }    // nasion DIP on the midline only
  if y < 30   { if col==0 { return 7 }  if col==1 { return 6 }  return 4 }    // brow: glabella thick, temple thin
  if col==0 { return 5 }
  if col==1 { return 4 }
  return 3                                                                    // temple -- thinnest on the head
368}
369// v1 kept as the midline column so the 1-D behaviour is still reachable and comparable
370func ss_tdepth(y: i64) -> i64 { return ss_tdepth2(y, 0) }
371func ss_f32(v: i64, scale: i64) -> i64 {
  // integer -> IEEE-754 single bits, value = v/scale
  if v == 0 { return 0 }
  var neg: i64 = 0
  var m: i64 = v
  if m < 0 { neg = 1; m = 0 - m }
  var e: i64 = 127
  // normalise m/scale into [1,2)
  var num: i64 = m
  var den: i64 = scale
  while num >= den*2 { den = den*2; e = e + 1 }
  while num < den { num = num*2; e = e - 1 }
  // mantissa = (num/den - 1) * 2^23
  let frac: i64 = ((num - den) * SS_MAGIC_8388608) / den
  var bits: i64 = (e << 23) | (frac & SS_MAGIC_8388607)
  if neg == 1 { bits = bits | (1 << 31) }
  return bits
388}
389func ss_wr32(b: *u8, o: i64, v: i64) -> i64 {
  b[o]   = (v & 255) as u8
  b[o+1] = ((v >> 8) & 255) as u8
  b[o+2] = ((v >> 16) & 255) as u8
  b[o+3] = ((v >> 24) & 255) as u8
  return 0
395}
396
397// ***REALISED THICKNESS -- THE OBJECTIVE THE DENSE-MAP LITERATURE ACTUALLY NEEDS, AND IT IS FREE HERE.
398// The 2-D table failed because writing depths into a FIELD is not the same as getting them on the
399// SURFACE: surface_nets redistributes them. So the thing to build is not a better table, it is a
400// MEASUREMENT OF WHAT THE SURFACE ACTUALLY REALISED. Our skull IS a distance function, so |field| at an
401// envelope vertex IS that vertex's realised tissue thickness over the bone -- no ray cast, no nearest-
402// triangle search. Same trick ss_fit already uses against the scanned reference.
403// Simultaneously the diagnostic (how much does the field-to-surface step redistribute a requested
404// depth) and the objective a coordinate descent would minimise.
405func ss_bandix(y: i64) -> i64 {
  if y < 0-78 { return 0 }
  if y < 0-60 { return 1 }
  if y < 0-38 { return 2 }
  if y < 0-30 { return 3 }
  if y < 0    { return 4 }
  if y < 8    { return 5 }
  if y < 22   { return 6 }
  if y < 30   { return 7 }
  return 8
415}
416func ss_band_req(ix: i64) -> i64 {
  if ix == 0 { return 11 }
  if ix == 1 { return 9 }
  if ix == 2 { return 11 }
  if ix == 3 { return 10 }
  if ix == 4 { return 7 }
  if ix == 5 { return 6 }
  if ix == 6 { return 3 }
  if ix == 7 { return 7 }
  return 5
426}
427func ss_rd32(b: *u8, o: i64) -> i64 {
  return (b[o] as i64) | ((b[o+1] as i64)<<8) | ((b[o+2] as i64)<<16) | ((b[o+3] as i64)<<24)
429}
430func ss_r_f32(bits: i64, scale: i64) -> i64 {
  let s: i64 = (bits >> 31) & 1
  let e: i64 = (bits >> 23) & 255
  let m: i64 = bits & SS_MAGIC_8388607
  if e == 0 { return 0 }
  if e == 255 { return 0 }
  let mant: i64 = SS_MAGIC_8388608 | m
  let sh: i64 = e - 127 - 23
  var v: i64 = 0
  if sh >= 0 { if sh > 30 { return 0 } v = (mant*scale) << sh }
  else { let rs: i64 = 0 - sh; if rs > 62 { return 0 } v = (mant*scale) >> rs }
  if s == 1 { return 0 - v }
  return v
443}
444// ★SCORE AGAINST THE REAL SCANNED REFERENCE, IN MILLIMETRES -- and the metric is FREE because our skull
445// IS a distance function: |field| at a reference vertex is the error there. No registration search, no
446// closest-triangle hunt. Eight rounds of hand-placing primitives matched the bounding box to 5mm while
447// the SHAPE stayed a cluster of lumps; a bounding box cannot see shape and an eyeball cannot be
448// optimized against. This can.
449// ⚠FRAME: the reference faces -z in a full-body frame, ours faces +z centred on the cranium. The
450// transform is DERIVED from the reference's own bbox, and z is negated -- without that we would be
451// scoring our face against the back of its skull.
452func ss_fit(path: *u8, sexf: i64, robust: i64, stride: i64) -> i64 {
  let ln: *i64 = sys_mmap(16) as *i64
  let buf: *u8 = sys_read_file(path, ln)
  if (buf as i64) == 0 { ss_puts("{\x22error\x22:\x22cannot read reference\x22}\n" as *u8); return 3 }
  let nlayer: i64 = ss_rd32(buf, 8)
  let nt: i64 = ss_rd32(buf, 12)
  let hdr: i64 = 16 + nlayer*24
  if nt <= 0 { ss_puts("{\x22error\x22:\x22no triangles\x22}\n" as *u8); return 4 }
  var lox: i64 = 0; var hix: i64 = 0
  var loy: i64 = 0; var hiy: i64 = 0
  var loz: i64 = 0; var hiz: i64 = 0
  var first: i64 = 1
  var t: i64 = 0
  while t < nt {
      let o: i64 = hdr + t*84
      var j: i64 = 0
      while j < 3 {
          let x: i64 = ss_r_f32(ss_rd32(buf,o+j*12),   1)
          let y: i64 = ss_r_f32(ss_rd32(buf,o+j*12+4), 1)
          let z: i64 = ss_r_f32(ss_rd32(buf,o+j*12+8), 1)
          if first == 1 { lox=x; hix=x; loy=y; hiy=y; loz=z; hiz=z; first=0 } else {
              if x<lox {lox=x}
              if x>hix {hix=x}
              if y<loy {loy=y}
              if y>hiy {hiy=y}
              if z<loz {loz=z}
              if z>hiz {hiz=z}
          }
          j = j + 1
      }
      t = t + 1
  }
  let cx: i64 = (lox+hix)/2
  let cy: i64 = (loy+hiy)/2
  let cz: i64 = (loz+hiz)/2
  var sum: i64 = 0
  var n: i64 = 0
  var worst: i64 = 0
  var over: i64 = 0
  t = 0
  while t < nt {
      if t % stride == 0 {
          let o: i64 = hdr + t*84
          let x: i64 = ss_r_f32(ss_rd32(buf,o),   1) - cx
          let y: i64 = ss_r_f32(ss_rd32(buf,o+4), 1) - cy
          let z: i64 = 0 - (ss_r_f32(ss_rd32(buf,o+8), 1) - cz)
          var d: i64 = ss_field(x, y, z, sexf, robust)
          if d < 0 { d = 0 - d }
          sum = sum + d
          n = n + 1
          if d > worst { worst = d }
          if d > 10 { over = over + 1 }
      }
      t = t + 1
  }
  if n == 0 { ss_puts("{\x22error\x22:\x22no samples\x22}\n" as *u8); return 5 }
  ss_puts("{\x22organ\x22:\x22nx_skullsdf\x22,\x22verb\x22:\x22fit\x22,\x22mean_err_mm\x22:" as *u8); ss_pn(sum/n)
  ss_puts(",\x22worst_err_mm\x22:" as *u8); ss_pn(worst)
  ss_puts(",\x22over_10mm_permil\x22:" as *u8); ss_pn(over*1000/n)
  ss_puts(",\x22samples\x22:" as *u8); ss_pn(n)
  ss_puts(",\x22ref_bbox_mm\x22:[" as *u8); ss_pn(hix-lox)
  ss_puts("," as *u8); ss_pn(hiy-loy); ss_puts("," as *u8); ss_pn(hiz-loz)
  ss_puts("]}\n" as *u8)
  return 0
516}
517
518// load reference vertices once into flat arrays, already transformed into our frame
519func ss_load_ref(path: *u8, RX: *i64, RY: *i64, RZ: *i64, cap: i64, stride: i64) -> i64 {
  let ln: *i64 = sys_mmap(16) as *i64
  let buf: *u8 = sys_read_file(path, ln)
  if (buf as i64) == 0 { return 0-1 }
  let nlayer: i64 = ss_rd32(buf, 8)
  let nt: i64 = ss_rd32(buf, 12)
  let hdr: i64 = 16 + nlayer*24
  var lox: i64 = 0; var hix: i64 = 0
  var loy: i64 = 0; var hiy: i64 = 0
  var loz: i64 = 0; var hiz: i64 = 0
  var first: i64 = 1
  var t: i64 = 0
  while t < nt {
      let o: i64 = hdr + t*84
      let x: i64 = ss_r_f32(ss_rd32(buf,o),   1)
      let y: i64 = ss_r_f32(ss_rd32(buf,o+4), 1)
      let z: i64 = ss_r_f32(ss_rd32(buf,o+8), 1)
      if first == 1 { lox=x; hix=x; loy=y; hiy=y; loz=z; hiz=z; first=0 } else {
          if x<lox {lox=x}
          if x>hix {hix=x}
          if y<loy {loy=y}
          if y>hiy {hiy=y}
          if z<loz {loz=z}
          if z>hiz {hiz=z}
      }
      t = t + 1
  }
  let cx: i64 = (lox+hix)/2
  let cy: i64 = (loy+hiy)/2
  let cz: i64 = (loz+hiz)/2
  var n: i64 = 0
  t = 0
  while t < nt {
      if t % stride == 0 {
          if n < cap {
              let o: i64 = hdr + t*84
              RX[n] = ss_r_f32(ss_rd32(buf,o),   1) - cx
              RY[n] = ss_r_f32(ss_rd32(buf,o+4), 1) - cy
              RZ[n] = 0 - (ss_r_f32(ss_rd32(buf,o+8), 1) - cz)
              n = n + 1
          }
      }
      t = t + 1
  }
  return n
564}
565// ★★THE OBJECTIVE IS SYMMETRIC, AND IT HAS TO BE. A one-directional score -- "how far is each REFERENCE
566// point from my surface" -- is trivially gamed by DELETING GEOMETRY: the first tuning run shrank the
567// orbits from 22mm to 8mm and flattened the maxilla from 30mm to 13mm, improving the number 40% by
568// filling in the eye sockets, because surface that does not exist cannot be wrong.
569// The reverse term fixes that by construction: sample points on OUR surface and measure how far they
570// are from the REFERENCE. A filled orbit puts our surface where the reference has a hole, and the
571// reverse term charges for it. Together they are a two-sided (Hausdorff-style) distance.
572// ⚠We have no distance function for the reference MESH, so the reverse term uses the nearest reference
573// VERTEX from a spatial grid. That is an upper bound on the true point-to-surface distance -- it can
574// overstate, never understate, which is the safe direction for a penalty.
575const SG_DIM: i64 = 24            // spatial hash grid, cells per axis
576const SG_EXT: i64 = 140           // half-extent covered, mm
577
578func sg_cell(x: i64, y: i64, z: i64) -> i64 {
  var i: i64 = (x + SG_EXT) * SG_DIM / (SG_EXT*2)
  var j: i64 = (y + SG_EXT) * SG_DIM / (SG_EXT*2)
  var k: i64 = (z + SG_EXT) * SG_DIM / (SG_EXT*2)
  if i < 0 { i = 0 }
  if j < 0 { j = 0 }
  if k < 0 { k = 0 }
  if i >= SG_DIM { i = SG_DIM-1 }
  if j >= SG_DIM { j = SG_DIM-1 }
  if k >= SG_DIM { k = SG_DIM-1 }
  return (i*SG_DIM + j)*SG_DIM + k
589}
590// bucket the reference points so the reverse term does not scan all of them per query
591func ss_bin_ref(RX: *i64, RY: *i64, RZ: *i64, n: i64, head: *i64, next: *i64) -> i64 {
  var c: i64 = 0
  while c < SG_DIM*SG_DIM*SG_DIM { head[c] = 0-1; c = c + 1 }
  var i: i64 = 0
  while i < n {
      let h: i64 = sg_cell(RX[i], RY[i], RZ[i])
      next[i] = head[h]
      head[h] = i
      i = i + 1
  }
  return 0
602}
603// nearest reference point to (x,y,z), searching the home cell then one ring out
604func ss_near_ref(x: i64, y: i64, z: i64, RX: *i64, RY: *i64, RZ: *i64, head: *i64, next: *i64) -> i64 {
  var ci: i64 = (x + SG_EXT) * SG_DIM / (SG_EXT*2)
  var cj: i64 = (y + SG_EXT) * SG_DIM / (SG_EXT*2)
  var ck: i64 = (z + SG_EXT) * SG_DIM / (SG_EXT*2)
  var best: i64 = 0-1
  var r: i64 = 0
  while r <= 1 {
      var di: i64 = 0 - r
      while di <= r {
          var dj: i64 = 0 - r
          while dj <= r {
              var dk: i64 = 0 - r
              while dk <= r {
                  let ii: i64 = ci+di
                  let jj: i64 = cj+dj
                  let kk: i64 = ck+dk
                  if ii >= 0 { if ii < SG_DIM { if jj >= 0 { if jj < SG_DIM { if kk >= 0 { if kk < SG_DIM {
                      var p: i64 = head[(ii*SG_DIM + jj)*SG_DIM + kk]
                      while p >= 0 {
                          let ddx: i64 = x-RX[p]
                          let ddy: i64 = y-RY[p]
                          let ddz: i64 = z-RZ[p]
                          let d2: i64 = ddx*ddx + ddy*ddy + ddz*ddz
                          if best < 0 { best = d2 } else { if d2 < best { best = d2 } }
                          p = next[p]
                      }
                  } } } } } }
                  dk = dk + 1
              }
              dj = dj + 1
          }
          di = di + 1
      }
      if best >= 0 { r = 2 } else { r = r + 1 }
  }
  if best < 0 { return SG_EXT }
  return ss_isqrt(best)
641}
642// forward term: how far each REFERENCE point is from our surface, straight off our own field
643func ss_score_fwd(RX: *i64, RY: *i64, RZ: *i64, n: i64, sexf: i64, robust: i64, P: *i64) -> i64 {
  var sum: i64 = 0
  var i: i64 = 0
  while i < n {
      var d: i64 = ss_field_p(RX[i], RY[i], RZ[i], sexf, robust, P)
      if d < 0 { d = 0 - d }
      sum = sum + d
      i = i + 1
  }
  if n == 0 { return 0 }
  return sum*100/n
654}
655// reverse term: walk a coarse lattice, keep points ON our surface, and charge for their distance to the
656// nearest reference point. This is what makes a deleted feature EXPENSIVE.
657func ss_score_rev(RX: *i64, RY: *i64, RZ: *i64, n: i64, head: *i64, next: *i64,
                sexf: i64, robust: i64, P: *i64, step: i64) -> i64 {
  var sum: i64 = 0
  var cnt: i64 = 0
  var x: i64 = 0 - SG_EXT
  while x <= SG_EXT {
      var y: i64 = 0 - SG_EXT
      while y <= SG_EXT {
          var z: i64 = 0 - SG_EXT
          while z <= SG_EXT {
              let d: i64 = ss_field_p(x, y, z, sexf, robust, P)
              // a lattice point within half a step of the zero level is ON our surface
              if d > 0 - step { if d < step {
                  sum = sum + ss_near_ref(x, y, z, RX, RY, RZ, head, next)
                  cnt = cnt + 1
              } }
              z = z + step
          }
          y = y + step
      }
      x = x + step
  }
  if cnt == 0 { return SG_EXT*100 }      // no surface at all is the worst possible answer
  return sum*100/cnt
681}
682// the objective: mean of both directions, so neither can be gamed alone
683func ss_score2(RX: *i64, RY: *i64, RZ: *i64, n: i64, head: *i64, next: *i64,
             sexf: i64, robust: i64, P: *i64, step: i64) -> i64 {
  let f: i64 = ss_score_fwd(RX,RY,RZ,n,sexf,robust,P)
  let r: i64 = ss_score_rev(RX,RY,RZ,n,head,next,sexf,robust,P,step)
  return (f + r)/2
688}
689// ★COORDINATE DESCENT. For each parameter try +step and -step; keep a move only if the MEASURED error
690// falls. Step halves each pass. No gradient needed, which suits an integer-only field, and no change is
691// ever kept on the strength of looking better.
692func ss_tune(path: *u8, sexf: i64, robust: i64, stride: i64, passes: i64) -> i64 {
  let cap: i64 = SS_MAGIC_40000
  let RX: *i64 = sys_mmap(cap*8) as *i64
  let RY: *i64 = sys_mmap(cap*8) as *i64
  let RZ: *i64 = sys_mmap(cap*8) as *i64
  let n: i64 = ss_load_ref(path, RX, RY, RZ, cap, stride)
  if n <= 0 { ss_puts("{\x22error\x22:\x22cannot load reference\x22}\n" as *u8); return 3 }
  let head: *i64 = sys_mmap(SG_DIM*SG_DIM*SG_DIM*8) as *i64
  let next: *i64 = sys_mmap(cap*8) as *i64
  ss_bin_ref(RX, RY, RZ, n, head, next)
  let P: *i64 = sys_mmap(SP_N*8) as *i64
  ss_defaults(P)
  let lat: i64 = 6                   // reverse-term lattice spacing, mm
  var best: i64 = ss_score2(RX,RY,RZ,n,head,next,sexf,robust,P,lat)
  let start: i64 = best
  let startf: i64 = ss_score_fwd(RX,RY,RZ,n,sexf,robust,P)
  let startr: i64 = ss_score_rev(RX,RY,RZ,n,head,next,sexf,robust,P,lat)
  var step: i64 = 8
  var pass: i64 = 0
  while pass < passes {
      var k: i64 = 0
      while k < SP_N {
          let orig: i64 = P[k]
          P[k] = orig + step
          let up: i64 = ss_score2(RX,RY,RZ,n,head,next,sexf,robust,P,lat)
          P[k] = orig - step
          let dn: i64 = ss_score2(RX,RY,RZ,n,head,next,sexf,robust,P,lat)
          P[k] = orig
          if up < best { if up <= dn { best = up; P[k] = orig + step } }
          if dn < best { if dn < up { best = dn; P[k] = orig - step } }
          k = k + 1
      }
      step = step/2
      if step < 1 { step = 1 }
      pass = pass + 1
  }
  let endf: i64 = ss_score_fwd(RX,RY,RZ,n,sexf,robust,P)
  let endr: i64 = ss_score_rev(RX,RY,RZ,n,head,next,sexf,robust,P,lat)
  ss_puts("{\x22organ\x22:\x22nx_skullsdf\x22,\x22verb\x22:\x22tune\x22,\x22samples\x22:" as *u8); ss_pn(n)
  ss_puts(",\x22start_err_mm\x22:" as *u8); ss_pn(start/100)
  ss_puts(",\x22final_err_mm\x22:" as *u8); ss_pn(best/100)
  ss_puts(",\x22start_centi\x22:" as *u8); ss_pn(start)
  ss_puts(",\x22final_centi\x22:" as *u8); ss_pn(best)
  ss_puts(",\x22params\x22:[" as *u8)
  var q: i64 = 0
  while q < SP_N {
      if q > 0 { ss_puts("," as *u8) }
      ss_pn(P[q])
      q = q + 1
  }
  ss_puts("]}\n" as *u8)
  return 0
744}
745
746// THE `thick` VERB: report, per height band, the depth we REQUESTED versus the thickness the emitted
747// envelope ACTUALLY realised over the bone. A gap between them is the field-to-surface redistribution
748// made visible, and its mean absolute error is the number a fit would drive to zero.
749func ss_thick(path: *u8, sexf: i64, robust: i64, stride: i64) -> i64 {
  let ln: *i64 = sys_mmap(16) as *i64
  let buf: *u8 = sys_read_file(path, ln)
  if (buf as i64) == 0 { ss_puts("{\x22error\x22:\x22cannot read envelope mesh\x22}\n" as *u8); return 3 }
  let nlayer: i64 = ss_rd32(buf, 8)
  let nt: i64 = ss_rd32(buf, 12)
  if nt <= 0 { ss_puts("{\x22error\x22:\x22no triangles\x22}\n" as *u8); return 4 }
  let hdr: i64 = 16 + nlayer*24
  let cnt: *i64 = sys_mmap(9*8) as *i64
  let sm:  *i64 = sys_mmap(9*8) as *i64
  let mn:  *i64 = sys_mmap(9*8) as *i64
  let mx:  *i64 = sys_mmap(9*8) as *i64
  var b: i64 = 0
  while b < 9 { cnt[b]=0; sm[b]=0; mn[b]=999999; mx[b]=0-999999; b=b+1 }
  var abserr: i64 = 0
  var n: i64 = 0
  var t: i64 = 0
  while t < nt {
      if t % stride == 0 {
          var j: i64 = 0
          while j < 3 {
              let o: i64 = hdr + t*84 + j*12
              let px: i64 = ss_r_f32(ss_rd32(buf,o),   1)
              let py: i64 = ss_r_f32(ss_rd32(buf,o+4), 1)
              let pz: i64 = ss_r_f32(ss_rd32(buf,o+8), 1)
              let d: i64 = ss_field(px, py, pz, sexf, robust)
              let ix: i64 = ss_bandix(py)
              cnt[ix] = cnt[ix] + 1
              sm[ix] = sm[ix] + d
              if d < mn[ix] { mn[ix] = d }
              if d > mx[ix] { mx[ix] = d }
              var e: i64 = d - ss_band_req(ix)
              if e < 0 { e = 0 - e }
              abserr = abserr + e
              n = n + 1
              j = j + 1
          }
      }
      t = t + 1
  }
  if n == 0 { ss_puts("{\x22error\x22:\x22no samples\x22}\n" as *u8); return 5 }
  ss_puts("{\x22organ\x22:\x22nx_skullsdf\x22,\x22verb\x22:\x22thick\x22,\x22samples\x22:" as *u8); ss_pn(n)
  ss_puts(",\x22mean_abs_err_mm\x22:" as *u8); ss_pn(abserr/n)
  ss_puts(",\x22bands\x22:[" as *u8)
  b = 0
  while b < 9 {
      if b > 0 { ss_puts("," as *u8) }
      ss_puts("{\x22band\x22:" as *u8); ss_pn(b)
      ss_puts(",\x22req\x22:" as *u8); ss_pn(ss_band_req(b))
      ss_puts(",\x22mean\x22:" as *u8)
      if cnt[b] > 0 { ss_pn(sm[b]/cnt[b]) } else { ss_pn(0-1) }
      ss_puts(",\x22min\x22:" as *u8)
      if cnt[b] > 0 { ss_pn(mn[b]) } else { ss_pn(0-1) }
      ss_puts(",\x22max\x22:" as *u8)
      if cnt[b] > 0 { ss_pn(mx[b]) } else { ss_pn(0-1) }
      ss_puts(",\x22n\x22:" as *u8); ss_pn(cnt[b])
      ss_puts("}" as *u8)
      b = b + 1
  }
  ss_puts("]}\n" as *u8)
  return 0
810}
811
812// ***THE `grad` VERB -- MEASURE |grad f| DIRECTLY INSTEAD OF INFERRING IT FROM SCATTER.
813// Every remaining hypothesis about the tissue-thickness scatter is a claim about how far this field is
814// from a TRUE distance function, where |grad f| = 1 everywhere. Rather than argue, sample it: walk a
815// coarse lattice, keep the points NEAR THE SURFACE (the only region that matters for an offset), and
816// report the distribution of |grad f| in per-mille. A true SDF reads 1000.
817// ***READ IT LIKE THIS: spread around 1000 is the offset error budget. If a requested 7mm offset lands
818// where |grad| is 700, the surface moves 10mm; at 1400 it moves 5mm. That IS the 3-6mm scatter, and this
819// verb says so directly instead of by inference. It also discriminates the two surviving suspects --
820// ss_smin composition (already exonerated by K=0) versus ss_ellipsoid's first-order approximation --
821// because you can re-run it with argv[5]=0 for a plain union and compare the SAME distribution.
822func ss_grad(sexf: i64, robust: i64, step: i64, near: i64) -> i64 {
  var lo: i64 = 999999
  var hi: i64 = 0-999999
  var sum: i64 = 0
  var n: i64 = 0
  var under: i64 = 0
  var over: i64 = 0
  var x: i64 = 0 - SS_EXT
  while x <= SS_EXT {
      var y: i64 = 0 - SS_EXT
      while y <= SS_EXT {
          var z: i64 = 0 - SS_EXT
          while z <= SS_EXT {
              let f: i64 = ss_field(x, y, z, sexf, robust)
              var af: i64 = f
              if af < 0 { af = 0 - af }
              if af <= near {
                  let gx: i64 = (ss_field(x+1,y,z,sexf,robust) - ss_field(x-1,y,z,sexf,robust)) * 1000 / 2
                  let gy: i64 = (ss_field(x,y+1,z,sexf,robust) - ss_field(x,y-1,z,sexf,robust)) * 1000 / 2
                  let gz: i64 = (ss_field(x,y,z+1,sexf,robust) - ss_field(x,y,z-1,sexf,robust)) * 1000 / 2
                  let g: i64 = ss_isqrt(gx*gx + gy*gy + gz*gz)
                  if g < lo { lo = g }
                  if g > hi { hi = g }
                  sum = sum + g
                  n = n + 1
                  if g < 800 { under = under + 1 }
                  if g > 1200 { over = over + 1 }
              }
              z = z + step
          }
          y = y + step
      }
      x = x + step
  }
  if n == 0 { ss_puts("{\x22error\x22:\x22no near-surface samples\x22}\n" as *u8); return 5 }
  ss_puts("{\x22organ\x22:\x22nx_skullsdf\x22,\x22verb\x22:\x22grad\x22,\x22samples\x22:" as *u8); ss_pn(n)
  ss_puts(",\x22true_sdf_is\x22:1000,\x22mean\x22:" as *u8); ss_pn(sum/n)
  ss_puts(",\x22min\x22:" as *u8); ss_pn(lo)
  ss_puts(",\x22max\x22:" as *u8); ss_pn(hi)
  ss_puts(",\x22under_800_permil\x22:" as *u8); ss_pn(under*1000/n)
  ss_puts(",\x22over_1200_permil\x22:" as *u8); ss_pn(over*1000/n)
  ss_puts(",\x22smooth_union_k\x22:" as *u8); ss_pn(ss_k())
  ss_puts("}\n" as *u8)
  return 0
866}
867
868func main(argc: i64, argv: *i64) -> i64 {
  if argc < 2 { ss_puts("usage: nx_skullsdf <out.nxmesh> [sex] [robust] [grid] | fit <ref> | tune <ref>\n" as *u8); return 2 }
  if ss_streq(argv[1] as *u8, "tune" as *u8) == 1 {
      if argc < 3 { ss_puts("usage: nx_skullsdf tune <ref.nxmesh> [sex] [robust] [stride] [passes]\n" as *u8); return 2 }
      var ts: i64 = 0
      if argc > 3 { ts = ss_atoi(argv[3] as *u8) }
      var tr: i64 = 500
      if argc > 4 { tr = ss_atoi(argv[4] as *u8) }
      var tst: i64 = 31
      if argc > 5 { tst = ss_atoi(argv[5] as *u8) }
      if tst < 1 { tst = 1 }
      var tp: i64 = 5
      if argc > 6 { tp = ss_atoi(argv[6] as *u8) }
      return ss_tune(argv[2] as *u8, ts, tr, tst, tp)
  }
  if ss_streq(argv[1] as *u8, "grad" as *u8) == 1 {
      var gs: i64 = 0
      if argc > 2 { gs = ss_atoi(argv[2] as *u8) }
      var gr: i64 = 500
      if argc > 3 { gr = ss_atoi(argv[3] as *u8) }
      var gp: i64 = 4
      if argc > 4 { gp = ss_atoi(argv[4] as *u8) }
      if gp < 1 { gp = 1 }
      if argc > 5 {
          SS_KVAL = ss_atoi(argv[5] as *u8)
          if SS_KVAL >= 0 { SS_KSET = 1 }
      }
      return ss_grad(gs, gr, gp, 3)
  }
  if ss_streq(argv[1] as *u8, "thick" as *u8) == 1 {
      if argc < 3 { ss_puts("usage: nx_skullsdf thick <envelope.nxmesh> [sex] [robust] [stride]\n" as *u8); return 2 }
      var ks: i64 = 0
      if argc > 3 { ks = ss_atoi(argv[3] as *u8) }
      var kr: i64 = 500
      if argc > 4 { kr = ss_atoi(argv[4] as *u8) }
      var kt: i64 = 7
      if argc > 5 { kt = ss_atoi(argv[5] as *u8) }
      if kt < 1 { kt = 1 }
      return ss_thick(argv[2] as *u8, ks, kr, kt)
  }
  if ss_streq(argv[1] as *u8, "fit" as *u8) == 1 {
      if argc < 3 { ss_puts("usage: nx_skullsdf fit <ref.nxmesh> [sex] [robust] [stride]\n" as *u8); return 2 }
      var fs: i64 = 0
      if argc > 3 { fs = ss_atoi(argv[3] as *u8) }
      var fr: i64 = 500
      if argc > 4 { fr = ss_atoi(argv[4] as *u8) }
      var st: i64 = 7
      if argc > 5 { st = ss_atoi(argv[5] as *u8) }
      if st < 1 { st = 1 }
      return ss_fit(argv[2] as *u8, fs, fr, st)
  }
  var sexf: i64 = 0
  if argc > 2 { sexf = ss_atoi(argv[2] as *u8) }
  var robust: i64 = 500
  if argc > 3 { robust = ss_atoi(argv[3] as *u8) }
  var G: i64 = SS_G
  if argc > 4 { G = ss_atoi(argv[4] as *u8) }
  // ★★CELL-SIZE-DRIVEN RESOLUTION (argv[5], MICROMETRES) -- the honest dial, additive so argv[4] still
  // means G for every existing caller.
  // WHY: `cell` below is INTEGER MILLIMETRES, so with a 320mm extent EVERY G from 161 to 319 yields
  // cell=2. Raising G in that range buys ZERO resolution while GROWING THE BOX (G=224 covers 448mm at
  // the SAME 2mm) and the allocation with it -- the dial is actively harmful in its dead zone.
  // MEASURED: G=160, 176 and 192 emit BYTE-IDENTICAL geometry (cell 2, verts 48814, tris 97660).
  // Asking for a CELL SIZE makes resolution monotonic and the box exactly the extent, with no waste.
  if argc > 5 {
      let cum: i64 = ss_atoi(argv[5] as *u8)
      if cum > 0 { G = (SS_EXT*2*1000 + cum - 1)/cum }
  }
936
  // ★TISSUE ENVELOPE (argv[6], per-mille of the published depths). ADDITIVE by construction: absent or 0
  // means SS_TISSUE stays 0 and the bone surface is emitted exactly as before.
  if argc > 6 {
      let tp: i64 = ss_atoi(argv[6] as *u8)
      if tp > 0 { SS_TISSUE = tp }
  }
  // SMOOTH-UNION RADIUS (argv[7], mm). Set 0 for a TRUE distance field with visible sutures.
  if argc > 7 {
      SS_KVAL = ss_atoi(argv[7] as *u8)
      if SS_KVAL >= 0 { SS_KSET = 1 }
  }
948
  // ⚠CEILING, not truncation. SS_EXT*2/G with 260mm over 144 cells gives cell=1, so the grid covered
  // only 144mm and CLIPPED the skull at its own boundary -- which is why width and depth both came
  // back as 142: they were not measurements of the skull, they were measurements of the box.
  let cell: i64 = (SS_EXT*2 + G - 1)/G
  if cell*G < SS_EXT*2 { ss_puts("{\x22error\x22:\x22grid does not cover the extent\x22}\n" as *u8); return 7 }
  // THE DIAL'S OTHER DEAD ZONE, AND IT IS THE SAME DEFECT ONE LEVEL DOWN. `cell` is an INTEGER
  // NUMBER OF MILLIMETRES, so the finest resolution this field can be sampled at is 1mm, reached at
  // G = SS_EXT*2. Every G ABOVE that still yields cell=1 -- but G*cell then EXCEEDS the extent, so the
  // grid silently covers a LARGER BOX at the SAME resolution: G=480 sampled 480mm instead of 240mm,
  // costing 8x the memory and 8x the time for ZERO extra detail, while still printing a `grid` field
  // that implies the caller got what they asked for.
  // That is exactly the failure the micrometre dial above was added to cure, so silently tolerating
  // it here would leave the cure with the disease inside it. REFUSE, and NAME the finest cell that is
  // actually expressible -- an honest non-answer beats a wrong mesh (the nx_memfloor law, applied to
  // over-resolution rather than over-allocation).
  if G > SS_EXT*2 {
      ss_puts("{\x22error\x22:\x22grid finer than the field can be sampled\x22,\x22requested_grid\x22:" as *u8); ss_pn(G)
      ss_puts(",\x22max_grid\x22:" as *u8); ss_pn(SS_EXT*2)
      ss_puts(",\x22finest_cell_mm\x22:1,\x22why\x22:\x22cell size is integer millimetres, so G above 2*SS_EXT grows the sampled box without adding resolution\x22}\n" as *u8)
      return 9
  }
  // ⚠CENTRE THE GRID ON THE SPAN IT ACTUALLY HAS. Ceiling division makes G*cell LARGER than 2*EXT, so
  // an origin of -EXT put the extra span entirely on the positive side and clipped the mandible off
  // the bottom -- which made the measured height depend on the grid rather than on the skull.
  let org: i64 = 0 - (G*cell)/2
  let n1: i64 = G+1
  // UPPER BOUND. The check above guards G being too SMALL; nothing guarded it being too LARGE, and
  // this allocation is O(G^3). On 2026-07-30 a G of ~1500 mapped 1501^3*8 = 27.06 GB on a 36 GB host
  // in under three minutes: swap hit 98%, load hit 41, and the mgmt API began refusing builds for
  // every other seat. seq1547 was the same shape in nx_ssdf and took mgmt, tools and sshd down.
  // Ask BEFORE mapping, and REFUSE rather than silently shrinking -- a caller who asked for 1500 and
  // quietly got 160 would get a wrong mesh, which is worse than an honest non-answer.
  if mf_admit("nx_skullsdf sdf grid" as *u8, n1*n1*n1*8) == 0 { return 8 }
  let grid: *i64 = sys_mmap(n1*n1*n1*8) as *i64
  var i: i64 = 0
  while i < n1 {
      let x: i64 = org + i*cell
      var j: i64 = 0
      while j < n1 {
          let y: i64 = org + j*cell
          var k: i64 = 0
          while k < n1 {
              let z: i64 = org + k*cell
              var fv: i64 = ss_field_world(x, y, z, sexf, robust)
              // SS_TISSUE = 0 leaves the bone iso-surface EXACTLY as it was, so every existing caller
              // is byte-identical; > 0 moves the zero level outward by the forensic depth at this height.
              // depth now varies with BOTH height and lateral distance (|x|), per the dense-map
              // literature; ss_tdepth2 at ax=0 reproduces the old midline column exactly.
              // ★★★MEASURED AND REVERTED TO THE MIDLINE COLUMN. The 2-D (height x lateral) table above is
              // RETAINED UNUSED, the GX-34 emitLimbTube precedent, because it MADE THE FACE WORSE on the
              // judge built to catch exactly this. A/B at grid 80 vs the cadaver skin oracle:
              // variance headline 128 -> 129 (noise), but PLACEMENT 135 -> 123 with recall 306 -> 278 and
              // precision unchanged at 444. For positional work this lane trusts PLACEMENT over variance.
              // ★★AND THE REASON IS STRUCTURAL, worth more than the revert: the midline depths in ss_tdepth2
              // are IDENTICAL to v1 by construction, yet the MIDLINE PROFILE STILL CHANGED. In an
              // ISO-SURFACE formulation the depths are NOT independent per-vertex knobs -- subtracting a
              // different depth off-midline moves the field in a neighbourhood, and surface_nets
              // interpolates that across cells, so a LATERAL edit propagates onto the MIDLINE SURFACE.
              // ★That is the difference from the offset formulation, where every vertex moved alone, and it
              // means the literature's DENSE TISSUE MAP cannot be transplanted cell-by-cell onto an SDF
              // envelope: the map must be fitted AGAINST THE RESULTING SURFACE, not applied to the field.
              // ***THE PER-POINT SUBTRACTION IS THE ONE THAT MEASURES BEST. I moved this into a
              // gradient-normalised second pass and it was WORSE BY A LOT -- see the disabled pass below.
              if SS_TISSUE > 0 { fv = fv - ss_tdepth(y)*SS_TISSUE/1000 }
              grid[(i*n1+j)*n1+k] = fv
              k = k + 1
          }
          j = j + 1
      }
      i = i + 1
  }
  // ***GRADIENT-NORMALISED TISSUE OFFSET -- THE FIX THE MEASUREMENT DEMANDED, NOT THE ONE I EXPECTED.
  // MEASURED: requesting a depth d realised 3-6mm of SCATTER around it, and that scatter barely moved
  // when the cell went 3mm -> 2mm (total spread 37 -> 34, 8 percent for 2.25x the cells). So it is NOT a
  // sampling artifact. THE CAUSE IS IN THIS FILE'S OWN HEADER: ss_smin subtracts h*h/(4k) on every
  // chained call, and 'the result is NOT a distance field -- gradient magnitude drifts far from 1'.
  // SUBTRACTING d FROM A FIELD WHOSE GRADIENT MAGNITUDE IS NOT 1 MOVES THE SURFACE BY d/|grad f|, NOT d.
  // With ~16 chained unions the drift is worst exactly where primitives overlap, which is why the nasal
  // and upper-lip bands scattered most and why everything came out systematically THIN (chained smin
  // pushes the field negative, so |grad| > 1 and d/|grad| lands short).
  // ***THE REMEDY IS THE STANDARD SDF ONE: divide the requested depth by the LOCAL GRADIENT MAGNITUDE,
  // estimated by central differences on the grid we have already built. It costs one extra pass and no
  // extra field evaluations. This also subsumes the -1mm bias, which was the same cause, not a second.
  // Gradient is carried in PER-MILLE so a true distance field reads 1000 and integer division stays exact.
  // ***DISABLED AND RETAINED (GX-34 precedent). MEASURED AT 3mm, normalised vs per-point:
  // chin req 11 realised 14 with range 8..62 (was 10, range 9..13); cheek 7 -> 8 range 4..24 (was 6,
  // range 5..8); mean_abs_err 0 -> 2. DIVIDING BY |grad f| MADE IT MUCH WORSE.
  // ***WHY, and it sharpens the diagnosis rather than excusing it: the gradient does not merely drift
  // ABOVE 1, it drifts BOTH WAYS, and where it drifts LOW the division AMPLIFIES -- a 62mm chin came
  // from a near-flat cell. My guard only caught g < 0.1; a g of 0.2 still multiplies the requested
  // depth by five. So the field is not slightly distorted, it is distorted enough that neither naive
  // remedy works: IGNORING |grad| scatters by 3-6mm, DIVIDING BY IT scatters by 50.
  // ***THE REAL FIX IS TO MAKE THE FIELD A TRUE SDF, not to compensate downstream: either drop SS_K to 0
  // (this file records having done exactly that once, for exactly this reason, before restoring 6mm for
  // appearance) and accept sutured seams, or REDISTANCE the grid -- an eikonal/fast-sweeping pass that
  // rebuilds |grad| = 1 everywhere before any offset is taken. Redistancing is the standard answer and
  // it operates on the grid we already build.
  if SS_TISSUE < 0 {
      let gm: *i64 = sys_mmap(n1*n1*n1*8) as *i64
      var gi: i64 = 0
      while gi < n1 {
          var gj: i64 = 0
          while gj < n1 {
              var gk: i64 = 0
              while gk < n1 {
                  var ai: i64 = gi+1
                  if ai > n1-1 { ai = n1-1 }
                  var bi: i64 = gi-1
                  if bi < 0 { bi = 0 }
                  var aj: i64 = gj+1
                  if aj > n1-1 { aj = n1-1 }
                  var bj: i64 = gj-1
                  if bj < 0 { bj = 0 }
                  var ak: i64 = gk+1
                  if ak > n1-1 { ak = n1-1 }
                  var bk: i64 = gk-1
                  if bk < 0 { bk = 0 }
                  let dx: i64 = (grid[(ai*n1+gj)*n1+gk] - grid[(bi*n1+gj)*n1+gk]) * 1000 / ((ai-bi)*cell)
                  let dy: i64 = (grid[(gi*n1+aj)*n1+gk] - grid[(gi*n1+bj)*n1+gk]) * 1000 / ((aj-bj)*cell)
                  let dz: i64 = (grid[(gi*n1+gj)*n1+ak] - grid[(gi*n1+gj)*n1+bk]) * 1000 / ((ak-bk)*cell)
                  var g: i64 = ss_isqrt(dx*dx + dy*dy + dz*dz)
                  // a degenerate gradient (flat field, e.g. deep inside a solid) carries no direction
                  // information; fall back to the unnormalised depth rather than dividing by ~0
                  if g < 100 { g = 1000 }
                  gm[(gi*n1+gj)*n1+gk] = g
                  gk = gk + 1
              }
              gj = gj + 1
          }
          gi = gi + 1
      }
      gi = 0
      while gi < n1 {
          let gx: i64 = org + gi*cell
          var gj: i64 = 0
          while gj < n1 {
              let gy: i64 = org + gj*cell
              var gk: i64 = 0
              while gk < n1 {
                  let ix: i64 = (gi*n1+gj)*n1+gk
                  let d: i64 = ss_tdepth(gy)*SS_TISSUE/1000
                  grid[ix] = grid[ix] - d*1000/gm[ix]
                  gk = gk + 1
              }
              gj = gj + 1
          }
          gi = gi + 1
      }
  }
  tm_reset()
  surface_nets(grid, G, G, G, org, org, org, cell, SS_ISO, SS_BONE)
  let nv: i64 = tm_nv()
  let nt: i64 = tm_nt()
  if nt <= 0 { ss_puts("{\x22error\x22:\x22no surface -- field never crosses the iso level\x22}\n" as *u8); return 5 }
1103
  // ---- write NXMSH2, one layer ("bone"), so the existing viewer and benches read it unchanged
  let hdr: i64 = 16 + 3*24
  let bytes: i64 = hdr + nt*84 + nt*4
  let buf: *u8 = sys_mmap(bytes + 64)
  buf[0]=78 as u8; buf[1]=88 as u8; buf[2]=77 as u8; buf[3]=83 as u8
  buf[4]=72 as u8; buf[5]=50 as u8; buf[6]=0 as u8; buf[7]=0 as u8
  ss_wr32(buf, 8, 3); ss_wr32(buf, 12, nt)
  var L: i64 = 0
  while L < 3 {
      let lb: i64 = 16 + L*24
      var q: i64 = 0
      while q < 16 { buf[lb+q]=0 as u8; q=q+1 }
      if L==2 { buf[lb]=98 as u8; buf[lb+1]=111 as u8; buf[lb+2]=110 as u8; buf[lb+3]=101 as u8 }
      if L==2 { ss_wr32(buf, lb+16, 0); ss_wr32(buf, lb+20, nt) } else { ss_wr32(buf, lb+16, 0); ss_wr32(buf, lb+20, 0) }
      L = L + 1
  }
  var t: i64 = 0
  while t < nt {
      let o: i64 = hdr + t*84
      let ia: i64 = tm_ta(t); let ib: i64 = tm_tb(t); let ic: i64 = tm_tc(t)
      ss_wr32(buf, o,    ss_f32(tm_vx(ia),1)); ss_wr32(buf, o+4,  ss_f32(tm_vy(ia),1)); ss_wr32(buf, o+8,  ss_f32(tm_vz(ia),1))
      ss_wr32(buf, o+12, ss_f32(tm_vx(ib),1)); ss_wr32(buf, o+16, ss_f32(tm_vy(ib),1)); ss_wr32(buf, o+20, ss_f32(tm_vz(ib),1))
      ss_wr32(buf, o+24, ss_f32(tm_vx(ic),1)); ss_wr32(buf, o+28, ss_f32(tm_vy(ic),1)); ss_wr32(buf, o+32, ss_f32(tm_vz(ic),1))
      // ⚠surface_nets writes gradient normals at 4096 scale (nx_isosurf.nx:68), NOT the Q14 16384 the
      // mesh format uses elsewhere. Reading them as Q14 made every normal a QUARTER length, so the
      // lambert term collapsed and the whole surface rendered dark and mottled -- which I spent three
      // passes blaming on the ellipsoid, the rasterizer and the z-buffer in turn.
      ss_wr32(buf, o+36, ss_f32(tm_vnx(ia),SS_NQ)); ss_wr32(buf, o+40, ss_f32(tm_vny(ia),SS_NQ)); ss_wr32(buf, o+44, ss_f32(tm_vnz(ia),SS_NQ))
      ss_wr32(buf, o+48, ss_f32(tm_vnx(ib),SS_NQ)); ss_wr32(buf, o+52, ss_f32(tm_vny(ib),SS_NQ)); ss_wr32(buf, o+56, ss_f32(tm_vnz(ib),SS_NQ))
      ss_wr32(buf, o+60, ss_f32(tm_vnx(ic),SS_NQ)); ss_wr32(buf, o+64, ss_f32(tm_vny(ic),SS_NQ)); ss_wr32(buf, o+68, ss_f32(tm_vnz(ic),SS_NQ))
      ss_wr32(buf, o+72, ss_f32(910,1000)); ss_wr32(buf, o+76, ss_f32(890,1000)); ss_wr32(buf, o+80, ss_f32(845,1000))
      ss_wr32(buf, hdr + nt*84 + t*4, 2)
      t = t + 1
  }
  let fd: i64 = sys_openat_wr(argv[1] as *u8, 420)
  sys_write(fd, buf, bytes)
  sys_close(fd)
1141
  // ★MEASURE THE RESULT AGAINST THE REFERENCE, in the organ, every run. The scale defect shipped to a
  // published page because nothing compared the emitted skull to the 151x209x215mm it is meant to be.
  var lox: i64 = 0; var hix: i64 = 0
  var loy: i64 = 0; var hiy: i64 = 0
  var loz: i64 = 0; var hiz: i64 = 0
  var vi: i64 = 0
  while vi < nv {
      let X: i64 = tm_vx(vi); let Y: i64 = tm_vy(vi); let Z: i64 = tm_vz(vi)
      if vi == 0 { lox=X; hix=X; loy=Y; hiy=Y; loz=Z; hiz=Z } else {
          if X < lox { lox = X }
          if X > hix { hix = X }
          if Y < loy { loy = Y }
          if Y > hiy { hiy = Y }
          if Z < loz { loz = Z }
          if Z > hiz { hiz = Z }
      }
      vi = vi + 1
  }
  let bw: i64 = hix-lox
  let bh: i64 = hiy-loy
  let bd: i64 = hiz-loz
  var fit: i64 = 1
  if ss_abs(bw - SS_REF_W) > SS_TOL { fit = 0 }
  if ss_abs(bh - SS_REF_H) > SS_TOL { fit = 0 }
  if ss_abs(bd - SS_REF_D) > SS_TOL { fit = 0 }
  ss_puts("{\x22organ\x22:\x22nx_skullsdf\x22,\x22bbox_mm\x22:[" as *u8); ss_pn(bw)
  ss_puts("," as *u8); ss_pn(bh); ss_puts("," as *u8); ss_pn(bd)
  ss_puts("],\x22reference_mm\x22:[" as *u8); ss_pn(SS_REF_W)
  ss_puts("," as *u8); ss_pn(SS_REF_H); ss_puts("," as *u8); ss_pn(SS_REF_D)
  ss_puts("],\x22dims_within_tolerance\x22:" as *u8); ss_pn(fit)
  ss_puts(",\x22grid\x22:" as *u8); ss_pn(G)
  ss_puts(",\x22cell\x22:" as *u8); ss_pn(cell)
  ss_puts(",\x22verts\x22:" as *u8); ss_pn(nv)
  ss_puts(",\x22tris\x22:" as *u8); ss_pn(nt)
  ss_puts(",\x22overflow\x22:" as *u8); ss_pn(tm_ovf())
  ss_puts(",\x22method\x22:\x22smooth-union of bone primitives, orbits and nasal aperture SUBTRACTED as real openings, polygonized by surface_nets\x22}\n" as *u8)
  return 0
1179}
nx_skullsdf.nx source

`nx_skullsdf.nx` source
