Merge hands/cultmath-lattice-weighted-shaders (cultmath-tapes cut 4b, lattice-weighted-shaders)

Spec cultmath-tapes:cut_spec:cut-lattice-weighted-shaders.r1; report h1; Soul s1 holds.

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>

packages/cultmath/README.md

@@ -34,10 +34,12 @@ shader semantics.
   `soft_gabriel_gate` gates a pair of sites by the empty-disc margin. Each is a loop over the shader steps
   `cultmath_power_score` / `cultmath_multiplicative_score`, `cultmath_site_cells_empty`, `cultmath_site_cells_insert`,
   `cultmath_site_cells_border`, `cultmath_power_border_step` (the exact power cell border, `power_border`) and `cultmath_gabriel_margin`; a shader loops over its own buffer.
-- Weighted lattice cells (C# only until the shader cut): `weighted_lattice_cells` returns `float4(F1, F2, smooth, id)` over a jittered,
+- Weighted lattice cells: `weighted_lattice_cells` returns `float4(F1, F2, smooth, id)` over a jittered,
   drifting lattice whose cell weights come from the exact power border of the body span at each cell centre, with a stretched
   metric and an exact ring search over the stated range (`LatticeMaxBoost`, `LatticeMaxStretch`, `LatticeMaxSmoothing`). It composes the
-  public steps `lattice_site`, `lattice_weight`, `lattice_distance` and `lattice_smooth_step`.
+  public steps `lattice_site`, `lattice_weight`, `lattice_distance` and `lattice_smooth_step`. The shaders carry the four steps as
+  `cultmath_lattice_site`, `cultmath_lattice_weight`, `cultmath_lattice_distance` and `cultmath_lattice_smooth_step`; the ring and box loops
+  are the shader caller's, written as the comment above them in `CultMath.hlsl` gives them, and the argument checks become its preconditions.
 - `shaders/CultMath.hlsl`, a canonical HLSL mirror include for shader-side
   parity. HLSL already owns `float2`, `float3`, and `float4`; the include
   exposes `cultmath_*` functions for shared semantics HLSL does not provide.

packages/cultmath/shaders/CultMath.glsl

@@ -688,6 +688,52 @@ float cultmath_gabriel_margin(vec3 a, vec3 b, vec3 other)
     return (cultmath_distance(other, (a + b) * 0.5) - r) / r;
 }
 
+// Weighted lattice cells: the four per-cell steps of math.Lattice.cs, statement for statement. A shader function cannot take a
+// span (design.md, "Sites"), so weighted_lattice_cells is the consumer's loop over its own body buffer, in two passes:
+//   vec2 q = p / cellSize; ivec2 c0 = (ivec2)floor(q); float f1 = 1.0e30, f2 = 1.0e30; int reach = 0;
+//   for (int k = 0; ; k++) {   // ring pass: Chebyshev rings 0, 1, 2, ... around c0, exact exit
+//       if (k > 1 && 0.5 * (k - 1) >= max(f2, f1 + 2.0 * smoothing)) break;   // k never reaches 38 in the accepted range
+//       for each cell on ring k: d = cultmath_lattice_distance(q, cultmath_lattice_site(cell, time, drift).xy, w, normal, stretch),
+//           w = cultmath_lattice_weight(site.z, border, boost, falloff), border = the .w of cultmath_power_border_step
+//           folded over the bodies (owner = the nearest body of the cell centre (cell + 0.5) * cellSize, z = 0);
+//           if (d < f1) { f2 = f1; f1 = d; } else if (d < f2) f2 = d;   store d for the box pass
+//       reach = k; }
+//   float m = f1 + smoothing;   // box pass: every stored cell, rows dz = -reach..reach, then dx = -reach..reach
+//   for each (dz, dx): m = cultmath_lattice_smooth_step(m, d, f1, smoothing);   // strict < for the winning id (earlier cell wins ties)
+// The preconditions the C# function throws for are the caller's in a shader: finite arguments, cellSize > 0, boost in [0, 4],
+// falloff > 0, smoothing in (0, 1], stretch in [1, 2], p within 2^23 cells. The normal is normalised as C# does: divide by its
+// largest component, then by its length (a zero normal means (1, 0) and needs stretch == 1). The ring bound is 37.
+vec3 cultmath_lattice_site(vec2 cell, float time, float drift)
+{
+    ivec3 h = cultmath_pcg3d(ivec3(int(cell.x), int(cell.y), 0));
+    vec2 phase = vec2(float(uint(h.x) >> 8) * (1.0 / 16777216.0), float(uint(h.y) >> 8) * (1.0 / 16777216.0));
+    vec2 site = cell + 0.5 + 0.5 * vec2(sin(drift * time + CULTMATH_TAU * phase.x), sin(drift * time + CULTMATH_TAU * phase.y));
+    return vec3(site, 0.5 + 0.5 * (float(uint(h.z) >> 8) * (1.0 / 16777216.0)));
+}
+
+float cultmath_lattice_weight(float base_weight, float border, float boost, float falloff)
+{
+    float t = border / falloff;
+    return base_weight * (1.0 + boost * exp(-(t * t)));
+}
+
+float cultmath_lattice_distance(vec2 q, vec2 site, float weight, vec2 normal, float stretch)
+{
+    vec2 v = site - q;
+    float a = dot(v, normal);
+    float c = v.x * normal.y - v.y * normal.x;
+    return weight * length(vec2(stretch * a, c));
+}
+
+float cultmath_lattice_smooth_step(float m, float d, float f1, float smoothing)
+{
+    if (d >= f1 + 2.0 * smoothing)
+        return m;
+    float h = cultmath_smoothstep(0.0, 1.0, 0.5 + 0.5 * (m - d) / smoothing);
+    float next = m + (d - m) * h - h * (1.0 - h) * smoothing / (1.0 + 3.0 * smoothing);
+    return min(next, f1 + smoothing);
+}
+
 vec2 cultmath_segment_closest(vec2 point_value, vec2 start, vec2 end)
 {
     vec2 segment = end - start;

packages/cultmath/shaders/CultMath.hlsl

@@ -688,6 +688,52 @@ float cultmath_gabriel_margin(float3 a, float3 b, float3 other)
     return (cultmath_distance(other, (a + b) * 0.5) - r) / r;
 }
 
+// Weighted lattice cells: the four per-cell steps of math.Lattice.cs, statement for statement. A shader function cannot take a
+// span (design.md, "Sites"), so weighted_lattice_cells is the consumer's loop over its own body buffer, in two passes:
+//   float2 q = p / cellSize; int2 c0 = (int2)floor(q); float f1 = 1.0e30, f2 = 1.0e30; int reach = 0;
+//   for (int k = 0; ; k++) {   // ring pass: Chebyshev rings 0, 1, 2, ... around c0, exact exit
+//       if (k > 1 && 0.5 * (k - 1) >= max(f2, f1 + 2.0 * smoothing)) break;   // k never reaches 38 in the accepted range
+//       for each cell on ring k: d = cultmath_lattice_distance(q, cultmath_lattice_site(cell, time, drift).xy, w, normal, stretch),
+//           w = cultmath_lattice_weight(site.z, border, boost, falloff), border = the .w of cultmath_power_border_step
+//           folded over the bodies (owner = the nearest body of the cell centre (cell + 0.5) * cellSize, z = 0);
+//           if (d < f1) { f2 = f1; f1 = d; } else if (d < f2) f2 = d;   store d for the box pass
+//       reach = k; }
+//   float m = f1 + smoothing;   // box pass: every stored cell, rows dz = -reach..reach, then dx = -reach..reach
+//   for each (dz, dx): m = cultmath_lattice_smooth_step(m, d, f1, smoothing);   // strict < for the winning id (earlier cell wins ties)
+// The preconditions the C# function throws for are the caller's in a shader: finite arguments, cellSize > 0, boost in [0, 4],
+// falloff > 0, smoothing in (0, 1], stretch in [1, 2], p within 2^23 cells. The normal is normalised as C# does: divide by its
+// largest component, then by its length (a zero normal means (1, 0) and needs stretch == 1). The ring bound is 37.
+float3 cultmath_lattice_site(float2 cell, float time, float drift)
+{
+    int3 h = cultmath_pcg3d(int3((int)cell.x, (int)cell.y, 0));
+    float2 phase = float2((float)((uint)h.x >> 8) * (1.0 / 16777216.0), (float)((uint)h.y >> 8) * (1.0 / 16777216.0));
+    float2 site = cell + 0.5 + 0.5 * float2(sin(drift * time + CULTMATH_TAU * phase.x), sin(drift * time + CULTMATH_TAU * phase.y));
+    return float3(site, 0.5 + 0.5 * ((float)((uint)h.z >> 8) * (1.0 / 16777216.0)));
+}
+
+float cultmath_lattice_weight(float base_weight, float border, float boost, float falloff)
+{
+    float t = border / falloff;
+    return base_weight * (1.0 + boost * exp(-(t * t)));
+}
+
+float cultmath_lattice_distance(float2 q, float2 site, float weight, float2 normal, float stretch)
+{
+    float2 v = site - q;
+    float a = dot(v, normal);
+    float c = v.x * normal.y - v.y * normal.x;
+    return weight * length(float2(stretch * a, c));
+}
+
+float cultmath_lattice_smooth_step(float m, float d, float f1, float smoothing)
+{
+    if (d >= f1 + 2.0 * smoothing)
+        return m;
+    float h = cultmath_smoothstep(0.0, 1.0, 0.5 + 0.5 * (m - d) / smoothing);
+    float next = m + (d - m) * h - h * (1.0 - h) * smoothing / (1.0 + 3.0 * smoothing);
+    return min(next, f1 + smoothing);
+}
+
 float2 cultmath_segment_closest(float2 point_value, float2 start, float2 end)
 {
     float2 segment = end - start;

packages/cultmath/tests/CultMath.Tests/GlslMirrorTests.cs

@@ -852,6 +852,34 @@ static int4 clamp(int4 x, int4 a, int4 b) { if (a.x > b.x || a.y > b.y || a.z >
             var a = Point3(r);
             return new object[] { a, r.Next(8) == 0 ? a : Point3(r), Point3(r) };
         }),
+        // The lattice steps. The cell is an integer-valued vec2 (negative and large included), time and drift span
+        // zero and the accepted range; the weight's border covers 0, near the falloff, and the 1.0e30 of no body.
+        new Family("vec3 cultmath_lattice_site(vec2, float, float)", "ulp-bounded", r =>
+            new object[] { new float2(r.Next(-4000, 4000), r.Next(-4000, 4000)), r.Next(6) == 0 ? 0.0f : Uniform(r, -200.0f, 200.0f), r.Next(6) == 0 ? 0.0f : Uniform(r, -3.0f, 3.0f) }),
+        new Family("float cultmath_lattice_weight(float, float, float, float)", "ulp-bounded", r =>
+        {
+            var falloff = Uniform(r, 0.05f, 40.0f);
+            var border = r.Next(5) switch { 0 => 0.0f, 1 => 1.0e30f, 2 => falloff * Uniform(r, 0.9f, 1.1f), _ => Uniform(r, 0.0f, 3.0f * falloff) };
+            var boost = r.Next(5) switch { 0 => 0.0f, 1 => 4.0f, _ => Uniform(r, 0.0f, 4.0f) };
+            return new object[] { Uniform(r, 0.5f, 1.0f), border, boost, falloff };
+        }),
+        new Family("float cultmath_lattice_distance(vec2, vec2, float, vec2, float)", "ulp-bounded", r =>
+        {
+            var angle = Uniform(r, 0.0f, 6.2831855f);
+            var normal = r.Next(6) == 0 ? new float2(1.0f, 0.0f) : new float2(MathF.Cos(angle), MathF.Sin(angle));
+            var stretch = r.Next(5) switch { 0 => 1.0f, 1 => 2.0f, _ => Uniform(r, 1.0f, 2.0f) };
+            return new object[] { Point2(r), Point2(r), Uniform(r, 0.5f, 5.0f), normal, stretch };
+        }),
+        // The smooth step: d exactly at f1 + 2 smoothing one in four (the equal branch), near it one in four, the
+        // smoothing near 0 and at 1, m anywhere up to f1 + smoothing.
+        new Family("float cultmath_lattice_smooth_step(float, float, float, float)", "ulp-bounded", r =>
+        {
+            var smoothing = r.Next(5) switch { 0 => 1.0f, 1 => Uniform(r, 1.0e-3f, 1.0e-2f), _ => Uniform(r, 0.01f, 1.0f) };
+            var f1 = Uniform(r, 0.0f, 10.0f);
+            var edge = f1 + 2.0f * smoothing;
+            var d = r.Next(4) switch { 0 => edge, 1 => edge * Uniform(r, 0.99f, 1.01f), _ => Uniform(r, f1, edge + 1.0f) };
+            return new object[] { Uniform(r, f1, f1 + smoothing), d, f1, smoothing };
+        }),
     }).ToArray();
 
     // A point of magnitude m, m log-uniform in [lo, hi]: one component at +-m, the other two uniform in [-m, m],

packages/cultmath/tests/CultMath.Tests/HlslSourceCompatibilityTests.cs

@@ -35,6 +35,10 @@ public sealed class HlslSourceCompatibilityTests
         Assert.NotNull(ShaderFunction(shader, "cultmath_site_cells_border", siteCells));
         Assert.NotNull(ShaderFunction(shader, "cultmath_gabriel_margin", typeof(float3), typeof(float3), typeof(float3)));
         Assert.NotNull(ShaderFunction(shader, "cultmath_power_border_step", typeof(float3), typeof(float4), typeof(float4), typeof(float4)));
+        Assert.NotNull(ShaderFunction(shader, "cultmath_lattice_site", typeof(float2), typeof(float), typeof(float)));
+        Assert.NotNull(ShaderFunction(shader, "cultmath_lattice_weight", typeof(float), typeof(float), typeof(float), typeof(float)));
+        Assert.NotNull(ShaderFunction(shader, "cultmath_lattice_distance", typeof(float2), typeof(float2), typeof(float), typeof(float2), typeof(float)));
+        Assert.NotNull(ShaderFunction(shader, "cultmath_lattice_smooth_step", typeof(float), typeof(float), typeof(float), typeof(float)));
         Assert.NotNull(ShaderFunction(shader, "cultmath_segment_closest", typeof(float2), typeof(float2), typeof(float2)));
         Assert.NotNull(ShaderFunction(shader, "cultmath_distance_to_segment", typeof(float2), typeof(float2), typeof(float2)));
         Assert.NotNull(ShaderFunction(shader, "cultmath_segment_closest", typeof(float3), typeof(float3), typeof(float3)));
@@ -200,7 +204,7 @@ public sealed class HlslSourceCompatibilityTests
         }
 
         Assert.True(mismatches.Count == 0, $"{mismatches.Count} mismatches:{Environment.NewLine}{string.Join(Environment.NewLine, mismatches.Take(12))}");
-        Assert.Equal(136, compared.Count);
+        Assert.Equal(140, compared.Count);
     }
 
     /// <summary>

packages/cultmath/tests/CultMath.Tests/fixtures/device-bounds-lavapipe.txt

@@ -20,14 +20,14 @@ lavapipe-glsl	15	vec2 cultmath_iv_min(vec2, vec2)	ulp-bounded	256	0	0	a324b35cb4
 lavapipe-glsl	16	vec2 cultmath_iv_max(vec2, vec2)	ulp-bounded	256	0	0	d68412262ca234c1da130fc5217ba6856da3e92e435c28c1fbdbf3692a89e1fa
 lavapipe-glsl	17	vec2 cultmath_iv_sqr(vec2)	ulp-bounded	256	0	0	dbbb0e0df015456393452377d689732428a9a8e24d8e2b407ee9620593b4c46b
 lavapipe-glsl	18	vec2 cultmath_iv_sqrt(vec2)	ulp-bounded	256	0	0	95bd15d1b283713fc632ced350f5da1b89f8f73e6618329773db1b52acd29991
-lavapipe-glsl	19	vec2 cultmath_iv_clamp(vec2, float, float)	ulp-bounded	256	0	0	abe9daf24930a5e3a49ec994c4cae3a0c27b9d019d6d93ec1963ec3daad664a0
+lavapipe-glsl	19	vec2 cultmath_iv_clamp(vec2, float, float)	ulp-bounded	256	0	0	268d61fd6d122e2b85e211c96daf410fb7e2d8ff83ec2082709f640504c852a7
 lavapipe-glsl	20	vec2 cultmath_iv_saturate(vec2)	ulp-bounded	256	0	0	0f844ef8c4d9a9f748c80677bbbfc36b5f6e682eb87c2d46e7e20635d5f55c26
 lavapipe-glsl	21	vec2 cultmath_iv_smoothstep(float, float, vec2)	ulp-bounded	256	0	0	3d5944a4c43feb91d6786924e0f5439c05285d28ff1f500b5582893758dd4ce5
 lavapipe-glsl	22	vec2 cultmath_iv_lerp(vec2, vec2, float)	ulp-bounded	256	0	0	96b09e90a3fbbfe81379a29a23b676e490bc7dc6bb731450197707e6cf4c573f
 lavapipe-glsl	23	vec2 cultmath_iv_snoise_ball(vec3, float)	ulp-bounded	242	54	0	570eb031260c8f4aab42edc57a5fa1d0da70e8a4e6f0b4bf68208c15506f7cb5
 lavapipe-glsl	24	vec2 cultmath_iv_fbm_ball(vec3, float, int, float, float)	ulp-bounded	250	56	0	9e7017426314537f84c58dcdd1f85188cbe8f4dd9ababed887f60776cf861ebf
 lavapipe-glsl	25	vec4 cultmath_iv_frustum_ball(vec2, float, float, float, float)	ulp-bounded	198	1.6457063576593662	0	327c306aa4d06aecbb2681d8808c6dbf0567e87b54a6067c68001e36b3e52169
-lavapipe-glsl	26	vec2 cultmath_iv_exp(vec2)	ulp-bounded, platform exp	7	7.526057804152758	0	b4af8232dc3dd782cc6d790e928ede0f6ba6dfdffd6c71dd9494fb58973e485c
+lavapipe-glsl	26	vec2 cultmath_iv_exp(vec2)	ulp-bounded, platform exp	7	7.526057804152758	0	1a46b0fa116f55e5abd70ec9f2a66de0befe8b3577fe472f9eaa98932aae8040
 lavapipe-glsl	27	CultPhasor cultmath_phacelle(vec3, vec3, float, float)	ulp-bounded, platform exp, sin, cos; across platforms |diff| <= 2^-20 max(|v|, 1); on a device |diff| <= 2^-18 max(|v|, 1)	0	18.5	0	705b4c18027a0838218645e9368c3749ae4b5bf75e0485985725e8e72b73ab88
 lavapipe-glsl	28	float cultmath_snoise(vec3)	ulp-bounded, on the simplex tie set	127	112	0	6929326e4f27726d7bbdbac3a7823209e2ecfcd301018ef164527c4c1a9f7ae8
 lavapipe-glsl	29	vec4 cultmath_snoise_grad(vec3)	ulp-bounded, on the simplex tie set	102	546.5	0	6173a812fd4059fa19bce84d34858c6035cdda98aa21a2b210e611cbd58c29d6
@@ -36,7 +36,7 @@ lavapipe-glsl	31	vec3 cultmath_af_symbol(float, float)	ulp-bounded	256	0	0	04147
 lavapipe-glsl	32	vec3 cultmath_af_from_iv(vec2)	ulp-bounded	256	0	0	306fe58a3268199fc8fd845a32d956f349a790422fa5c87d5a0824636cb55424
 lavapipe-glsl	33	vec2 cultmath_af_range(vec3)	ulp-bounded	256	0	0	6245eeba19473d69d0d8155e20e2e6089a6843140723d23ed5d501064023a44a
 lavapipe-glsl	34	vec3 cultmath_af_add(vec3, vec3)	ulp-bounded	256	0	0	cb1cb3fc69224837342de767525d332687b9d3e17b3de255c28e2f0f65f32640
-lavapipe-glsl	35	vec3 cultmath_af_sub(vec3, vec3)	ulp-bounded	256	0	0	a8fad8ea86cf61841430293fdd9840a54008160250114040380c9634c63bb17e
+lavapipe-glsl	35	vec3 cultmath_af_sub(vec3, vec3)	ulp-bounded	256	0	0	df44c501a8be20dc46a54faac9583da13f4367adc501a33fe14624f10e54b558
 lavapipe-glsl	36	vec3 cultmath_af_neg(vec3)	ulp-bounded	256	0	0	e485acf8ee21c6d880621cc6216b3b2a78318f56f5864b33c5509be27e22a694
 lavapipe-glsl	37	vec3 cultmath_af_scale(vec3, float)	ulp-bounded	256	0	0	8b0c8a540fea82fe058efc42ffa38dbd69850e579cefe5fdbc4c164b715ec15d
 lavapipe-glsl	38	vec3 cultmath_af_add_iv(vec3, vec2)	ulp-bounded	256	0	0	620f747e6ba53014c9714a8dbfaa3ff93f281c80938bd035ef64657e3bdc1a16
@@ -50,7 +50,7 @@ lavapipe-glsl	45	vec3 cultmath_af_snoise(vec3, vec3, float)	ulp-bounded, reach 1
 lavapipe-glsl	46	vec3 cultmath_af_fbm(vec3, vec3, float, int, float, float)	ulp-bounded, reach 1e-6 to 1e-3	27	102.5	0	42246db4e19a1da20433517cdc7016dda375ea70dc90d1a777679bfd76fb59e8
 lavapipe-glsl	47	float cultmath_cycles_divide(float, float)	ulp-bounded	256	0	0	87f143c57806ad52c3295cde67e97f31e39c8572b8c0a4b8c577e6fcd8ecbebf
 lavapipe-glsl	48	float cultmath_cycles_power(float, float)	ulp-bounded, platform pow	136	4.918926113980705	0	0e62db5ea32fdb9fdd3a9b135a914ddadd3231bdee0ff15c709102b26bb89186
-lavapipe-glsl	49	float cultmath_cycles_logarithm(float, float)	ulp-bounded, platform log	146	4.94622778071426	0	5b2bf1411512c7e5a3f4b335a16fc3ba00ba0784bb87acb14b7d1b9dd551b2f3
+lavapipe-glsl	49	float cultmath_cycles_logarithm(float, float)	ulp-bounded, platform log	147	4.94622778071426	0	5b2bf1411512c7e5a3f4b335a16fc3ba00ba0784bb87acb14b7d1b9dd551b2f3
 lavapipe-glsl	50	float cultmath_cycles_sqrt(float)	ulp-bounded	256	0	0	6d4beb34e93ae304b3d9d30f203fb6c2ba222affc0efc35bb5441528e9062a9a
 lavapipe-glsl	51	float cultmath_cycles_inverse_sqrt(float)	ulp-bounded	256	0	0	71aadd5bd384b9ca2eb89827de53af810a1350b02177de1987e9405e4a6e9ad8
 lavapipe-glsl	52	float cultmath_cycles_modulo(float, float)	ulp-bounded	256	0	0	cf055cafcb5b2d4789a0a2d5cfbc8bc79f52df646b60f5e47db3f994680949e9
@@ -96,16 +96,16 @@ lavapipe-glsl	91	vec3 cultmath_cycles_mix_val(float, vec3, vec3)	ulp-bounded	256
 lavapipe-glsl	92	vec3 cultmath_cycles_mix_color(float, vec3, vec3)	ulp-bounded	256	0	0	00067b1567bcd6c07a81fa5002f145dfca22437a3f3df5389b2665334d14909b
 lavapipe-glsl	93	vec3 cultmath_cycles_mix_soft(float, vec3, vec3)	ulp-bounded	157	1.9750388068880254	0	ed7c5508ca0543cc20a5f0c5624e75e3ca2a2d6044d481816eeda2edc50c0592
 lavapipe-glsl	94	vec3 cultmath_cycles_mix_linear(float, vec3, vec3)	ulp-bounded	256	0	0	672435cc30bcbbb253cce7316ee0712b1a18f06924bc89cea2d3388dd164a15d
-lavapipe-glsl	95	float cultmath_cycles_arcsine(float)	ulp-bounded, platform asin	154	2734.286809678319	0	f28f3ed0a53ffeebdfa84865d2d3d41590e6b46fc1578d40e1215e2a9e1af585
+lavapipe-glsl	95	float cultmath_cycles_arcsine(float)	ulp-bounded, platform asin	155	2734.286809678319	0	f28f3ed0a53ffeebdfa84865d2d3d41590e6b46fc1578d40e1215e2a9e1af585
 lavapipe-glsl	96	float cultmath_cycles_arccosine(float)	ulp-bounded, platform acos	79	1046.8674409774287	0	22a2c38ab5a232cdbb33cf0c133362581a398f64a4d0d5d6dd89dc5af06bd890
-lavapipe-glsl	97	float cultmath_cycles_arctan2(float, float)	ulp-bounded, platform atan	6	25.5	0	2c60447d80186f6dc9726f19c09fa96ec3f66d8f5688968da533d9195ea463c4
+lavapipe-glsl	97	float cultmath_cycles_arctan2(float, float)	ulp-bounded, platform atan	7	25.5	0	2c60447d80186f6dc9726f19c09fa96ec3f66d8f5688968da533d9195ea463c4
 lavapipe-glsl	98	mat3 cultmath_snoise_hessian(vec3)	ulp-bounded	30	1358.4375	0	62bbafb8420ed5aaa0ce11d1470ca98945e690b186c33a1e7cf4d71478396465
 lavapipe-glsl	99	mat3 cultmath_snoise_hessian(vec3)	ulp-bounded, on the simplex tie set	110	1317.4754224467295	0	0efd9b3a637b46033ed0351f64de274db4d9ce05bb83dd1ce57afb3ceaea26bc
 lavapipe-glsl	100	float cultmath_integral_clamp_linear(float, float, float, float, float, float)	ulp-bounded	256	0	0	84bf9c9a2126b3114a692507cc54f58d313afc33de8a1cac83969cc508433cbe
 lavapipe-glsl	101	float cultmath_integral_clamp_linear(float, float, float, float, float, float)	ulp-bounded, lo above hi and infinite bounds	256	0	0	ff999094d7794aa525e0f9f9a067aa21408a59559aa546cace3b1bb4a8c7f96d
 lavapipe-glsl	102	float cultmath_integral_clamp_linear(float, float, float, float, float, float)	ulp-bounded, zero-length spans and flat infinite clamps	256	0	0	c3cc48f4edcac6801b9223f12d289934916431bdfaea8f68af33a1b833ab9860
 lavapipe-glsl	103	SpanNoise cultmath_span_fbm(SpanPath, SpanStage, int, float, float)	ulp-bounded	7	1012477.3459086476	0	97c531c3a690e056d95e949e243ae74111d4a93a39fd22c0358a103b3bb14bc1
-lavapipe-glsl	104	SpanNoise cultmath_span_ridged(SpanPath, SpanStage, int, float, float)	ulp-bounded	8	948534.9108393334	0	54fd229d69439ff3318690b7802143f8410dc7ece30ad0d56ccc4b68bf39bec2
+lavapipe-glsl	104	SpanNoise cultmath_span_ridged(SpanPath, SpanStage, int, float, float)	ulp-bounded	8	948534.9108393334	0	c5d55a1d05403f6a1a7b7946c3a4c9556277f217fc660d338b3894efbb333e43
 lavapipe-glsl	105	vec4 cultmath_snoise_grad(vec3)	ulp-bounded, coordinate bands 1e-4 to 1e2	116	249.5	0	fff9658a8ec055766c9327ee9b680cf7fb83736c472ae90a11e50d6d2a053fdc
 lavapipe-glsl	106	vec4 cultmath_snoise_grad(vec3)	ulp-bounded, coordinate bands 1e2 to 4e6	70	11866336.625	0	833484714ebcea59d86e0fbc2eaa4ae247c29541703763989e6758547dbf6db8
 lavapipe-glsl	107	mat3 cultmath_snoise_hessian(vec3)	ulp-bounded, coordinate bands 1e-4 to 1e2	120	980.7417469278579	0	3ea43dabe0091ea8e994c1dfc65c7274ed38b9343d4d1d06f7caa09c806c91df
@@ -117,9 +117,13 @@ lavapipe-glsl	112	vec3 cultmath_segment_closest(vec3, vec3, vec3)	ulp-bounded	21
 lavapipe-glsl	113	vec4 cultmath_power_border_step(vec3, vec4, vec4, vec4)	ulp-bounded	214	43	0	fdfdff73434a146489b002af5e80663658b2dd7b86105a7e65bdab755ab54a5e
 lavapipe-glsl	114	vec4 cultmath_power_score(vec3, vec4)	ulp-bounded	207	1.4619722193127032	0	dc1aa639ae1dc44003a0f5d8c7c99b2e3d7f51b158c96b3c3bd7a9f7df6d927e
 lavapipe-glsl	115	vec4 cultmath_multiplicative_score(vec3, vec4)	ulp-bounded	234	1.5529504197086745	0	ee1af26ac82489e8d363e7a6b6b59da7dacfb397d4bc9a723dd68607a69da41a
-lavapipe-glsl	116	CultSiteCells cultmath_site_cells_insert(CultSiteCells, vec4, int)	ulp-bounded	256	0	0	bfad8b369011cfbf14644fec68ce65620694fcbf3cd3804f54953d55587313fc
+lavapipe-glsl	116	CultSiteCells cultmath_site_cells_insert(CultSiteCells, vec4, int)	ulp-bounded	256	0	0	b8687b139aaa865e9f28fbc84fe37dd4a1d4873d5ff8e2074922c07f56551576
 lavapipe-glsl	117	vec4 cultmath_site_cells_border(CultSiteCells)	ulp-bounded	228	1.069496760346883	0	d7b478bef7e6f80902d0b5b255cb4fca30757ff6b9d25dac2030b037a8d342ce
 lavapipe-glsl	118	float cultmath_gabriel_margin(vec3, vec3, vec3)	ulp-bounded	201	2	0	6a80fbef486de496a08b7c8e7f9f65e2cc0f5b9f93abe50c43e84ad88d1ed034
+lavapipe-glsl	119	vec3 cultmath_lattice_site(vec2, float, float)	ulp-bounded	256	0	0	84df739c336796638dcf0a99c328a4b8c150c25d80e02248d4b6d023dc13161f
+lavapipe-glsl	120	float cultmath_lattice_weight(float, float, float, float)	ulp-bounded	231	2.0671110200639147	0	434cdf5603abc2942aa624b9d2e98d5f1231706c86180a80439bc8b72bdd066e
+lavapipe-glsl	121	float cultmath_lattice_distance(vec2, vec2, float, vec2, float)	ulp-bounded	256	0	0	622d0e1ea0fcf0e2700558dbdaea92b8ce02e44048dbf35944c23b5088c3e40c
+lavapipe-glsl	122	float cultmath_lattice_smooth_step(float, float, float, float)	ulp-bounded	256	0	0	e6c9aeb52c5e63ebf3c8525dd39b5b88d5f890fd4f23f4894a92232807a3d94e
 lavapipe-hlsl	0	float cultmath_snoise(vec3)	ulp-bounded	94	122.6875	0	5d41c14241a13124f2e1b49f230f5df0c48d0d69fb1be9ef2f33dc1702bf0b0a
 lavapipe-hlsl	1	float cultmath_snoise(vec2)	ulp-bounded	204	1	0	81d9c62726afdccbbe4ffef173b5c92731eb6bf5927b3979d653e50dbd5d4064
 lavapipe-hlsl	2	vec4 cultmath_snoise_grad(vec3)	ulp-bounded	71	617.5	0	f7e9ed1707cdb015efaba0e0150193309da0d4c125349518f8b7c60a17b25790
@@ -139,14 +143,14 @@ lavapipe-hlsl	15	vec2 cultmath_iv_min(vec2, vec2)	ulp-bounded	256	0	0	a324b35cb4
 lavapipe-hlsl	16	vec2 cultmath_iv_max(vec2, vec2)	ulp-bounded	256	0	0	d68412262ca234c1da130fc5217ba6856da3e92e435c28c1fbdbf3692a89e1fa
 lavapipe-hlsl	17	vec2 cultmath_iv_sqr(vec2)	ulp-bounded	256	0	0	dbbb0e0df015456393452377d689732428a9a8e24d8e2b407ee9620593b4c46b
 lavapipe-hlsl	18	vec2 cultmath_iv_sqrt(vec2)	ulp-bounded	256	0	0	95bd15d1b283713fc632ced350f5da1b89f8f73e6618329773db1b52acd29991
-lavapipe-hlsl	19	vec2 cultmath_iv_clamp(vec2, float, float)	ulp-bounded	256	0	0	abe9daf24930a5e3a49ec994c4cae3a0c27b9d019d6d93ec1963ec3daad664a0
+lavapipe-hlsl	19	vec2 cultmath_iv_clamp(vec2, float, float)	ulp-bounded	256	0	0	268d61fd6d122e2b85e211c96daf410fb7e2d8ff83ec2082709f640504c852a7
 lavapipe-hlsl	20	vec2 cultmath_iv_saturate(vec2)	ulp-bounded	256	0	0	0f844ef8c4d9a9f748c80677bbbfc36b5f6e682eb87c2d46e7e20635d5f55c26
 lavapipe-hlsl	21	vec2 cultmath_iv_smoothstep(float, float, vec2)	ulp-bounded	256	0	0	3d5944a4c43feb91d6786924e0f5439c05285d28ff1f500b5582893758dd4ce5
 lavapipe-hlsl	22	vec2 cultmath_iv_lerp(vec2, vec2, float)	ulp-bounded	256	0	0	96b09e90a3fbbfe81379a29a23b676e490bc7dc6bb731450197707e6cf4c573f
 lavapipe-hlsl	23	vec2 cultmath_iv_snoise_ball(vec3, float)	ulp-bounded	244	54	0	f36530a4cd8c9fdc1c73e7ddb6782cd11cbf8493e2ee7b0656e818812504267e
 lavapipe-hlsl	24	vec2 cultmath_iv_fbm_ball(vec3, float, int, float, float)	ulp-bounded	252	75	0	a1677ea42ce91a5d2b6f83fa7c44879b7a184ed4631108d7a1c6e710bf26ff02
 lavapipe-hlsl	25	vec4 cultmath_iv_frustum_ball(vec2, float, float, float, float)	ulp-bounded	198	1.6457063576593662	0	327c306aa4d06aecbb2681d8808c6dbf0567e87b54a6067c68001e36b3e52169
-lavapipe-hlsl	26	vec2 cultmath_iv_exp(vec2)	ulp-bounded, platform exp	7	7.526057804152758	0	b4af8232dc3dd782cc6d790e928ede0f6ba6dfdffd6c71dd9494fb58973e485c
+lavapipe-hlsl	26	vec2 cultmath_iv_exp(vec2)	ulp-bounded, platform exp	7	7.526057804152758	0	1a46b0fa116f55e5abd70ec9f2a66de0befe8b3577fe472f9eaa98932aae8040
 lavapipe-hlsl	27	CultPhasor cultmath_phacelle(vec3, vec3, float, float)	ulp-bounded, platform exp, sin, cos; across platforms |diff| <= 2^-20 max(|v|, 1); on a device |diff| <= 2^-18 max(|v|, 1)	0	18.5	0	705b4c18027a0838218645e9368c3749ae4b5bf75e0485985725e8e72b73ab88
 lavapipe-hlsl	28	float cultmath_snoise(vec3)	ulp-bounded, on the simplex tie set	144	99	0	be76512b18eb678194dad0c4726c0aef9ba34012b60b79d24c2df27989707145
 lavapipe-hlsl	29	vec4 cultmath_snoise_grad(vec3)	ulp-bounded, on the simplex tie set	111	546.5	0	124d4be07cbb66edab644e649c081cb7c8be5d99b6c1d84fec5d7ef65c76ed0f
@@ -155,7 +159,7 @@ lavapipe-hlsl	31	vec3 cultmath_af_symbol(float, float)	ulp-bounded	256	0	0	04147
 lavapipe-hlsl	32	vec3 cultmath_af_from_iv(vec2)	ulp-bounded	256	0	0	306fe58a3268199fc8fd845a32d956f349a790422fa5c87d5a0824636cb55424
 lavapipe-hlsl	33	vec2 cultmath_af_range(vec3)	ulp-bounded	256	0	0	6245eeba19473d69d0d8155e20e2e6089a6843140723d23ed5d501064023a44a
 lavapipe-hlsl	34	vec3 cultmath_af_add(vec3, vec3)	ulp-bounded	256	0	0	cb1cb3fc69224837342de767525d332687b9d3e17b3de255c28e2f0f65f32640
-lavapipe-hlsl	35	vec3 cultmath_af_sub(vec3, vec3)	ulp-bounded	256	0	0	a8fad8ea86cf61841430293fdd9840a54008160250114040380c9634c63bb17e
+lavapipe-hlsl	35	vec3 cultmath_af_sub(vec3, vec3)	ulp-bounded	256	0	0	df44c501a8be20dc46a54faac9583da13f4367adc501a33fe14624f10e54b558
 lavapipe-hlsl	36	vec3 cultmath_af_neg(vec3)	ulp-bounded	256	0	0	e485acf8ee21c6d880621cc6216b3b2a78318f56f5864b33c5509be27e22a694
 lavapipe-hlsl	37	vec3 cultmath_af_scale(vec3, float)	ulp-bounded	256	0	0	8b0c8a540fea82fe058efc42ffa38dbd69850e579cefe5fdbc4c164b715ec15d
 lavapipe-hlsl	38	vec3 cultmath_af_add_iv(vec3, vec2)	ulp-bounded	256	0	0	620f747e6ba53014c9714a8dbfaa3ff93f281c80938bd035ef64657e3bdc1a16
@@ -169,7 +173,7 @@ lavapipe-hlsl	45	vec3 cultmath_af_snoise(vec3, vec3, float)	ulp-bounded, reach 1
 lavapipe-hlsl	46	vec3 cultmath_af_fbm(vec3, vec3, float, int, float, float)	ulp-bounded, reach 1e-6 to 1e-3	24	122.75	0	7f941b1f0c76d9f2121027a555ae7f2a741cc164402f0df75237198ac97f850b
 lavapipe-hlsl	47	float cultmath_cycles_divide(float, float)	ulp-bounded	256	0	0	87f143c57806ad52c3295cde67e97f31e39c8572b8c0a4b8c577e6fcd8ecbebf
 lavapipe-hlsl	48	float cultmath_cycles_power(float, float)	ulp-bounded, platform pow	136	4.918926113980705	0	0e62db5ea32fdb9fdd3a9b135a914ddadd3231bdee0ff15c709102b26bb89186
-lavapipe-hlsl	49	float cultmath_cycles_logarithm(float, float)	ulp-bounded, platform log	146	4.94622778071426	0	5b2bf1411512c7e5a3f4b335a16fc3ba00ba0784bb87acb14b7d1b9dd551b2f3
+lavapipe-hlsl	49	float cultmath_cycles_logarithm(float, float)	ulp-bounded, platform log	147	4.94622778071426	0	5b2bf1411512c7e5a3f4b335a16fc3ba00ba0784bb87acb14b7d1b9dd551b2f3
 lavapipe-hlsl	50	float cultmath_cycles_sqrt(float)	ulp-bounded	256	0	0	6d4beb34e93ae304b3d9d30f203fb6c2ba222affc0efc35bb5441528e9062a9a
 lavapipe-hlsl	51	float cultmath_cycles_inverse_sqrt(float)	ulp-bounded	256	0	0	71aadd5bd384b9ca2eb89827de53af810a1350b02177de1987e9405e4a6e9ad8
 lavapipe-hlsl	52	float cultmath_cycles_modulo(float, float)	ulp-bounded	256	0	0	cf055cafcb5b2d4789a0a2d5cfbc8bc79f52df646b60f5e47db3f994680949e9
@@ -215,16 +219,16 @@ lavapipe-hlsl	91	vec3 cultmath_cycles_mix_val(float, vec3, vec3)	ulp-bounded	256
 lavapipe-hlsl	92	vec3 cultmath_cycles_mix_color(float, vec3, vec3)	ulp-bounded	256	0	0	00067b1567bcd6c07a81fa5002f145dfca22437a3f3df5389b2665334d14909b
 lavapipe-hlsl	93	vec3 cultmath_cycles_mix_soft(float, vec3, vec3)	ulp-bounded	157	1.9750388068880254	0	ed7c5508ca0543cc20a5f0c5624e75e3ca2a2d6044d481816eeda2edc50c0592
 lavapipe-hlsl	94	vec3 cultmath_cycles_mix_linear(float, vec3, vec3)	ulp-bounded	256	0	0	672435cc30bcbbb253cce7316ee0712b1a18f06924bc89cea2d3388dd164a15d
-lavapipe-hlsl	95	float cultmath_cycles_arcsine(float)	ulp-bounded, platform asin	154	2734.286809678319	0	f28f3ed0a53ffeebdfa84865d2d3d41590e6b46fc1578d40e1215e2a9e1af585
+lavapipe-hlsl	95	float cultmath_cycles_arcsine(float)	ulp-bounded, platform asin	155	2734.286809678319	0	f28f3ed0a53ffeebdfa84865d2d3d41590e6b46fc1578d40e1215e2a9e1af585
 lavapipe-hlsl	96	float cultmath_cycles_arccosine(float)	ulp-bounded, platform acos	79	1046.8674409774287	0	22a2c38ab5a232cdbb33cf0c133362581a398f64a4d0d5d6dd89dc5af06bd890
-lavapipe-hlsl	97	float cultmath_cycles_arctan2(float, float)	ulp-bounded, platform atan	6	25.5	0	2c60447d80186f6dc9726f19c09fa96ec3f66d8f5688968da533d9195ea463c4
+lavapipe-hlsl	97	float cultmath_cycles_arctan2(float, float)	ulp-bounded, platform atan	7	25.5	0	2c60447d80186f6dc9726f19c09fa96ec3f66d8f5688968da533d9195ea463c4
 lavapipe-hlsl	98	mat3 cultmath_snoise_hessian(vec3)	ulp-bounded	33	2377.8799856935966	0	a64853839f394cc7c367ba5e107caa8bb396f07cf202263aa917095dd1c939f7
 lavapipe-hlsl	99	mat3 cultmath_snoise_hessian(vec3)	ulp-bounded, on the simplex tie set	132	1317.4754224467295	0	9066a49e50731881583ffca16c949171bb61578a1dfd497c54dafe773ab49488
 lavapipe-hlsl	100	float cultmath_integral_clamp_linear(float, float, float, float, float, float)	ulp-bounded	256	0	0	84bf9c9a2126b3114a692507cc54f58d313afc33de8a1cac83969cc508433cbe
 lavapipe-hlsl	101	float cultmath_integral_clamp_linear(float, float, float, float, float, float)	ulp-bounded, lo above hi and infinite bounds	256	0	0	ff999094d7794aa525e0f9f9a067aa21408a59559aa546cace3b1bb4a8c7f96d
 lavapipe-hlsl	102	float cultmath_integral_clamp_linear(float, float, float, float, float, float)	ulp-bounded, zero-length spans and flat infinite clamps	256	0	0	c3cc48f4edcac6801b9223f12d289934916431bdfaea8f68af33a1b833ab9860
 lavapipe-hlsl	103	SpanNoise cultmath_span_fbm(SpanPath, SpanStage, int, float, float)	ulp-bounded	3	1024946.5723514018	0	f6395b9f2609d914894c35b442719be3cc3e11d07c5f0bae5a8719651e60cd4e
-lavapipe-hlsl	104	SpanNoise cultmath_span_ridged(SpanPath, SpanStage, int, float, float)	ulp-bounded	7	948534.9108393334	0	2adfdc4e6c81ee0bc7bb7869c55207f5033b4176104bc36dce1528ae0a5fe39b
+lavapipe-hlsl	104	SpanNoise cultmath_span_ridged(SpanPath, SpanStage, int, float, float)	ulp-bounded	7	948534.9108393334	0	bfda3536007373bdbef75a5c7bb63a7192f1c90b082984588f23e5b4eb767867
 lavapipe-hlsl	105	vec4 cultmath_snoise_grad(vec3)	ulp-bounded, coordinate bands 1e-4 to 1e2	119	423.1430718408491	0	a94c38d1baa651a6faa510920cbe9d1f9528c0adb863ba6e35d835588ad00a58
 lavapipe-hlsl	106	vec4 cultmath_snoise_grad(vec3)	ulp-bounded, coordinate bands 1e2 to 4e6	73	13116827.1875	0	9ad0fd577b26aa717534c0693df97ee41bcded0768f442739b98f505e4a2a430
 lavapipe-hlsl	107	mat3 cultmath_snoise_hessian(vec3)	ulp-bounded, coordinate bands 1e-4 to 1e2	122	980.7417469278579	0	0977fa6f446e4f916a9b938ce24ea32df6aa912dc991c182014d309dc0efb1cb
@@ -236,6 +240,10 @@ lavapipe-hlsl	112	vec3 cultmath_segment_closest(vec3, vec3, vec3)	ulp-bounded	21
 lavapipe-hlsl	113	vec4 cultmath_power_border_step(vec3, vec4, vec4, vec4)	ulp-bounded	214	43	0	fdfdff73434a146489b002af5e80663658b2dd7b86105a7e65bdab755ab54a5e
 lavapipe-hlsl	114	vec4 cultmath_power_score(vec3, vec4)	ulp-bounded	207	1.4619722193127032	0	dc1aa639ae1dc44003a0f5d8c7c99b2e3d7f51b158c96b3c3bd7a9f7df6d927e
 lavapipe-hlsl	115	vec4 cultmath_multiplicative_score(vec3, vec4)	ulp-bounded	234	1.5529504197086745	0	ee1af26ac82489e8d363e7a6b6b59da7dacfb397d4bc9a723dd68607a69da41a
-lavapipe-hlsl	116	CultSiteCells cultmath_site_cells_insert(CultSiteCells, vec4, int)	ulp-bounded	256	0	0	bfad8b369011cfbf14644fec68ce65620694fcbf3cd3804f54953d55587313fc
+lavapipe-hlsl	116	CultSiteCells cultmath_site_cells_insert(CultSiteCells, vec4, int)	ulp-bounded	256	0	0	b8687b139aaa865e9f28fbc84fe37dd4a1d4873d5ff8e2074922c07f56551576
 lavapipe-hlsl	117	vec4 cultmath_site_cells_border(CultSiteCells)	ulp-bounded	228	1.069496760346883	0	d7b478bef7e6f80902d0b5b255cb4fca30757ff6b9d25dac2030b037a8d342ce
 lavapipe-hlsl	118	float cultmath_gabriel_margin(vec3, vec3, vec3)	ulp-bounded	201	2	0	6a80fbef486de496a08b7c8e7f9f65e2cc0f5b9f93abe50c43e84ad88d1ed034
+lavapipe-hlsl	119	vec3 cultmath_lattice_site(vec2, float, float)	ulp-bounded	256	0	0	84df739c336796638dcf0a99c328a4b8c150c25d80e02248d4b6d023dc13161f
+lavapipe-hlsl	120	float cultmath_lattice_weight(float, float, float, float)	ulp-bounded	231	2.0671110200639147	0	434cdf5603abc2942aa624b9d2e98d5f1231706c86180a80439bc8b72bdd066e
+lavapipe-hlsl	121	float cultmath_lattice_distance(vec2, vec2, float, vec2, float)	ulp-bounded	256	0	0	622d0e1ea0fcf0e2700558dbdaea92b8ce02e44048dbf35944c23b5088c3e40c
+lavapipe-hlsl	122	float cultmath_lattice_smooth_step(float, float, float, float)	ulp-bounded	256	0	0	e6c9aeb52c5e63ebf3c8525dd39b5b88d5f890fd4f23f4894a92232807a3d94e

packages/cultmath/unity/org.gamecult.cultmath/Shaders/CultMath.hlsl

@@ -688,6 +688,52 @@ float cultmath_gabriel_margin(float3 a, float3 b, float3 other)
     return (cultmath_distance(other, (a + b) * 0.5) - r) / r;
 }
 
+// Weighted lattice cells: the four per-cell steps of math.Lattice.cs, statement for statement. A shader function cannot take a
+// span (design.md, "Sites"), so weighted_lattice_cells is the consumer's loop over its own body buffer, in two passes:
+//   float2 q = p / cellSize; int2 c0 = (int2)floor(q); float f1 = 1.0e30, f2 = 1.0e30; int reach = 0;
+//   for (int k = 0; ; k++) {   // ring pass: Chebyshev rings 0, 1, 2, ... around c0, exact exit
+//       if (k > 1 && 0.5 * (k - 1) >= max(f2, f1 + 2.0 * smoothing)) break;   // k never reaches 38 in the accepted range
+//       for each cell on ring k: d = cultmath_lattice_distance(q, cultmath_lattice_site(cell, time, drift).xy, w, normal, stretch),
+//           w = cultmath_lattice_weight(site.z, border, boost, falloff), border = the .w of cultmath_power_border_step
+//           folded over the bodies (owner = the nearest body of the cell centre (cell + 0.5) * cellSize, z = 0);
+//           if (d < f1) { f2 = f1; f1 = d; } else if (d < f2) f2 = d;   store d for the box pass
+//       reach = k; }
+//   float m = f1 + smoothing;   // box pass: every stored cell, rows dz = -reach..reach, then dx = -reach..reach
+//   for each (dz, dx): m = cultmath_lattice_smooth_step(m, d, f1, smoothing);   // strict < for the winning id (earlier cell wins ties)
+// The preconditions the C# function throws for are the caller's in a shader: finite arguments, cellSize > 0, boost in [0, 4],
+// falloff > 0, smoothing in (0, 1], stretch in [1, 2], p within 2^23 cells. The normal is normalised as C# does: divide by its
+// largest component, then by its length (a zero normal means (1, 0) and needs stretch == 1). The ring bound is 37.
+float3 cultmath_lattice_site(float2 cell, float time, float drift)
+{
+    int3 h = cultmath_pcg3d(int3((int)cell.x, (int)cell.y, 0));
+    float2 phase = float2((float)((uint)h.x >> 8) * (1.0 / 16777216.0), (float)((uint)h.y >> 8) * (1.0 / 16777216.0));
+    float2 site = cell + 0.5 + 0.5 * float2(sin(drift * time + CULTMATH_TAU * phase.x), sin(drift * time + CULTMATH_TAU * phase.y));
+    return float3(site, 0.5 + 0.5 * ((float)((uint)h.z >> 8) * (1.0 / 16777216.0)));
+}
+
+float cultmath_lattice_weight(float base_weight, float border, float boost, float falloff)
+{
+    float t = border / falloff;
+    return base_weight * (1.0 + boost * exp(-(t * t)));
+}
+
+float cultmath_lattice_distance(float2 q, float2 site, float weight, float2 normal, float stretch)
+{
+    float2 v = site - q;
+    float a = dot(v, normal);
+    float c = v.x * normal.y - v.y * normal.x;
+    return weight * length(float2(stretch * a, c));
+}
+
+float cultmath_lattice_smooth_step(float m, float d, float f1, float smoothing)
+{
+    if (d >= f1 + 2.0 * smoothing)
+        return m;
+    float h = cultmath_smoothstep(0.0, 1.0, 0.5 + 0.5 * (m - d) / smoothing);
+    float next = m + (d - m) * h - h * (1.0 - h) * smoothing / (1.0 + 3.0 * smoothing);
+    return min(next, f1 + smoothing);
+}
+
 float2 cultmath_segment_closest(float2 point_value, float2 start, float2 end)
 {
     float2 segment = end - start;