aperiodic: improve aa

Calculate colors after accumulating raw data and use standard fwidth
trick to anti-alias edges. The cells themselves are not yet anti
aliased.

1 files changed, 57 insertions, 44 deletions

diff --git a/aperiodic_tiling.cginc b/aperiodic_tiling.cginc
index 5e12ee0..142a3de 100644
--- a/aperiodic_tiling.cginc
+++ b/aperiodic_tiling.cginc
@@ -43,11 +43,6 @@ float2x2 inv2x2(float2x2 m) {
   return float2x2(m[1][1], -m[0][1], -m[1][0], m[0][0]) / d;
 }
 
-struct AperiodicTileSample {
-  float coverage;
-  float2 barycentric;
-};
-
 float2 tile5_barycentric(float4 p03, float p44, float2x2 m, float2 s,
                          float4 a03, float a44, float4 b03, float b44) {
   float2 q = mul(s, m);
@@ -61,13 +56,6 @@ float tile5_distance_from_barycentric(float2 barycentric) {
   return 0.5 - max(f.x, f.y);
 }
 
-float aperiodic_edge_coverage(float distance_to_edge) {
-  float edge_width = saturate(_Aperiodic_Tiling_Edge_Thickness * 2.0) * 0.5;
-  float signed_distance = distance_to_edge - edge_width;
-  float aa_width = max(fwidth(signed_distance), 1e-4);
-  return smoothstep(-aa_width, aa_width, signed_distance);
-}
-
 #if defined(_APERIODIC_TILING_NORMALS)
 float3 aperiodic_tiling_normal(float2 barycentric) {
   float bevel_width = min(_Aperiodic_Tiling_Normal_Thickness, 0.5);
@@ -85,13 +73,18 @@ float3 aperiodic_tiling_normal(float2 barycentric) {
 void choose_aperiodic_candidate(float2 barycentric, inout float distance_to_edge,
                                 inout float2 best_barycentric) {
   float candidate_distance = tile5_distance_from_barycentric(barycentric);
-  if (candidate_distance > distance_to_edge) {
-    distance_to_edge = candidate_distance;
-    best_barycentric = barycentric;
-  }
+  bool better = (candidate_distance > distance_to_edge);
+  distance_to_edge = better ? candidate_distance : distance_to_edge;
+  best_barycentric = better ? barycentric : best_barycentric;
 }
 
-AperiodicTileSample sample_aperiodic_orientation(
+struct AperiodicTileSample {
+  float distance_to_edge;
+  float2 barycentric;
+  uint face_id;
+};
+
+AperiodicTileSample sample_lattice(
     float4 p03, float p44, float4 a03, float a44, float4 b03, float b44) {
   float2 pa = proj5(a03, a44);
   float2 pb = proj5(b03, b44);
@@ -112,22 +105,17 @@ AperiodicTileSample sample_aperiodic_orientation(
       distance_to_edge, best_barycentric);
 
   AperiodicTileSample sample;
-  sample.coverage = aperiodic_edge_coverage(distance_to_edge);
+  sample.distance_to_edge = distance_to_edge;
   sample.barycentric = best_barycentric;
   return sample;
 }
 
-void apply_aperiodic_orientation(float3 face_color,
-                                 float4 p03, float p44,
-                                 float4 a03, float a44, float4 b03, float b44,
-                                 float3 edge_color,
-                                 inout float3 albedo, inout float2 normal_xy_acc) {
-  AperiodicTileSample sample =
-      sample_aperiodic_orientation(p03, p44, a03, a44, b03, b44);
-  albedo += (face_color - edge_color) * sample.coverage;
-#if defined(_APERIODIC_TILING_NORMALS)
-  normal_xy_acc += aperiodic_tiling_normal(sample.barycentric).xy * sample.coverage;
-#endif
+void accumulate_best(AperiodicTileSample candidate, uint face_id,
+                                  inout AperiodicTileSample best) {
+  bool better = (candidate.distance_to_edge > best.distance_to_edge);
+  best.distance_to_edge = better ? candidate.distance_to_edge : best.distance_to_edge;
+  best.barycentric = better ? candidate.barycentric : best.barycentric;
+  best.face_id = better ? face_id : best.face_id;
 }
 
 void sample_aperiodic_tiling(float2 uv, out float3 albedo
@@ -137,24 +125,49 @@ void sample_aperiodic_tiling(float2 uv, out float3 albedo
   float p44 = uv.x * basis_u5_44 + uv.y * basis_v5_44;
 
   float2 u = float2(0, 1);
+
+  // Accumulate best sample across all 10 face orientations = C(5,2) pairs
+  AperiodicTileSample best;
+  best.distance_to_edge = -1e10;
+  best.barycentric = 0;
+  best.face_id = 0;
+
+  accumulate_best(sample_lattice(p03, p44, u.yxxx, u.x, u.xyxx, u.x), 0, best);
+  accumulate_best(sample_lattice(p03, p44, u.yxxx, u.x, u.xxyx, u.x), 1, best);
+  accumulate_best(sample_lattice(p03, p44, u.yxxx, u.x, u.xxxy, u.x), 2, best);
+  accumulate_best(sample_lattice(p03, p44, u.yxxx, u.x, u.xxxx, u.y), 3, best);
+  accumulate_best(sample_lattice(p03, p44, u.xyxx, u.x, u.xxyx, u.x), 4, best);
+  accumulate_best(sample_lattice(p03, p44, u.xyxx, u.x, u.xxxy, u.x), 5, best);
+  accumulate_best(sample_lattice(p03, p44, u.xyxx, u.x, u.xxxx, u.y), 6, best);
+  accumulate_best(sample_lattice(p03, p44, u.xxyx, u.x, u.xxxy, u.x), 7, best);
+  accumulate_best(sample_lattice(p03, p44, u.xxyx, u.x, u.xxxx, u.y), 8, best);
+  accumulate_best(sample_lattice(p03, p44, u.xxxy, u.x, u.xxxx, u.y), 9, best);
+
+  // Compute edge coverage from distance
+  float edge_width = saturate(_Aperiodic_Tiling_Edge_Thickness * 2.0) * 0.5;
+  float edge_sd = best.distance_to_edge - edge_width;
+  float edge_sd_aa = max(abs(fwidth(edge_sd)), 1e-4);
+  float edge_mask = smoothstep(-edge_sd_aa * 0.5, edge_sd_aa * 0.5, edge_sd);
+
+  // Select face color and composite
+  float3 face_colors[10];
+  face_colors[0] = _Aperiodic_Tiling_Color_0.rgb;
+  face_colors[1] = _Aperiodic_Tiling_Color_1.rgb;
+  face_colors[2] = _Aperiodic_Tiling_Color_2.rgb;
+  face_colors[3] = _Aperiodic_Tiling_Color_3.rgb;
+  face_colors[4] = _Aperiodic_Tiling_Color_4.rgb;
+  face_colors[5] = _Aperiodic_Tiling_Color_5.rgb;
+  face_colors[6] = _Aperiodic_Tiling_Color_6.rgb;
+  face_colors[7] = _Aperiodic_Tiling_Color_7.rgb;
+  face_colors[8] = _Aperiodic_Tiling_Color_8.rgb;
+  face_colors[9] = _Aperiodic_Tiling_Color_9.rgb;
+
   float3 edge = _Aperiodic_Tiling_Edge_Color.rgb;
-  albedo = edge;
-  float2 normal_xy_accum = 0;
-
-  // 10 face orientations = C(5,2) pairs of 5D axes
-  apply_aperiodic_orientation(_Aperiodic_Tiling_Color_0.rgb, p03, p44, u.yxxx, u.x, u.xyxx, u.x, edge, albedo, normal_xy_accum);
-  apply_aperiodic_orientation(_Aperiodic_Tiling_Color_1.rgb, p03, p44, u.yxxx, u.x, u.xxyx, u.x, edge, albedo, normal_xy_accum);
-  apply_aperiodic_orientation(_Aperiodic_Tiling_Color_2.rgb, p03, p44, u.yxxx, u.x, u.xxxy, u.x, edge, albedo, normal_xy_accum);
-  apply_aperiodic_orientation(_Aperiodic_Tiling_Color_3.rgb, p03, p44, u.yxxx, u.x, u.xxxx, u.y, edge, albedo, normal_xy_accum);
-  apply_aperiodic_orientation(_Aperiodic_Tiling_Color_4.rgb, p03, p44, u.xyxx, u.x, u.xxyx, u.x, edge, albedo, normal_xy_accum);
-  apply_aperiodic_orientation(_Aperiodic_Tiling_Color_5.rgb, p03, p44, u.xyxx, u.x, u.xxxy, u.x, edge, albedo, normal_xy_accum);
-  apply_aperiodic_orientation(_Aperiodic_Tiling_Color_6.rgb, p03, p44, u.xyxx, u.x, u.xxxx, u.y, edge, albedo, normal_xy_accum);
-  apply_aperiodic_orientation(_Aperiodic_Tiling_Color_7.rgb, p03, p44, u.xxyx, u.x, u.xxxy, u.x, edge, albedo, normal_xy_accum);
-  apply_aperiodic_orientation(_Aperiodic_Tiling_Color_8.rgb, p03, p44, u.xxyx, u.x, u.xxxx, u.y, edge, albedo, normal_xy_accum);
-  apply_aperiodic_orientation(_Aperiodic_Tiling_Color_9.rgb, p03, p44, u.xxxy, u.x, u.xxxx, u.y, edge, albedo, normal_xy_accum);
+  albedo = lerp(edge, face_colors[best.face_id], edge_mask);
 
 #if defined(_APERIODIC_TILING_NORMALS)
-  tiling_normal_tangent = normalize(float3(normal_xy_accum, 1.0));
+  float3 tile_normal = aperiodic_tiling_normal(best.barycentric);
+  tiling_normal_tangent = normalize(float3(tile_normal.xy * edge_mask, 1.0));
 #else
   tiling_normal_tangent = 0;
 #endif