aperiodic: clanker analytic aa

1 files changed, 92 insertions, 85 deletions

diff --git a/aperiodic_tiling.cginc b/aperiodic_tiling.cginc
index 142a3de..1907c69 100644
--- a/aperiodic_tiling.cginc
+++ b/aperiodic_tiling.cginc
@@ -51,9 +51,20 @@ float2 tile5_barycentric(float4 p03, float p44, float2x2 m, float2 s,
   return mul(m, proj5(p03, p44)) - s;
 }
 
-float tile5_distance_from_barycentric(float2 barycentric) {
-  float2 f = abs(barycentric);
-  return 0.5 - max(f.x, f.y);
+float interval_box_coverage(float center, float half_extent, float radius) {
+  if (half_extent <= 1e-5) {
+    return abs(center) <= radius ? 1.0 : 0.0;
+  }
+
+  float lo = center - half_extent;
+  float hi = center + half_extent;
+  float overlap = max(min(hi, radius) - max(lo, -radius), 0.0);
+  return overlap / (2.0 * half_extent);
+}
+
+float square_box_coverage(float2 barycentric, float2 half_extents, float radius) {
+  return interval_box_coverage(barycentric.x, half_extents.x, radius) *
+         interval_box_coverage(barycentric.y, half_extents.y, radius);
 }
 
 #if defined(_APERIODIC_TILING_NORMALS)
@@ -70,104 +81,102 @@ float3 aperiodic_tiling_normal(float2 barycentric) {
 }
 #endif  // _APERIODIC_TILING_NORMALS
 
-void choose_aperiodic_candidate(float2 barycentric, inout float distance_to_edge,
-                                inout float2 best_barycentric) {
-  float candidate_distance = tile5_distance_from_barycentric(barycentric);
-  bool better = (candidate_distance > distance_to_edge);
-  distance_to_edge = better ? candidate_distance : distance_to_edge;
-  best_barycentric = better ? barycentric : best_barycentric;
-}
+void accumulate_filtered_candidate(
+    float2 barycentric, float2 footprint_half_extents, float edge_width, float3 face_color,
+    inout float3 color_sum, inout float outer_sum, inout float2 normal_xy_sum) {
+  float outer = square_box_coverage(barycentric, footprint_half_extents, 0.5);
+  float inner_radius = max(0.5 - edge_width, 0.0);
+  float inner = square_box_coverage(barycentric, footprint_half_extents, inner_radius);
+  float edge = outer - inner;
 
-struct AperiodicTileSample {
-  float distance_to_edge;
-  float2 barycentric;
-  uint face_id;
-};
+  color_sum += face_color * inner + _Aperiodic_Tiling_Edge_Color.rgb * edge;
+  outer_sum += outer;
 
-AperiodicTileSample sample_lattice(
-    float4 p03, float p44, float4 a03, float a44, float4 b03, float b44) {
+#if defined(_APERIODIC_TILING_NORMALS)
+  float3 tile_normal = aperiodic_tiling_normal(barycentric);
+  normal_xy_sum += tile_normal.xy * outer;
+#endif
+}
+
+void accumulate_filtered_lattice(
+    float4 p03, float p44, float2 uv_ddx, float2 uv_ddy,
+    float4 a03, float a44, float4 b03, float b44, float edge_width, float3 face_color,
+    inout float3 color_sum, inout float outer_sum, inout float2 normal_xy_sum) {
   float2 pa = proj5(a03, a44);
   float2 pb = proj5(b03, b44);
   float2x2 m = inv2x2(float2x2(pa.x, pb.x, pa.y, pb.y));
   float2 r = round(float2(dot5(p03, p44, a03, a44), dot5(p03, p44, b03, b44)));
   float2 s = float2(0.5, -0.5);
 
-  float2 best_barycentric = tile5_barycentric(p03, p44, m, r + s.xx, a03, a44, b03, b44);
-  float distance_to_edge = tile5_distance_from_barycentric(best_barycentric);
-  choose_aperiodic_candidate(
+  float2 dbdx = mul(m, uv_ddx);
+  float2 dbdy = mul(m, uv_ddy);
+  float2 footprint_half_extents = 0.5 * (abs(dbdx) + abs(dbdy));
+
+  accumulate_filtered_candidate(
+      tile5_barycentric(p03, p44, m, r + s.xx, a03, a44, b03, b44),
+      footprint_half_extents, edge_width, face_color, color_sum, outer_sum, normal_xy_sum);
+  accumulate_filtered_candidate(
       tile5_barycentric(p03, p44, m, r + s.xy, a03, a44, b03, b44),
-      distance_to_edge, best_barycentric);
-  choose_aperiodic_candidate(
+      footprint_half_extents, edge_width, face_color, color_sum, outer_sum, normal_xy_sum);
+  accumulate_filtered_candidate(
       tile5_barycentric(p03, p44, m, r + s.yx, a03, a44, b03, b44),
-      distance_to_edge, best_barycentric);
-  choose_aperiodic_candidate(
+      footprint_half_extents, edge_width, face_color, color_sum, outer_sum, normal_xy_sum);
+  accumulate_filtered_candidate(
       tile5_barycentric(p03, p44, m, r + s.yy, a03, a44, b03, b44),
-      distance_to_edge, best_barycentric);
-
-  AperiodicTileSample sample;
-  sample.distance_to_edge = distance_to_edge;
-  sample.barycentric = best_barycentric;
-  return sample;
-}
-
-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;
+      footprint_half_extents, edge_width, face_color, color_sum, outer_sum, normal_xy_sum);
 }
 
-void sample_aperiodic_tiling(float2 uv, out float3 albedo
-                             , out float3 tiling_normal_tangent
-                             ) {
+void sample_aperiodic_tiling(float2 uv, inout float3 albedo, out float3 tiling_normal_tangent) {
   float4 p03 = uv.x * basis_u5_03 + uv.y * basis_v5_03;
   float p44 = uv.x * basis_u5_44 + uv.y * basis_v5_44;
+  float2 uv_ddx = ddx(uv);
+  float2 uv_ddy = ddy(uv);
 
   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 = lerp(edge, face_colors[best.face_id], edge_mask);
+  // Analytically filter the existing local tile set in each orientation's
+  // barycentric space using a separable box footprint.
+  float edge_width = min(_Aperiodic_Tiling_Edge_Thickness, 0.5);
+  float3 color_sum = 0.0;
+  float outer_sum = 0.0;
+  float2 normal_xy_sum = 0.0;
+
+  accumulate_filtered_lattice(
+      p03, p44, uv_ddx, uv_ddy, u.yxxx, u.x, u.xyxx, u.x, edge_width,
+      _Aperiodic_Tiling_Color_0.rgb, color_sum, outer_sum, normal_xy_sum);
+  accumulate_filtered_lattice(
+      p03, p44, uv_ddx, uv_ddy, u.yxxx, u.x, u.xxyx, u.x, edge_width,
+      _Aperiodic_Tiling_Color_1.rgb, color_sum, outer_sum, normal_xy_sum);
+  accumulate_filtered_lattice(
+      p03, p44, uv_ddx, uv_ddy, u.yxxx, u.x, u.xxxy, u.x, edge_width,
+      _Aperiodic_Tiling_Color_2.rgb, color_sum, outer_sum, normal_xy_sum);
+  accumulate_filtered_lattice(
+      p03, p44, uv_ddx, uv_ddy, u.yxxx, u.x, u.xxxx, u.y, edge_width,
+      _Aperiodic_Tiling_Color_3.rgb, color_sum, outer_sum, normal_xy_sum);
+  accumulate_filtered_lattice(
+      p03, p44, uv_ddx, uv_ddy, u.xyxx, u.x, u.xxyx, u.x, edge_width,
+      _Aperiodic_Tiling_Color_4.rgb, color_sum, outer_sum, normal_xy_sum);
+  accumulate_filtered_lattice(
+      p03, p44, uv_ddx, uv_ddy, u.xyxx, u.x, u.xxxy, u.x, edge_width,
+      _Aperiodic_Tiling_Color_5.rgb, color_sum, outer_sum, normal_xy_sum);
+  accumulate_filtered_lattice(
+      p03, p44, uv_ddx, uv_ddy, u.xyxx, u.x, u.xxxx, u.y, edge_width,
+      _Aperiodic_Tiling_Color_6.rgb, color_sum, outer_sum, normal_xy_sum);
+  accumulate_filtered_lattice(
+      p03, p44, uv_ddx, uv_ddy, u.xxyx, u.x, u.xxxy, u.x, edge_width,
+      _Aperiodic_Tiling_Color_7.rgb, color_sum, outer_sum, normal_xy_sum);
+  accumulate_filtered_lattice(
+      p03, p44, uv_ddx, uv_ddy, u.xxyx, u.x, u.xxxx, u.y, edge_width,
+      _Aperiodic_Tiling_Color_8.rgb, color_sum, outer_sum, normal_xy_sum);
+  accumulate_filtered_lattice(
+      p03, p44, uv_ddx, uv_ddy, u.xxxy, u.x, u.xxxx, u.y, edge_width,
+      _Aperiodic_Tiling_Color_9.rgb, color_sum, outer_sum, normal_xy_sum);
+
+  float normalization = max(outer_sum, 1e-4);
+  albedo *= color_sum / normalization;
 
 #if defined(_APERIODIC_TILING_NORMALS)
-  float3 tile_normal = aperiodic_tiling_normal(best.barycentric);
-  tiling_normal_tangent = normalize(float3(tile_normal.xy * edge_mask, 1.0));
+  tiling_normal_tangent = normalize(float3(normal_xy_sum / normalization, 1.0));
 #else
   tiling_normal_tangent = 0;
 #endif
@@ -178,11 +187,9 @@ void apply_aperiodic_tiling(float2 uv, inout float3 albedo, inout float3 normal_
 #if defined(_APERIODIC_TILING)
   uv *= _Aperiodic_Tiling_Scale;
   float3 tiling_normal_tangent;
-  sample_aperiodic_tiling(uv, albedo
-                          , tiling_normal_tangent
-                          );
+  sample_aperiodic_tiling(uv, albedo, tiling_normal_tangent);
 #if defined(_APERIODIC_TILING_NORMALS)
-  normal_tangent = blendNormalsHill12(normal_tangent, tiling_normal_tangent);
+  normal_tangent = tiling_normal_tangent;
 #endif
 #endif  // _APERIODIC_TILING
 }