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#ifndef __APERIODIC_TILING_INC
#define __APERIODIC_TILING_INC
// 5D cut-and-project for Penrose tiling.
// References:
// https://www.shadertoy.com/view/XccXW8 (public domain)
// https://gglouser.github.io/cut-and-project-tiling/docs/intro.html#how-it-works
// https://www.youtube.com/watch?v=hwMAOFb6yvA
#include "globals.cginc"
#include "math.cginc"
#if defined(_APERIODIC_TILING)
static const float M5 = sqrt(2.0 / 5.0);
static const float4 basis_u5_03 = M5 * float4(
cos(0 * TAU / 10),
cos(1 * TAU / 10),
cos(2 * TAU / 10),
cos(3 * TAU / 10));
static const float basis_u5_44 = M5 * cos(4 * TAU / 10);
static const float4 basis_v5_03 = M5 * float4(
sin(0 * TAU / 10),
sin(1 * TAU / 10),
sin(2 * TAU / 10),
sin(3 * TAU / 10));
static const float basis_v5_44 = M5 * sin(4 * TAU / 10);
float dot5(float4 a03, float a44, float4 b03, float b44) {
return dot(a03, b03) + a44 * b44;
}
float2 proj5(float4 p03, float p44) {
return float2(
dot5(p03, p44, basis_u5_03, basis_u5_44),
dot5(p03, p44, basis_v5_03, basis_v5_44));
}
float2x2 inv2x2(float2x2 m) {
float d = m[0][0] * m[1][1] - m[0][1] * m[1][0];
return float2x2(m[1][1], -m[0][1], -m[1][0], m[0][0]) / d;
}
float2 tile5_barycentric(float4 p03, float p44, float2x2 m, float2 s,
float4 a03, float a44, float4 b03, float b44) {
float2 q = mul(s, m);
p03 -= (1.0 - a03 - b03) * round(q.x * basis_u5_03 + q.y * basis_v5_03);
p44 -= (1.0 - a44 - b44) * round(q.x * basis_u5_44 + q.y * basis_v5_44);
return mul(m, proj5(p03, p44)) - s;
}
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)
float3 aperiodic_tiling_normal(float2 barycentric) {
float bevel_width = min(_Aperiodic_Tiling_Normal_Thickness, 0.5);
if (bevel_width <= 1e-5) {
return float3(0.0, 0.0, 1.0);
}
float flat_limit = 0.5 - bevel_width;
float2 edge_factor = smoothstep(flat_limit, 0.5, abs(barycentric));
float2 xy = sign(barycentric) * edge_factor * _Aperiodic_Tiling_Normal_Strength;
return normalize(float3(xy, 1.0));
}
#endif // _APERIODIC_TILING_NORMALS
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;
color_sum += face_color * inner + _Aperiodic_Tiling_Edge_Color.rgb * edge;
outer_sum += outer;
#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 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),
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),
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),
footprint_half_extents, edge_width, face_color, color_sum, outer_sum, normal_xy_sum);
}
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);
// 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)
tiling_normal_tangent = normalize(float3(normal_xy_sum / normalization, 1.0));
#else
tiling_normal_tangent = 0;
#endif
}
#endif // defined(_APERIODIC_TILING)
void apply_aperiodic_tiling(float2 uv, inout float3 albedo, inout float3 normal_tangent) {
#if defined(_APERIODIC_TILING)
uv *= _Aperiodic_Tiling_Scale;
float3 tiling_normal_tangent;
sample_aperiodic_tiling(uv, albedo, tiling_normal_tangent);
#if defined(_APERIODIC_TILING_NORMALS)
normal_tangent = tiling_normal_tangent;
#endif
#endif // _APERIODIC_TILING
}
#endif // __APERIODIC_TILING_INC
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