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1 | 1 | #ifndef UNITY_AREA_LIGHTING_INCLUDED |
2 | 2 | #define UNITY_AREA_LIGHTING_INCLUDED |
3 | 3 |
|
4 | | -#define SPHERE_LIGHT_APPROXIMATION |
| 4 | +#define APPROXIMATE_POLY_LIGHT_AS_SPHERE_LIGHT |
| 5 | +#define APPROXIMATE_SPHERE_LIGHT_NUMERICALLY |
5 | 6 |
|
6 | 7 | // Not normalized by the factor of 1/TWO_PI. |
7 | 8 | float3 ComputeEdgeFactor(float3 V1, float3 V2) |
@@ -40,102 +41,103 @@ float IntegrateEdge(float3 V1, float3 V2) |
40 | 41 | // N.b.: this function accounts for horizon clipping. |
41 | 42 | float DiffuseSphereLightIrradiance(float sinSqSigma, float cosOmega) |
42 | 43 | { |
43 | | -#if 1 // Use a numerical fit for the sphere light approximation found in Mathematica. |
| 44 | +#ifdef APPROXIMATE_SPHERE_LIGHT_NUMERICALLY |
44 | 45 | float x = sinSqSigma; |
45 | 46 | float y = cosOmega; |
46 | 47 |
|
47 | | - // For most of the domain, the absolute error is pretty low, under 0.005. |
48 | | - // You can use the following Mathematica code to reproduce our results: |
49 | | - // t = Flatten[Table[{x, y, f[x, y]}, {x, 0, 0.999999, 0.001}, {y, -0.999999, 0.999999, 0.002}], 1] |
50 | | - // m = NonlinearModelFit[t, x * (y + e) * (0.5 + (y - e) * (a + b * x + c * x^2 + d * x^3)), {a, b, c, d, e}, {x, y}] |
51 | | - return saturate(x * (0.9245867471551246 + y) * (0.5 + (-0.9245867471551246 + y) * (0.5359050373687144 + x * (-1.0054221851257754 + x * (1.8199061187417047 - x * 1.3172081704209504))))); |
| 48 | + #if 1 |
| 49 | + // Use a numerical fit found in Mathematica. |
| 50 | + // For most of the domain, the absolute error is fairly low, under 0.005. |
| 51 | + // You can use the following Mathematica code to reproduce our results: |
| 52 | + // t = Flatten[Table[{x, y, f[x, y]}, {x, 0, 0.999999, 0.001}, {y, -0.999999, 0.999999, 0.002}], 1] |
| 53 | + // m = NonlinearModelFit[t, x * (y + e) * (0.5 + (y - e) * (a + b * x + c * x^2 + d * x^3)), {a, b, c, d, e}, {x, y}] |
| 54 | + return saturate(x * (0.9245867471551246 + y) * (0.5 + (-0.9245867471551246 + y) * (0.5359050373687144 + x * (-1.0054221851257754 + x * (1.8199061187417047 - x * 1.3172081704209504))))); |
| 55 | + #else |
| 56 | + // Another fit found with Mathematica. The absolute error is larger (around 0.02 on average), but the function is very smooth. |
| 57 | + // You can use the following Mathematica code to reproduce our results: |
| 58 | + // t = Flatten[Table[{x, y, f[x, y]}, {x, 0, 0.999999, 0.001}, {y, -0.999999, 0.999999, 0.002}], 1] |
| 59 | + // m = NonlinearModelFit[t, 1 - (1 - x)^(a * (y + 1) + b * (y + 1)^2 + c * (y + 1)^3 + d * (y + 1)^4)}, {a, b, c, d}, {x, y}] |
| 60 | + float p = saturate(0.14506085844485772 + y * (0.2858221675641456 + y * (0.23405929637528905 + y * (0.20682928702038633 + y * 0.1135312997643852)))); |
| 61 | + return saturate(1 - pow(1 - x, p)); |
| 62 | + #endif |
52 | 63 | #else |
53 | | - float x = sinSqSigma; |
54 | | - float y = cosOmega; |
55 | | - |
56 | | - // Another fit found with Mathematica. The error is larger (around 0.02 on average), but the function is very smooth. |
57 | | - // You can use the following Mathematica code to reproduce our results: |
58 | | - // t = Flatten[Table[{x, y, f[x, y]}, {x, 0, 0.999999, 0.001}, {y, -0.999999, 0.999999, 0.002}], 1] |
59 | | - // m = NonlinearModelFit[t, 1 - (1 - x)^(a * (y + 1) + b * (y + 1)^2 + c * (y + 1)^3 + d * (y + 1)^4)}, {a, b, c, d}, {x, y}] |
60 | | - float p = saturate(0.14506085844485772 + y * (0.2858221675641456 + y * (0.23405929637528905 + y * (0.20682928702038633 + y * 0.1135312997643852)))); |
61 | | - return saturate(1 - pow(1 - x, p)); |
62 | | -#endif |
63 | | -#if 0 // Ref: Area Light Sources for Real-Time Graphics, page 4 (1996). |
64 | | - float sinSqOmega = saturate(1 - cosOmega * cosOmega); |
65 | | - float cosSqSigma = saturate(1 - sinSqSigma); |
66 | | - float sinSqGamma = saturate(cosSqSigma / sinSqOmega); |
67 | | - float cosSqGamma = saturate(1 - sinSqGamma); |
| 64 | + #if 0 // Ref: Area Light Sources for Real-Time Graphics, page 4 (1996). |
| 65 | + float sinSqOmega = saturate(1 - cosOmega * cosOmega); |
| 66 | + float cosSqSigma = saturate(1 - sinSqSigma); |
| 67 | + float sinSqGamma = saturate(cosSqSigma / sinSqOmega); |
| 68 | + float cosSqGamma = saturate(1 - sinSqGamma); |
68 | 69 |
|
69 | | - float sinSigma = sqrt(sinSqSigma); |
70 | | - float sinGamma = sqrt(sinSqGamma); |
71 | | - float cosGamma = sqrt(cosSqGamma); |
| 70 | + float sinSigma = sqrt(sinSqSigma); |
| 71 | + float sinGamma = sqrt(sinSqGamma); |
| 72 | + float cosGamma = sqrt(cosSqGamma); |
72 | 73 |
|
73 | | - float sigma = asin(sinSigma); |
74 | | - float omega = acos(cosOmega); |
75 | | - float gamma = asin(sinGamma); |
| 74 | + float sigma = asin(sinSigma); |
| 75 | + float omega = acos(cosOmega); |
| 76 | + float gamma = asin(sinGamma); |
76 | 77 |
|
77 | | - if (omega >= HALF_PI + sigma) |
78 | | - { |
79 | | - // Full horizon occlusion (case #4). |
80 | | - return 0; |
81 | | - } |
82 | | - |
83 | | - float e = sinSqSigma * cosOmega; |
| 78 | + if (omega >= HALF_PI + sigma) |
| 79 | + { |
| 80 | + // Full horizon occlusion (case #4). |
| 81 | + return 0; |
| 82 | + } |
84 | 83 |
|
85 | | - [branch] |
86 | | - if (omega < HALF_PI - sigma) |
87 | | - { |
88 | | - // No horizon occlusion (case #1). |
89 | | - return e; |
90 | | - } |
91 | | - else |
92 | | - { |
93 | | - float g = (-2 * sqrt(sinSqOmega * cosSqSigma) + sinGamma) * cosGamma + (HALF_PI - gamma); |
94 | | - float h = cosOmega * (cosGamma * sqrt(saturate(sinSqSigma - cosSqGamma)) + sinSqSigma * asin(saturate(cosGamma / sinSigma))); |
| 84 | + float e = sinSqSigma * cosOmega; |
95 | 85 |
|
96 | | - if (omega < HALF_PI) |
| 86 | + [branch] |
| 87 | + if (omega < HALF_PI - sigma) |
97 | 88 | { |
98 | | - // Partial horizon occlusion (case #2). |
99 | | - return saturate(e + INV_PI * (g - h)); |
| 89 | + // No horizon occlusion (case #1). |
| 90 | + return e; |
100 | 91 | } |
101 | 92 | else |
102 | 93 | { |
103 | | - // Partial horizon occlusion (case #3). |
104 | | - return saturate(INV_PI * (g + h)); |
| 94 | + float g = (-2 * sqrt(sinSqOmega * cosSqSigma) + sinGamma) * cosGamma + (HALF_PI - gamma); |
| 95 | + float h = cosOmega * (cosGamma * sqrt(saturate(sinSqSigma - cosSqGamma)) + sinSqSigma * asin(saturate(cosGamma / sinSigma))); |
| 96 | + |
| 97 | + if (omega < HALF_PI) |
| 98 | + { |
| 99 | + // Partial horizon occlusion (case #2). |
| 100 | + return saturate(e + INV_PI * (g - h)); |
| 101 | + } |
| 102 | + else |
| 103 | + { |
| 104 | + // Partial horizon occlusion (case #3). |
| 105 | + return saturate(INV_PI * (g + h)); |
| 106 | + } |
105 | 107 | } |
106 | | - } |
107 | | -#else // Ref: Moving Frostbite to Physically Based Rendering, page 47 (2015, optimized). |
108 | | - float cosSqOmega = cosOmega * cosOmega; // y^2 |
| 108 | + #else // Ref: Moving Frostbite to Physically Based Rendering, page 47 (2015, optimized). |
| 109 | + float cosSqOmega = cosOmega * cosOmega; // y^2 |
109 | 110 |
|
110 | | - [branch] |
111 | | - if (cosSqOmega > sinSqSigma) // (y^2)>x |
112 | | - { |
113 | | - return saturate(sinSqSigma * cosOmega); // Clip[x*y,{0,1}] |
114 | | - } |
115 | | - else |
116 | | - { |
117 | | - float cotSqSigma = rcp(sinSqSigma) - 1; // 1/x-1 |
118 | | - float tanSqSigma = rcp(cotSqSigma); // x/(1-x) |
119 | | - float sinSqOmega = 1 - cosSqOmega; // 1-y^2 |
| 111 | + [branch] |
| 112 | + if (cosSqOmega > sinSqSigma) // (y^2)>x |
| 113 | + { |
| 114 | + return saturate(sinSqSigma * cosOmega); // Clip[x*y,{0,1}] |
| 115 | + } |
| 116 | + else |
| 117 | + { |
| 118 | + float cotSqSigma = rcp(sinSqSigma) - 1; // 1/x-1 |
| 119 | + float tanSqSigma = rcp(cotSqSigma); // x/(1-x) |
| 120 | + float sinSqOmega = 1 - cosSqOmega; // 1-y^2 |
120 | 121 |
|
121 | | - float w = sinSqOmega * tanSqSigma; // (1-y^2)*(x/(1-x)) |
122 | | - float x = -cosOmega * rsqrt(w); // -y*Sqrt[(1/x-1)/(1-y^2)] |
123 | | - float y = sqrt(sinSqOmega * tanSqSigma - cosSqOmega); // Sqrt[(1-y^2)*(x/(1-x))-y^2] |
124 | | - float z = y * cotSqSigma; // Sqrt[(1-y^2)*(x/(1-x))-y^2]*(1/x-1) |
| 122 | + float w = sinSqOmega * tanSqSigma; // (1-y^2)*(x/(1-x)) |
| 123 | + float x = -cosOmega * rsqrt(w); // -y*Sqrt[(1/x-1)/(1-y^2)] |
| 124 | + float y = sqrt(sinSqOmega * tanSqSigma - cosSqOmega); // Sqrt[(1-y^2)*(x/(1-x))-y^2] |
| 125 | + float z = y * cotSqSigma; // Sqrt[(1-y^2)*(x/(1-x))-y^2]*(1/x-1) |
125 | 126 |
|
126 | | - float a = cosOmega * acos(x) - z; // y*ArcCos[-y*Sqrt[(1/x-1)/(1-y^2)]]-Sqrt[(1-y^2)*(x/(1-x))-y^2]*(1/x-1) |
127 | | - float b = atan(y); // ArcTan[Sqrt[(1-y^2)*(x/(1-x))-y^2]] |
| 127 | + float a = cosOmega * acos(x) - z; // y*ArcCos[-y*Sqrt[(1/x-1)/(1-y^2)]]-Sqrt[(1-y^2)*(x/(1-x))-y^2]*(1/x-1) |
| 128 | + float b = atan(y); // ArcTan[Sqrt[(1-y^2)*(x/(1-x))-y^2]] |
128 | 129 |
|
129 | | - // Replacing max() with saturate() results in a 12 cycle SGPR forwarding stall on PS4. |
130 | | - return max(INV_PI * (a * sinSqSigma + b), 0); // (a/Pi)*x+(b/Pi) |
131 | | - } |
| 130 | + // Replacing max() with saturate() results in a 12 cycle SGPR forwarding stall on PS4. |
| 131 | + return max(INV_PI * (a * sinSqSigma + b), 0); // (a/Pi)*x+(b/Pi) |
| 132 | + } |
| 133 | + #endif |
132 | 134 | #endif |
133 | 135 | } |
134 | 136 |
|
135 | 137 | // Expects non-normalized vertex positions. |
136 | 138 | float PolygonIrradiance(float4x3 L) |
137 | 139 | { |
138 | | -#ifdef SPHERE_LIGHT_APPROXIMATION |
| 140 | +#ifdef APPROXIMATE_POLY_LIGHT_AS_SPHERE_LIGHT |
139 | 141 | [unroll] |
140 | 142 | for (uint i = 0; i < 4; i++) |
141 | 143 | { |
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