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#ifndef UNITY_AREA_LIGHTING_INCLUDED
#define UNITY_AREA_LIGHTING_INCLUDED
float IntegrateEdge(float3 v1, float3 v2)
{
float cosTheta = dot(v1, v2);
// Clamp to avoid artifacts. This particular constant gives the best results.
cosTheta = Clamp(cosTheta, -0.9999, 0.9999);
float theta = FastACos(cosTheta);
float res = cross(v1, v2).z * theta * rsqrt(1.0f - cosTheta * cosTheta); // optimization from * 1 / sin(theta)
return res;
}
// Baum's equation
// Expects non-normalized vertex positions
float PolygonRadiance(float4x3 L, bool twoSided)
{
// 1. ClipQuadToHorizon
// detect clipping config
uint config = 0;
if (L[0].z > 0) config += 1;
if (L[1].z > 0) config += 2;
if (L[2].z > 0) config += 4;
if (L[3].z > 0) config += 8;
// The fifth vertex for cases when clipping cuts off one corner.
// Due to a compiler bug, copying L into a vector array with 5 rows
// messes something up, so we need to stick with the matrix + the L4 vertex.
float3 L4 = L[3];
// This switch is surprisingly fast. Tried replacing it with a lookup array of vertices.
// Even though that replaced the switch with just some indexing and no branches, it became
// way, way slower - mem fetch stalls?
// clip
uint n = 0;
switch (config)
{
case 0: // clip all
break;
case 1: // V1 clip V2 V3 V4
n = 3;
L[1] = -L[1].z * L[0] + L[0].z * L[1];
L[2] = -L[3].z * L[0] + L[0].z * L[3];
break;
case 2: // V2 clip V1 V3 V4
n = 3;
L[0] = -L[0].z * L[1] + L[1].z * L[0];
L[2] = -L[2].z * L[1] + L[1].z * L[2];
break;
case 3: // V1 V2 clip V3 V4
n = 4;
L[2] = -L[2].z * L[1] + L[1].z * L[2];
L[3] = -L[3].z * L[0] + L[0].z * L[3];
break;
case 4: // V3 clip V1 V2 V4
n = 3;
L[0] = -L[3].z * L[2] + L[2].z * L[3];
L[1] = -L[1].z * L[2] + L[2].z * L[1];
break;
case 5: // V1 V3 clip V2 V4: impossible
break;
case 6: // V2 V3 clip V1 V4
n = 4;
L[0] = -L[0].z * L[1] + L[1].z * L[0];
L[3] = -L[3].z * L[2] + L[2].z * L[3];
break;
case 7: // V1 V2 V3 clip V4
n = 5;
L4 = -L[3].z * L[0] + L[0].z * L[3];
L[3] = -L[3].z * L[2] + L[2].z * L[3];
break;
case 8: // V4 clip V1 V2 V3
n = 3;
L[0] = -L[0].z * L[3] + L[3].z * L[0];
L[1] = -L[2].z * L[3] + L[3].z * L[2];
L[2] = L[3];
break;
case 9: // V1 V4 clip V2 V3
n = 4;
L[1] = -L[1].z * L[0] + L[0].z * L[1];
L[2] = -L[2].z * L[3] + L[3].z * L[2];
break;
case 10: // V2 V4 clip V1 V3: impossible
break;
case 11: // V1 V2 V4 clip V3
n = 5;
L[3] = -L[2].z * L[3] + L[3].z * L[2];
L[2] = -L[2].z * L[1] + L[1].z * L[2];
break;
case 12: // V3 V4 clip V1 V2
n = 4;
L[1] = -L[1].z * L[2] + L[2].z * L[1];
L[0] = -L[0].z * L[3] + L[3].z * L[0];
break;
case 13: // V1 V3 V4 clip V2
n = 5;
L[3] = L[2];
L[2] = -L[1].z * L[2] + L[2].z * L[1];
L[1] = -L[1].z * L[0] + L[0].z * L[1];
break;
case 14: // V2 V3 V4 clip V1
n = 5;
L4 = -L[0].z * L[3] + L[3].z * L[0];
L[0] = -L[0].z * L[1] + L[1].z * L[0];
break;
case 15: // V1 V2 V3 V4
n = 4;
break;
}
if (n == 0) return 0;
// 2. Project onto sphere
L[0] = normalize(L[0]);
L[1] = normalize(L[1]);
L[2] = normalize(L[2]);
switch (n)
{
case 3:
L[3] = L[0];
break;
case 4:
L[3] = normalize(L[3]);
L4 = L[0];
break;
case 5:
L[3] = normalize(L[3]);
L4 = normalize(L4);
break;
}
// 3. Integrate
float sum = 0;
sum += IntegrateEdge(L[0], L[1]);
sum += IntegrateEdge(L[1], L[2]);
sum += IntegrateEdge(L[2], L[3]);
if (n >= 4)
sum += IntegrateEdge(L[3], L4);
if (n == 5)
sum += IntegrateEdge(L4, L[0]);
sum *= INV_TWO_PI; // Normalization
return twoSided ? abs(sum) : max(sum, 0.0);
}
// For polygonal lights.
float LTCEvaluate(float4x3 L, float3 V, float3 N, float NdotV, bool twoSided, float3x3 invM)
{
// Construct local orthonormal basis around N, aligned with N
// TODO: it could be stored in PreLightData. All LTC lights compute it more than once!
// Also consider using 'bsdfData.tangentWS', 'bsdfData.bitangentWS', 'bsdfData.normalWS'.
float3x3 basis;
basis[0] = normalize(V - N * NdotV);
basis[1] = normalize(cross(N, basis[0]));
basis[2] = N;
// rotate area light in local basis
invM = mul(transpose(basis), invM);
L = mul(L, invM);
// Polygon radiance in transformed configuration - specular
return PolygonRadiance(L, twoSided);
}
float LineFpo(float tLDDL, float lrcpD, float rcpD)
{
// Compute: ((l / d) / (d * d + l * l)) + (1.0 / (d * d)) * atan(l / d).
return tLDDL + (rcpD * rcpD) * FastATan(lrcpD);
}
float LineFwt(float tLDDL, float l)
{
// Compute: l * ((l / d) / (d * d + l * l)).
return l * tLDDL;
}
// Computes the integral of the clamped cosine over the line segment.
// 'l1' and 'l2' define the integration interval.
// 'tangent' is the line's tangent direction.
// 'normal' is the direction orthogonal to the tangent. It is the shortest vector between
// the shaded point and the line, pointing away from the shaded point.
float LineIrradiance(float l1, float l2, float3 normal, float3 tangent)
{
float d = length(normal);
float l1rcpD = l1 * rcp(d);
float l2rcpD = l2 * rcp(d);
float tLDDL1 = l1rcpD / (d * d + l1 * l1);
float tLDDL2 = l2rcpD / (d * d + l2 * l2);
float intWt = LineFwt(tLDDL2, l2) - LineFwt(tLDDL1, l1);
float intP0 = LineFpo(tLDDL2, l2rcpD, rcp(d)) - LineFpo(tLDDL1, l1rcpD, rcp(d));
return intP0 * normal.z + intWt * tangent.z;
}
// Computes 1.0 / length(mul(ortho, transpose(inverse(invM)))).
float ComputeLineWidthFactor(float3x3 invM, float3 ortho)
{
// transpose(inverse(M)) = (1.0 / determinant(M)) * cofactor(M).
// Take into account that m12 = m21 = m23 = m32 = 0 and m33 = 1.
float det = invM._11 * invM._22 - invM._22 * invM._31 * invM._13;
float3x3 cof = {invM._22, 0.0, -invM._22 * invM._31,
0.0, invM._11 - invM._13 * invM._31, 0.0,
-invM._13 * invM._22, 0.0, invM._11 * invM._22};
// 1.0 / length(mul(V, (1.0 / s * M))) = abs(s) / length(mul(V, M)).
return abs(det) / length(mul(ortho, cof));
}
// For line lights.
float LTCEvaluate(float3 P1, float3 P2, float3 B, float3x3 invM)
{
// Inverse-transform the endpoints.
P1 = mul(P1, invM);
P2 = mul(P2, invM);
// Terminate the algorithm if both points are below the horizon.
if (P1.z <= 0.0 && P2.z <= 0.0) return 0.0;
float width = ComputeLineWidthFactor(invM, B);
if (P1.z > P2.z)
{
// Convention: 'P2' is above 'P1', with the tangent pointing upwards.
Swap(P1, P2);
}
// Recompute the length and the tangent in the new coordinate system.
float len = length(P2 - P1);
float3 T = normalize(P2 - P1);
// Clip the part of the light below the horizon.
if (P1.z <= 0.0)
{
// P = P1 + t * T; P.z == 0.
float t = -P1.z / T.z;
P1 = float3(P1.xy + t * T.xy, 0.0);
// Set the length of the visible part of the light.
len -= t;
}
// Compute the normal direction to the line, s.t. it is the shortest vector
// between the shaded point and the line, pointing away from the shaded point.
// Can be interpreted as a point on the line, since the shaded point is at the origin.
float proj = dot(P1, T);
float3 P0 = P1 - proj * T;
// Compute the parameterization: distances from 'P1' and 'P2' to 'P0'.
float l1 = proj;
float l2 = l1 + len;
// Integrate the clamped cosine over the line segment.
float irradiance = LineIrradiance(l1, l2, P0, T);
// Guard against numerical precision issues.
return max(INV_PI * width * irradiance, 0.0);
}
#endif // UNITY_AREA_LIGHTING_INCLUDED