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/* Mainly From https://eheitzresearch.wordpress.com/415-2/ */
#define USE_LTC
#define LTC_LUT_SIZE 64
uniform sampler2D ltcMat;
uniform sampler2D ltcMag;
/* from Real-Time Area Lighting: a Journey from Research to Production
* Stephen Hill and Eric Heitz */
float edge_integral(vec3 p1, vec3 p2)
{
#if 0
/* more accurate replacement of acos */
float x = dot(p1, p2);
float y = abs(x);
float a = 5.42031 + (3.12829 + 0.0902326 * y) * y;
float b = 3.45068 + (4.18814 + y) * y;
float theta_sintheta = a / b;
if (x < 0.0) {
theta_sintheta = (M_PI / sqrt(1.0 - x * x)) - theta_sintheta;
}
vec3 u = cross(p1, p2);
return theta_sintheta * dot(u, N);
#endif
float cos_theta = dot(p1, p2);
cos_theta = clamp(cos_theta, -0.9999, 0.9999);
float theta = acos(cos_theta);
vec3 u = normalize(cross(p1, p2));
return theta * cross(p1, p2).z / sin(theta);
}
int clip_quad_to_horizon(inout vec3 L[5])
{
/* detect clipping config */
int config = 0;
if (L[0].z > 0.0) config += 1;
if (L[1].z > 0.0) config += 2;
if (L[2].z > 0.0) config += 4;
if (L[3].z > 0.0) config += 8;
/* clip */
int n = 0;
if (config == 0)
{
/* clip all */
}
else if (config == 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];
}
else if (config == 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];
}
else if (config == 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];
}
else if (config == 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];
}
else if (config == 5) /* V1 V3 clip V2 V4) impossible */
{
n = 0;
}
else if (config == 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];
}
else if (config == 7) /* V1 V2 V3 clip V4 */
{
n = 5;
L[4] = -L[3].z * L[0] + L[0].z * L[3];
L[3] = -L[3].z * L[2] + L[2].z * L[3];
}
else if (config == 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];
}
else if (config == 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];
}
else if (config == 10) /* V2 V4 clip V1 V3) impossible */
{
n = 0;
}
else if (config == 11) /* V1 V2 V4 clip V3 */
{
n = 5;
L[4] = L[3];
L[3] = -L[2].z * L[3] + L[3].z * L[2];
L[2] = -L[2].z * L[1] + L[1].z * L[2];
}
else if (config == 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];
}
else if (config == 13) /* V1 V3 V4 clip V2 */
{
n = 5;
L[4] = L[3];
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];
}
else if (config == 14) /* V2 V3 V4 clip V1 */
{
n = 5;
L[4] = -L[0].z * L[3] + L[3].z * L[0];
L[0] = -L[0].z * L[1] + L[1].z * L[0];
}
else if (config == 15) /* V1 V2 V3 V4 */
{
n = 4;
}
if (n == 3)
L[3] = L[0];
if (n == 4)
L[4] = L[0];
return n;
}
vec2 ltc_coords(float cosTheta, float roughness)
{
float theta = acos(cosTheta);
vec2 coords = vec2(roughness, theta/(0.5*3.14159));
/* scale and bias coordinates, for correct filtered lookup */
return coords * (LTC_LUT_SIZE - 1.0) / LTC_LUT_SIZE + 0.5 / LTC_LUT_SIZE;
}
mat3 ltc_matrix(vec2 coord)
{
/* load inverse matrix */
vec4 t = texture(ltcMat, coord);
mat3 Minv = mat3(
vec3( 1, 0, t.y),
vec3( 0, t.z, 0),
vec3(t.w, 0, t.x)
);
return Minv;
}
float ltc_evaluate(vec3 N, vec3 V, mat3 Minv, vec3 corners[4])
{
/* construct orthonormal basis around N */
vec3 T1, T2;
T1 = normalize(V - N*dot(V, N));
T2 = cross(N, T1);
/* rotate area light in (T1, T2, R) basis */
Minv = Minv * transpose(mat3(T1, T2, N));
/* polygon (allocate 5 vertices for clipping) */
vec3 L[5];
L[0] = Minv * corners[0];
L[1] = Minv * corners[1];
L[2] = Minv * corners[2];
L[3] = Minv * corners[3];
int n = clip_quad_to_horizon(L);
if (n == 0)
return 0.0;
/* project onto sphere */
L[0] = normalize(L[0]);
L[1] = normalize(L[1]);
L[2] = normalize(L[2]);
L[3] = normalize(L[3]);
L[4] = normalize(L[4]);
/* integrate */
float sum = 0.0;
sum += edge_integral(L[0], L[1]);
sum += edge_integral(L[1], L[2]);
sum += edge_integral(L[2], L[3]);
if (n >= 4)
sum += edge_integral(L[3], L[4]);
if (n == 5)
sum += edge_integral(L[4], L[0]);
return abs(sum);
}
/* Aproximate circle with an octogone */
#define LTC_CIRCLE_RES 8
float ltc_evaluate_circle(vec3 N, vec3 V, mat3 Minv, vec3 p[LTC_CIRCLE_RES])
{
/* construct orthonormal basis around N */
vec3 T1, T2;
T1 = normalize(V - N*dot(V, N));
T2 = cross(N, T1);
/* rotate area light in (T1, T2, R) basis */
Minv = Minv * transpose(mat3(T1, T2, N));
for (int i = 0; i < LTC_CIRCLE_RES; ++i) {
p[i] = Minv * p[i];
/* clip to horizon */
p[i].z = max(0.0, p[i].z);
/* project onto sphere */
p[i] = normalize(p[i]);
}
/* integrate */
float sum = 0.0;
for (int i = 0; i < LTC_CIRCLE_RES - 1; ++i) {
sum += edge_integral(p[i], p[i + 1]);
}
sum += edge_integral(p[LTC_CIRCLE_RES - 1], p[0]);
return max(0.0, sum);
}
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