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Eevee: Implement new LTC algorithm for Sphere Lights. 

This is an improvement on the old spining quad method that was giving artifacts when the reflection ray was nearly aligned with the sphere center.
This might be a bit heavier but it's worth it.
This commit is contained in:
Clément Foucault 2018-01-18 16:19:04 +01:00
parent 97e2b0c594
commit 8ed0161aa7
6 changed files with 742 additions and 54 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

2
source/blender/draw/engines/clay/clay_engine.c
View File

@ -317,7 +317,7 @@ static struct GPUTexture *create_jitter_texture(int num_samples)
jitter[i][2] = bn * num_samples_inv;
}
UNUSED_VARS(bsdf_split_sum_ggx, btdf_split_sum_ggx, ltc_mag_ggx, ltc_mat_ggx);
UNUSED_VARS(bsdf_split_sum_ggx, btdf_split_sum_ggx, ltc_mag_ggx, ltc_mat_ggx, ltc_disk_integral);
return DRW_texture_create_2D(64, 64, DRW_TEX_RGB_16, DRW_TEX_FILTER | DRW_TEX_WRAP, &jitter[0][0]);
}

515
source/blender/draw/engines/eevee/eevee_lut.h
View File

@ -3345,6 +3345,521 @@ static float bsdf_split_sum_ggx[64 * 64 * 2] = {
0.626953f, 0.023544f, 0.616699f, 0.022186f, 0.605957f, 0.020920f, 0.594727f, 0.019730f
};
static float ltc_disk_integral[64 * 64] = {
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0.119617f, 0.131957f, 0.144591f, 0.157503f, 0.170682f, 0.184117f, 0.197799f, 0.211720f,
0.225873f, 0.240253f, 0.254854f, 0.269673f, 0.284707f, 0.299953f, 0.315408f, 0.331073f,
0.346946f, 0.363028f, 0.379318f, 0.395818f, 0.412530f, 0.429457f, 0.446602f, 0.463968f,
0.481561f, 0.499386f, 0.517450f, 0.535761f, 0.554328f, 0.573162f, 0.592275f, 0.611681f,
0.631398f, 0.651445f, 0.671845f, 0.692628f, 0.713827f, 0.735484f, 0.757650f, 0.780390f,
0.803789f, 0.827960f, 0.853056f, 0.879298f, 0.907014f, 0.936691f, 0.968254f, 1.000000f,
0.000000f, 0.000000f, 0.000617f, 0.003679f, 0.008674f, 0.015068f, 0.022531f, 0.030851f,
0.039880f, 0.049515f, 0.059675f, 0.070300f, 0.081343f, 0.092764f, 0.104533f, 0.116624f,
0.129015f, 0.141687f, 0.154626f, 0.167818f, 0.181252f, 0.194918f, 0.208807f, 0.222913f,
0.237229f, 0.251750f, 0.266473f, 0.281392f, 0.296505f, 0.311811f, 0.327306f, 0.342991f,
0.358864f, 0.374925f, 0.391176f, 0.407616f, 0.424249f, 0.441076f, 0.458100f, 0.475324f,
0.492754f, 0.510394f, 0.528251f, 0.546331f, 0.564644f, 0.583198f, 0.602005f, 0.621078f,
0.640434f, 0.660089f, 0.680066f, 0.700390f, 0.721094f, 0.742215f, 0.763800f, 0.785912f,
0.808628f, 0.832055f, 0.856338f, 0.881690f, 0.908441f, 0.937125f, 0.968254f, 1.000000f,
0.000000f, 0.000000f, 0.001477f, 0.005732f, 0.011826f, 0.019212f, 0.027573f, 0.036710f,
0.046487f, 0.056807f, 0.067598f, 0.078806f, 0.090386f, 0.102304f, 0.114532f, 0.127047f,
0.139828f, 0.152861f, 0.166130f, 0.179624f, 0.193332f, 0.207247f, 0.221360f, 0.235666f,
0.250158f, 0.264832f, 0.279684f, 0.294711f, 0.309911f, 0.325280f, 0.340819f, 0.356524f,
0.372397f, 0.388438f, 0.404645f, 0.421022f, 0.437569f, 0.454287f, 0.471181f, 0.488253f,
0.505507f, 0.522947f, 0.540580f, 0.558412f, 0.576449f, 0.594701f, 0.613178f, 0.631892f,
0.650856f, 0.670088f, 0.689606f, 0.709434f, 0.729600f, 0.750138f, 0.771093f, 0.792519f,
0.814488f, 0.837097f, 0.860481f, 0.884842f, 0.910494f, 0.937985f, 0.968254f, 1.000000f,
0.000000f, 0.000096f, 0.003012f, 0.008704f, 0.016071f, 0.024590f, 0.033968f, 0.044025f,
0.054641f, 0.065728f, 0.077225f, 0.089081f, 0.101260f, 0.113731f, 0.126469f, 0.139454f,
0.152670f, 0.166101f, 0.179736f, 0.193565f, 0.207578f, 0.221769f, 0.236130f, 0.250656f,
0.265343f, 0.280187f, 0.295183f, 0.310330f, 0.325624f, 0.341065f, 0.356650f, 0.372380f,
0.388253f, 0.404269f, 0.420430f, 0.436735f, 0.453187f, 0.469786f, 0.486536f, 0.503439f,
0.520498f, 0.537717f, 0.555102f, 0.572657f, 0.590390f, 0.608307f, 0.626419f, 0.644733f,
0.663264f, 0.682025f, 0.701032f, 0.720308f, 0.739875f, 0.759764f, 0.780014f, 0.800673f,
0.821803f, 0.843492f, 0.865860f, 0.889087f, 0.913466f, 0.939520f, 0.968350f, 1.000000f,
0.000000f, 0.000727f, 0.005696f, 0.013170f, 0.022074f, 0.031940f, 0.042520f, 0.053660f,
0.065258f, 0.077243f, 0.089562f, 0.102175f, 0.115050f, 0.128164f, 0.141495f, 0.155026f,
0.168745f, 0.182639f, 0.196699f, 0.210915f, 0.225282f, 0.239792f, 0.254440f, 0.269223f,
0.284135f, 0.299174f, 0.314337f, 0.329622f, 0.345026f, 0.360549f, 0.376189f, 0.391946f,
0.407819f, 0.423808f, 0.439914f, 0.456137f, 0.472479f, 0.488940f, 0.505523f, 0.522230f,
0.539064f, 0.556028f, 0.573125f, 0.590361f, 0.607741f, 0.625270f, 0.642957f, 0.660809f,
0.678836f, 0.697050f, 0.715465f, 0.734098f, 0.752968f, 0.772101f, 0.791529f, 0.811290f,
0.831438f, 0.852044f, 0.873210f, 0.895090f, 0.917932f, 0.942204f, 0.968981f, 1.000000f,
0.000000f, 0.002796f, 0.010764f, 0.020645f, 0.031576f, 0.043202f, 0.055340f, 0.067877f,
0.080740f, 0.093877f, 0.107250f, 0.120832f, 0.134598f, 0.148533f, 0.162620f, 0.176849f,
0.191210f, 0.205694f, 0.220294f, 0.235005f, 0.249820f, 0.264737f, 0.279751f, 0.294859f,
0.310058f, 0.325346f, 0.340721f, 0.356181f, 0.371725f, 0.387353f, 0.403063f, 0.418854f,
0.434727f, 0.450682f, 0.466718f, 0.482837f, 0.499038f, 0.515324f, 0.531695f, 0.548153f,
0.564700f, 0.581338f, 0.598070f, 0.614900f, 0.631830f, 0.648865f, 0.666011f, 0.683273f,
0.700659f, 0.718176f, 0.735834f, 0.753646f, 0.771625f, 0.789790f, 0.808162f, 0.826771f,
0.845654f, 0.864863f, 0.884472f, 0.904592f, 0.925407f, 0.947271f, 0.971050f, 1.000000f,
0.000000f, 0.015873f, 0.031746f, 0.047619f, 0.063492f, 0.079365f, 0.095238f, 0.111111f,
0.126984f, 0.142857f, 0.158730f, 0.174603f, 0.190476f, 0.206349f, 0.222222f, 0.238095f,
0.253968f, 0.269841f, 0.285714f, 0.301587f, 0.317460f, 0.333333f, 0.349206f, 0.365079f,
0.380952f, 0.396825f, 0.412698f, 0.428571f, 0.444444f, 0.460317f, 0.476190f, 0.492063f,
0.507937f, 0.523810f, 0.539683f, 0.555556f, 0.571429f, 0.587302f, 0.603175f, 0.619048f,
0.634921f, 0.650794f, 0.666667f, 0.682540f, 0.698413f, 0.714286f, 0.730159f, 0.746032f,
0.761905f, 0.777778f, 0.793651f, 0.809524f, 0.825397f, 0.841270f, 0.857143f, 0.873016f,
0.888889f, 0.904762f, 0.920635f, 0.936508f, 0.952381f, 0.968254f, 0.984127f, 1.000000f
};
static float btdf_split_sum_ggx[32][64 * 64] = {
{
0.000000f, 1.000000f, 0.999512f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 0.999512f, 1.000000f,

1
source/blender/draw/engines/eevee/eevee_materials.c
View File

@ -447,6 +447,7 @@ static void eevee_init_util_texture(void)
texels_layer[i][0] = bsdf_split_sum_ggx[i * 2 + 0];
texels_layer[i][1] = bsdf_split_sum_ggx[i * 2 + 1];
texels_layer[i][2] = ltc_mag_ggx[i];
texels_layer[i][3] = ltc_disk_integral[i];
}
texels_layer += 64 * 64;

2
source/blender/draw/engines/eevee/shaders/bsdf_common_lib.glsl
View File

@ -549,7 +549,7 @@ vec3 F_schlick(vec3 f0, float cos_theta)
/* Fresnel approximation for LTC area lights (not MRP) */
vec3 F_area(vec3 f0, vec2 lut)
{
vec2 fac = normalize(lut.xy);
vec2 fac = normalize(lut.xy); /* XXX FIXME this does not work!!! */
/* Unreal specular matching : if specular color is below 2% intensity,
* treat as shadowning */

50
source/blender/draw/engines/eevee/shaders/bsdf_direct_lib.glsl
View File

@ -106,51 +106,32 @@ vec3 direct_ggx_sun(LightData ld, vec3 N, vec3 V, float roughness, vec3 f0)
#ifdef USE_LTC
vec3 direct_ggx_sphere(LightData ld, vec3 N, vec3 V, vec4 l_vector, float roughness, vec3 f0)
{
vec3 L = l_vector.xyz / l_vector.w;
vec3 spec_dir = get_specular_reflection_dominant_dir(N, V, roughness);
vec3 P = line_aligned_plane_intersect(vec3(0.0), spec_dir, l_vector.xyz);
vec3 Px = normalize(P - l_vector.xyz) * ld.l_radius;
vec3 Py = cross(Px, L);
roughness = clamp(roughness, 0.0008, 0.999); /* Fix low roughness artifacts. */
vec2 uv = lut_coords(dot(N, V), sqrt(roughness));
vec3 brdf_lut = texture(utilTex, vec3(uv, 1.0)).rgb;
vec4 ltc_lut = texture(utilTex, vec3(uv, 0.0)).rgba;
mat3 ltc_mat = ltc_matrix(ltc_lut);
// #define HIGHEST_QUALITY
#ifdef HIGHEST_QUALITY
vec3 Pxy1 = normalize( Px + Py) * ld.l_radius;
vec3 Pxy2 = normalize(-Px + Py) * ld.l_radius;
/* Make orthonormal basis. */
vec3 L = l_vector.xyz / l_vector.w;
vec3 Px, Py;
make_orthonormal_basis(L, Px, Py);
Px *= ld.l_radius;
Py *= ld.l_radius;
/* counter clockwise */
vec3 points[8];
points[0] = l_vector.xyz + Px;
points[1] = l_vector.xyz - Pxy2;
points[2] = l_vector.xyz - Py;
points[3] = l_vector.xyz - Pxy1;
points[4] = l_vector.xyz - Px;
points[5] = l_vector.xyz + Pxy2;
points[6] = l_vector.xyz + Py;
points[7] = l_vector.xyz + Pxy1;
float bsdf = ltc_evaluate_circle(N, V, ltc_mat, points);
#else
vec3 points[4];
points[0] = l_vector.xyz + Px;
points[1] = l_vector.xyz - Py;
points[2] = l_vector.xyz - Px;
points[3] = l_vector.xyz + Py;
float bsdf = ltc_evaluate(N, V, ltc_mat, points);
/* sqrt(pi/2) difference between square and disk area */
bsdf *= 1.25331413731;
#endif
vec3 points[3];
points[0] = l_vector.xyz - Px - Py;
points[1] = l_vector.xyz + Px - Py;
points[2] = l_vector.xyz + Px + Py;
float bsdf = ltc_evaluate_disk(N, V, ltc_mat, points);
bsdf *= brdf_lut.b; /* Bsdf intensity */
bsdf *= M_1_2PI * M_1_PI;
bsdf *= M_1_PI;
vec3 spec = F_area(f0, brdf_lut.xy) * bsdf;
return spec;
return vec3(bsdf);
}
vec3 direct_ggx_rectangle(LightData ld, vec3 N, vec3 V, vec4 l_vector, float roughness, vec3 f0)
@ -165,13 +146,14 @@ vec3 direct_ggx_rectangle(LightData ld, vec3 N, vec3 V, vec4 l_vector, float rou
vec3 brdf_lut = texture(utilTex, vec3(uv, 1.0)).rgb;
vec4 ltc_lut = texture(utilTex, vec3(uv, 0.0)).rgba;
mat3 ltc_mat = ltc_matrix(ltc_lut);
float bsdf = ltc_evaluate(N, V, ltc_mat, corners);
bsdf *= brdf_lut.b; /* Bsdf intensity */
bsdf *= M_1_2PI;
vec3 spec = F_area(f0, brdf_lut.xy) * bsdf;
return spec;
return vec3(bsdf);
}
#endif

226
source/blender/draw/engines/eevee/shaders/ltc_lib.glsl
View File

@ -1,4 +1,10 @@
/* Mainly From https://eheitzresearch.wordpress.com/415-2/ */
/**
* Adapted from :
* Real-Time Polygonal-Light Shading with Linearly Transformed Cosines.
* Eric Heitz, Jonathan Dupuy, Stephen Hill and David Neubelt.
* ACM Transactions on Graphics (Proceedings of ACM SIGGRAPH 2016) 35(4), 2016.
* Project page: https://eheitzresearch.wordpress.com/415-2/
**/
#define USE_LTC
@ -8,6 +14,99 @@ uniform sampler2DArray utilTex;
#define texelfetch_noise_tex(coord) texelFetch(utilTex, ivec3(ivec2(coord) % LUT_SIZE, 2.0), 0)
#endif /* UTIL_TEX */
/**
* An extended version of the implementation from
* "How to solve a cubic equation, revisited"
* http://momentsingraphics.de/?p=105
**/
vec3 solve_cubic(vec4 coefs)
{
/* Normalize the polynomial */
coefs.xyz /= coefs.w;
/* Divide middle coefficients by three */
coefs.yz /= 3.0;
float A = coefs.w;
float B = coefs.z;
float C = coefs.y;
float D = coefs.x;
/* Compute the Hessian and the discriminant */
vec3 delta = vec3(
-coefs.z*coefs.z + coefs.y,
-coefs.y*coefs.z + coefs.x,
dot(vec2(coefs.z, -coefs.y), coefs.xy)
);
/* Discriminant */
float discr = dot(vec2(4.0 * delta.x, -delta.y), delta.zy);
vec2 xlc, xsc;
/* Algorithm A */
{
float A_a = 1.0;
float C_a = delta.x;
float D_a = -2.0 * B * delta.x + delta.y;
/* Take the cubic root of a normalized complex number */
float theta = atan(sqrt(discr), -D_a) / 3.0;
float x_1a = 2.0 * sqrt(-C_a) * cos(theta);
float x_3a = 2.0 * sqrt(-C_a) * cos(theta + (2.0 / 3.0) * M_PI);
float xl;
if ((x_1a + x_3a) > 2.0 * B) {
xl = x_1a;
}
else {
xl = x_3a;
}
xlc = vec2(xl - B, A);
}
/* Algorithm D */
{
float A_d = D;
float C_d = delta.z;
float D_d = -D * delta.y + 2.0 * C * delta.z;
/* Take the cubic root of a normalized complex number */
float theta = atan(D * sqrt(discr), -D_d) / 3.0;
float x_1d = 2.0 * sqrt(-C_d) * cos(theta);
float x_3d = 2.0 * sqrt(-C_d) * cos(theta + (2.0 / 3.0) * M_PI);
float xs;
if (x_1d + x_3d < 2.0 * C)
xs = x_1d;
else
xs = x_3d;
xsc = vec2(-D, xs + C);
}
float E = xlc.y * xsc.y;
float F = -xlc.x * xsc.y - xlc.y * xsc.x;
float G = xlc.x * xsc.x;
vec2 xmc = vec2(C * F - B * G, -B * F + C * E);
vec3 root = vec3(xsc.x / xsc.y,
xmc.x / xmc.y,
xlc.x / xlc.y);
if (root.x < root.y && root.x < root.z) {
root.xyz = root.yxz;
}
else if (root.z < root.x && root.z < root.y) {
root.xyz = root.xzy;
}
return root;
}
/* from Real-Time Area Lighting: a Journey from Research to Production
* Stephen Hill and Eric Heitz */
float edge_integral(vec3 p1, vec3 p2)
@ -206,9 +305,13 @@ float ltc_evaluate(vec3 N, vec3 V, mat3 Minv, vec3 corners[4])
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])
float diffuseSphereIntegralCheap(vec3 F, float l)
{
return max((l*l + F.z) / (l+1.0), 0.0);
}
/* disk_points are WS vectors from the shading point to the disk "bounding domain" */
float ltc_evaluate_disk(vec3 N, vec3 V, mat3 Minv, vec3 disk_points[3])
{
/* Avoid dot(N, V) == 1 in ortho mode, leading T1 normalize to fail. */
V = normalize(V + 1e-8);
@ -219,23 +322,110 @@ float ltc_evaluate_circle(vec3 N, vec3 V, mat3 Minv, vec3 p[LTC_CIRCLE_RES])
T2 = cross(N, T1);
/* rotate area light in (T1, T2, R) basis */
Minv = Minv * transpose(mat3(T1, T2, N));
mat3 R = 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]);
/* Intermediate step: init ellipse. */
vec3 L_[3];
L_[0] = mul(R, disk_points[0]);
L_[1] = mul(R, disk_points[1]);
L_[2] = mul(R, disk_points[2]);
vec3 C = 0.5 * (L_[0] + L_[2]);
vec3 V1 = 0.5 * (L_[1] - L_[2]);
vec3 V2 = 0.5 * (L_[1] - L_[0]);
/* Transform ellipse by Minv. */
C = Minv * C;
V1 = Minv * V1;
V2 = Minv * V2;
/* Compute eigenvectors of new ellipse. */
float d11 = dot(V1, V1);
float d22 = dot(V2, V2);
float d12 = dot(V1, V2);
float a, b; /* Eigenvalues */
const float threshold = 0.0007; /* Can be adjusted. Fix artifacts. */
if (abs(d12) / sqrt(d11 * d22) > threshold) {
float tr = d11 + d22;
float det = -d12 * d12 + d11 * d22;
/* use sqrt matrix to solve for eigenvalues */
det = sqrt(det);
float u = 0.5 * sqrt(tr - 2.0 * det);
float v = 0.5 * sqrt(tr + 2.0 * det);
float e_max = (u + v);
float e_min = (u - v);
e_max *= e_max;
e_min *= e_min;
vec3 V1_, V2_;
if (d11 > d22) {
V1_ = d12 * V1 + (e_max - d11) * V2;
V2_ = d12 * V1 + (e_min - d11) * V2;
}
else {
V1_ = d12 * V2 + (e_max - d22) * V1;
V2_ = d12 * V2 + (e_min - d22) * V1;
}
a = 1.0 / e_max;
b = 1.0 / e_min;
V1 = normalize(V1_);
V2 = normalize(V2_);
}
else {
a = 1.0 / d11;
b = 1.0 / d22;
V1 *= sqrt(a);
V2 *= sqrt(b);
}
/* 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]);
/* Now find front facing ellipse with same solid angle. */
return max(0.0, sum);
vec3 V3 = normalize(cross(V1, V2));
if (dot(C, V3) < 0.0)
V3 *= -1.0;
float L = dot(V3, C);
float x0 = dot(V1, C) / L;
float y0 = dot(V2, C) / L;
a *= L*L;
b *= L*L;
float c0 = a * b;
float c1 = a * b * (1.0 + x0 * x0 + y0 * y0) - a - b;
float c2 = 1.0 - a * (1.0 + x0 * x0) - b * (1.0 + y0 * y0);
float c3 = 1.0;
vec3 roots = solve_cubic(vec4(c0, c1, c2, c3));
float e1 = roots.x;
float e2 = roots.y;
float e3 = roots.z;
vec3 avgDir = vec3(a * x0 / (a - e2), b * y0 / (b - e2), 1.0);
mat3 rotate = mat3(V1, V2, V3);
avgDir = rotate * avgDir;
avgDir = normalize(avgDir);
/* L1, L2 are the extends of the front facing ellipse. */
float L1 = sqrt(-e2/e3);
float L2 = sqrt(-e2/e1);
/* Find the sphere and compute lighting. */
float formFactor = L1 * L2 * inversesqrt((1.0 + L1 * L1) * (1.0 + L2 * L2));
/* use tabulated horizon-clipped sphere */
vec2 uv = vec2(avgDir.z * 0.5 + 0.5, formFactor);
uv = uv * (64.0 - 1.0) / 64.0 + 0.5 / 64.0;
float sphere_cosine_integral = formFactor * texture(utilTex, vec3(uv, 1.0)).w;
/* Less accurate version, a bit cheaper. */
//float sphere_cosine_integral = formFactor * diffuseSphereIntegralCheap(avgDir, formFactor);
return max(0.0, sphere_cosine_integral);
}