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Diffstat (limited to 'source/blender/draw/engines/eevee/shaders/ltc_lib.glsl')
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diff --git a/source/blender/draw/engines/eevee/shaders/ltc_lib.glsl b/source/blender/draw/engines/eevee/shaders/ltc_lib.glsl
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+/**
+ * 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
+
+#ifndef UTIL_TEX
+#define UTIL_TEX
+uniform sampler2DArray utilTex;
+#define texelfetch_noise_tex(coord) texelFetch(utilTex, ivec3(ivec2(coord) % LUT_SIZE, 2.0), 0)
+#endif /* UTIL_TEX */
+
+/* Diffuse *clipped* sphere integral. */
+float diffuse_sphere_integral_lut(float avg_dir_z, float form_factor)
+{
+ vec2 uv = vec2(avg_dir_z * 0.5 + 0.5, form_factor);
+ uv = uv * (LUT_SIZE - 1.0) / LUT_SIZE + 0.5 / LUT_SIZE;
+
+ return texture(utilTex, vec3(uv, 1.0)).w;
+}
+
+float diffuse_sphere_integral_cheap(float avg_dir_z, float form_factor)
+{
+ return max((form_factor * form_factor + avg_dir_z) / (form_factor + 1.0), 0.0);
+}
+
+/**
+ * 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 */
+vec3 edge_integral_vec(vec3 v1, vec3 v2)
+{
+ float x = dot(v1, v2);
+ float y = abs(x);
+
+ float a = 0.8543985 + (0.4965155 + 0.0145206 * y) * y;
+ float b = 3.4175940 + (4.1616724 + y) * y;
+ float v = a / b;
+
+ float theta_sintheta = (x > 0.0) ? v : 0.5 * inversesqrt(max(1.0 - x * x, 1e-7)) - v;
+
+ return cross(v1, v2) * theta_sintheta;
+}
+
+mat3 ltc_matrix(vec4 lut)
+{
+ /* load inverse matrix */
+ mat3 Minv = mat3(
+ vec3( 1, 0, lut.y),
+ vec3( 0, lut.z, 0),
+ vec3(lut.w, 0, lut.x)
+ );
+
+ return Minv;
+}
+
+void ltc_transform_quad(vec3 N, vec3 V, mat3 Minv, inout vec3 corners[4])
+{
+ /* Avoid dot(N, V) == 1 in ortho mode, leading T1 normalize to fail. */
+ V = normalize(V + 1e-8);
+
+ /* construct orthonormal basis around N */
+ vec3 T1, T2;
+ T1 = normalize(V - N * dot(N, V));
+ T2 = cross(N, T1);
+
+ /* rotate area light in (T1, T2, R) basis */
+ Minv = Minv * transpose(mat3(T1, T2, N));
+
+ /* Apply LTC inverse matrix. */
+ corners[0] = normalize(Minv * corners[0]);
+ corners[1] = normalize(Minv * corners[1]);
+ corners[2] = normalize(Minv * corners[2]);
+ corners[3] = normalize(Minv * corners[3]);
+}
+
+/* If corners have already pass through ltc_transform_quad(), then N **MUST** be vec3(0.0, 0.0, 1.0),
+ * corresponding to the Up axis of the shading basis. */
+float ltc_evaluate_quad(vec3 corners[4], vec3 N)
+{
+ /* Approximation using a sphere of the same solid angle than the quad.
+ * Finding the clipped sphere diffuse integral is easier than clipping the quad. */
+ vec3 avg_dir;
+ avg_dir = edge_integral_vec(corners[0], corners[1]);
+ avg_dir += edge_integral_vec(corners[1], corners[2]);
+ avg_dir += edge_integral_vec(corners[2], corners[3]);
+ avg_dir += edge_integral_vec(corners[3], corners[0]);
+
+ float form_factor = length(avg_dir);
+ float avg_dir_z = dot(N, avg_dir / form_factor);
+
+#if 1 /* use tabulated horizon-clipped sphere */
+ return form_factor * diffuse_sphere_integral_lut(avg_dir_z, form_factor);
+#else /* Less accurate version, a bit cheaper. */
+ return form_factor * diffuse_sphere_integral_cheap(avg_dir_z, form_factor);
+#endif
+}
+
+/* If disk does not need to be transformed and is already front facing. */
+float ltc_evaluate_disk_simple(float disk_radius, float NL)
+{
+ float r_sqr = disk_radius * disk_radius;
+ float one_r_sqr = 1.0 + r_sqr;
+ float form_factor = r_sqr * inversesqrt(one_r_sqr * one_r_sqr);
+
+#if 1 /* use tabulated horizon-clipped sphere */
+ return form_factor * diffuse_sphere_integral_lut(NL, form_factor);
+#else /* Less accurate version, a bit cheaper. */
+ return form_factor * diffuse_sphere_integral_cheap(NL, form_factor);
+#endif
+}
+
+/* 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);
+
+ /* 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 */
+ mat3 R = transpose(mat3(T1, T2, N));
+
+ /* 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);
+ }
+
+ /* Now find front facing ellipse with same solid angle. */
+
+ 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 avg_dir = vec3(a * x0 / (a - e2), b * y0 / (b - e2), 1.0);
+
+ mat3 rotate = mat3(V1, V2, V3);
+
+ avg_dir = rotate * avg_dir;
+ avg_dir = normalize(avg_dir);
+
+ /* 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 form_factor = max(0.0, L1 * L2 * inversesqrt((1.0 + L1 * L1) * (1.0 + L2 * L2)));
+
+#if 1 /* use tabulated horizon-clipped sphere */
+ return form_factor * diffuse_sphere_integral_lut(avg_dir.z, form_factor);
+#else /* Less accurate version, a bit cheaper. */
+ return form_factor * diffuse_sphere_integral_cheap(avg_dir.z, form_factor);
+#endif
+}
+