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|
/* SPDX-License-Identifier: Apache-2.0
* Copyright 2011-2022 Blender Foundation */
#ifdef __MNEE__
# include "kernel/light/sample.h"
/*
* Manifold Next Event Estimation
*
* This code adds manifold next event estimation through refractive surface(s) as a new sampling
* technique for direct lighting, i.e. finding the point on the refractive surface(s) along the
* path to a light sample, which satisfies fermat's principle for a given microfacet normal and
* the path's end points. This technique involves walking on the "specular manifold" using a pseudo
* newton solver. Such a manifold is defined by the specular constraint matrix from the manifold
* exploration framework [2]. For each refractive interface, this constraint is defined by
* enforcing that the generalized half-vector projection onto the interface local tangent plane is
* null. The newton solver guides the walk by linearizing the manifold locally before reprojecting
* the linear solution onto the refractive surface. See paper [1] for more details about
* the technique itself and [3] for the half-vector light transport formulation, from which it is
* derived.
*
* [1] Manifold Next Event Estimation
* Johannes Hanika, Marc Droske, and Luca Fascione. 2015.
* Comput. Graph. Forum 34, 4 (July 2015), 87–97.
* https://jo.dreggn.org/home/2015_mnee.pdf
*
* [2] Manifold exploration: a Markov Chain Monte Carlo technique for rendering scenes with
* difficult specular transport Wenzel Jakob and Steve Marschner. 2012. ACM Trans. Graph. 31, 4,
* Article 58 (July 2012), 13 pages.
* https://www.cs.cornell.edu/projects/manifolds-sg12/
*
* [3] The Natural-Constraint Representation of the Path Space for Efficient Light Transport
* Simulation Anton S. Kaplanyan, Johannes Hanika, and Carsten Dachsbacher. 2014. ACM Trans. Graph.
* 33, 4, Article 102 (July 2014), 13 pages.
* https://cg.ivd.kit.edu/english/HSLT.php
*/
# define MNEE_MAX_ITERATIONS 32
# define MNEE_MAX_INTERSECTION_COUNT 10
# define MNEE_SOLVER_THRESHOLD 0.001f
# define MNEE_MINIMUM_STEP_SIZE 0.0001f
# define MNEE_MAX_CAUSTIC_CASTERS 6
# define MNEE_MIN_DISTANCE 0.001f
# define MNEE_MIN_PROGRESS_DISTANCE 0.0001f
# define MNEE_MIN_DETERMINANT 0.0001f
# define MNEE_PROJECTION_DISTANCE_MULTIPLIER 2.f
CCL_NAMESPACE_BEGIN
/* Manifold struct containing the local differential geometry quantity */
typedef ccl_private struct ManifoldVertex {
/* Position and partials */
float3 p;
float3 dp_du;
float3 dp_dv;
/* Normal and partials */
float3 n;
float3 ng;
float3 dn_du;
float3 dn_dv;
/* geometric info */
float2 uv;
int object;
int prim;
int shader;
/* closure info */
float eta;
ccl_private ShaderClosure *bsdf;
float2 n_offset;
/* constraint and its derivative matrices */
float2 constraint;
float4 a;
float4 b;
float4 c;
} ManifoldVertex;
/* Multiplication of a 2x2 matrix encoded in a row-major order float4 by a vector */
ccl_device_inline float2 mat22_mult(const float4 a, const float2 b)
{
return make_float2(a.x * b.x + a.y * b.y, a.z * b.x + a.w * b.y);
}
/* Multiplication of 2x2 matrices encoded in a row-major order float4 */
ccl_device_inline float4 mat22_mult(const float4 a, const float4 b)
{
return make_float4(
a.x * b.x + a.y * b.z, a.x * b.y + a.y * b.w, a.z * b.x + a.w * b.z, a.z * b.y + a.w * b.w);
}
/* Determinant of a 2x2 matrix encoded in a row-major order float4 */
ccl_device_inline float mat22_determinant(const float4 m)
{
return m.x * m.w - m.y * m.z;
}
/* Inverse of a 2x2 matrix encoded in a row-major order float4 */
ccl_device_inline float mat22_inverse(const float4 m, ccl_private float4 &m_inverse)
{
float det = mat22_determinant(m);
if (fabsf(det) < MNEE_MIN_DETERMINANT)
return 0.f;
m_inverse = make_float4(m.w, -m.y, -m.z, m.x) / det;
return det;
}
/* Update light sample */
ccl_device_forceinline void mnee_update_light_sample(KernelGlobals kg,
const float3 P,
ccl_private LightSample *ls)
{
/* correct light sample position/direction and pdf
* NOTE: preserve pdf in area measure */
const ccl_global KernelLight *klight = &kernel_tex_fetch(__lights, ls->lamp);
if (ls->type == LIGHT_POINT || ls->type == LIGHT_SPOT) {
ls->D = normalize_len(ls->P - P, &ls->t);
ls->Ng = -ls->D;
float2 uv = map_to_sphere(ls->Ng);
ls->u = uv.x;
ls->v = uv.y;
float invarea = klight->spot.invarea;
ls->eval_fac = (0.25f * M_1_PI_F) * invarea;
ls->pdf = invarea;
if (ls->type == LIGHT_SPOT) {
/* spot light attenuation */
float3 dir = make_float3(klight->spot.dir[0], klight->spot.dir[1], klight->spot.dir[2]);
ls->eval_fac *= spot_light_attenuation(
dir, klight->spot.spot_angle, klight->spot.spot_smooth, ls->Ng);
}
}
else if (ls->type == LIGHT_AREA) {
ls->D = normalize_len(ls->P - P, &ls->t);
ls->pdf = fabsf(klight->area.invarea);
}
}
/* Compute orthonormal basis
* https://graphics.pixar.com/library/OrthonormalB/paper.pdf */
ccl_device_forceinline void mnee_make_orthonormals(const float3 n,
ccl_private float3 *dp_du,
ccl_private float3 *dp_dv)
{
if (n.z < 0.0f) {
const float a = 1.0f / (1.0f - n.z);
const float b = n.x * n.y * a;
*dp_du = make_float3(1.0f - n.x * n.x * a, -b, n.x);
*dp_dv = make_float3(b, n.y * n.y * a - 1.0f, -n.y);
}
else {
const float a = 1.0f / (1.0f + n.z);
const float b = -n.x * n.y * a;
*dp_du = make_float3(1.0f - n.x * n.x * a, b, -n.x);
*dp_dv = make_float3(b, 1.0f - n.y * n.y * a, -n.y);
}
}
/* Manifold vertex setup from ray and intersection data */
ccl_device_forceinline void mnee_setup_manifold_vertex(KernelGlobals kg,
ccl_private ManifoldVertex *vtx,
ccl_private ShaderClosure *bsdf,
const float eta,
const float2 n_offset,
ccl_private const Ray *ray,
ccl_private const Intersection *isect,
ccl_private ShaderData *sd_vtx,
bool seed)
{
sd_vtx->object = (isect->object == OBJECT_NONE) ? kernel_tex_fetch(__prim_object, isect->prim) :
isect->object;
sd_vtx->type = isect->type;
sd_vtx->flag = 0;
sd_vtx->object_flag = kernel_tex_fetch(__object_flag, sd_vtx->object);
/* Matrices and time. */
shader_setup_object_transforms(kg, sd_vtx, ray->time);
sd_vtx->time = ray->time;
sd_vtx->prim = isect->prim;
sd_vtx->ray_length = isect->t;
sd_vtx->u = isect->u;
sd_vtx->v = isect->v;
sd_vtx->shader = kernel_tex_fetch(__tri_shader, sd_vtx->prim);
float3 verts[3];
float3 normals[3];
if (sd_vtx->type & PRIMITIVE_TRIANGLE) {
/* Load triangle vertices and normals. */
triangle_vertices_and_normals(kg, sd_vtx->prim, verts, normals);
/* Compute refined position (same code as in triangle_point_from_uv). */
sd_vtx->P = isect->u * verts[0] + isect->v * verts[1] + (1.f - isect->u - isect->v) * verts[2];
if (!(sd_vtx->object_flag & SD_OBJECT_TRANSFORM_APPLIED)) {
const Transform tfm = object_get_transform(kg, sd_vtx);
sd_vtx->P = transform_point(&tfm, sd_vtx->P);
}
}
else { /* if (sd_vtx->type & PRIMITIVE_MOTION_TRIANGLE) */
/* Load triangle vertices and normals. */
motion_triangle_vertices_and_normals(
kg, sd_vtx->object, sd_vtx->prim, sd_vtx->time, verts, normals);
/* Compute refined position. */
sd_vtx->P = motion_triangle_point_from_uv(
kg, sd_vtx, isect->object, isect->prim, isect->u, isect->v, verts);
}
/* Instance transform. */
if (!(sd_vtx->object_flag & SD_OBJECT_TRANSFORM_APPLIED)) {
object_position_transform_auto(kg, sd_vtx, &verts[0]);
object_position_transform_auto(kg, sd_vtx, &verts[1]);
object_position_transform_auto(kg, sd_vtx, &verts[2]);
object_normal_transform_auto(kg, sd_vtx, &normals[0]);
object_normal_transform_auto(kg, sd_vtx, &normals[1]);
object_normal_transform_auto(kg, sd_vtx, &normals[2]);
}
/* Tangent space (position derivatives) WRT barycentric (u, v). */
float3 dp_du = verts[0] - verts[2];
float3 dp_dv = verts[1] - verts[2];
/* Geometric normal. */
vtx->ng = normalize(cross(dp_du, dp_dv));
if (sd_vtx->object_flag & SD_OBJECT_NEGATIVE_SCALE_APPLIED)
vtx->ng = -vtx->ng;
/* Shading normals: Interpolate normals between vertices. */
float n_len;
vtx->n = normalize_len(normals[0] * sd_vtx->u + normals[1] * sd_vtx->v +
normals[2] * (1.0f - sd_vtx->u - sd_vtx->v),
&n_len);
/* Shading normal derivatives WRT barycentric (u, v)
* we calculate the derivative of n = |u*n0 + v*n1 + (1-u-v)*n2| using:
* d/du [f(u)/|f(u)|] = [d/du f(u)]/|f(u)| - f(u)/|f(u)|^3 <f(u), d/du f(u)>. */
const float inv_n_len = 1.f / n_len;
float3 dn_du = inv_n_len * (normals[0] - normals[2]);
float3 dn_dv = inv_n_len * (normals[1] - normals[2]);
dn_du -= vtx->n * dot(vtx->n, dn_du);
dn_dv -= vtx->n * dot(vtx->n, dn_dv);
/* Orthonormalize (dp_du,dp_dv) using a linear transformation, which
* we use on (dn_du,dn_dv) as well so the new (u,v) are consistent. */
const float inv_len_dp_du = 1.f / len(dp_du);
dp_du *= inv_len_dp_du;
dn_du *= inv_len_dp_du;
const float dpdu_dot_dpdv = dot(dp_du, dp_dv);
dp_dv -= dpdu_dot_dpdv * dp_du;
dn_dv -= dpdu_dot_dpdv * dn_du;
const float inv_len_dp_dv = 1.f / len(dp_dv);
dp_dv *= inv_len_dp_dv;
dn_dv *= inv_len_dp_dv;
/* Final local differential geometry. */
if (seed) {
vtx->dp_du = dp_du;
vtx->dp_dv = dp_dv;
vtx->dn_du = dn_du;
vtx->dn_dv = dn_dv;
}
else {
/* Find angle subtended by reference direction (travel direction). */
const float3 reference_direction = normalize(sd_vtx->P - vtx->p);
const float reference_theta = atan2(dot(reference_direction, vtx->dp_dv),
dot(reference_direction, vtx->dp_du));
const float current_theta = atan2(dot(reference_direction, dp_dv),
dot(reference_direction, dp_du));
const float theta = reference_theta - current_theta;
/* Rotate (dp_du,dp_dv) to be consistent with previous tangent frame. */
float cos_theta, sin_theta;
fast_sincosf(theta, &sin_theta, &cos_theta);
vtx->dp_du = cos_theta * dp_du - sin_theta * dp_dv;
vtx->dp_dv = sin_theta * dp_du + cos_theta * dp_dv;
vtx->dn_du = cos_theta * dn_du - sin_theta * dn_dv;
vtx->dn_dv = sin_theta * dn_du + cos_theta * dn_dv;
}
/* Manifold vertex position. */
vtx->p = sd_vtx->P;
/* Initialize constraint and its derivates. */
vtx->a = vtx->c = zero_float4();
vtx->b = make_float4(1.f, 0.f, 0.f, 1.f);
vtx->constraint = zero_float2();
vtx->n_offset = n_offset;
/* Closure information. */
vtx->bsdf = bsdf;
vtx->eta = eta;
/* Geometric information. */
vtx->uv = make_float2(isect->u, isect->v);
vtx->object = sd_vtx->object;
vtx->prim = sd_vtx->prim;
vtx->shader = sd_vtx->shader;
}
/* Compute constraint derivatives. */
ccl_device_forceinline bool mnee_compute_constraint_derivatives(
int vertex_count,
ccl_private ManifoldVertex *vertices,
ccl_private const float3 &surface_sample_pos,
const bool light_fixed_direction,
const float3 light_sample)
{
for (int vi = 0; vi < vertex_count; vi++) {
ccl_private ManifoldVertex &v = vertices[vi];
/* Direction toward surface sample. */
float3 wi = (vi == 0) ? surface_sample_pos - v.p : vertices[vi - 1].p - v.p;
float ili = len(wi);
if (ili < MNEE_MIN_DISTANCE)
return false;
ili = 1.f / ili;
wi *= ili;
/* Direction toward light sample. */
float3 wo = (vi == vertex_count - 1) ?
(light_fixed_direction ? light_sample : light_sample - v.p) :
vertices[vi + 1].p - v.p;
float ilo = len(wo);
if (ilo < MNEE_MIN_DISTANCE)
return false;
ilo = 1.f / ilo;
wo *= ilo;
/* Invert ior if coming from inside. */
float eta = v.eta;
if (dot(wi, v.ng) < .0f)
eta = 1.f / eta;
/* Half vector. */
float3 H = -(wi + eta * wo);
float ilh = 1.f / len(H);
H *= ilh;
ilo *= eta * ilh;
ili *= ilh;
/* Local shading frame. */
float dp_du_dot_n = dot(v.dp_du, v.n);
float3 s = v.dp_du - dp_du_dot_n * v.n;
float inv_len_s = 1.f / len(s);
s *= inv_len_s;
float3 t = cross(v.n, s);
float3 dH_du, dH_dv;
/* Constraint derivatives WRT previous vertex. */
if (vi > 0) {
ccl_private ManifoldVertex &v_prev = vertices[vi - 1];
dH_du = (v_prev.dp_du - wi * dot(wi, v_prev.dp_du)) * ili;
dH_dv = (v_prev.dp_dv - wi * dot(wi, v_prev.dp_dv)) * ili;
dH_du -= H * dot(dH_du, H);
dH_dv -= H * dot(dH_dv, H);
dH_du = -dH_du;
dH_dv = -dH_dv;
v.a = make_float4(dot(dH_du, s), dot(dH_dv, s), dot(dH_du, t), dot(dH_dv, t));
}
/* Constraint derivatives WRT current vertex. */
if (vi == vertex_count - 1 && light_fixed_direction) {
dH_du = ili * (-v.dp_du + wi * dot(wi, v.dp_du));
dH_dv = ili * (-v.dp_dv + wi * dot(wi, v.dp_dv));
}
else {
dH_du = -v.dp_du * (ili + ilo) + wi * (dot(wi, v.dp_du) * ili) +
wo * (dot(wo, v.dp_du) * ilo);
dH_dv = -v.dp_dv * (ili + ilo) + wi * (dot(wi, v.dp_dv) * ili) +
wo * (dot(wo, v.dp_dv) * ilo);
}
dH_du -= H * dot(dH_du, H);
dH_dv -= H * dot(dH_dv, H);
dH_du = -dH_du;
dH_dv = -dH_dv;
float3 ds_du = -inv_len_s * (dot(v.dp_du, v.dn_du) * v.n + dp_du_dot_n * v.dn_du);
float3 ds_dv = -inv_len_s * (dot(v.dp_du, v.dn_dv) * v.n + dp_du_dot_n * v.dn_dv);
ds_du -= s * dot(s, ds_du);
ds_dv -= s * dot(s, ds_dv);
float3 dt_du = cross(v.dn_du, s) + cross(v.n, ds_du);
float3 dt_dv = cross(v.dn_dv, s) + cross(v.n, ds_dv);
v.b = make_float4(dot(dH_du, s) + dot(H, ds_du),
dot(dH_dv, s) + dot(H, ds_dv),
dot(dH_du, t) + dot(H, dt_du),
dot(dH_dv, t) + dot(H, dt_dv));
/* Constraint derivatives WRT next vertex. */
if (vi < vertex_count - 1) {
ccl_private ManifoldVertex &v_next = vertices[vi + 1];
dH_du = (v_next.dp_du - wo * dot(wo, v_next.dp_du)) * ilo;
dH_dv = (v_next.dp_dv - wo * dot(wo, v_next.dp_dv)) * ilo;
dH_du -= H * dot(dH_du, H);
dH_dv -= H * dot(dH_dv, H);
dH_du = -dH_du;
dH_dv = -dH_dv;
v.c = make_float4(dot(dH_du, s), dot(dH_dv, s), dot(dH_du, t), dot(dH_dv, t));
}
/* Constraint vector WRT. the local shading frame. */
v.constraint = make_float2(dot(s, H), dot(t, H)) - v.n_offset;
}
return true;
}
/* Invert (block) constraint derivative matrix and solve linear system so we can map dh back to dx:
* dh / dx = A
* dx = inverse(A) x dh
* to use for specular specular manifold walk
* (See for example http://faculty.washington.edu/finlayso/ebook/algebraic/advanced/LUtri.htm
* for block tridiagonal matrix based linear system solve) */
ccl_device_forceinline bool mnee_solve_matrix_h_to_x(int vertex_count,
ccl_private ManifoldVertex *vertices,
ccl_private float2 *dx)
{
float4 Li[MNEE_MAX_CAUSTIC_CASTERS];
float2 C[MNEE_MAX_CAUSTIC_CASTERS];
/* Block tridiagonal LU factorization. */
float4 Lk = vertices[0].b;
if (mat22_inverse(Lk, Li[0]) == 0.f)
return false;
C[0] = vertices[0].constraint;
for (int k = 1; k < vertex_count; k++) {
float4 A = mat22_mult(vertices[k].a, Li[k - 1]);
Lk = vertices[k].b - mat22_mult(A, vertices[k - 1].c);
if (mat22_inverse(Lk, Li[k]) == 0.f)
return false;
C[k] = vertices[k].constraint - mat22_mult(A, C[k - 1]);
}
dx[vertex_count - 1] = mat22_mult(Li[vertex_count - 1], C[vertex_count - 1]);
for (int k = vertex_count - 2; k > -1; k--)
dx[k] = mat22_mult(Li[k], C[k] - mat22_mult(vertices[k].c, dx[k + 1]));
return true;
}
/* Newton solver to walk on specular manifold. */
ccl_device_forceinline bool mnee_newton_solver(KernelGlobals kg,
ccl_private const ShaderData *sd,
ccl_private ShaderData *sd_vtx,
ccl_private const LightSample *ls,
int vertex_count,
ccl_private ManifoldVertex *vertices)
{
float2 dx[MNEE_MAX_CAUSTIC_CASTERS];
ManifoldVertex tentative[MNEE_MAX_CAUSTIC_CASTERS];
Ray projection_ray;
projection_ray.self.light_object = OBJECT_NONE;
projection_ray.self.light_prim = PRIM_NONE;
projection_ray.dP = differential_make_compact(sd->dP);
projection_ray.dD = differential_zero_compact();
projection_ray.time = sd->time;
Intersection projection_isect;
const bool light_fixed_direction = (ls->t == FLT_MAX);
const float3 light_sample = light_fixed_direction ? ls->D : ls->P;
/* We start gently, potentially ramping up to beta = 1, since target configurations
* far from the seed path can send the proposed solution further than the linearized
* local differential geometric quantities are meant for (especially dn/du and dn/dv). */
float beta = .1f;
bool reduce_stepsize = false;
bool resolve_constraint = true;
for (int iteration = 0; iteration < MNEE_MAX_ITERATIONS; iteration++) {
if (resolve_constraint) {
/* Calculate constraint and its derivatives for vertices. */
if (!mnee_compute_constraint_derivatives(
vertex_count, vertices, sd->P, light_fixed_direction, light_sample))
return false;
/* Calculate constraint norm. */
float constraint_norm = 0.f;
for (int vi = 0; vi < vertex_count; vi++)
constraint_norm = fmaxf(constraint_norm, len(vertices[vi].constraint));
/* Return if solve successful. */
if (constraint_norm < MNEE_SOLVER_THRESHOLD)
return true;
/* Invert derivative matrix. */
if (!mnee_solve_matrix_h_to_x(vertex_count, vertices, dx))
return false;
}
/* Construct tentative new vertices and project back onto surface. */
for (int vi = 0; vi < vertex_count; vi++) {
ccl_private ManifoldVertex &mv = vertices[vi];
/* Tentative new position on linearized manifold (tangent plane). */
float3 tentative_p = mv.p - beta * (dx[vi].x * mv.dp_du + dx[vi].y * mv.dp_dv);
/* For certain configs, the first solve ends up below the receiver. */
if (vi == 0) {
const float3 wo = tentative_p - sd->P;
if (dot(sd->Ng, wo) <= 0.f) {
/* Change direction for the 1st interface. */
tentative_p = mv.p + beta * (dx[vi].x * mv.dp_du + dx[vi].y * mv.dp_dv);
}
}
/* Project tentative point from tangent plane back to surface
* we ignore all other intersections since this tentative path could lead
* valid to a valid path even if occluded. */
if (vi == 0) {
projection_ray.self.object = sd->object;
projection_ray.self.prim = sd->prim;
projection_ray.P = sd->P;
}
else {
ccl_private const ManifoldVertex &pv = vertices[vi - 1];
projection_ray.self.object = pv.object;
projection_ray.self.prim = pv.prim;
projection_ray.P = pv.p;
}
projection_ray.D = normalize_len(tentative_p - projection_ray.P, &projection_ray.t);
projection_ray.t *= MNEE_PROJECTION_DISTANCE_MULTIPLIER;
bool projection_success = false;
for (int isect_count = 0; isect_count < MNEE_MAX_INTERSECTION_COUNT; isect_count++) {
bool hit = scene_intersect(kg, &projection_ray, PATH_RAY_TRANSMIT, &projection_isect);
if (!hit)
break;
int hit_object = (projection_isect.object == OBJECT_NONE) ?
kernel_tex_fetch(__prim_object, projection_isect.prim) :
projection_isect.object;
if (hit_object == mv.object) {
projection_success = true;
break;
}
projection_ray.self.object = projection_isect.object;
projection_ray.self.prim = projection_isect.prim;
projection_ray.P += projection_isect.t * projection_ray.D;
projection_ray.t -= projection_isect.t;
}
if (!projection_success) {
reduce_stepsize = true;
break;
}
/* Initialize tangent frame, which will be used as reference. */
ccl_private ManifoldVertex &tv = tentative[vi];
tv.p = mv.p;
tv.dp_du = mv.dp_du;
tv.dp_dv = mv.dp_dv;
/* Setup corrected manifold vertex. */
mnee_setup_manifold_vertex(kg,
&tv,
mv.bsdf,
mv.eta,
mv.n_offset,
&projection_ray,
&projection_isect,
sd_vtx,
false);
/* Fail newton solve if we are not making progress, probably stuck trying to move off the
* edge of the mesh. */
const float distance = len(tv.p - mv.p);
if (distance < MNEE_MIN_PROGRESS_DISTANCE)
return false;
}
/* Check that tentative path is still transmissive. */
if (!reduce_stepsize) {
for (int vi = 0; vi < vertex_count; vi++) {
ccl_private ManifoldVertex &tv = tentative[vi];
/* Direction toward surface sample. */
const float3 wi = (vi == 0 ? sd->P : tentative[vi - 1].p) - tv.p;
/* Direction toward light sample. */
const float3 wo = (vi == vertex_count - 1) ? light_fixed_direction ? ls->D : ls->P - tv.p :
tentative[vi + 1].p - tv.p;
if (dot(tv.n, wi) * dot(tv.n, wo) >= 0.f) {
reduce_stepsize = true;
break;
}
}
}
if (reduce_stepsize) {
/* Adjust step if can't land on right surface. */
reduce_stepsize = false;
resolve_constraint = false;
beta *= .5f;
/* Fail newton solve if the stepsize is too small. */
if (beta < MNEE_MINIMUM_STEP_SIZE)
return false;
continue;
}
/* Copy tentative vertices to main vertex list. */
for (int vi = 0; vi < vertex_count; vi++)
vertices[vi] = tentative[vi];
/* Increase the step to get back to 1. */
resolve_constraint = true;
beta = min(1.f, 2.f * beta);
}
return false;
}
/* Sample bsdf in half-vector measure. */
ccl_device_forceinline float2
mnee_sample_bsdf_dh(ClosureType type, float alpha_x, float alpha_y, float sample_u, float sample_v)
{
float alpha2;
float cos_phi, sin_phi;
if (alpha_x == alpha_y) {
float phi = sample_v * M_2PI_F;
fast_sincosf(phi, &sin_phi, &cos_phi);
alpha2 = alpha_x * alpha_x;
}
else {
float phi = atanf(alpha_y / alpha_x * tanf(M_2PI_F * sample_v + M_PI_2_F));
if (sample_v > .5f)
phi += M_PI_F;
fast_sincosf(phi, &sin_phi, &cos_phi);
float alpha_x2 = alpha_x * alpha_x;
float alpha_y2 = alpha_y * alpha_y;
alpha2 = 1.f / (cos_phi * cos_phi / alpha_x2 + sin_phi * sin_phi / alpha_y2);
}
/* Map sampled angles to micro-normal direction h. */
float tan2_theta = alpha2;
if (type == CLOSURE_BSDF_MICROFACET_BECKMANN_REFRACTION_ID) {
tan2_theta *= -logf(1.0f - sample_u);
}
else { /* type == CLOSURE_BSDF_MICROFACET_GGX_REFRACTION_ID assumed */
tan2_theta *= sample_u / (1.0f - sample_u);
}
float cos2_theta = 1.0f / (1.0f + tan2_theta);
float sin_theta = safe_sqrtf(1.0f - cos2_theta);
return make_float2(cos_phi * sin_theta, sin_phi * sin_theta);
}
/* Evaluate product term inside eq.6 at solution interface vi
* divided by corresponding sampled pdf:
* fr(vi)_do / pdf_dh(vi) x |do/dh| x |n.wo / n.h|
* We assume here that the pdf (in half-vector measure) is the same as
* the one calculation when sampling the microfacet normals from the
* specular chain above: this allows us to simplify the bsdf weight */
ccl_device_forceinline float3 mnee_eval_bsdf_contribution(ccl_private ShaderClosure *closure,
float3 wi,
float3 wo)
{
ccl_private MicrofacetBsdf *bsdf = (ccl_private MicrofacetBsdf *)closure;
float cosNO = dot(bsdf->N, wi);
float cosNI = dot(bsdf->N, wo);
float3 Ht = normalize(-(bsdf->ior * wo + wi));
float cosHO = dot(Ht, wi);
float alpha2 = bsdf->alpha_x * bsdf->alpha_y;
float cosThetaM = dot(bsdf->N, Ht);
float G;
if (bsdf->type == CLOSURE_BSDF_MICROFACET_BECKMANN_REFRACTION_ID) {
/* Eq. 26, 27: now calculate G1(i,m) and G1(o,m). */
G = bsdf_beckmann_G1(bsdf->alpha_x, cosNO) * bsdf_beckmann_G1(bsdf->alpha_x, cosNI);
}
else { /* bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_REFRACTION_ID assumed */
/* Eq. 34: now calculate G1(i,m) and G1(o,m). */
G = (2.f / (1.f + safe_sqrtf(1.f + alpha2 * (1.f - cosNO * cosNO) / (cosNO * cosNO)))) *
(2.f / (1.f + safe_sqrtf(1.f + alpha2 * (1.f - cosNI * cosNI) / (cosNI * cosNI))));
}
/*
* bsdf_do = (1 - F) * D_do * G * |h.wi| / (n.wi * n.wo)
* pdf_dh = D_dh * cosThetaM
* D_do = D_dh * |dh/do|
*
* contribution = bsdf_do * |do/dh| * |n.wo / n.h| / pdf_dh
* = (1 - F) * G * |h.wi / (n.wi * n.h^2)|
*/
return bsdf->weight * G * fabsf(cosHO / (cosNO * sqr(cosThetaM)));
}
/* Compute transfer matrix determinant |T1| = |dx1/dxn| (and |dh/dx| in the process) */
ccl_device_forceinline bool mnee_compute_transfer_matrix(ccl_private const ShaderData *sd,
ccl_private const LightSample *ls,
int vertex_count,
ccl_private ManifoldVertex *vertices,
ccl_private float *dx1_dxlight,
ccl_private float *dh_dx)
{
/* Simplified block tridiagonal LU factorization. */
float4 Li;
float4 U[MNEE_MAX_CAUSTIC_CASTERS - 1];
float4 Lk = vertices[0].b;
float Lk_det = mat22_inverse(Lk, Li);
if (Lk_det == 0.f)
return false;
float det_dh_dx = Lk_det;
for (int k = 1; k < vertex_count; k++) {
U[k - 1] = mat22_mult(Li, vertices[k - 1].c);
Lk = vertices[k].b - mat22_mult(vertices[k].a, U[k - 1]);
Lk_det = mat22_inverse(Lk, Li);
if (Lk_det == 0.f)
return false;
det_dh_dx *= Lk_det;
}
/* Fill out constraint derivatives WRT light vertex param. */
/* Local shading frame at last free vertex. */
int mi = vertex_count - 1;
ccl_private const ManifoldVertex &m = vertices[mi];
float3 s = normalize(m.dp_du - dot(m.dp_du, m.n) * m.n);
float3 t = cross(m.n, s);
/* Local differential geometry. */
float3 dp_du, dp_dv;
mnee_make_orthonormals(ls->Ng, &dp_du, &dp_dv);
/* Direction toward surface sample. */
float3 wi = vertex_count == 1 ? sd->P - m.p : vertices[mi - 1].p - m.p;
float ili = 1.f / len(wi);
wi *= ili;
/* Invert ior if coming from inside. */
float eta = m.eta;
if (dot(wi, m.ng) < .0f)
eta = 1.f / eta;
float dxn_dwn;
float4 dc_dlight;
if (ls->t == FLT_MAX) {
/* Constant direction toward light sample. */
float3 wo = ls->D;
/* Half vector. */
float3 H = -(wi + eta * wo);
float ilh = 1.f / len(H);
H *= ilh;
float ilo = -eta * ilh;
float cos_theta = dot(wo, m.n);
float sin_theta = safe_sqrtf(1.f - sqr(cos_theta));
float cos_phi = dot(wo, s);
float sin_phi = safe_sqrtf(1.f - sqr(cos_phi));
/* Wo = (cos_phi * sin_theta) * s + (sin_phi * sin_theta) * t + cos_theta * n. */
float3 dH_dtheta = ilo * (cos_theta * (cos_phi * s + sin_phi * t) - sin_theta * m.n);
float3 dH_dphi = ilo * sin_theta * (-sin_phi * s + cos_phi * t);
dH_dtheta -= H * dot(dH_dtheta, H);
dH_dphi -= H * dot(dH_dphi, H);
/* Constraint derivatives WRT light direction expressed
* in spherical coordinates (theta, phi). */
dc_dlight = make_float4(
dot(dH_dtheta, s), dot(dH_dphi, s), dot(dH_dtheta, t), dot(dH_dphi, t));
/* Jacobian to convert dtheta x dphi to dw measure. */
dxn_dwn = 1.f / fmaxf(MNEE_MIN_DISTANCE, fabsf(sin_theta));
}
else {
/* Direction toward light sample. */
float3 wo = ls->P - m.p;
float ilo = 1.f / len(wo);
wo *= ilo;
/* Half vector. */
float3 H = -(wi + eta * wo);
float ilh = 1.f / len(H);
H *= ilh;
ilo *= eta * ilh;
float3 dH_du = (dp_du - wo * dot(wo, dp_du)) * ilo;
float3 dH_dv = (dp_dv - wo * dot(wo, dp_dv)) * ilo;
dH_du -= H * dot(dH_du, H);
dH_dv -= H * dot(dH_dv, H);
dH_du = -dH_du;
dH_dv = -dH_dv;
dc_dlight = make_float4(dot(dH_du, s), dot(dH_dv, s), dot(dH_du, t), dot(dH_dv, t));
/* Neutral value since dc_dlight is already in the desired vertex area measure. */
dxn_dwn = 1.f;
}
/* Compute transfer matrix. */
float4 Tp = -mat22_mult(Li, dc_dlight);
for (int k = vertex_count - 2; k > -1; k--)
Tp = -mat22_mult(U[k], Tp);
*dx1_dxlight = fabsf(mat22_determinant(Tp)) * dxn_dwn;
*dh_dx = fabsf(det_dh_dx);
return true;
}
/* Calculate the path contribution. */
ccl_device_forceinline bool mnee_path_contribution(KernelGlobals kg,
IntegratorState state,
ccl_private ShaderData *sd,
ccl_private ShaderData *sd_mnee,
ccl_private LightSample *ls,
int vertex_count,
ccl_private ManifoldVertex *vertices,
ccl_private BsdfEval *throughput)
{
float wo_len;
float3 wo = normalize_len(vertices[0].p - sd->P, &wo_len);
/* Initialize throughput and evaluate receiver bsdf * |n.wo|. */
shader_bsdf_eval(kg, sd, wo, false, throughput, ls->shader);
/* Update light sample with new position / direct.ion
* and keep pdf in vertex area measure */
mnee_update_light_sample(kg, vertices[vertex_count - 1].p, ls);
/* Evaluate light sample
* in case the light has a node-based shader:
* 1. sd_mnee will be used to store light data, which is why we need to do
* this evaluation here. sd_mnee needs to contain the solution's last
* interface data at the end of the call for the shadow ray setup to work.
* 2. ls needs to contain the last interface data for the light shader to
* evaluate properly */
float3 light_eval = light_sample_shader_eval(kg, state, sd_mnee, ls, sd->time);
bsdf_eval_mul3(throughput, light_eval / ls->pdf);
/* Generalized geometry term. */
float dh_dx;
float dx1_dxlight;
if (!mnee_compute_transfer_matrix(sd, ls, vertex_count, vertices, &dx1_dxlight, &dh_dx))
return false;
/* Receiver bsdf eval above already contains |n.wo|. */
const float dw0_dx1 = fabsf(dot(wo, vertices[0].n)) / sqr(wo_len);
/* Clamp since it has a tendency to be unstable. */
const float G = fminf(dw0_dx1 * dx1_dxlight, 2.f);
bsdf_eval_mul(throughput, G);
/* Specular reflectance. */
/* Probe ray / isect. */
Ray probe_ray;
probe_ray.self.light_object = ls->object;
probe_ray.self.light_prim = ls->prim;
probe_ray.dP = differential_make_compact(sd->dP);
probe_ray.dD = differential_zero_compact();
probe_ray.time = sd->time;
Intersection probe_isect;
probe_ray.self.object = sd->object;
probe_ray.self.prim = sd->prim;
probe_ray.P = sd->P;
float3 wi;
float wi_len;
for (int vi = 0; vi < vertex_count; vi++) {
ccl_private const ManifoldVertex &v = vertices[vi];
/* Check visibility. */
probe_ray.D = normalize_len(v.p - probe_ray.P, &probe_ray.t);
if (scene_intersect(kg, &probe_ray, PATH_RAY_TRANSMIT, &probe_isect)) {
int hit_object = (probe_isect.object == OBJECT_NONE) ?
kernel_tex_fetch(__prim_object, probe_isect.prim) :
probe_isect.object;
/* Test whether the ray hit the appropriate object at its intended location. */
if (hit_object != v.object || fabsf(probe_ray.t - probe_isect.t) > MNEE_MIN_DISTANCE)
return false;
}
probe_ray.self.object = v.object;
probe_ray.self.prim = v.prim;
probe_ray.P = v.p;
/* Set view looking dir. */
wi = -wo;
wi_len = wo_len;
/* Setup shader data for vertex vi. */
shader_setup_from_sample(kg,
sd_mnee,
v.p,
v.n,
wi,
v.shader,
v.object,
v.prim,
v.uv.x,
v.uv.y,
wi_len,
sd->time,
false,
LAMP_NONE);
/* Evaluate shader nodes at solution vi. */
shader_eval_surface<KERNEL_FEATURE_NODE_MASK_SURFACE_SHADOW>(
kg, state, sd_mnee, NULL, PATH_RAY_DIFFUSE, true);
/* Set light looking dir. */
wo = (vi == vertex_count - 1) ? (ls->t == FLT_MAX ? ls->D : ls->P - v.p) :
vertices[vi + 1].p - v.p;
wo = normalize_len(wo, &wo_len);
/* Evaluate product term inside eq.6 at solution interface. vi
* divided by corresponding sampled pdf:
* fr(vi)_do / pdf_dh(vi) x |do/dh| x |n.wo / n.h| */
float3 bsdf_contribution = mnee_eval_bsdf_contribution(v.bsdf, wi, wo);
bsdf_eval_mul3(throughput, bsdf_contribution);
}
return true;
}
/* Manifold next event estimation path sampling. */
ccl_device_forceinline bool kernel_path_mnee_sample(KernelGlobals kg,
IntegratorState state,
ccl_private ShaderData *sd,
ccl_private ShaderData *sd_mnee,
ccl_private const RNGState *rng_state,
ccl_private LightSample *ls,
ccl_private BsdfEval *throughput)
{
/*
* 1. send seed ray from shading point to light sample position (or along sampled light
* direction), making sure it intersects a caustic caster at least once, ignoring all other
* intersections (the final path could be valid even though objects could occlude the light
* this seed point), building an array of manifold vertices.
*/
/* Setup probe ray. */
Ray probe_ray;
probe_ray.self.object = sd->object;
probe_ray.self.prim = sd->prim;
probe_ray.self.light_object = ls->object;
probe_ray.self.light_prim = ls->prim;
probe_ray.P = sd->P;
if (ls->t == FLT_MAX) {
/* Distant / env light. */
probe_ray.D = ls->D;
probe_ray.t = ls->t;
}
else {
/* Other lights, avoid self-intersection. */
probe_ray.D = ls->P - probe_ray.P;
probe_ray.D = normalize_len(probe_ray.D, &probe_ray.t);
}
probe_ray.dP = differential_make_compact(sd->dP);
probe_ray.dD = differential_zero_compact();
probe_ray.time = sd->time;
Intersection probe_isect;
ManifoldVertex vertices[MNEE_MAX_CAUSTIC_CASTERS];
int vertex_count = 0;
for (int isect_count = 0; isect_count < MNEE_MAX_INTERSECTION_COUNT; isect_count++) {
bool hit = scene_intersect(kg, &probe_ray, PATH_RAY_TRANSMIT, &probe_isect);
if (!hit)
break;
const int object_flags = intersection_get_object_flags(kg, &probe_isect);
if (object_flags & SD_OBJECT_CAUSTICS_CASTER) {
/* Do we have enough slots. */
if (vertex_count >= MNEE_MAX_CAUSTIC_CASTERS)
return false;
/* Reject caster if it is not a triangles mesh. */
if (!(probe_isect.type & PRIMITIVE_TRIANGLE))
return false;
ccl_private ManifoldVertex &mv = vertices[vertex_count++];
/* Setup shader data on caustic caster and evaluate context. */
shader_setup_from_ray(kg, sd_mnee, &probe_ray, &probe_isect);
/* Reject caster if smooth normals are not available: Manifold exploration assumes local
* differential geometry can be created at any point on the surface which is not possible if
* normals are not smooth. */
if (!(sd_mnee->shader & SHADER_SMOOTH_NORMAL))
return false;
/* Last bool argument is the MNEE flag (for TINY_MAX_CLOSURE cap in kernel_shader.h). */
shader_eval_surface<KERNEL_FEATURE_NODE_MASK_SURFACE_SHADOW>(
kg, state, sd_mnee, NULL, PATH_RAY_DIFFUSE, true);
/* Get and sample refraction bsdf */
bool found_transimissive_microfacet_bsdf = false;
for (int ci = 0; ci < sd_mnee->num_closure; ci++) {
ccl_private ShaderClosure *bsdf = &sd_mnee->closure[ci];
if (bsdf->type == CLOSURE_BSDF_MICROFACET_BECKMANN_REFRACTION_ID ||
bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_REFRACTION_ID ||
bsdf->type == CLOSURE_BSDF_MICROFACET_MULTI_GGX_GLASS_ID ||
bsdf->type == CLOSURE_BSDF_MICROFACET_MULTI_GGX_GLASS_FRESNEL_ID) {
/* Note that CLOSURE_BSDF_MICROFACET_MULTI_GGX_GLASS_ID and
* CLOSURE_BSDF_MICROFACET_MULTI_GGX_GLASS_FRESNEL_ID are treated as
* CLOSURE_BSDF_MICROFACET_GGX_REFRACTION_ID further below. */
found_transimissive_microfacet_bsdf = true;
ccl_private MicrofacetBsdf *microfacet_bsdf = (ccl_private MicrofacetBsdf *)bsdf;
/* Figure out appropriate index of refraction ratio. */
const float eta = (sd_mnee->flag & SD_BACKFACING) ? 1.0f / microfacet_bsdf->ior :
microfacet_bsdf->ior;
/* Sample transmissive microfacet bsdf. */
float bsdf_u, bsdf_v;
path_state_rng_2D(kg, rng_state, PRNG_BSDF_U, &bsdf_u, &bsdf_v);
float2 h = mnee_sample_bsdf_dh(
bsdf->type, microfacet_bsdf->alpha_x, microfacet_bsdf->alpha_y, bsdf_u, bsdf_v);
/* Setup differential geometry on vertex. */
mnee_setup_manifold_vertex(
kg, &mv, bsdf, eta, h, &probe_ray, &probe_isect, sd_mnee, true);
break;
}
}
if (!found_transimissive_microfacet_bsdf)
return false;
}
probe_ray.self.object = probe_isect.object;
probe_ray.self.prim = probe_isect.prim;
probe_ray.P += probe_isect.t * probe_ray.D;
if (ls->t != FLT_MAX)
probe_ray.t -= probe_isect.t;
};
/* Mark the manifold walk invalid to keep mollification on by default. */
INTEGRATOR_STATE_WRITE(state, path, mnee) &= ~PATH_MNEE_VALID;
if (vertex_count == 0)
return false;
/* Check whether the transmission depth limit is reached before continuing. */
const int transmission_bounce = INTEGRATOR_STATE(state, path, transmission_bounce) +
vertex_count;
if (transmission_bounce >= kernel_data.integrator.max_transmission_bounce)
return false;
/* Check whether the diffuse depth limit is reached before continuing. */
const int diffuse_bounce = INTEGRATOR_STATE(state, path, diffuse_bounce) + 1;
if (diffuse_bounce >= kernel_data.integrator.max_diffuse_bounce)
return false;
/* Check whether the overall depth limit is reached before continuing. */
const int bounce = INTEGRATOR_STATE(state, path, bounce) + diffuse_bounce + transmission_bounce;
if (bounce >= kernel_data.integrator.max_bounce)
return false;
/* Mark the manifold walk valid to turn off mollification regardless of how successful the walk
* is: this is noticeable when another mnee is performed deeper in the path, for an internally
* reflected ray for example. If mollification was active for the reflection, a clear
* discontinuity is visible between direct and indirect contributions */
INTEGRATOR_STATE_WRITE(state, path, mnee) |= PATH_MNEE_VALID;
/* 2. Walk on the specular manifold to find vertices on the
* casters that satisfy snell's law for each interface
*/
if (mnee_newton_solver(kg, sd, sd_mnee, ls, vertex_count, vertices)) {
/* 3. If a solution exists, calculate contribution of the corresponding path */
if (!mnee_path_contribution(kg, state, sd, sd_mnee, ls, vertex_count, vertices, throughput))
return false;
return true;
}
return false;
}
CCL_NAMESPACE_END
#endif /* __MNEE__ */
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