blender/intern/cycles/kernel/kernel_subsurface.h

/*
 * Copyright 2011-2013 Blender Foundation
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 * http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License
 */

CCL_NAMESPACE_BEGIN

/* NEW BSSRDF: See "BSSRDF Importance Sampling", SIGGRAPH 2013 */

/* TODO:
 * - test using power heuristic for combing bssrdfs
 * - try to reduce one sample model variance
 */

#define BSSRDF_MULTI_EVAL

ccl_device ShaderClosure *subsurface_scatter_pick_closure(KernelGlobals *kg, ShaderData *sd, float *probability)
{
	/* sum sample weights of bssrdf and bsdf */
	float bsdf_sum = 0.0f;
	float bssrdf_sum = 0.0f;

	for(int i = 0; i < sd->num_closure; i++) {
		ShaderClosure *sc = &sd->closure[i];
		
		if(CLOSURE_IS_BSDF(sc->type))
			bsdf_sum += sc->sample_weight;
		else if(CLOSURE_IS_BSSRDF(sc->type))
			bssrdf_sum += sc->sample_weight;
	}

	/* use bsdf or bssrdf? */
	float r = sd->randb_closure*(bsdf_sum + bssrdf_sum);

	if(r < bsdf_sum) {
		/* use bsdf, and adjust randb so we can reuse it for picking a bsdf */
		sd->randb_closure = r/bsdf_sum;
		*probability = (bsdf_sum > 0.0f)? (bsdf_sum + bssrdf_sum)/bsdf_sum: 1.0f;
		return NULL;
	}

	/* use bssrdf */
	r -= bsdf_sum;

	float sum = 0.0f;

	for(int i = 0; i < sd->num_closure; i++) {
		ShaderClosure *sc = &sd->closure[i];
		
		if(CLOSURE_IS_BSSRDF(sc->type)) {
			sum += sc->sample_weight;

			if(r <= sum) {
				sd->randb_closure = (r - (sum - sc->sample_weight))/sc->sample_weight;

#ifdef BSSRDF_MULTI_EVAL
				*probability = (bssrdf_sum > 0.0f)? (bsdf_sum + bssrdf_sum)/bssrdf_sum: 1.0f;
#else
				*probability = (bssrdf_sum > 0.0f)? (bsdf_sum + bssrdf_sum)/sc->sample_weight: 1.0f;
#endif
				return sc;
			}
		}
	}

	/* should never happen */
	sd->randb_closure = 0.0f;
	*probability = 1.0f;
	return NULL;
}

ccl_device float3 subsurface_scatter_eval(ShaderData *sd, ShaderClosure *sc, float disk_r, float r, bool all)
{
#ifdef BSSRDF_MULTI_EVAL
	/* this is the veach one-sample model with balance heuristic, some pdf
	 * factors drop out when using balance heuristic weighting */
	float3 eval_sum = make_float3(0.0f, 0.0f, 0.0f);
	float pdf_sum = 0.0f;
	float sample_weight_sum = 0.0f;
	int num_bssrdf = 0;

	for(int i = 0; i < sd->num_closure; i++) {
		sc = &sd->closure[i];
		
		if(CLOSURE_IS_BSSRDF(sc->type)) {
			float sample_weight = (all)? 1.0f: sc->sample_weight;
			sample_weight_sum += sample_weight;
		}
	}

	float sample_weight_inv = 1.0f/sample_weight_sum;

	//printf("num closures %d\n", sd->num_closure);

	for(int i = 0; i < sd->num_closure; i++) {
		sc = &sd->closure[i];
		
		if(CLOSURE_IS_BSSRDF(sc->type)) {
			/* in case of branched path integrate we sample all bssrdf's once,
			 * for path trace we pick one, so adjust pdf for that */
			float sample_weight = (all)? 1.0f: sc->sample_weight * sample_weight_inv;

			/* compute pdf */
			float pdf = bssrdf_pdf(sc, r);
			float disk_pdf = bssrdf_pdf(sc, disk_r);

			/* TODO power heuristic is not working correct here */
			eval_sum += sc->weight*pdf; //*sample_weight*disk_pdf;
			pdf_sum += sample_weight*disk_pdf; //*sample_weight*disk_pdf;

			num_bssrdf++;
		}
	}

	return (pdf_sum > 0.0f)? eval_sum / pdf_sum : make_float3(0.0f, 0.0f, 0.0f);
#else
	float pdf = bssrdf_pdf(pick_sc, r);
	float disk_pdf = bssrdf_pdf(pick_sc, disk_r);

	return pick_sc->weight * pdf / disk_pdf;
#endif
}

/* replace closures with a single diffuse bsdf closure after scatter step */
ccl_device void subsurface_scatter_setup_diffuse_bsdf(ShaderData *sd, float3 weight, bool hit, float3 N)
{
	sd->flag &= ~SD_CLOSURE_FLAGS;
	sd->randb_closure = 0.0f;

	if(hit) {
		ShaderClosure *sc = &sd->closure[0];
		sd->num_closure = 1;

		sc->weight = weight;
		sc->sample_weight = 1.0f;
		sc->data0 = 0.0f;
		sc->data1 = 0.0f;
		sc->N = N;
		sd->flag |= bsdf_diffuse_setup(sc);

		/* replace CLOSURE_BSDF_DIFFUSE_ID with this special ID so render passes
		 * can recognize it as not being a regular diffuse closure */
		sc->type = CLOSURE_BSDF_BSSRDF_ID;
	}
	else
		sd->num_closure = 0;
}

/* optionally do blurring of color and/or bump mapping, at the cost of a shader evaluation */
ccl_device float3 subsurface_color_pow(float3 color, float exponent)
{
	color = max(color, make_float3(0.0f, 0.0f, 0.0f));

	if(exponent == 1.0f) {
		/* nothing to do */
	}
	else if(exponent == 0.5f) {
		color.x = sqrtf(color.x);
		color.y = sqrtf(color.y);
		color.z = sqrtf(color.z);
	}
	else {
		color.x = powf(color.x, exponent);
		color.y = powf(color.y, exponent);
		color.z = powf(color.z, exponent);
	}

	return color;
}

ccl_device void subsurface_color_bump_blur(KernelGlobals *kg, ShaderData *out_sd, ShaderData *in_sd, int state_flag, float3 *eval, float3 *N)
{
	/* average color and texture blur at outgoing point */
	float texture_blur;
	float3 out_color = shader_bssrdf_sum(out_sd, NULL, &texture_blur);

	/* do we have bump mapping? */
	bool bump = (out_sd->flag & SD_HAS_BSSRDF_BUMP) != 0;

	if(bump || texture_blur > 0.0f) {
		/* average color and normal at incoming point */
		shader_eval_surface(kg, in_sd, 0.0f, state_flag, SHADER_CONTEXT_SSS);
		float3 in_color = shader_bssrdf_sum(in_sd, (bump)? N: NULL, NULL);

		/* we simply divide out the average color and multiply with the average
		 * of the other one. we could try to do this per closure but it's quite
		 * tricky to match closures between shader evaluations, their number and
		 * order may change, this is simpler */
		if(texture_blur > 0.0f) {
			out_color = subsurface_color_pow(out_color, texture_blur);
			in_color = subsurface_color_pow(in_color, texture_blur);

			*eval *= safe_divide_color(in_color, out_color);
		}
	}
}

/* subsurface scattering step, from a point on the surface to other nearby points on the same object */
ccl_device int subsurface_scatter_multi_step(KernelGlobals *kg, ShaderData *sd, ShaderData bssrdf_sd[BSSRDF_MAX_HITS],
	int state_flag, ShaderClosure *sc, uint *lcg_state, float disk_u, float disk_v, bool all)
{
	/* pick random axis in local frame and point on disk */
	float3 disk_N, disk_T, disk_B;
	float pick_pdf_N, pick_pdf_T, pick_pdf_B;
	
	disk_N = sd->Ng;
	make_orthonormals(disk_N, &disk_T, &disk_B);

	/* reusing variable for picking the closure gives a bit nicer stratification
	 * for path tracer, for branched we do all closures so it doesn't help */
	float axisu = (all)? disk_u: sd->randb_closure;

	if(axisu < 0.5f) {
		pick_pdf_N = 0.5f;
		pick_pdf_T = 0.25f;
		pick_pdf_B = 0.25f;
		if(all)
			disk_u *= 2.0f;
	}
	else if(axisu < 0.75f) {
		float3 tmp = disk_N;
		disk_N = disk_T;
		disk_T = tmp;
		pick_pdf_N = 0.25f;
		pick_pdf_T = 0.5f;
		pick_pdf_B = 0.25f;
		if(all)
			disk_u = (disk_u - 0.5f)*4.0f;
	}
	else {
		float3 tmp = disk_N;
		disk_N = disk_B;
		disk_B = tmp;
		pick_pdf_N = 0.25f;
		pick_pdf_T = 0.25f;
		pick_pdf_B = 0.5f;
		if(all)
			disk_u = (disk_u - 0.75f)*4.0f;
	}

	/* sample point on disk */
    float phi = M_2PI_F * disk_u;
    float disk_r = disk_v;
	float disk_height;

	bssrdf_sample(sc, disk_r, &disk_r, &disk_height);

	float3 disk_P = (disk_r*cosf(phi)) * disk_T + (disk_r*sinf(phi)) * disk_B;

	/* create ray */
	Ray ray;
	ray.P = sd->P + disk_N*disk_height + disk_P;
	ray.D = -disk_N;
	ray.t = 2.0f*disk_height;
	ray.dP = sd->dP;
	ray.dD = differential3_zero();
	ray.time = sd->time;

	/* intersect with the same object. if multiple intersections are found it
	 * will use at most BSSRDF_MAX_HITS hits, a random subset of all hits */
	Intersection isect[BSSRDF_MAX_HITS];
	uint num_hits = scene_intersect_subsurface(kg, &ray, isect, sd->object, lcg_state, BSSRDF_MAX_HITS);

	/* evaluate bssrdf */
	float3 eval = make_float3(0.0f, 0.0f, 0.0f);
	int num_eval_hits = min(num_hits, BSSRDF_MAX_HITS);

	for(int hit = 0; hit < num_eval_hits; hit++) {
		ShaderData *bsd = &bssrdf_sd[hit];

		/* setup new shading point */
		*bsd = *sd;
		shader_setup_from_subsurface(kg, bsd, &isect[hit], &ray);

		/* probability densities for local frame axes */
		float pdf_N = pick_pdf_N * fabsf(dot(disk_N, bsd->Ng));
		float pdf_T = pick_pdf_T * fabsf(dot(disk_T, bsd->Ng));
		float pdf_B = pick_pdf_B * fabsf(dot(disk_B, bsd->Ng));
		
		/* multiple importance sample between 3 axes, power heuristic
		 * found to be slightly better than balance heuristic */
		float mis_weight = power_heuristic_3(pdf_N, pdf_T, pdf_B);

		/* real distance to sampled point */
		float r = len(bsd->P - sd->P);

		/* evaluate */
		float w = mis_weight / pdf_N;
		if(num_hits > BSSRDF_MAX_HITS)
			w *= num_hits/(float)BSSRDF_MAX_HITS;
		eval = subsurface_scatter_eval(bsd, sc, disk_r, r, all) * w;

		/* optionally blur colors and bump mapping */
		float3 N = bsd->N;
		subsurface_color_bump_blur(kg, sd, bsd, state_flag, &eval, &N);

		/* setup diffuse bsdf */
		subsurface_scatter_setup_diffuse_bsdf(bsd, eval, true, N);
	}

	return num_eval_hits;
}

/* subsurface scattering step, from a point on the surface to another nearby point on the same object */
ccl_device void subsurface_scatter_step(KernelGlobals *kg, ShaderData *sd,
	int state_flag, ShaderClosure *sc, uint *lcg_state, float disk_u, float disk_v, bool all)
{
	float3 eval = make_float3(0.0f, 0.0f, 0.0f);
	uint num_hits = 0;

	/* pick random axis in local frame and point on disk */
	float3 disk_N, disk_T, disk_B;
	float pick_pdf_N, pick_pdf_T, pick_pdf_B;
	
	disk_N = sd->Ng;
	make_orthonormals(disk_N, &disk_T, &disk_B);

	if(sd->randb_closure < 0.5f) {
		pick_pdf_N = 0.5f;
		pick_pdf_T = 0.25f;
		pick_pdf_B = 0.25f;
	}
	else if(sd->randb_closure < 0.75f) {
		float3 tmp = disk_N;
		disk_N = disk_T;
		disk_T = tmp;
		pick_pdf_N = 0.25f;
		pick_pdf_T = 0.5f;
		pick_pdf_B = 0.25f;
	}
	else {
		float3 tmp = disk_N;
		disk_N = disk_B;
		disk_B = tmp;
		pick_pdf_N = 0.25f;
		pick_pdf_T = 0.25f;
		pick_pdf_B = 0.5f;
	}

	/* sample point on disk */
	float phi = M_2PI_F * disk_u;
	float disk_r = disk_v;
	float disk_height;

	bssrdf_sample(sc, disk_r, &disk_r, &disk_height);

	float3 disk_P = (disk_r*cosf(phi)) * disk_T + (disk_r*sinf(phi)) * disk_B;

	/* create ray */
	Ray ray;
	ray.P = sd->P + disk_N*disk_height + disk_P;
	ray.D = -disk_N;
	ray.t = 2.0f*disk_height;
	ray.dP = sd->dP;
	ray.dD = differential3_zero();
	ray.time = sd->time;

	/* intersect with the same object. if multiple intersections are
	 * found it will randomly pick one of them */
	Intersection isect;
	num_hits = scene_intersect_subsurface(kg, &ray, &isect, sd->object, lcg_state, 1);

	/* evaluate bssrdf */
	if(num_hits > 0) {
		float3 origP = sd->P;

		/* setup new shading point */
		shader_setup_from_subsurface(kg, sd, &isect, &ray);

		/* probability densities for local frame axes */
		float pdf_N = pick_pdf_N * fabsf(dot(disk_N, sd->Ng));
		float pdf_T = pick_pdf_T * fabsf(dot(disk_T, sd->Ng));
		float pdf_B = pick_pdf_B * fabsf(dot(disk_B, sd->Ng));
		
		/* multiple importance sample between 3 axes, power heuristic
		 * found to be slightly better than balance heuristic */
		float mis_weight = power_heuristic_3(pdf_N, pdf_T, pdf_B);

		/* real distance to sampled point */
		float r = len(sd->P - origP);

		/* evaluate */
		float w = (mis_weight * num_hits) / pdf_N;
		eval = subsurface_scatter_eval(sd, sc, disk_r, r, all) * w;
	}

	/* optionally blur colors and bump mapping */
	float3 N = sd->N;
	subsurface_color_bump_blur(kg, sd, sd, state_flag, &eval, &N);

	/* setup diffuse bsdf */
	subsurface_scatter_setup_diffuse_bsdf(sd, eval, (num_hits > 0), N);
}

CCL_NAMESPACE_END