/*
 * 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

/* BSSRDF using disk based importance sampling.
 *
 * BSSRDF Importance Sampling, SIGGRAPH 2013
 * http://library.imageworks.com/pdfs/imageworks-library-BSSRDF-sampling.pdf
 *
 */

/* 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_inline 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;

	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;
	sd->num_closure = 0;
	sd->num_closure_extra = 0;

	if(hit) {
		DiffuseBsdf *bsdf = (DiffuseBsdf*)bsdf_alloc(sd, sizeof(DiffuseBsdf), weight);

		if(bsdf) {
			bsdf->N = N;
			sd->flag |= bsdf_diffuse_setup(bsdf);

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

/* 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 *sd,
                                           PathState *state,
                                           int state_flag,
                                           float3 *eval,
                                           float3 *N)
{
	/* average color and texture blur at outgoing point */
	float texture_blur;
	float3 out_color = shader_bssrdf_sum(sd, NULL, &texture_blur);

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

	if(bump || texture_blur > 0.0f) {
		/* average color and normal at incoming point */
		shader_eval_surface(kg, sd, NULL, state, 0.0f, state_flag, SHADER_CONTEXT_SSS);
		float3 in_color = shader_bssrdf_sum(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_inline int subsurface_scatter_multi_intersect(
        KernelGlobals *kg,
        SubsurfaceIntersection *ss_isect,
        ShaderData *sd,
        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 = &ss_isect->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 */
	scene_intersect_subsurface(kg,
	                           ray,
	                           ss_isect,
	                           sd->object,
	                           lcg_state,
	                           BSSRDF_MAX_HITS);
	int num_eval_hits = min(ss_isect->num_hits, BSSRDF_MAX_HITS);

	for(int hit = 0; hit < num_eval_hits; hit++) {
		/* Quickly retrieve P and Ng without setting up ShaderData. */
		float3 hit_P;
		if(ccl_fetch(sd, type) & PRIMITIVE_TRIANGLE) {
			hit_P = triangle_refine_subsurface(kg,
			                                   sd,
			                                   &ss_isect->hits[hit],
			                                   ray);
		}
#ifdef __OBJECT_MOTION__
		else  if(ccl_fetch(sd, type) & PRIMITIVE_MOTION_TRIANGLE) {
			float3 verts[3];
			motion_triangle_vertices(
			        kg,
			        ccl_fetch(sd, object),
			        kernel_tex_fetch(__prim_index, ss_isect->hits[hit].prim),
			        ccl_fetch(sd, time),
			        verts);
			hit_P = motion_triangle_refine_subsurface(kg,
			                                          sd,
			                                          &ss_isect->hits[hit],
			                                          ray,
			                                          verts);
		}
#endif  /* __OBJECT_MOTION__ */
		else {
			ss_isect->weight[hit] = make_float3(0.0f, 0.0f, 0.0f);
			continue;
		}

		float3 hit_Ng = ss_isect->Ng[hit];
		if(ss_isect->hits[hit].object != OBJECT_NONE) {
			object_normal_transform(kg, sd, &hit_Ng);
		}

		/* probability densities for local frame axes */
		float pdf_N = pick_pdf_N * fabsf(dot(disk_N, hit_Ng));
		float pdf_T = pick_pdf_T * fabsf(dot(disk_T, hit_Ng));
		float pdf_B = pick_pdf_B * fabsf(dot(disk_B, hit_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(hit_P - sd->P);

		/* evaluate */
		float w = mis_weight / pdf_N;
		if(ss_isect->num_hits > BSSRDF_MAX_HITS)
			w *= ss_isect->num_hits/(float)BSSRDF_MAX_HITS;
		float3 eval = subsurface_scatter_eval(sd, sc, disk_r, r, all) * w;

		ss_isect->weight[hit] = eval;
	}

	return num_eval_hits;
}

ccl_device_noinline void subsurface_scatter_multi_setup(
        KernelGlobals *kg,
        SubsurfaceIntersection* ss_isect,
        int hit,
        ShaderData *sd,
        PathState *state,
        int state_flag,
        ShaderClosure *sc,
        bool all)
{
	/* Setup new shading point. */
	shader_setup_from_subsurface(kg, sd, &ss_isect->hits[hit], &ss_isect->ray);

	/* Optionally blur colors and bump mapping. */
	float3 weight = ss_isect->weight[hit];
	float3 N = sd->N;
	subsurface_color_bump_blur(kg, sd, state, state_flag, &weight, &N);

	/* Setup diffuse BSDF. */
	subsurface_scatter_setup_diffuse_bsdf(sd, weight, true, N);
}

/* 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, PathState *state,
	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);

	/* 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 */
	SubsurfaceIntersection ss_isect;
	scene_intersect_subsurface(kg, &ray, &ss_isect, sd->object, lcg_state, 1);

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

		/* setup new shading point */
		shader_setup_from_subsurface(kg, sd, &ss_isect.hits[0], &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 * ss_isect.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, state, state_flag, &eval, &N);

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

CCL_NAMESPACE_END

