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|
/*
* 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
typedef enum VolumeIntegrateResult {
VOLUME_PATH_SCATTERED = 0,
VOLUME_PATH_ATTENUATED = 1,
VOLUME_PATH_MISSED = 2
} VolumeIntegrateResult;
/* Volume shader properties
*
* extinction coefficient = absorption coefficient + scattering coefficient
* sigma_t = sigma_a + sigma_s */
typedef struct VolumeShaderCoefficients {
float3 sigma_a;
float3 sigma_s;
float3 emission;
} VolumeShaderCoefficients;
/* evaluate shader to get extinction coefficient at P */
ccl_device bool volume_shader_extinction_sample(KernelGlobals *kg, ShaderData *sd, PathState *state, float3 P, float3 *extinction)
{
sd->P = P;
shader_eval_volume(kg, sd, state->volume_stack, PATH_RAY_SHADOW, SHADER_CONTEXT_SHADOW);
if(!(sd->flag & (SD_ABSORPTION|SD_SCATTER)))
return false;
float3 sigma_t = make_float3(0.0f, 0.0f, 0.0f);
for(int i = 0; i < sd->num_closure; i++) {
const ShaderClosure *sc = &sd->closure[i];
if(CLOSURE_IS_VOLUME(sc->type))
sigma_t += sc->weight;
}
*extinction = sigma_t;
return true;
}
/* evaluate shader to get absorption, scattering and emission at P */
ccl_device bool volume_shader_sample(KernelGlobals *kg, ShaderData *sd, PathState *state, float3 P, VolumeShaderCoefficients *coeff)
{
sd->P = P;
shader_eval_volume(kg, sd, state->volume_stack, state->flag, SHADER_CONTEXT_VOLUME);
if(!(sd->flag & (SD_ABSORPTION|SD_SCATTER|SD_EMISSION)))
return false;
coeff->sigma_a = make_float3(0.0f, 0.0f, 0.0f);
coeff->sigma_s = make_float3(0.0f, 0.0f, 0.0f);
coeff->emission = make_float3(0.0f, 0.0f, 0.0f);
for(int i = 0; i < sd->num_closure; i++) {
const ShaderClosure *sc = &sd->closure[i];
if(sc->type == CLOSURE_VOLUME_ABSORPTION_ID)
coeff->sigma_a += sc->weight;
else if(sc->type == CLOSURE_EMISSION_ID)
coeff->emission += sc->weight;
else if(CLOSURE_IS_VOLUME(sc->type))
coeff->sigma_s += sc->weight;
}
/* when at the max number of bounces, treat scattering as absorption */
if(sd->flag & SD_SCATTER) {
if(state->volume_bounce >= kernel_data.integrator.max_volume_bounce) {
coeff->sigma_a += coeff->sigma_s;
coeff->sigma_s = make_float3(0.0f, 0.0f, 0.0f);
sd->flag &= ~SD_SCATTER;
sd->flag |= SD_ABSORPTION;
}
}
return true;
}
ccl_device float3 volume_color_attenuation(float3 sigma, float t)
{
return make_float3(expf(-sigma.x * t), expf(-sigma.y * t), expf(-sigma.z * t));
}
ccl_device bool volume_stack_is_heterogeneous(KernelGlobals *kg, VolumeStack *stack)
{
for(int i = 0; stack[i].shader != SHADER_NO_ID; i++) {
int shader_flag = kernel_tex_fetch(__shader_flag, (stack[i].shader & SHADER_MASK)*2);
if(shader_flag & SD_HETEROGENEOUS_VOLUME)
return true;
}
return false;
}
/* Volume Shadows
*
* These functions are used to attenuate shadow rays to lights. Both absorption
* and scattering will block light, represented by the extinction coefficient. */
/* homogeneous volume: assume shader evaluation at the starts gives
* the extinction coefficient for the entire line segment */
ccl_device void kernel_volume_shadow_homogeneous(KernelGlobals *kg, PathState *state, Ray *ray, ShaderData *sd, float3 *throughput)
{
float3 sigma_t;
if(volume_shader_extinction_sample(kg, sd, state, ray->P, &sigma_t))
*throughput *= volume_color_attenuation(sigma_t, ray->t);
}
/* heterogeneous volume: integrate stepping through the volume until we
* reach the end, get absorbed entirely, or run out of iterations */
ccl_device void kernel_volume_shadow_heterogeneous(KernelGlobals *kg, PathState *state, Ray *ray, ShaderData *sd, float3 *throughput)
{
float3 tp = *throughput;
const float tp_eps = 1e-10f; /* todo: this is likely not the right value */
/* prepare for stepping */
int max_steps = kernel_data.integrator.volume_max_steps;
float step = kernel_data.integrator.volume_step_size;
float random_jitter_offset = lcg_step_float(&state->rng_congruential) * step;
/* compute extinction at the start */
float t = 0.0f;
float3 P = ray->P;
float3 sigma_t;
if(!volume_shader_extinction_sample(kg, sd, state, P, &sigma_t))
sigma_t = make_float3(0.0f, 0.0f, 0.0f);
for(int i = 0; i < max_steps; i++) {
/* advance to new position */
float new_t = min(ray->t, t + random_jitter_offset + i * step);
float3 new_P = ray->P + ray->D * new_t;
float3 new_sigma_t;
/* compute attenuation over segment */
if(volume_shader_extinction_sample(kg, sd, state, new_P, &new_sigma_t)) {
/* todo: we could avoid computing expf() for each step by summing,
* because exp(a)*exp(b) = exp(a+b), but we still want a quick
* tp_eps check too */
tp *= volume_color_attenuation(0.5f*(sigma_t + new_sigma_t), new_t - t);
/* stop if nearly all light blocked */
if(tp.x < tp_eps && tp.y < tp_eps && tp.z < tp_eps)
break;
sigma_t = new_sigma_t;
}
else {
/* skip empty space */
sigma_t = make_float3(0.0f, 0.0f, 0.0f);
}
/* stop if at the end of the volume */
t = new_t;
if(t == ray->t)
break;
}
*throughput = tp;
}
/* get the volume attenuation over line segment defined by ray, with the
* assumption that there are no surfaces blocking light between the endpoints */
ccl_device_noinline void kernel_volume_shadow(KernelGlobals *kg, PathState *state, Ray *ray, float3 *throughput)
{
ShaderData sd;
shader_setup_from_volume(kg, &sd, ray, state->bounce);
if(volume_stack_is_heterogeneous(kg, state->volume_stack))
kernel_volume_shadow_heterogeneous(kg, state, ray, &sd, throughput);
else
kernel_volume_shadow_homogeneous(kg, state, ray, &sd, throughput);
}
/* Volume Path */
/* homogeneous volume: assume shader evaluation at the start gives
* the volume shading coefficient for the entire line segment */
ccl_device VolumeIntegrateResult kernel_volume_integrate_homogeneous(KernelGlobals *kg,
PathState *state, Ray *ray, ShaderData *sd, PathRadiance *L, float3 *throughput,
RNG *rng)
{
VolumeShaderCoefficients coeff;
if(!volume_shader_sample(kg, sd, state, ray->P, &coeff))
return VOLUME_PATH_MISSED;
int closure_flag = sd->flag;
float t = ray->t;
float3 new_tp;
float3 transmittance;
/* randomly scatter, and if we do t is shortened */
if(closure_flag & SD_SCATTER) {
float3 sigma_t = coeff.sigma_a + coeff.sigma_s;
/* set up variables for sampling */
float rphase = path_state_rng_1D(kg, rng, state, PRNG_PHASE);
int channel = (int)(rphase*3.0f);
sd->randb_closure = rphase*3.0f - channel;
/* pick random color channel, we use the Veach one-sample
* model with balance heuristic for the channels */
float sample_sigma_t;
if(channel == 0)
sample_sigma_t = sigma_t.x;
else if(channel == 1)
sample_sigma_t = sigma_t.y;
else
sample_sigma_t = sigma_t.z;
/* distance sampling */
if(kernel_data.integrator.volume_homogeneous_sampling == 0 || !kernel_data.integrator.num_all_lights) {
/* xi is [0, 1[ so log(0) should never happen, division by zero is
* avoided because sample_sigma_t > 0 when SD_SCATTER is set */
float xi = path_state_rng_1D(kg, rng, state, PRNG_SCATTER_DISTANCE);
float sample_t = min(t, -logf(1.0f - xi)/sample_sigma_t);
transmittance = volume_color_attenuation(sigma_t, sample_t);
if(sample_t < t) {
float pdf = dot(sigma_t, transmittance);
new_tp = *throughput * coeff.sigma_s * transmittance * (3.0f / pdf);
t = sample_t;
}
else {
float pdf = (transmittance.x + transmittance.y + transmittance.z);
new_tp = *throughput * transmittance * (3.0f / pdf);
}
}
/* equi-angular sampling */
else {
/* decide if we are going to scatter or not, based on sigma_t. this
* is not ideal, instead we should perhaps split the path here and
* do both, and at least add multiple importance sampling */
float xi = path_state_rng_1D(kg, rng, state, PRNG_SCATTER_DISTANCE);
float sample_transmittance = expf(-sample_sigma_t * t);
if(xi < sample_transmittance) {
/* no scattering */
transmittance = volume_color_attenuation(sigma_t, t);
float pdf = (transmittance.x + transmittance.y + transmittance.z);
new_tp = *throughput * transmittance * (3.0f / pdf);
}
else {
/* rescale random number so we can reuse it */
xi = (xi - sample_transmittance)/(1.0f - sample_transmittance);
/* equi-angular scattering somewhere on segment 0..t */
/* see "Importance Sampling Techniques for Path Tracing in Participating Media" */
/* light RNGs */
float light_t = path_state_rng_1D(kg, rng, state, PRNG_LIGHT);
float light_u, light_v;
path_state_rng_2D(kg, rng, state, PRNG_LIGHT_U, &light_u, &light_v);
/* light sample */
LightSample ls;
light_sample(kg, light_t, light_u, light_v, ray->time, ray->P, &ls);
if(ls.pdf == 0.0f)
return VOLUME_PATH_MISSED;
/* sampling */
float delta = dot((ls.P - ray->P) , ray->D);
float D = sqrtf(len_squared(ls.P - ray->P) - delta * delta);
float theta_a = -atan2f(delta, D);
float theta_b = atan2f(t - delta, D);
float t_ = D * tan((xi * theta_b) + (1 - xi) * theta_a);
float pdf = D / ((theta_b - theta_a) * (D * D + t_ * t_));
float sample_t = min(t, delta + t_);
transmittance = volume_color_attenuation(sigma_t, sample_t);
new_tp = *throughput * coeff.sigma_s * transmittance / ((1.0f - sample_transmittance) * pdf);
t = sample_t;
}
}
}
else if(closure_flag & SD_ABSORPTION) {
/* absorption only, no sampling needed */
transmittance = volume_color_attenuation(coeff.sigma_a, t);
new_tp = *throughput * transmittance;
}
/* integrate emission attenuated by extinction
* integral E * exp(-sigma_t * t) from 0 to t = E * (1 - exp(-sigma_t * t))/sigma_t
* this goes to E * t as sigma_t goes to zero
*
* todo: we should use an epsilon to avoid precision issues near zero sigma_t */
if(closure_flag & SD_EMISSION) {
float3 emission = coeff.emission;
if(closure_flag & SD_ABSORPTION) {
float3 sigma_t = coeff.sigma_a + coeff.sigma_s;
emission.x *= (sigma_t.x > 0.0f)? (1.0f - transmittance.x)/sigma_t.x: t;
emission.y *= (sigma_t.y > 0.0f)? (1.0f - transmittance.y)/sigma_t.y: t;
emission.z *= (sigma_t.z > 0.0f)? (1.0f - transmittance.z)/sigma_t.z: t;
}
else
emission *= t;
path_radiance_accum_emission(L, *throughput, emission, state->bounce);
}
/* modify throughput */
if(closure_flag & (SD_ABSORPTION|SD_SCATTER)) {
*throughput = new_tp;
/* prepare to scatter to new direction */
if(t < ray->t) {
/* adjust throughput and move to new location */
sd->P = ray->P + t*ray->D;
return VOLUME_PATH_SCATTERED;
}
}
return VOLUME_PATH_ATTENUATED;
}
/* heterogeneous volume: integrate stepping through the volume until we
* reach the end, get absorbed entirely, or run out of iterations */
ccl_device VolumeIntegrateResult kernel_volume_integrate_heterogeneous(KernelGlobals *kg,
PathState *state, Ray *ray, ShaderData *sd, PathRadiance *L, float3 *throughput, RNG *rng)
{
VolumeShaderCoefficients coeff;
float3 tp = *throughput;
const float tp_eps = 1e-10f; /* todo: this is likely not the right value */
/* prepare for stepping */
int max_steps = kernel_data.integrator.volume_max_steps;
float step = kernel_data.integrator.volume_step_size;
float random_jitter_offset = lcg_step_float(&state->rng_congruential) * step;
/* compute coefficients at the start */
float t = 0.0f;
float3 P = ray->P;
if(!volume_shader_sample(kg, sd, state, P, &coeff)) {
coeff.sigma_a = make_float3(0.0f, 0.0f, 0.0f);
coeff.sigma_s = make_float3(0.0f, 0.0f, 0.0f);
coeff.emission = make_float3(0.0f, 0.0f, 0.0f);
}
/* accumulate these values so we can use a single stratified number to sample */
float3 accum_transmittance = make_float3(1.0f, 1.0f, 1.0f);
float3 accum_sigma_t = make_float3(0.0f, 0.0f, 0.0f);
float3 accum_sigma_s = make_float3(0.0f, 0.0f, 0.0f);
/* cache some constant variables */
float nlogxi;
int channel = -1;
bool has_scatter = false;
for(int i = 0; i < max_steps; i++) {
/* advance to new position */
float new_t = min(ray->t, t + random_jitter_offset + i * step);
float3 new_P = ray->P + ray->D * new_t;
VolumeShaderCoefficients new_coeff;
/* compute segment */
if(volume_shader_sample(kg, sd, state, new_P, &new_coeff)) {
int closure_flag = sd->flag;
float dt = new_t - t;
float3 new_tp;
float3 transmittance;
bool scatter = false;
/* randomly scatter, and if we do dt and new_t are shortened */
if((closure_flag & SD_SCATTER) || (has_scatter && (closure_flag & SD_ABSORPTION))) {
has_scatter = true;
/* average sigma_t and sigma_s over segment */
float3 last_sigma_t = coeff.sigma_a + coeff.sigma_s;
float3 new_sigma_t = new_coeff.sigma_a + new_coeff.sigma_s;
float3 sigma_t = 0.5f*(last_sigma_t + new_sigma_t);
float3 sigma_s = 0.5f*(coeff.sigma_s + new_coeff.sigma_s);
/* lazily set up variables for sampling */
if(channel == -1) {
float xi = path_state_rng_1D(kg, rng, state, PRNG_SCATTER_DISTANCE);
nlogxi = -logf(1.0f - xi);
float rphase = path_state_rng_1D(kg, rng, state, PRNG_PHASE);
channel = (int)(rphase*3.0f);
sd->randb_closure = rphase*3.0f - channel;
}
/* pick random color channel, we use the Veach one-sample
* model with balance heuristic for the channels */
float sample_sigma_t;
if(channel == 0)
sample_sigma_t = accum_sigma_t.x + dt*sigma_t.x;
else if(channel == 1)
sample_sigma_t = accum_sigma_t.y + dt*sigma_t.y;
else
sample_sigma_t = accum_sigma_t.z + dt*sigma_t.z;
if(nlogxi < sample_sigma_t) {
/* compute sampling distance */
sample_sigma_t /= new_t;
new_t = nlogxi/sample_sigma_t;
dt = new_t - t;
transmittance = volume_color_attenuation(sigma_t, dt);
accum_transmittance *= transmittance;
accum_sigma_t = (accum_sigma_t + dt*sigma_t)/new_t;
accum_sigma_s = (accum_sigma_s + dt*sigma_s)/new_t;
/* todo: it's not clear to me that this is correct if we move
* through a color volume, needs verification */
float pdf = dot(accum_sigma_t, accum_transmittance);
new_tp = tp * accum_sigma_s * transmittance * (3.0f / pdf);
scatter = true;
}
else {
transmittance = volume_color_attenuation(sigma_t, dt);
accum_transmittance *= transmittance;
accum_sigma_t += dt*sigma_t;
accum_sigma_s += dt*sigma_s;
new_tp = tp * transmittance;
}
}
else if(closure_flag & SD_ABSORPTION) {
/* absorption only, no sampling needed */
float3 sigma_a = 0.5f*(coeff.sigma_a + new_coeff.sigma_a);
transmittance = volume_color_attenuation(sigma_a, dt);
accum_transmittance *= transmittance;
accum_sigma_t += dt*sigma_a;
new_tp = tp * transmittance;
/* todo: we could avoid computing expf() for each step by summing,
* because exp(a)*exp(b) = exp(a+b), but we still want a quick
* tp_eps check too */
}
/* integrate emission attenuated by absorption
* integral E * exp(-sigma_t * t) from 0 to t = E * (1 - exp(-sigma_t * t))/sigma_t
* this goes to E * t as sigma_t goes to zero
*
* todo: we should use an epsilon to avoid precision issues near zero sigma_t */
if(closure_flag & SD_EMISSION) {
float3 emission = 0.5f*(coeff.emission + new_coeff.emission);
if(closure_flag & SD_ABSORPTION) {
float3 sigma_t = 0.5f*(coeff.sigma_a + coeff.sigma_s + new_coeff.sigma_a + new_coeff.sigma_s);
emission.x *= (sigma_t.x > 0.0f)? (1.0f - transmittance.x)/sigma_t.x: dt;
emission.y *= (sigma_t.y > 0.0f)? (1.0f - transmittance.y)/sigma_t.y: dt;
emission.z *= (sigma_t.z > 0.0f)? (1.0f - transmittance.z)/sigma_t.z: dt;
}
else
emission *= dt;
path_radiance_accum_emission(L, tp, emission, state->bounce);
}
/* modify throughput */
if(closure_flag & (SD_ABSORPTION|SD_SCATTER)) {
tp = new_tp;
/* stop if nearly all light blocked */
if(tp.x < tp_eps && tp.y < tp_eps && tp.z < tp_eps) {
tp = make_float3(0.0f, 0.0f, 0.0f);
break;
}
/* prepare to scatter to new direction */
if(scatter) {
/* adjust throughput and move to new location */
sd->P = ray->P + new_t*ray->D;
*throughput = tp;
return VOLUME_PATH_SCATTERED;
}
}
coeff = new_coeff;
}
else {
/* skip empty space */
coeff.sigma_a = make_float3(0.0f, 0.0f, 0.0f);
coeff.sigma_s = make_float3(0.0f, 0.0f, 0.0f);
coeff.emission = make_float3(0.0f, 0.0f, 0.0f);
}
/* stop if at the end of the volume */
t = new_t;
if(t == ray->t)
break;
}
/* include pdf for volumes with scattering */
if(has_scatter) {
float pdf = (accum_transmittance.x + accum_transmittance.y + accum_transmittance.z);
if(pdf > 0.0f)
tp *= (3.0f/pdf);
}
*throughput = tp;
return VOLUME_PATH_ATTENUATED;
}
/* get the volume attenuation and emission over line segment defined by
* ray, with the assumption that there are no surfaces blocking light
* between the endpoints */
ccl_device_noinline VolumeIntegrateResult kernel_volume_integrate(KernelGlobals *kg,
PathState *state, ShaderData *sd, Ray *ray, PathRadiance *L, float3 *throughput, RNG *rng)
{
/* workaround to fix correlation bug in T38710, can find better solution
* in random number generator later, for now this is done here to not impact
* performance of rendering without volumes */
RNG tmp_rng = cmj_hash(*rng, state->rng_offset);
shader_setup_from_volume(kg, sd, ray, state->bounce);
if(volume_stack_is_heterogeneous(kg, state->volume_stack))
return kernel_volume_integrate_heterogeneous(kg, state, ray, sd, L, throughput, &tmp_rng);
else
return kernel_volume_integrate_homogeneous(kg, state, ray, sd, L, throughput, &tmp_rng);
}
/* Volume Stack
*
* This is an array of object/shared ID's that the current segment of the path
* is inside of. */
ccl_device void kernel_volume_stack_init(KernelGlobals *kg, VolumeStack *stack)
{
/* todo: this assumes camera is always in air, need to detect when it isn't */
if(kernel_data.background.volume_shader == SHADER_NO_ID) {
stack[0].shader = SHADER_NO_ID;
}
else {
stack[0].shader = kernel_data.background.volume_shader;
stack[0].object = ~0;
stack[1].shader = SHADER_NO_ID;
}
}
ccl_device void kernel_volume_stack_enter_exit(KernelGlobals *kg, ShaderData *sd, VolumeStack *stack)
{
/* todo: we should have some way for objects to indicate if they want the
* world shader to work inside them. excluding it by default is problematic
* because non-volume objects can't be assumed to be closed manifolds */
if(!(sd->flag & SD_HAS_VOLUME))
return;
if(sd->flag & SD_BACKFACING) {
/* exit volume object: remove from stack */
for(int i = 0; stack[i].shader != SHADER_NO_ID; i++) {
if(stack[i].object == sd->object) {
/* shift back next stack entries */
do {
stack[i] = stack[i+1];
i++;
}
while(stack[i].shader != SHADER_NO_ID);
return;
}
}
}
else {
/* enter volume object: add to stack */
int i;
for(i = 0; stack[i].shader != SHADER_NO_ID; i++) {
/* already in the stack? then we have nothing to do */
if(stack[i].object == sd->object)
return;
}
/* if we exceed the stack limit, ignore */
if(i >= VOLUME_STACK_SIZE-1)
return;
/* add to the end of the stack */
stack[i].shader = sd->shader;
stack[i].object = sd->object;
stack[i+1].shader = SHADER_NO_ID;
}
}
CCL_NAMESPACE_END
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