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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
*/
#include "bssrdf.h"
#include "util_algorithm.h"
#include "util_math.h"
#include "util_types.h"
#include "kernel_types.h"
#include "kernel_montecarlo.h"
CCL_NAMESPACE_BEGIN
static float bssrdf_cubic(float ld, float r)
{
if(ld == 0.0f)
return (r == 0.0f)? 1.0f: 0.0f;
return powf(ld - min(r, ld), 3.0f) * 4.0f/powf(ld, 4.0f);
}
/* Cumulative density function utilities */
static float cdf_lookup_inverse(const vector<float>& table, float2 range, float x)
{
int index = upper_bound(table.begin(), table.end(), x) - table.begin();
if(index == 0)
return range[0];
else if(index == table.size())
return range[1];
else
index--;
float t = (x - table[index])/(table[index+1] - table[index]);
float y = ((index + t)/(table.size() - 1));
return y*(range[1] - range[0]) + range[0];
}
static void cdf_invert(vector<float>& to, float2 to_range, const vector<float>& from, float2 from_range)
{
float step = 1.0f/(float)(to.size() - 1);
for(int i = 0; i < to.size(); i++) {
float x = (i*step)*(from_range[1] - from_range[0]) + from_range[0];
to[i] = cdf_lookup_inverse(from, to_range, x);
}
}
/* BSSRDF */
static void bssrdf_lookup_table_create(float ld, vector<float>& sample_table, vector<float>& pdf_table)
{
const int size = BSSRDF_RADIUS_TABLE_SIZE;
vector<float> cdf(size);
vector<float> pdf(size);
float step = 1.0f/(float)(size - 1);
float max_radius = ld;
float pdf_sum = 0.0f;
/* compute the probability density function */
for(int i = 0; i < pdf.size(); i++) {
float x = (i*step)*max_radius;
pdf[i] = bssrdf_cubic(ld, x);
pdf_sum += pdf[i];
}
/* adjust for area covered by each distance */
for(int i = 0; i < pdf.size(); i++) {
float x = (i*step)*max_radius;
pdf[i] *= M_2PI_F*x;
}
/* normalize pdf, we multiply in reflectance later */
if(pdf_sum > 0.0f)
for(int i = 0; i < pdf.size(); i++)
pdf[i] /= pdf_sum;
/* sum to account for sampling which uses overlapping sphere */
for(int i = pdf.size() - 2; i >= 0; i--)
pdf[i] = pdf[i] + pdf[i+1];
/* compute the cumulative density function */
cdf[0] = 0.0f;
for(int i = 1; i < size; i++)
cdf[i] = cdf[i-1] + 0.5f*(pdf[i-1] + pdf[i])*step*max_radius;
/* invert cumulative density function for importance sampling */
float2 cdf_range = make_float2(0.0f, cdf[size - 1]);
float2 table_range = make_float2(0.0f, max_radius);
cdf_invert(sample_table, table_range, cdf, cdf_range);
/* copy pdf table */
for(int i = 0; i < pdf.size(); i++)
pdf_table[i] = pdf[i];
}
void bssrdf_table_build(vector<float>& table)
{
vector<float> sample_table(BSSRDF_RADIUS_TABLE_SIZE);
vector<float> pdf_table(BSSRDF_RADIUS_TABLE_SIZE);
table.resize(BSSRDF_LOOKUP_TABLE_SIZE);
/* create a 2D lookup table, for reflection x sample radius */
for(int i = 0; i < BSSRDF_REFL_TABLE_SIZE; i++) {
float radius = 1.0f;
bssrdf_lookup_table_create(radius, sample_table, pdf_table);
memcpy(&table[i*BSSRDF_RADIUS_TABLE_SIZE], &sample_table[0], BSSRDF_RADIUS_TABLE_SIZE*sizeof(float));
memcpy(&table[BSSRDF_PDF_TABLE_OFFSET + i*BSSRDF_RADIUS_TABLE_SIZE], &pdf_table[0], BSSRDF_RADIUS_TABLE_SIZE*sizeof(float));
}
}
CCL_NAMESPACE_END
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