chi-square test on the sphere, improved microflake code
Wenzel Jakob
parent
9aa5c13daa
commit
d3ad21f0da
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@ -0,0 +1,278 @@
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/*
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This file is part of Mitsuba, a physically based rendering system.
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Copyright (c) 2007-2010 by Wenzel Jakob and others.
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Mitsuba is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License Version 3
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as published by the Free Software Foundation.
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Mitsuba is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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#if !defined(__CHI_SQUARE_TEST_H)
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#define __CHI_SQUARE_TEST_H
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#include <mitsuba/core/fresolver.h>
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#include <mitsuba/core/quad.h>
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#include <mitsuba/core/timer.h>
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#include <mitsuba/core/random.h>
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#include <boost/bind.hpp>
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#include <boost/math/distributions/chi_squared.hpp>
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MTS_NAMESPACE_BEGIN
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/**
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* \brief Chi-square goodness-of-fit test on the sphere
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*
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* This class performs a chi-square goodness-of-fit test of the null hypothesis
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* that a specified sampling procedure produces samples that are distributed
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* according to a supplied density function. This is very useful to verify BRDF
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* and phase function sampling codes for their correctness.
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*
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* This implementation works by generating a large batch of samples, which are
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* then accumulated into rectangular bins in spherical coordinates. To obtain
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* reference bin counts, the provided density function is numerically
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* integrated over the area of each bin. Comparing the actual and reference
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* bin counts yields the desired test statistic.
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*
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* Given a BSDF/phase function with the following interface
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* <code>
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* class MyDistribution {
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* Vector sample(const Point2 &uniformSample) const;
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* Float pdf(const Vector &direction) const;
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* };
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* </code>
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*
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* the code in this class might be used as follows
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*
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* <code>
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* MyDistribution myDistrInstance;
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* ChiSquareTest chiSqr;
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*
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* // Initialize the tables used by the chi-square test
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* chiSqr.fill(
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* boost::bind(&MyDistribution::sample, myDistrInstance, _1),
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* boost::bind(&MyDistribution::pdf, myDistrInstance, _1)
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* );
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*
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* // Optional: dump the tables to a MATLAB file for external analysis
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* chiSqr.dumpTables("debug.m");
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*
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* // (the folowing assumes that the distribution has 1 parameter, e.g. exponent value)
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* if (!chiSqr.runTest(1))
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* Log(EError, "Uh oh -- test failed, the implementation is probably incorrect!");
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* </code>
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*/
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class ChiSquareTest {
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public:
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/**
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* \brief Create a new Chi-square test instance with the given
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* resolution and sample count
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*
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* \param thetaBins
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* Number of bins wrt. latitude. The default is 10
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*
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* \param phiBins
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* Number of bins wrt. azimuth. The default is to use
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* twice the number of \c thetaBins
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*
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* \param sampleCount
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* Number of samples to be used when computing the bin
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* values. The default is \c thetaBins*phiBins*1000
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*/
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ChiSquareTest(int thetaBins = 10, int phiBins = 0, size_t sampleCount = 0)
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: m_thetaBins(thetaBins), m_phiBins(phiBins), m_sampleCount(sampleCount) {
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if (m_phiBins == 0)
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m_phiBins = 2*m_thetaBins;
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if (m_sampleCount == 0)
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m_sampleCount = m_thetaBins * m_phiBins * 1000;
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m_table = new uint32_t[m_thetaBins*m_phiBins];
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m_refTable = new Float[m_thetaBins*m_phiBins];
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}
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/// Release all memory
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~ChiSquareTest() {
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delete[] m_table;
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delete[] m_refTable;
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}
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/**
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* \brief Fill the actual and reference bin counts
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*
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* Please see the class documentation for a description
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* on how to invoke this function
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*/
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void fill(
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const boost::function<Vector (const Point2 &)> &sampleFn,
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const boost::function<Float (const Vector &)> &pdfFn) {
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ref<Random> random = new Random();
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memset(m_table, 0, m_thetaBins*m_phiBins*sizeof(uint32_t));
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SLog(EInfo, "Accumulating " SIZE_T_FMT " samples into a %ix%i"
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" contingency table", m_sampleCount, m_thetaBins, m_phiBins);
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Point2 factor(m_thetaBins / M_PI, m_phiBins / (2*M_PI));
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ref<Timer> timer = new Timer();
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for (size_t i=0; i<m_sampleCount; ++i) {
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Point2 sample(random->nextFloat(), random->nextFloat());
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Point2 sphCoords = toSphericalCoordinates(sampleFn(sample));
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int thetaBin = std::min(std::max(0,
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floorToInt(sphCoords.x * factor.x)), m_thetaBins-1);
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int phiBin = std::min(std::max(0,
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floorToInt(sphCoords.y * factor.y)), m_phiBins-1);
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++m_table[thetaBin * m_phiBins + phiBin];
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}
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SLog(EInfo, "Done, took %i ms.", timer->getMilliseconds());
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factor = Point2(M_PI / m_thetaBins, (2*M_PI) / m_phiBins);
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SLog(EInfo, "Integrating reference contingency table");
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timer->reset();
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Float min[2], max[2];
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size_t idx = 0;
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NDIntegrator integrator(1, 2, 50000, 0, 1e-6f);
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Float maxError = 0, integral = 0;
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for (int i=0; i<m_thetaBins; ++i) {
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min[0] = i * factor.x;
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max[0] = (i+1) * factor.x;
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for (int j=0; j<m_phiBins; ++j) {
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min[1] = j * factor.y;
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max[1] = (j+1) * factor.y;
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Float result, error;
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size_t evals;
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integrator.integrateVectorized(
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boost::bind(&ChiSquareTest::integrand, pdfFn, _1, _2, _3),
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min, max, &result, &error, evals
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);
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integral += result;
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m_refTable[idx++] = result * m_sampleCount;
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maxError = std::max(maxError, error);
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}
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}
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SLog(EInfo, "Done, took %i ms (max error = %f, integral=%f).",
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timer->getMilliseconds(), maxError, integral);
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}
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/**
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* \brief Dump the bin counts to a file using MATLAB format
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*/
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void dumpTables(const fs::path &filename) {
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fs::ofstream out(filename);
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out << "tbl_counts = [ ";
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for (int i=0; i<m_thetaBins; ++i) {
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for (int j=0; j<m_phiBins; ++j) {
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out << m_table[i*m_phiBins+j];
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if (j+1 < m_phiBins)
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out << ", ";
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}
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if (i+1 < m_thetaBins)
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out << "; ";
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}
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out << " ];" << endl
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<< "tbl_ref = [ ";
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for (int i=0; i<m_thetaBins; ++i) {
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for (int j=0; j<m_phiBins; ++j) {
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out << m_refTable[i*m_phiBins+j];
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if (j+1 < m_phiBins)
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out << ", ";
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}
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if (i+1 < m_thetaBins)
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out << "; ";
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}
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out << " ];" << endl;
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out.close();
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}
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/**
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* \brief Perform the actual chi-square test
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*
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* \param distParams
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* Number of parameters of the distribution in question.
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* Anything such as lobe width, indices of refraction, etc.
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* should be counted.
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*
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* \param pvalThresh
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* The implementation will reject the null hypothesis
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* when the computed p-value lies below this parameter
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* (default: 0.01f)
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*
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* \return \c false if the null hypothesis was rejected
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* and \c true otherwise.
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*/
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bool runTest(int distParams, Float pvalThresh = 0.01f) {
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/* Compute the chi-square statistic */
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Float chsq = 0.0f;
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Float pooledCounts = 0, pooledRef = 0;
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int pooledCells = 0;
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int df = 0;
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for (int i=0; i<m_thetaBins*m_phiBins; ++i) {
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if (m_refTable[i] < 5) {
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pooledCounts += m_table[i];
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pooledRef += m_refTable[i];
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++pooledCells;
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} else {
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Float diff = m_table[i]-m_refTable[i];
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chsq += (diff*diff) / m_refTable[i];
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++df;
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}
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}
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if (pooledCells > 0) {
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SLog(EInfo, "Pooled %i cells with an expected "
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"number of < 5 entries!", pooledCells);
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if (pooledRef < 5) {
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SLog(EWarn, "Even after pooling, the expected "
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"number of entries is < 5 (%f), expect badness!",
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pooledRef);
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}
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Float diff = pooledCounts - pooledRef;
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chsq += (diff*diff) / pooledRef;
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++df;
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}
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df -= distParams + 1;
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SLog(EInfo, "Chi-square statistic = %e (df=%i)", chsq, df);
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boost::math::chi_squared chSqDist(df);
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/* Probability of obtaining a test statistic at least
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as extreme as the one observed under the assumption
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that the distributions match */
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Float pval = 1 - boost::math::cdf(chSqDist, chsq);
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SLog(EInfo, "P-value = %e", pval);
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if (pval < pvalThresh) {
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SLog(EWarn, "Rejecting the null hypothesis");
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return false;
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}
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return true;
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}
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protected:
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static void integrand(
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const boost::function<Float (const Vector &)> &pdfFn,
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size_t nPts, const Float *in, Float *out) {
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#pragma omp parallel for
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for (size_t i=0; i<nPts; ++i)
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out[i] = pdfFn(sphericalDirection(in[2*i], in[2*i+1])) * std::sin(in[2*i]);
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}
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private:
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int m_thetaBins, m_phiBins;
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size_t m_sampleCount;
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uint32_t *m_table;
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Float *m_refTable;
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};
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MTS_NAMESPACE_END
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#endif /* __CHI_SQUARE_TEST_H */
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@ -88,76 +88,8 @@ namespace std {
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};
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using std::select2nd;
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using std::compose1;
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#endif
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/* Forward declarations */
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MTS_NAMESPACE_BEGIN
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extern MTS_EXPORT_CORE void * __restrict allocAligned(size_t size);
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extern MTS_EXPORT_CORE void freeAligned(void *ptr);
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/**
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* \brief Aligned memory allocator for use with SSE2-based code
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* \headerfile mitsuba/core/stl.h mitsuba/mitsuba.h
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*
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* Basic implementaiton, which forwards all calls to \ref allocAligned.
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*/
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template <typename T> class aligned_allocator {
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public:
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typedef size_t size_type;
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typedef ptrdiff_t difference_type;
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typedef T* pointer;
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typedef const T* const_pointer;
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typedef T& reference;
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typedef const T& const_reference;
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typedef T value_type;
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/// \cond
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template <class U> struct rebind {
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typedef aligned_allocator<U> other;
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};
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/// \endcond
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pointer address (reference value) const {
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return &value;
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}
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const_pointer address (const_reference value) const {
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return &value;
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}
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aligned_allocator() throw() { }
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aligned_allocator(const aligned_allocator&) throw() { }
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template <class U> aligned_allocator (const aligned_allocator<U>&) throw() { }
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~aligned_allocator() throw() { }
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size_type max_size () const throw() {
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return INT_MAX;
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}
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T* __restrict allocate (size_type num, const_pointer *hint = 0) {
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return (T *) mitsuba::allocAligned(num*sizeof(T));
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}
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void construct (pointer p, const T& value) {
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*p=value;
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}
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void destroy (pointer p) {
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p->~T();
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};
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void deallocate (pointer p, size_type num) {
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freeAligned(p);
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}
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};
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MTS_NAMESPACE_END
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#if defined(WIN32)
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inline bool mts_isnan(float f) {
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int classification = ::_fpclass(f);
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@ -616,10 +616,13 @@ Point2 squareToTriangle(const Point2 &sample) {
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}
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Point2 toSphericalCoordinates(const Vector &v) {
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return Point2(
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Point2 result(
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std::acos(v.z),
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std::atan2(v.y, v.x)
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);
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if (result.y < 0)
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result.y += 2*M_PI;
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return result;
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}
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Point2 squareToDiskConcentric(const Point2 &sample) {
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@ -1,736 +0,0 @@
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/*
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This file is part of Mitsuba, a physically based rendering system.
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Copyright (c) 2007-2010 by Wenzel Jakob and others.
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Mitsuba is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License Version 3
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as published by the Free Software Foundation.
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Mitsuba is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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#include <mitsuba/render/scene.h>
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#include <mitsuba/render/volume.h>
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#include <mitsuba/core/fstream.h>
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#include <mitsuba/core/brent.h>
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#include <mitsuba/core/shvector4d.h>
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#include <mitsuba/core/statistics.h>
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#include <fstream>
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/*
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* When inverting an integral of the form f(t):=\int_0^t [...] dt
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* using composite Simpson's rule quadrature, the following constant
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* specified how many times the step size will be reduced when we
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* have almost reached the desired value.
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*/
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#define NUM_REFINES 8
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/**
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* Allow to stop integrating densities when the resulting segment
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* has a throughput of less than 'Epsilon'
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*/
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#define HET_EARLY_EXIT 1
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/// Header identification record for phase function caches
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#define PHASE_FUNCTION_HEADER 0x40044004
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#define USE_REJECTION_SAMPLING 1
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#define USE_COSTHETA_DISTR 1
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MTS_NAMESPACE_BEGIN
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static StatsCounter totalSamples("Micro-flake model", "Sample generations");
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static StatsCounter avgSampleIterations("Micro-flake model", "Average rejection sampling iterations", EAverage);
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static StatsCounter brentSolves("Micro-flake model", "Brent solver calls");
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static StatsCounter avgBrentFunEvals("Micro-flake model", "Average Brent solver function evaluations", EAverage);
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struct AbsCos {
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Float operator()(const Vector &w) const { return std::abs(w.z); }
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};
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#define USE_COSTHETA_DISTR 1
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enum EMode {
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ESinP = 0,
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ECosP
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};
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struct FlakeDistr {
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Float exp;
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EMode mode;
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FlakeDistr() { }
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FlakeDistr(EMode mode, Float exp) : exp(exp), mode(mode) { }
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inline Float operator()(const Vector &w) const {
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switch (mode) {
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case ESinP:
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return std::pow(1-std::pow(w.z, 2), exp/2.0f);
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case ECosP:
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return std::pow(std::abs(w.z), exp);
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default:
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SLog(EError, "Invalid flake distribution!");
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return 0.0f;
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}
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}
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};
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template <typename Distr> struct FlakePhaseFunctor {
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Distr d;
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FlakePhaseFunctor(Distr d) : d(d) { }
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inline Float operator()(const Vector &wi, const Vector &wo) const {
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Vector H = normalize(wi + wo);
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return d(H) + d(-H);
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}
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};
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class HeterogeneousFlakeMedium;
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class FlakePhaseFunction : public PhaseFunction {
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public:
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FlakePhaseFunction(const SHVector &sigmaT, int samplingRecursions, const SHVector4D *phaseExpansion,
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Float exponent, Float normalization, EMode mode, HeterogeneousFlakeMedium *medium) : PhaseFunction(Properties()),
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m_sigmaT(sigmaT), m_samplingRecursions(samplingRecursions), m_distr(mode, exponent), m_phaseExpansion(phaseExpansion),
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m_exponent(exponent), m_normalization(normalization), m_mode(mode), m_medium(medium) {
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||||
initialize();
|
||||
}
|
||||
|
||||
FlakePhaseFunction(Stream *stream, InstanceManager *manager) :
|
||||
PhaseFunction(stream, manager) {
|
||||
/* Not implemented */
|
||||
}
|
||||
|
||||
void serialize(Stream *stream, InstanceManager *manager) const {
|
||||
PhaseFunction::serialize(stream, manager);
|
||||
/* Not implemented */
|
||||
}
|
||||
|
||||
void initialize() {
|
||||
m_shSampler = new SHSampler(m_phaseExpansion->getBands(), m_samplingRecursions);
|
||||
Log(EInfo, "Constructing a SH sampler: %s", m_shSampler->toString().c_str());
|
||||
}
|
||||
|
||||
virtual ~FlakePhaseFunction() { }
|
||||
|
||||
/* Implementations are below */
|
||||
Spectrum f(const PhaseFunctionQueryRecord &pRec) const;
|
||||
|
||||
Spectrum sample(PhaseFunctionQueryRecord &pRec,
|
||||
Float &pdf, Sampler *sampler) const;
|
||||
|
||||
Spectrum sample(PhaseFunctionQueryRecord &pRec,
|
||||
Sampler *sampler) const;
|
||||
|
||||
Float pdf(const PhaseFunctionQueryRecord &pRec) const;
|
||||
|
||||
std::string toString() const {
|
||||
return "FlakePhaseFunction[]";
|
||||
}
|
||||
|
||||
MTS_DECLARE_CLASS()
|
||||
private:
|
||||
SHVector m_sigmaT;
|
||||
ref<SHSampler> m_shSampler;
|
||||
int m_samplingRecursions;
|
||||
FlakeDistr m_distr;
|
||||
const SHVector4D *m_phaseExpansion;
|
||||
mutable PrimitiveThreadLocal<SHVector> m_temp;
|
||||
Float m_exponent;
|
||||
Float m_normalization;
|
||||
EMode m_mode;
|
||||
const HeterogeneousFlakeMedium *m_medium;
|
||||
};
|
||||
|
||||
class HeterogeneousFlakeMedium : public Medium {
|
||||
public:
|
||||
HeterogeneousFlakeMedium(const Properties &props)
|
||||
: Medium(props) {
|
||||
m_stepSize = props.getFloat("stepSize", 0);
|
||||
|
||||
/* Flake model configuration */
|
||||
int bands = props.getInteger("bands", 7);
|
||||
int phaseBands = props.getInteger("phaseBands", bands);
|
||||
Assert(bands > 0 && phaseBands > 0);
|
||||
|
||||
m_samplingRecursions = props.getInteger("samplingRecursions", 10);
|
||||
std::string mode = props.getString("mode", "sinp");
|
||||
|
||||
if (mode == "sinp") {
|
||||
m_mode = ESinP;
|
||||
} else if (mode == "cosp") {
|
||||
m_mode = ECosP;
|
||||
} else {
|
||||
Log(EError, "Unknown mode: %s!", mode.c_str());
|
||||
}
|
||||
|
||||
const int numSamples = 80;
|
||||
ref<FileStream> stream;
|
||||
|
||||
SHVector absCos = SHVector(bands);
|
||||
absCos.project(AbsCos(), numSamples);
|
||||
Float absCosError = absCos.l2Error(AbsCos(), numSamples);
|
||||
|
||||
m_exponent = props.getFloat("exponent", 4);
|
||||
FlakeDistr distrFunc(m_mode, m_exponent);
|
||||
|
||||
m_D = SHVector(bands);
|
||||
m_D.project(distrFunc, numSamples);
|
||||
m_normalization = 1 / (m_D(0, 0) * 2 * std::sqrt(M_PI));
|
||||
Float dError = m_D.l2Error(distrFunc, numSamples);
|
||||
m_D.normalize();
|
||||
|
||||
Log(EInfo, "======= Flake medium properties =======");
|
||||
Log(EInfo, " distribution type = %s", mode.c_str());
|
||||
Log(EInfo, " distribution exponent = %f", m_exponent);
|
||||
Log(EInfo, " SH bands (D, sigmaT) = %i", bands);
|
||||
Log(EInfo, " SH bands (phase fct) = %i", phaseBands);
|
||||
Log(EInfo, " |cos| projection error = %f", absCosError);
|
||||
Log(EInfo, " D projection error = %f", dError);
|
||||
Log(EInfo, " sampling recursions = %i", m_samplingRecursions);
|
||||
|
||||
bool computePhaseProjection = true;
|
||||
if (fs::exists("flake-phase.dat")) {
|
||||
/* Avoid recomputing this every time */
|
||||
stream = new FileStream("flake-phase.dat", FileStream::EReadOnly);
|
||||
unsigned int header = stream->readUInt();
|
||||
int nBands = stream->readInt();
|
||||
int mode = stream->readInt();
|
||||
Float exponent = stream->readFloat();
|
||||
if (header == PHASE_FUNCTION_HEADER && nBands == phaseBands
|
||||
&& exponent == m_exponent && mode == m_mode) {
|
||||
m_phaseExpansion = SHVector4D(stream);
|
||||
computePhaseProjection = false;
|
||||
}
|
||||
stream->close();
|
||||
}
|
||||
|
||||
if (computePhaseProjection) {
|
||||
int res = 50;
|
||||
FlakePhaseFunctor<FlakeDistr> phaseFunctor(distrFunc);
|
||||
m_phaseExpansion = SHVector4D(res, 2*res, phaseBands);
|
||||
Log(EDebug, "Phase function parameterization: %s", m_phaseExpansion.toString().c_str());
|
||||
m_phaseExpansion.project(phaseFunctor, numSamples);
|
||||
m_phaseExpansion.normalize();
|
||||
stream = new FileStream("flake-phase.dat", FileStream::ETruncReadWrite);
|
||||
stream->writeInt(PHASE_FUNCTION_HEADER);
|
||||
stream->writeInt(phaseBands);
|
||||
stream->writeInt(m_mode);
|
||||
stream->writeFloat(m_exponent);
|
||||
m_phaseExpansion.serialize(stream);
|
||||
stream->close();
|
||||
}
|
||||
|
||||
for (int i=0; i<phaseBands; ++i)
|
||||
Log(EInfo, "Energy in phase function band %i: %f", i, m_phaseExpansion.energy(i));
|
||||
|
||||
/* Compute sigma_t except for the a*rho factor */
|
||||
m_sigmaT = SHVector(m_D);
|
||||
m_sigmaT.convolve(absCos);
|
||||
Assert(m_sigmaT.isAzimuthallyInvariant());
|
||||
m_kdTree = new ShapeKDTree();
|
||||
}
|
||||
|
||||
/* Unserialize from a binary data stream */
|
||||
HeterogeneousFlakeMedium(Stream *stream, InstanceManager *manager)
|
||||
: Medium(stream, manager) {
|
||||
m_kdTree = new ShapeKDTree();
|
||||
size_t shapeCount = stream->readUInt();
|
||||
for (size_t i=0; i<shapeCount; ++i)
|
||||
addChild("", static_cast<Shape *>(manager->getInstance(stream)));
|
||||
m_densities = static_cast<VolumeDataSource *>(manager->getInstance(stream));
|
||||
m_albedo = static_cast<VolumeDataSource *>(manager->getInstance(stream));
|
||||
m_orientations = static_cast<VolumeDataSource *>(manager->getInstance(stream));
|
||||
m_stepSize = stream->readFloat();
|
||||
m_exponent = stream->readFloat();
|
||||
m_normalization = stream->readFloat();
|
||||
m_mode = (EMode) stream->readInt();
|
||||
m_D = SHVector(stream);
|
||||
m_sigmaT = SHVector(stream);
|
||||
m_phaseExpansion = SHVector4D(stream);
|
||||
m_samplingRecursions = stream->readInt();
|
||||
configure();
|
||||
}
|
||||
|
||||
virtual ~HeterogeneousFlakeMedium() {
|
||||
for (size_t i=0; i<m_shapes.size(); ++i)
|
||||
m_shapes[i]->decRef();
|
||||
}
|
||||
|
||||
/* Serialize the volume to a binary data stream */
|
||||
void serialize(Stream *stream, InstanceManager *manager) const {
|
||||
Medium::serialize(stream, manager);
|
||||
stream->writeUInt((uint32_t) m_shapes.size());
|
||||
for (size_t i=0; i<m_shapes.size(); ++i)
|
||||
manager->serialize(stream, m_shapes[i]);
|
||||
manager->serialize(stream, m_densities.get());
|
||||
manager->serialize(stream, m_albedo.get());
|
||||
manager->serialize(stream, m_orientations.get());
|
||||
stream->writeFloat(m_stepSize);
|
||||
stream->writeFloat(m_exponent);
|
||||
stream->writeFloat(m_normalization);
|
||||
stream->writeInt(m_mode);
|
||||
m_D.serialize(stream);
|
||||
m_sigmaT.serialize(stream);
|
||||
m_phaseExpansion.serialize(stream);
|
||||
stream->writeInt(m_samplingRecursions);
|
||||
}
|
||||
|
||||
void configure() {
|
||||
Medium::configure();
|
||||
if (m_densities.get() == NULL)
|
||||
Log(EError, "No densities specified!");
|
||||
if (m_albedo.get() == NULL)
|
||||
Log(EError, "No albedo specified!");
|
||||
if (m_orientations.get() == NULL)
|
||||
Log(EError, "No orientations specified!");
|
||||
|
||||
if (m_stepSize == 0) {
|
||||
m_stepSize = std::min(std::min(
|
||||
m_densities->getStepSize(),
|
||||
m_albedo->getStepSize()),
|
||||
m_orientations->getStepSize());
|
||||
|
||||
if (m_stepSize == std::numeric_limits<Float>::infinity())
|
||||
Log(EError, "Unable to infer step size, please specify!");
|
||||
}
|
||||
|
||||
m_phaseFunction = new FlakePhaseFunction(m_sigmaT, m_samplingRecursions,
|
||||
&m_phaseExpansion, m_exponent, m_normalization, m_mode, this);
|
||||
|
||||
if (m_shapes.size() > 0) {
|
||||
m_kdTree->build();
|
||||
m_aabb = m_kdTree->getAABB();
|
||||
} else {
|
||||
m_aabb = m_densities->getAABB();
|
||||
}
|
||||
}
|
||||
|
||||
void setParent(ConfigurableObject *parent) {
|
||||
if (parent->getClass()->derivesFrom(MTS_CLASS(Shape)))
|
||||
Log(EError, "Medium cannot be a parent of a shape");
|
||||
}
|
||||
|
||||
|
||||
void addChild(const std::string &name, ConfigurableObject *child) {
|
||||
if (child->getClass()->derivesFrom(MTS_CLASS(Shape))) {
|
||||
Shape *shape = static_cast<Shape *>(child);
|
||||
if (shape->isCompound()) {
|
||||
int ctr = 0;
|
||||
while (true) {
|
||||
ref<Shape> childShape = shape->getElement(ctr++);
|
||||
if (!childShape)
|
||||
break;
|
||||
addChild("", childShape);
|
||||
}
|
||||
} else {
|
||||
m_kdTree->addShape(shape);
|
||||
shape->incRef();
|
||||
m_shapes.push_back(shape);
|
||||
}
|
||||
} else if (child->getClass()->derivesFrom(MTS_CLASS(VolumeDataSource))) {
|
||||
VolumeDataSource *volume = static_cast<VolumeDataSource *>(child);
|
||||
|
||||
if (name == "albedo") {
|
||||
Assert(volume->supportsSpectrumLookups());
|
||||
m_albedo = volume;
|
||||
} else if (name == "density") {
|
||||
Assert(volume->supportsFloatLookups());
|
||||
m_densities = volume;
|
||||
} else if (name == "orientations") {
|
||||
Assert(volume->supportsVectorLookups());
|
||||
m_orientations = volume;
|
||||
}
|
||||
} else {
|
||||
Medium::addChild(name, child);
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
* \brief Intersect a ray with the stencil and
|
||||
* determine whether it started on the inside
|
||||
*/
|
||||
inline bool rayIntersect(const Ray &ray, Float &t, bool &inside) const {
|
||||
if (m_shapes.size() != 0) {
|
||||
Intersection its;
|
||||
if (!m_kdTree->rayIntersect(ray, its))
|
||||
return false;
|
||||
inside = dot(its.geoFrame.n, ray.d) > 0;
|
||||
t = its.t;
|
||||
} else {
|
||||
Float mint, maxt;
|
||||
if (!m_aabb.rayIntersect(ray, mint, maxt))
|
||||
return false;
|
||||
if (mint <= ray.mint && maxt <= ray.mint)
|
||||
return false;
|
||||
inside = mint <= 0 && maxt > 0;
|
||||
t = (mint <= 0) ? maxt : mint;
|
||||
}
|
||||
return true;
|
||||
}
|
||||
|
||||
inline Vector lookupOrientation(const Point &p) const {
|
||||
Vector orientation = m_orientations->lookupVector(p);
|
||||
Float lengthSqr = orientation.lengthSquared();
|
||||
if (lengthSqr != 0)
|
||||
return orientation / std::sqrt(lengthSqr);
|
||||
else
|
||||
return Vector(0.0f);
|
||||
}
|
||||
|
||||
inline Float sigmaT(const Point &p, const Vector &d) const {
|
||||
/**
|
||||
* Double the densities so that a uniform flake distribution
|
||||
* reproduces isotropic scattering
|
||||
*/
|
||||
Float density = 2 * m_densities->lookupFloat(p) * m_densityMultiplier;
|
||||
if (density == 0)
|
||||
return 0.0f;
|
||||
Vector orientation = lookupOrientation(p);
|
||||
if (orientation == Vector(0.0f))
|
||||
return 0.0f;
|
||||
|
||||
Vector localD = Frame(orientation).toLocal(d);
|
||||
|
||||
return density * m_sigmaT.evalAzimuthallyInvariant(localD);
|
||||
}
|
||||
|
||||
/// Integrate densities using the composite Simpson's rule
|
||||
inline Float integrateDensity(Ray ray, Float length) const {
|
||||
if (length == 0)
|
||||
return 0.0f;
|
||||
int nParts = (int) std::ceil(length/m_stepSize);
|
||||
nParts += nParts % 2;
|
||||
const Float stepSize = length/nParts;
|
||||
const Vector increment = ray.d * stepSize;
|
||||
|
||||
Float m = 4;
|
||||
Float accumulatedDensity =
|
||||
sigmaT(ray.o, ray.d) + sigmaT(ray(length), ray.d);
|
||||
#ifdef HET_EARLY_EXIT
|
||||
const Float stopAfterDensity = -std::log(Epsilon);
|
||||
const Float stopValue = stopAfterDensity*3/stepSize;
|
||||
#endif
|
||||
|
||||
ray.o += increment;
|
||||
for (int i=1; i<nParts; ++i) {
|
||||
Float value = sigmaT(ray.o, ray.d);
|
||||
accumulatedDensity += value*m;
|
||||
Point tmp = ray.o;
|
||||
ray.o += increment;
|
||||
|
||||
if (ray.o == tmp) {
|
||||
Log(EWarn, "integrateDensity(): failed to make forward progress -- "
|
||||
"round-off error issues? The step size was %.18f", stepSize);
|
||||
break;
|
||||
}
|
||||
|
||||
#ifdef HET_EARLY_EXIT
|
||||
if (accumulatedDensity > stopValue) // Stop early
|
||||
return std::numeric_limits<Float>::infinity();
|
||||
#endif
|
||||
m = 6 - m;
|
||||
}
|
||||
accumulatedDensity *= stepSize/3;
|
||||
|
||||
return accumulatedDensity;
|
||||
}
|
||||
|
||||
/**
|
||||
* \brief Integrate the density covered by the specified ray
|
||||
* segment, while clipping the volume to the underlying
|
||||
* stencil volume.
|
||||
*/
|
||||
inline Float integrateDensity(const Ray &r) const {
|
||||
Ray ray(r(r.mint), r.d,
|
||||
0, std::numeric_limits<Float>::infinity(), 0.0f);
|
||||
Float integral = 0, remaining = r.maxt - r.mint;
|
||||
int iterations = 0;
|
||||
bool inside = false;
|
||||
Float t = 0;
|
||||
|
||||
while (remaining > 0 && rayIntersect(ray, t, inside)) {
|
||||
if (inside)
|
||||
integral += integrateDensity(ray, std::min(remaining, t));
|
||||
|
||||
remaining -= t;
|
||||
ray.o = ray(t);
|
||||
ray.mint = Epsilon;
|
||||
|
||||
if (++iterations > 100) {
|
||||
/// Just a precaution..
|
||||
Log(EWarn, "integrateDensity(): round-off error issues?");
|
||||
break;
|
||||
}
|
||||
}
|
||||
return integral;
|
||||
}
|
||||
|
||||
/**
|
||||
* Attempts to solve the following 1D integral equation for 't'
|
||||
* \int_0^t density(ray.o + x * ray.d) * dx + accumulatedDensity == desiredDensity.
|
||||
* When no solution can be found in [0, maxDist] the function returns
|
||||
* false. For convenience, the function returns the current values of sigmaT
|
||||
* and the albedo, as well as the 3D position 'ray.o+t*ray.d' upon
|
||||
* success.
|
||||
*/
|
||||
bool invertDensityIntegral(Ray ray, Float maxDist,
|
||||
Float &accumulatedDensity, Float desiredDensity,
|
||||
Float ¤tSigmaT, Spectrum ¤tAlbedo,
|
||||
Point ¤tPoint) const {
|
||||
if (maxDist == 0)
|
||||
return std::numeric_limits<Float>::infinity();
|
||||
int nParts = (int) std::ceil(maxDist/m_stepSize);
|
||||
Float stepSize = maxDist/nParts;
|
||||
Vector fullIncrement = ray.d * stepSize,
|
||||
halfIncrement = fullIncrement * .5f;
|
||||
Float t = 0;
|
||||
int numRefines = 0;
|
||||
bool success = false;
|
||||
Float node1 = sigmaT(ray.o, ray.d);
|
||||
|
||||
while (t <= maxDist) {
|
||||
Float node2 = sigmaT(ray.o + halfIncrement, ray.d);
|
||||
Float node3 = sigmaT(ray.o + fullIncrement, ray.d);
|
||||
const Float newDensity = accumulatedDensity +
|
||||
(node1+node2*4+node3) * (stepSize/6);
|
||||
|
||||
if (newDensity > desiredDensity) {
|
||||
if (t+stepSize/2 <= maxDist) {
|
||||
/* Record the last "good" scattering event */
|
||||
success = true;
|
||||
if (EXPECT_TAKEN(node2 != 0)) {
|
||||
currentPoint = ray.o + halfIncrement;
|
||||
currentSigmaT = node2;
|
||||
} else if (node3 != 0 && t+stepSize <= maxDist) {
|
||||
currentPoint = ray.o + fullIncrement;
|
||||
currentSigmaT = node3;
|
||||
} else if (node1 != 0) {
|
||||
currentPoint = ray.o;
|
||||
currentSigmaT = node1;
|
||||
}
|
||||
}
|
||||
|
||||
if (++numRefines > NUM_REFINES)
|
||||
break;
|
||||
|
||||
stepSize *= .5f;
|
||||
fullIncrement = halfIncrement;
|
||||
halfIncrement *= .5f;
|
||||
continue;
|
||||
}
|
||||
|
||||
if (ray.o+fullIncrement == ray.o) /* Unable to make forward progress - stop */
|
||||
break;
|
||||
|
||||
accumulatedDensity = newDensity;
|
||||
node1 = node3;
|
||||
t += stepSize;
|
||||
ray.o += fullIncrement;
|
||||
}
|
||||
|
||||
if (success)
|
||||
currentAlbedo = m_albedo->lookupSpectrum(currentPoint);
|
||||
|
||||
return success;
|
||||
}
|
||||
|
||||
/// Evaluate the transmittance along a ray segment
|
||||
Spectrum tau(const Ray &ray) const {
|
||||
return Spectrum(std::exp(-integrateDensity(ray)));
|
||||
}
|
||||
|
||||
bool sampleDistance(const Ray &r, MediumSamplingRecord &mRec,
|
||||
Sampler *sampler) const {
|
||||
Ray ray(r(r.mint), r.d, 0.0f);
|
||||
Float distSurf = r.maxt - r.mint,
|
||||
desiredDensity = -std::log(1-sampler->next1D()),
|
||||
accumulatedDensity = 0.0f,
|
||||
currentSigmaT = 0.0f;
|
||||
Spectrum currentAlbedo(0.0f);
|
||||
int iterations = 0;
|
||||
bool inside = false, success = false;
|
||||
Float t = 0;
|
||||
Float sigmaTOrigin = sigmaT(ray.o, ray.d);
|
||||
|
||||
while (rayIntersect(ray, t, inside)) {
|
||||
if (inside) {
|
||||
Point currentPoint(0.0f);
|
||||
success = invertDensityIntegral(ray, std::min(t, distSurf),
|
||||
accumulatedDensity, desiredDensity, currentSigmaT, currentAlbedo,
|
||||
currentPoint);
|
||||
if (success) {
|
||||
/* A medium interaction occurred */
|
||||
mRec.p = currentPoint;
|
||||
mRec.t = (mRec.p-r.o).length();
|
||||
success = true;
|
||||
break;
|
||||
}
|
||||
}
|
||||
|
||||
distSurf -= t;
|
||||
|
||||
if (distSurf < 0) {
|
||||
/* A surface interaction occurred */
|
||||
break;
|
||||
}
|
||||
ray.o = ray(t);
|
||||
ray.mint = Epsilon;
|
||||
|
||||
if (++iterations > 100) {
|
||||
/// Just a precaution..
|
||||
Log(EWarn, "sampleDistance(): round-off error issues?");
|
||||
break;
|
||||
}
|
||||
}
|
||||
Float expVal = std::max(Epsilon, std::exp(-accumulatedDensity));
|
||||
|
||||
if (success)
|
||||
mRec.orientation = lookupOrientation(mRec.p);
|
||||
|
||||
mRec.pdfFailure = expVal;
|
||||
mRec.pdfSuccess = expVal * std::max((Float) Epsilon, currentSigmaT);
|
||||
mRec.pdfSuccessRev = expVal * std::max((Float) Epsilon, sigmaTOrigin);
|
||||
mRec.transmittance = Spectrum(expVal);
|
||||
|
||||
if (!success)
|
||||
return false;
|
||||
|
||||
mRec.sigmaS = currentAlbedo * currentSigmaT;
|
||||
mRec.sigmaA = Spectrum(currentSigmaT) - mRec.sigmaS;
|
||||
mRec.albedo = currentAlbedo.max();
|
||||
mRec.medium = this;
|
||||
return true;
|
||||
}
|
||||
|
||||
void pdfDistance(const Ray &ray, Float t, MediumSamplingRecord &mRec) const {
|
||||
Float expVal = std::exp(-integrateDensity(Ray(ray, 0, t)));
|
||||
|
||||
mRec.transmittance = Spectrum(expVal);
|
||||
mRec.pdfFailure = expVal;
|
||||
mRec.pdfSuccess = expVal * std::max((Float) Epsilon,
|
||||
sigmaT(ray(t), ray.d));
|
||||
mRec.pdfSuccessRev = expVal * std::max((Float) Epsilon,
|
||||
sigmaT(ray(ray.mint), ray.d));
|
||||
}
|
||||
|
||||
std::string toString() const {
|
||||
std::ostringstream oss;
|
||||
oss << "HeterogeneousFlakeMedium[" << endl
|
||||
<< " albedo=" << indent(m_albedo.toString()) << "," << endl
|
||||
<< " orientations=" << indent(m_orientations.toString()) << "," << endl
|
||||
<< " densities=" << indent(m_densities.toString()) << "," << endl
|
||||
<< " stepSize=" << m_stepSize << "," << endl
|
||||
<< " densityMultiplier=" << m_densityMultiplier << endl
|
||||
<< "]";
|
||||
return oss.str();
|
||||
}
|
||||
MTS_DECLARE_CLASS()
|
||||
private:
|
||||
ref<VolumeDataSource> m_densities;
|
||||
ref<VolumeDataSource> m_albedo;
|
||||
ref<VolumeDataSource> m_orientations;
|
||||
ref<ShapeKDTree> m_kdTree;
|
||||
std::vector<Shape *> m_shapes;
|
||||
Float m_stepSize;
|
||||
/* Flake model-related */
|
||||
SHVector m_D, m_sigmaT;
|
||||
SHVector4D m_phaseExpansion;
|
||||
int m_samplingRecursions;
|
||||
EMode m_mode;
|
||||
Float m_exponent, m_normalization;
|
||||
};
|
||||
|
||||
Spectrum FlakePhaseFunction::f(const PhaseFunctionQueryRecord &pRec) const {
|
||||
Frame frame(pRec.mRec.orientation);
|
||||
Vector wi = frame.toLocal(pRec.wi);
|
||||
Vector wo = frame.toLocal(pRec.wo);
|
||||
#if defined(FLAKE_EVAL_APPROXIMATION)
|
||||
/* Evaluate spherical harmonics representation - might be inaccurate */
|
||||
SHVector temp(m_phaseExpansion->getBands());
|
||||
m_phaseExpansion->lookup(wi, temp);
|
||||
Float result = std::max((Float) 0, temp.eval(wo));
|
||||
return Spectrum(result);
|
||||
#else
|
||||
/* Evaluate the real phase function */
|
||||
Float sigmaT = m_sigmaT.evalAzimuthallyInvariant(wi);
|
||||
Vector H = wi + wo;
|
||||
Float length = H.length();
|
||||
|
||||
if (length == 0)
|
||||
return Spectrum(0.0f);
|
||||
else
|
||||
H /= length;
|
||||
|
||||
Float result = m_distr(H) / (2*sigmaT);
|
||||
result *= m_normalization;
|
||||
return Spectrum(result);
|
||||
#endif
|
||||
}
|
||||
|
||||
Spectrum FlakePhaseFunction::sample(PhaseFunctionQueryRecord &pRec,
|
||||
Float &_pdf, Sampler *sampler) const {
|
||||
#if defined(FLAKE_SAMPLE_UNIFORM)
|
||||
/* Uniform sampling */
|
||||
pRec.wo = squareToSphere(sampler->next2D());
|
||||
_pdf = 1/(4*M_PI);
|
||||
return f(pRec);
|
||||
#else
|
||||
Point2 sample(sampler->next2D());
|
||||
Frame frame(pRec.mRec.orientation);
|
||||
Vector wi = frame.toLocal(pRec.wi);
|
||||
/* Importance sampling using the interpolated phase function */
|
||||
SHVector &temp = m_temp.get();
|
||||
if (EXPECT_NOT_TAKEN(temp.getBands() == 0))
|
||||
temp = SHVector(m_phaseExpansion->getBands());
|
||||
m_phaseExpansion->lookup(wi, temp);
|
||||
_pdf = m_shSampler->warp(temp, sample);
|
||||
|
||||
Vector wo = sphericalDirection(sample.x, sample.y);
|
||||
pRec.wo = frame.toWorld(wo);
|
||||
#if defined(FLAKE_EVAL_APPROXIMATION)
|
||||
return Spectrum(std::max((Float) 0, temp.eval(sample.x, sample.y)));
|
||||
#else
|
||||
return f(pRec);
|
||||
#endif
|
||||
#endif
|
||||
}
|
||||
|
||||
Spectrum FlakePhaseFunction::sample(PhaseFunctionQueryRecord &pRec,
|
||||
Sampler *sampler) const {
|
||||
Float pdf;
|
||||
Spectrum result = FlakePhaseFunction::sample(pRec, pdf, sampler);
|
||||
if (!result.isZero())
|
||||
return result / pdf;
|
||||
else
|
||||
return Spectrum(0.0f);
|
||||
}
|
||||
|
||||
Float FlakePhaseFunction::pdf(const PhaseFunctionQueryRecord &pRec) const {
|
||||
#if defined(FLAKE_SAMPLE_UNIFORM)
|
||||
return 1/(4*M_PI);
|
||||
#else
|
||||
Frame frame(pRec.mRec.orientation);
|
||||
Vector wi = frame.toLocal(pRec.wi);
|
||||
Vector wo = frame.toLocal(pRec.wo);
|
||||
SHVector temp(m_phaseExpansion->getBands());
|
||||
m_phaseExpansion->lookup(wi, temp);
|
||||
|
||||
return std::max((Float) 0, temp.eval(wo));
|
||||
#endif
|
||||
}
|
||||
|
||||
MTS_IMPLEMENT_CLASS_S(HeterogeneousFlakeMedium, false, Medium)
|
||||
MTS_IMPLEMENT_CLASS_S(FlakePhaseFunction, false, PhaseFunction)
|
||||
MTS_EXPORT_PLUGIN(HeterogeneousFlakeMedium, "Heterogeneous micro-flake medium");
|
||||
MTS_NAMESPACE_END
|
||||
|
||||
|
|
@ -356,7 +356,7 @@ public:
|
|||
|
||||
x -= fx/dfx;
|
||||
|
||||
if (x <= a || x >= b || dfx == 0)
|
||||
if (EXPECT_NOT_TAKEN(x <= a || x >= b || dfx == 0))
|
||||
x = 0.5f * (b + a);
|
||||
|
||||
/* Integrated version of the above Lagrange polynomial */
|
||||
|
|
|
|||
|
|
@ -16,16 +16,24 @@
|
|||
along with this program. If not, see <http://www.gnu.org/licenses/>.
|
||||
*/
|
||||
|
||||
#include <mitsuba/core/chisquare.h>
|
||||
#include <mitsuba/render/phase.h>
|
||||
#include <mitsuba/render/sampler.h>
|
||||
#include "microflake.h"
|
||||
#include "microflake_fiber.h"
|
||||
|
||||
MTS_NAMESPACE_BEGIN
|
||||
|
||||
class MicroflakePhaseFunction : public PhaseFunction {
|
||||
public:
|
||||
MicroflakePhaseFunction(const Properties &props)
|
||||
: PhaseFunction(props) {
|
||||
MicroflakePhaseFunction(const Properties &props) : PhaseFunction(props) {
|
||||
m_fiberDistr = GaussianFiberDistribution(props.getFloat("stddev"));
|
||||
ChiSquareTest test(7);
|
||||
test.fill(
|
||||
boost::bind(&GaussianFiberDistribution::sample, m_fiberDistr, _1),
|
||||
boost::bind(&GaussianFiberDistribution::pdf, m_fiberDistr, _1)
|
||||
);
|
||||
test.dumpTables("test.m");
|
||||
test.runTest(1);
|
||||
}
|
||||
|
||||
MicroflakePhaseFunction(Stream *stream, InstanceManager *manager)
|
||||
|
|
@ -60,10 +68,16 @@ public:
|
|||
}
|
||||
|
||||
std::string toString() const {
|
||||
return "MicroflakePhaseFunction[]";
|
||||
std::ostringstream oss;
|
||||
oss << "MicroflakePhaseFunction[" << endl
|
||||
<< " fiberDistr = " << indent(m_fiberDistr.toString()) << endl
|
||||
<< "]";
|
||||
return oss.str();
|
||||
}
|
||||
|
||||
MTS_DECLARE_CLASS()
|
||||
private:
|
||||
GaussianFiberDistribution m_fiberDistr;
|
||||
};
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -16,20 +16,30 @@
|
|||
along with this program. If not, see <http://www.gnu.org/licenses/>.
|
||||
*/
|
||||
|
||||
#if !defined(__MICROFLAKE_SIGMA_T_H)
|
||||
#define __MICROFLAKE_SIGMA_T_H
|
||||
#if !defined(__MICROFLAKE_FIBER_DIST_H)
|
||||
#define __MICROFLAKE_FIBER_DIST_H
|
||||
|
||||
#include <mitsuba/core/statistics.h>
|
||||
#include <mitsuba/core/brent.h>
|
||||
#include <boost/math/special_functions/erf.hpp>
|
||||
#include <boost/bind.hpp>
|
||||
#include <boost/math/special_functions/erf.hpp>
|
||||
|
||||
MTS_NAMESPACE_BEGIN
|
||||
|
||||
#define SIGMA_T_RANGE_MIN 4e-08
|
||||
#define SIGMA_T_RANGE_MAX 4
|
||||
#define SIGMA_T_ELEMENTS 100
|
||||
#define SIGMA_T_COEFFS 10
|
||||
FINLINE Float mts_erf(Float arg) {
|
||||
#if defined(__GNUC__) && defined(SINGLE_PRECISION)
|
||||
return erff(arg);
|
||||
#elif defined(__GNUC__) && defined(DOUBLE_PRECISION)
|
||||
return erf(arg);
|
||||
#else
|
||||
return boost::math::erf<Float>(arg);
|
||||
#endif
|
||||
}
|
||||
|
||||
#define FIBERDIST_STDDEV_MIN 4e-08
|
||||
#define FIBERDIST_STDDEV_MAX 4
|
||||
#define FIBERDIST_SIGMA_T_ELEMENTS 100
|
||||
#define FIBERDIST_SIGMA_T_COEFFS 10
|
||||
|
||||
/**
|
||||
* Each row of this table table stores an expansion of \sigma_t in terms of
|
||||
|
|
@ -37,11 +47,11 @@ MTS_NAMESPACE_BEGIN
|
|||
* fiber axis and the incident direction. The standard deviation of the
|
||||
* underlying distribution increases from row to row using a nonlinear
|
||||
* mapping to capture the `interesting' parts more efficiently (see
|
||||
* \ref sigmaT_fiberGaussian())
|
||||
* \ref sigmaT_fiberSigmaT())
|
||||
*
|
||||
* The implementation here has an average absolute error of 3.17534e-05.
|
||||
*/
|
||||
const double fiberGaussianCoeffs[SIGMA_T_ELEMENTS][SIGMA_T_COEFFS] = {
|
||||
const double fiberSigmaTCoeffs[FIBERDIST_SIGMA_T_ELEMENTS][FIBERDIST_SIGMA_T_COEFFS] = {
|
||||
{ 2.5037347588631811e-08, 6.3661860705430207e-01, 1.7827351092236654e-05, -1.3015084365974872e-04, 5.2848718115683369e-04, -1.2810825925271274e-03, 1.8970200528656278e-03, -1.6818874867112754e-03, 8.1991128831759852e-04, -1.6898472595983094e-04 },
|
||||
{ 4.0059757909494120e-07, 6.3660112034736627e-01, 2.8523763553955916e-04, -2.0824136415171779e-03, 8.4557955473769653e-03, -2.0497323170502568e-02, 3.0352323203715059e-02, -2.6910202150020268e-02, 1.3118581833396092e-02, -2.7037558688078889e-03 },
|
||||
{ 2.0280252492606374e-06, 6.3652534713591225e-01, 1.4440155345667449e-03, -1.0542219099960448e-02, 4.2807465147063795e-02, -1.0376769900017280e-01, 1.5365863698661997e-01, -1.3623289910560743e-01, 6.6412820861387445e-02, -1.3687764171763206e-02 },
|
||||
|
|
@ -144,27 +154,27 @@ const double fiberGaussianCoeffs[SIGMA_T_ELEMENTS][SIGMA_T_COEFFS] = {
|
|||
{ 4.9740122861160618e-01, 4.9788891152147130e-06, 3.7427454517739989e-03, 1.2662117029549336e-03, -3.7139444921194809e-03, 2.9874687143092160e-03, 6.6568975580594270e-03, -1.6932579956119298e-02, 1.3976501563774946e-02, -4.0922961870819563e-03 }
|
||||
};
|
||||
|
||||
double sigmaT_fiberGaussian(double stddev, double sinTheta) {
|
||||
double sigmaT_fiberDist(double stddev, double sinTheta) {
|
||||
/* Undo the nonlinear mapping */
|
||||
const double factor = SIGMA_T_ELEMENTS / std::pow(SIGMA_T_RANGE_MAX, 0.25);
|
||||
const double factor = FIBERDIST_SIGMA_T_ELEMENTS / std::pow(FIBERDIST_STDDEV_MAX, 0.25);
|
||||
double pos = std::pow(stddev, 0.25) * factor - 1;
|
||||
|
||||
/* Clamp to the supported parameter range */
|
||||
pos = std::min(std::max(0.0, pos), (double) (SIGMA_T_ELEMENTS-1));
|
||||
pos = std::min(std::max(0.0, pos), (double) (FIBERDIST_SIGMA_T_ELEMENTS-1));
|
||||
|
||||
/* Linearly interpolate coefficients using \c alpha */
|
||||
int idx0 = (int) std::floor(pos), idx1 = (int) std::ceil(pos);
|
||||
double alpha = pos - idx0, base = 1, result = 0;
|
||||
|
||||
SAssert(
|
||||
idx0 >= 0 && idx0 < SIGMA_T_ELEMENTS &&
|
||||
idx1 >= 0 && idx1 < SIGMA_T_ELEMENTS
|
||||
idx0 >= 0 && idx0 < FIBERDIST_SIGMA_T_ELEMENTS &&
|
||||
idx1 >= 0 && idx1 < FIBERDIST_SIGMA_T_ELEMENTS
|
||||
);
|
||||
|
||||
/* Compute the expansion */
|
||||
for (int i=0; i<SIGMA_T_COEFFS; ++i) {
|
||||
result += base * ((1-alpha) * fiberGaussianCoeffs[idx0][i]
|
||||
+ alpha * fiberGaussianCoeffs[idx1][i]);
|
||||
/* Evaluate the expansion */
|
||||
for (int i=0; i<FIBERDIST_SIGMA_T_COEFFS; ++i) {
|
||||
result += base * ((1-alpha) * fiberSigmaTCoeffs[idx0][i]
|
||||
+ alpha * fiberSigmaTCoeffs[idx1][i]);
|
||||
base *= sinTheta;
|
||||
}
|
||||
|
||||
|
|
@ -176,56 +186,106 @@ static StatsCounter brentSolves("Micro-flake model",
|
|||
static StatsCounter avgBrentFunEvals("Micro-flake model",
|
||||
"Average Brent solver function evaluations", EAverage);
|
||||
|
||||
struct GaussianFiberDistribution {
|
||||
class GaussianFiberDistribution {
|
||||
public:
|
||||
inline GaussianFiberDistribution() {}
|
||||
|
||||
inline GaussianFiberDistribution(Float stddev) : m_stddev(stddev) {
|
||||
m_normalization = 1/(std::sqrt(2*M_PI) * m_stddev *
|
||||
boost::math::erf<Float>(1/(SQRT_TWO * m_stddev)));
|
||||
m_c1 = 1.0f/boost::math::erf<Float>(1/(SQRT_TWO * m_stddev));
|
||||
m_normalization = 1/(std::pow(2*M_PI, 3.0f/2.0f) * m_stddev *
|
||||
mts_erf(1/(SQRT_TWO * m_stddev)));
|
||||
m_c1 = 1.0f/mts_erf(1/(SQRT_TWO * m_stddev));
|
||||
|
||||
if (stddev < FIBERDIST_STDDEV_MIN || stddev > FIBERDIST_STDDEV_MAX)
|
||||
SLog(EError, "Standard deviation parameter is out of range (must "
|
||||
"be in [%f, %f])!", FIBERDIST_STDDEV_MIN, FIBERDIST_STDDEV_MAX);
|
||||
|
||||
/* Determine expansion coefficients of sigma_t for a fixed stddev */
|
||||
Float pos = std::pow(stddev / FIBERDIST_STDDEV_MAX, 0.25) *
|
||||
FIBERDIST_SIGMA_T_ELEMENTS - 1;
|
||||
|
||||
pos = std::min(std::max((Float) 0, pos), (Float) (FIBERDIST_SIGMA_T_ELEMENTS-1));
|
||||
|
||||
int idx0 = (int) std::floor(pos), idx1 = (int) std::ceil(pos);
|
||||
Float alpha = pos - idx0;
|
||||
|
||||
for (int i=0; i<FIBERDIST_SIGMA_T_COEFFS; ++i)
|
||||
m_coeffs[i] = (Float) (((1-alpha) * fiberSigmaTCoeffs[idx0][i]
|
||||
+ alpha * fiberSigmaTCoeffs[idx1][i]));
|
||||
}
|
||||
|
||||
/// Evaluate \sigma_t as a function of \cos\theta
|
||||
Float sigmaT(Float cosTheta) const {
|
||||
return sigmaT_fiberGaussian(m_stddev,
|
||||
std::sqrt(std::max((Float) 0, 1-cosTheta*cosTheta)));
|
||||
inline Float sigmaT(Float cosTheta) const {
|
||||
Float sinTheta = std::sqrt(std::max(
|
||||
(Float) 0, 1-cosTheta*cosTheta)),
|
||||
base = 1.0f, result = 0.0f;
|
||||
|
||||
/* Evaluate the expansion */
|
||||
for (int i=0; i<FIBERDIST_SIGMA_T_COEFFS; ++i) {
|
||||
result += base * m_coeffs[i];
|
||||
base *= sinTheta;
|
||||
}
|
||||
|
||||
return result;
|
||||
}
|
||||
|
||||
/// Evaluate the longitudinal density as a function of \cos\theta
|
||||
Float pdfCosTheta(Float cosTheta) const {
|
||||
return std::exp(-cosTheta*cosTheta/(2*m_stddev*m_stddev)) * m_normalization;
|
||||
/// Evaluate the density as a function of \cos\theta
|
||||
inline Float pdfCosTheta(Float cosTheta) const {
|
||||
return std::exp(-cosTheta*cosTheta
|
||||
/ (2*m_stddev*m_stddev)) * m_normalization;
|
||||
}
|
||||
|
||||
/// Evaluate the longitudinal CDF as a function of \cos\theta
|
||||
inline Float cdf(Float theta) const {
|
||||
return 0.5f * (1.0f -
|
||||
boost::math::erf<Float>(std::cos(theta)/(SQRT_TWO * m_stddev))*m_c1);
|
||||
/// Evaluate the density as a function of direction
|
||||
inline Float pdf(const Vector &d) const {
|
||||
return std::exp(-d.z*d.z
|
||||
/ (2*m_stddev*m_stddev)) * m_normalization;
|
||||
}
|
||||
|
||||
/**
|
||||
* Apply the inversion method to sample \theta given
|
||||
* a uniformly distributed \xi on [0, 1]
|
||||
* \brief Apply the inversion method to sample \cos\theta given
|
||||
* a uniformly distributed r.v. \xi on [0, 1]
|
||||
*/
|
||||
Float sample(Float xi) const {
|
||||
Vector sample(const Point2 &sample) const {
|
||||
BrentSolver brentSolver(100, 1e-6f);
|
||||
BrentSolver::Result result = brentSolver.solve(
|
||||
boost::bind(&GaussianFiberDistribution::cdfFunctor, this, xi, _1), 0, M_PI);
|
||||
boost::bind(&GaussianFiberDistribution::cdfFunctor,
|
||||
this, sample.x, _1), -1, 1);
|
||||
SAssert(result.success);
|
||||
avgBrentFunEvals.incrementBase();
|
||||
++brentSolves;
|
||||
return result.x;
|
||||
}
|
||||
private:
|
||||
Float cdfFunctor(Float theta, Float xi) const {
|
||||
++avgBrentFunEvals;
|
||||
return cdf(theta)-xi;
|
||||
|
||||
Float cosTheta = result.x,
|
||||
sinTheta = std::sqrt(std::max((Float) 0, 1-cosTheta*cosTheta)),
|
||||
phi = 2 * M_PI * sample.y,
|
||||
sinPhi = std::sin(phi), cosPhi = std::cos(phi);
|
||||
|
||||
return Vector(sinTheta * cosPhi, sinTheta * sinPhi, cosTheta);
|
||||
}
|
||||
|
||||
std::string toString() const {
|
||||
std::ostringstream oss;
|
||||
oss << "GaussianFiberDistribution[stddev="
|
||||
<< m_stddev << "]";
|
||||
return oss.str();
|
||||
}
|
||||
protected:
|
||||
/// Evaluate the longitudinal CDF as a function of \cos\theta
|
||||
inline Float cdf(Float cosTheta) const {
|
||||
return 0.5f * (1.0f -
|
||||
mts_erf(cosTheta / (SQRT_TWO * m_stddev)) * m_c1);
|
||||
}
|
||||
|
||||
Float cdfFunctor(Float xi, Float cosTheta) const {
|
||||
++avgBrentFunEvals;
|
||||
return cdf(cosTheta)-xi;
|
||||
}
|
||||
|
||||
protected:
|
||||
Float m_stddev;
|
||||
Float m_normalization;
|
||||
Float m_c1;
|
||||
Float m_coeffs[FIBERDIST_SIGMA_T_COEFFS];
|
||||
};
|
||||
|
||||
|
||||
MTS_NAMESPACE_END
|
||||
|
||||
#endif /* __MICROFLAKE_SIGMA_T_H */
|
||||
#endif /* __MICROFLAKE_FIBER_DIST_H */
|
||||
Loading…
Reference in New Issue