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done with the smooth conductor, started working on the rough dielectric

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Wenzel Jakob 2011-07-07 03:07:32 +02:00
parent bd4301bd1e
commit a13583db34
18 changed files with 250 additions and 105 deletions
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1
data/ior/Cu.eta.spd
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@ -2,6 +2,7 @@
# ; Optical constants for Cu
# ;
# ; Lambda (A) n k
# ;-----------------------------------------
302.400421 1.380000
306.133759 1.358438
309.960449 1.340000

1
data/ior/Cu.k.spd
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@ -3,7 +3,6 @@
# ;
# ; Lambda (A) n k
# ;-----------------------------------------
298.757050 1.662125
302.400421 1.687000
306.133759 1.703313
309.960449 1.720000

3
data/tests/test_bsdf.xml
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@ -24,4 +24,7 @@
<rgb name="transmittance" value="0 .5 0"/>
</bsdf>
</bsdf>
<!-- Test the conductor model -->
<bsdf type="conductor"/>
</scene>

1
doc/format.tex
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@ -127,6 +127,7 @@ Passing strings is straightforward:
<string name="stringProperty" value="This is a string"/>
\end{xml}
\subsubsection{Color spectra}
\label{sec:format-spectra}
Depending on the compilation flags of Mitsuba (see \secref{compiling-flags} for
details), the renderer internally either represents colors using discretized color spectra
(when \texttt{SPECTRUM\_SAMPLES} is set to a value other than 3), or it

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1
doc/macros.sty
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@ -3,6 +3,7 @@
\newcommand{\figref}[1]{\mbox{Figure~\ref{fig:#1}}}
\newcommand{\secref}[1]{\mbox{Section~\ref{sec:#1}}}
\newcommand{\lstref}[1]{\mbox{Listing~\ref{lst:#1}}}
\newcommand{\tblref}[1]{\mbox{Table~\ref{tbl:#1}}}
\newcommand{\code}[1]{\texttt{#1}}
% Macros that are used in the plugin documentation

7
doc/main.bib
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@ -21,3 +21,10 @@
year = {2005},
publisher = {AK Peters, Ltd.}
}
@book{Palik1998Handbook,
title = {Handbook of optical constants of solids},
author = {Palik, E.D. and Ghosh, G.},
year = {1998},
publisher = {Academic press}
}

8
include/mitsuba/core/util.h
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@ -453,14 +453,14 @@ extern MTS_EXPORT_CORE Float fresnel(Float cosThetaI, Float etaExt,
* Calculates the unpolarized fresnel reflection coefficient on
* an interface to a conductor.
*
* \param cosTheta
* \param cosThetaI
* Cosine of the angle between the normal and the incident ray
* \param eta
* Relative refractive index (per wavelength)
* Real refractive index (wavelength-dependent)
* \param k
* Absorption coefficient (per wavelength)
* Imaginary refractive index (wavelength-dependent)
*/
extern MTS_EXPORT_CORE Spectrum fresnelConductor(Float cosTheta,
extern MTS_EXPORT_CORE Spectrum fresnelConductor(Float cosThetaI,
const Spectrum &eta, const Spectrum &k);
/*! @} */

2
src/bsdfs/SConscript
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@ -6,7 +6,7 @@ plugins += env.SharedLibrary('conductor', ['conductor.cpp'])
plugins += env.SharedLibrary('diffuse', ['diffuse.cpp'])
#plugins += env.SharedLibrary('plastic', ['plastic.cpp'])
#plugins += env.SharedLibrary('roughdielectric', ['roughdielectric.cpp'])
plugins += env.SharedLibrary('roughdielectric', ['roughdielectric.cpp'])
#plugins += env.SharedLibrary('roughconductor', ['roughconductor.cpp'])
#plugins += env.SharedLibrary('roughdiffuse', ['roughdiffuse.cpp'])
#plugins += env.SharedLibrary('roughplastic', ['roughplastic.cpp'])

2
src/bsdfs/coating.cpp
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@ -21,7 +21,7 @@
MTS_NAMESPACE_BEGIN
/*! \plugin{varnish}{Smooth varnish layer}
/*! \plugin{coating}{Smooth coating layer}
*
* \parameters{
* \parameter{intIOR}{\Float}{Interior index of refraction \default{1.5046}}

144
src/bsdfs/conductor.cpp
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@ -18,13 +18,75 @@
#include <mitsuba/render/bsdf.h>
#include <mitsuba/render/consttexture.h>
#include "ior.h"
#include <mitsuba/core/fresolver.h>
MTS_NAMESPACE_BEGIN
/*! \plugin{conductor}{Smooth conductor}
* \parameters{
* \parameter{preset}{\String}{Name of a material preset, see \tblref{conductor-iors}.\!\default{\texttt{Cu} / copper}}
* \parameter{eta}{\Spectrum}{Real part of the material's index of refraction \default{based on the value of \texttt{preset}}}
* \parameter{k}{\Spectrum}{Imaginary part of the material's index of refraction, also known as absorption coefficient.
* \default{based on the value of \texttt{preset}}}
* \lastparameter{specular\showbreak Reflectance}{\Spectrum\Or\Texture}{Optional
* factor used to modulate the reflectance component\default{1.0}}
* }
* \renderings{
* \rendering{Measured copper material (the default)}{bsdf_conductor_copper.jpg}
* \rendering{Measured gold material (\lstref{conductor-gold})}{bsdf_conductor_gold.jpg}
* }
* This plugin implements a perfectly smooth interface to a conducting material,
* such as a metal. For a similar model that instead describes a rough surface
* microstructure, take a look at the seperately available
* \pluginref{roughconductor} plugin.
* In contrast to dielectric materials, conductors do not transmit
* any light. Their index of refraction is complex-valued and tends to undergo
* considerable changes throughout the visible color spectrum.
*
* \begin{table}
* To faciliate the tedious task of specifying spectrally-varying index of
* refraction information, Mitsuba ships with a set of measured data for a
* several materials, where visible-spectrum information was publicly available\footnote{
* These index of refraction values are identical to the data distributed with PBRT.
* They are originally from the Luxpop database (\url{www.luxpop.com}) and
* are based on data by Palik et al. \cite{Palik1998Handbook} and measurements
* of atomic scattering factors made by the Center For X-Ray Optics (CXRO)
* at Berkeley and the Lawrence Livermore National Laboratory (LLNL).
* }.
*
* Note that \tblref{conductor-iors} also includes several popular optical coatings, which are
* not actually conductors. These materials can also be used with this plugin,
* though note that the plugin will ignore any refraction component that the actual
* material might have had.
* The table also contains a few birefingent materials, which are split into
* separate measurements correponding to their two indices of
* refraction (named ``ordinary'' and ``extraordinary ray'').
*
* When using this plugin, you should compile Mitsuba with support for spectral
* renderings to get the most accurate results. While it also works in RGB mode,
* the computations will be much more approximate in this case.
*
* \begin{xml}[caption=Material configuration for a smooth conductor with measured gold data, label=lst:conductor-gold]
* <shape type="...">
* <bsdf type="conductor">
* <string name="preset" value="Au"/>
* </bsdf>
* <shape>
* \end{xml}
* \vspace{5mm}
* It is also possible to load spectrally varying index of refraction data from
* two external files (see \secref{format-spectra} for details on the file format):
* \begin{xml}[caption=Rendering a smooth conductor with custom data]
* <shape type="...">
* <bsdf type="conductor">
* <spectrum name="eta" filename="conductorIOR.eta.spd"/>
* <spectrum name="k" filename="conductorIOR.k.spd"/>
* </bsdf>
* <shape>
* \end{xml}
* \vspace{1.5cm}
* \begin{table}[hb!]
* \centering
* \scriptsize
* \begin{tabular}{>{\ttfamily}llp{1mm}>{\ttfamily}ll}
@ -55,24 +117,33 @@ MTS_NAMESPACE_BEGIN
* \bottomrule
* \end{tabular}
* \caption{
* \label{tbl:dielectric-iors}
* \label{tbl:conductor-iors}
* This table lists all supported material names that can be passed into the
* \pluginref{conductor} plugin. In most cases, there are two separate
* measurements of the same material made using different approaches.
* \pluginref{conductor} plugin. Note that some of them are not actually
* conductors---this is not a problem, they can be used regardless (though only
* the reflection component and no transmission will be simulated).
* In most cases, there are multiple entries for each material, which
* represent different measurements.
* }
* \end{table}
**
*/
class SmoothConductor : public BSDF {
public:
SmoothConductor(const Properties &props) : BSDF(props) {
ref<FileResolver> fResolver = Thread::getThread()->getFileResolver();
m_specularReflectance = new ConstantSpectrumTexture(
props.getSpectrum("specularReflectance", Spectrum(1.0f)));
std::string preset = props.getString("preset", "Cu");
Spectrum presetEta, presetK;
presetEta.fromContinuousSpectrum(InterpolatedSpectrum(
fResolver->resolve("data/ior/" + preset + ".eta.spd")));
presetK.fromContinuousSpectrum(InterpolatedSpectrum(
fResolver->resolve("data/ior/" + preset + ".k.spd")));
//m_eta = props.getSpectrum("eta", presetEta);
// m_k = props.getSpectrum("k", presetK);
m_eta = props.getSpectrum("eta", presetEta);
m_k = props.getSpectrum("k", presetK);
m_components.push_back(EDeltaReflection | EFrontSide);
m_usesRayDifferentials = false;
@ -106,20 +177,63 @@ public:
}
}
Spectrum sample(BSDFQueryRecord &bRec, const Point2 &sample) const {
return Spectrum(0.0f);
/// Reflection in local coordinates
inline Vector reflect(const Vector &wi) const {
return Vector(-wi.x, -wi.y, wi.z);
}
Spectrum eval(const BSDFQueryRecord &bRec, EMeasure measure) const {
return Spectrum(0.0f);
}
bool sampleReflection = (bRec.typeMask & EDeltaReflection)
&& (bRec.component == -1 || bRec.component == 0);
Spectrum sample(BSDFQueryRecord &bRec, Float &pdf, const Point2 &sample) const {
return Spectrum(0.0f);
if (!sampleReflection || measure != EDiscrete ||
Frame::cosTheta(bRec.wi) <= 0 ||
Frame::cosTheta(bRec.wo) <= 0)
return Spectrum(0.0f);
return m_specularReflectance->getValue(bRec.its) *
fresnelConductor(Frame::cosTheta(bRec.wi), m_eta, m_k);
}
Float pdf(const BSDFQueryRecord &bRec, EMeasure measure) const {
return 0.0f;
bool sampleReflection = (bRec.typeMask & EDeltaReflection)
&& (bRec.component == -1 || bRec.component == 0);
if (!sampleReflection || measure != EDiscrete ||
Frame::cosTheta(bRec.wi) <= 0 ||
Frame::cosTheta(bRec.wo) <= 0)
return 0.0f;
return 1.0f;
}
Spectrum sample(BSDFQueryRecord &bRec, const Point2 &sample) const {
bool sampleReflection = (bRec.typeMask & EDeltaReflection)
&& (bRec.component == -1 || bRec.component == 0);
if (!sampleReflection || Frame::cosTheta(bRec.wi) <= 0)
return Spectrum(0.0f);
bRec.sampledComponent = 0;
bRec.sampledType = EDeltaReflection;
bRec.wo = reflect(bRec.wi);
return m_specularReflectance->getValue(bRec.its) *
fresnelConductor(Frame::cosTheta(bRec.wi), m_eta, m_k);
}
Spectrum sample(BSDFQueryRecord &bRec, Float &pdf, const Point2 &sample) const {
bool sampleReflection = (bRec.typeMask & EDeltaReflection)
&& (bRec.component == -1 || bRec.component == 0);
if (!sampleReflection || Frame::cosTheta(bRec.wi) <= 0)
return Spectrum(0.0f);
bRec.sampledComponent = 0;
bRec.sampledType = EDeltaReflection;
bRec.wo = reflect(bRec.wi);
pdf = 1;
return m_specularReflectance->getValue(bRec.its) *
fresnelConductor(Frame::cosTheta(bRec.wi), m_eta, m_k);
}
std::string toString() const {

96
src/bsdfs/dielectric.cpp
View File

@ -196,6 +196,54 @@ public:
return Vector(-eta*wi.x, -eta*wi.y, cosThetaT);
}
Spectrum eval(const BSDFQueryRecord &bRec, EMeasure measure) const {
bool sampleReflection = (bRec.typeMask & EDeltaReflection)
&& (bRec.component == -1 || bRec.component == 0);
bool sampleTransmission = (bRec.typeMask & EDeltaTransmission)
&& (bRec.component == -1 || bRec.component == 1);
bool reflection = Frame::cosTheta(bRec.wo) * Frame::cosTheta(bRec.wi) > 0;
if ((reflection && !sampleReflection) ||
(!reflection && !sampleTransmission) || measure != EDiscrete)
return Spectrum(0.0f);
Float fr = fresnel(Frame::cosTheta(bRec.wi), m_extIOR, m_intIOR);
if (reflection) {
return m_specularReflectance->getValue(bRec.its) * fr;
} else {
Float etaI = m_extIOR, etaT = m_intIOR;
bool entering = Frame::cosTheta(bRec.wi) > 0.0f;
if (!entering)
std::swap(etaI, etaT);
Float factor = (bRec.quantity == ERadiance)
? (etaI*etaI) / (etaT*etaT) : 1.0f;
return m_specularTransmittance->getValue(bRec.its) * factor * (1 - fr);
}
}
Float pdf(const BSDFQueryRecord &bRec, EMeasure measure) const {
bool sampleReflection = (bRec.typeMask & EDeltaReflection)
&& (bRec.component == -1 || bRec.component == 0);
bool sampleTransmission = (bRec.typeMask & EDeltaTransmission)
&& (bRec.component == -1 || bRec.component == 1);
bool reflection = Frame::cosTheta(bRec.wo)
* Frame::cosTheta(bRec.wi) > 0;
if ((reflection && !sampleReflection) ||
(!reflection && !sampleTransmission) || measure != EDiscrete)
return 0.0f;
if (sampleTransmission && sampleReflection) {
Float Fr = fresnel(Frame::cosTheta(bRec.wi), m_extIOR, m_intIOR);
return reflection ? Fr : (1 - Fr);
} else {
return 1.0f;
}
}
Spectrum sample(BSDFQueryRecord &bRec, const Point2 &sample) const {
bool sampleReflection = (bRec.typeMask & EDeltaReflection)
&& (bRec.component == -1 || bRec.component == 0);
@ -278,54 +326,6 @@ public:
}
}
Spectrum eval(const BSDFQueryRecord &bRec, EMeasure measure) const {
bool sampleReflection = (bRec.typeMask & EDeltaReflection)
&& (bRec.component == -1 || bRec.component == 0);
bool sampleTransmission = (bRec.typeMask & EDeltaTransmission)
&& (bRec.component == -1 || bRec.component == 1);
bool reflection = Frame::cosTheta(bRec.wo) * Frame::cosTheta(bRec.wi) > 0;
if ((reflection && !sampleReflection) ||
(!reflection && !sampleTransmission) || measure != EDiscrete)
return Spectrum(0.0f);
Float fr = fresnel(Frame::cosTheta(bRec.wi), m_extIOR, m_intIOR);
if (reflection) {
return m_specularReflectance->getValue(bRec.its) * fr;
} else {
Float etaI = m_extIOR, etaT = m_intIOR;
bool entering = Frame::cosTheta(bRec.wi) > 0.0f;
if (!entering)
std::swap(etaI, etaT);
Float factor = (bRec.quantity == ERadiance)
? (etaI*etaI) / (etaT*etaT) : 1.0f;
return m_specularTransmittance->getValue(bRec.its) * factor * (1 - fr);
}
}
Float pdf(const BSDFQueryRecord &bRec, EMeasure measure) const {
bool sampleReflection = (bRec.typeMask & EDeltaReflection)
&& (bRec.component == -1 || bRec.component == 0);
bool sampleTransmission = (bRec.typeMask & EDeltaTransmission)
&& (bRec.component == -1 || bRec.component == 1);
bool reflection = Frame::cosTheta(bRec.wo)
* Frame::cosTheta(bRec.wi) > 0;
if ((reflection && !sampleReflection) ||
(!reflection && !sampleTransmission) || measure != EDiscrete)
return 0.0f;
if (sampleTransmission && sampleReflection) {
Float Fr = fresnel(Frame::cosTheta(bRec.wi), m_extIOR, m_intIOR);
return reflection ? Fr : (1 - Fr);
} else {
return 1.0f;
}
}
Spectrum sample(BSDFQueryRecord &bRec, Float &pdf, const Point2 &sample) const {
bool sampleReflection = (bRec.typeMask & EDeltaReflection)
&& (bRec.component == -1 || bRec.component == 0);

22
src/bsdfs/microfacet.h
View File

@ -50,8 +50,7 @@ public:
* (ggx/phong/beckmann)
*/
MicrofacetDistribution(const std::string &name) {
std::string distr =
boost::to_lower_copy(props.getString("distribution", "beckmann"));
std::string distr = boost::to_lower_copy(name);
if (distr == "beckmann")
m_type = EBeckmann;
@ -171,8 +170,8 @@ public:
* \brief Smith's shadow-masking function G1 for each
* of the supported microfacet distributions
*
* \param m The microsurface normal
* \param v An arbitrary direction
* \param m The microsurface normal
* \param alpha The surface roughness
*/
Float smithG1(const Vector &v, const Vector &m, Float alpha) const {
@ -219,8 +218,21 @@ public:
}
}
/**
* \brief Smith's shadow-masking function G1 for each
* of the supported microfacet distributions
*
* \param wi The incident direction
* \param wo The exitant direction
* \param m The microsurface normal
* \param alpha The surface roughness
*/
Float smithG(const Vector &wi, const Vector &wo, const Vector &m, Float alpha) const {
return smithG1(wi, m, alpha) * smithG1(wo, m, alpha);
}
std::string toString() const {
switch (m_distribution) {
switch (m_type) {
case EBeckmann: return "beckmann"; break;
case EPhong: return "phong"; break;
case EGGX: return "ggx"; break;
@ -230,7 +242,7 @@ public:
}
}
private:
EType type;
EType m_type;
};
MTS_NAMESPACE_END

41
src/bsdfs/roughdielectric.cpp
View File

@ -127,15 +127,6 @@ public:
m_specularTransmittance = new ConstantSpectrumTexture(
props.getSpectrum("specularTransmittance", Spectrum(1.0f)));
Float alpha;
if (props.hasProperty("alphaB")) {
Log(EWarn, "Deprecation warning: the 'alphaB' parameter "
"has been renamed to 'alpha'");
alpha = props.getFloat("alphaB");
} else {
alpha = props.getFloat("alpha", 0.1f);
}
m_intIOR = props.getFloat("intIOR", 1.5046f);
m_extIOR = props.getFloat("extIOR", 1.0f);
@ -145,10 +136,11 @@ public:
"refraction must be positive and differ!");
m_distribution = MicrofacetDistribution(
m_props.getString("distribution", "beckmann")
props.getString("distribution", "beckmann")
);
m_alpha = new ConstantFloatTexture(alpha);
m_alpha = new ConstantFloatTexture(
props.getFloat("alpha", 0.1f));
m_components.push_back(
EGlossyReflection | EFrontSide | EBackSide | ECanUseSampler);
@ -184,7 +176,10 @@ public:
return (value < 0) ? -1.0f : 1.0f;
}
Spectrum eval(const BSDFQueryRecord &bRec) const {
Spectrum eval(const BSDFQueryRecord &bRec, EMeasure measure) const {
if (measure != ESolidAngle)
return Spectrum(0.0f);
/* Determine the type of interaction */
bool reflect = Frame::cosTheta(bRec.wi)
* Frame::cosTheta(bRec.wo) > 0;
@ -219,7 +214,7 @@ public:
}
/* Evaluate the roughness */
Float alpha = m_distribution.transform(
Float alpha = m_distribution.transformRoughness(
m_alpha->getValue(bRec.its).average());
/* Microsurface normal distribution */
@ -231,7 +226,7 @@ public:
const Float F = fresnel(dot(bRec.wi, H), m_extIOR, m_intIOR);
/* Smith's shadow-masking function */
const Float G = smithG1(bRec.wi, H, alpha) * smithG1(bRec.wo, H, alpha);
const Float G = m_distribution.smithG(bRec.wi, bRec.wo, H, alpha);
if (reflect) {
/* Calculate the total amount of reflection */
@ -255,7 +250,10 @@ public:
}
}
Float pdf(const BSDFQueryRecord &bRec) const {
Float pdf(const BSDFQueryRecord &bRec, EMeasure measure) const {
if (measure != ESolidAngle)
return 0.0f;
/* Determine the type of interaction */
bool sampleReflection = ((bRec.component == -1 || bRec.component == 0)
&& (bRec.typeMask & EGlossyReflection)),
@ -303,7 +301,7 @@ public:
}
/* Evaluate the roughness */
Float alpha = m_distribution.transform(
Float alpha = m_distribution.transformRoughness(
m_alpha->getValue(bRec.its).average());
/* Suggestion by Bruce Walter: sample using a slightly different
@ -386,7 +384,7 @@ public:
}
/* Evaluate the roughness */
Float alpha = m_distribution.transform(
Float alpha = m_distribution.transformRoughness(
m_alpha->getValue(bRec.its).average());
/* Suggestion by Bruce Walter: sample using a slightly different
@ -396,7 +394,7 @@ public:
std::abs(Frame::cosTheta(bRec.wi))));
/* Sample M, the microsurface normal */
const Normal m = sampleD(sample, sampleAlpha);
const Normal m = m_distribution.sampleD(sample, sampleAlpha);
if (sampleExactFresnelTerm) {
sampleF = fresnel(dot(bRec.wi, m), m_extIOR, m_intIOR);
@ -438,8 +436,7 @@ public:
}
Float numerator = m_distribution.eval(m, alpha)
* m_distribution.smithG1(bRec.wi, m, alpha)
* m_distribution.smithG1(bRec.wo, m, alpha)
* m_distribution.smithG(bRec.wi, bRec.wo, m, alpha)
* dot(bRec.wi, m);
Float denominator = m_distribution.eval(m, sampleAlpha)
@ -508,7 +505,7 @@ public:
}
/* Evaluate the roughness */
Float alpha = m_distribution.transform(
Float alpha = m_distribution.transformRoughness(
m_alpha->getValue(bRec.its).average());
/* Suggestion by Bruce Walter: sample using a slightly different
@ -518,7 +515,7 @@ public:
std::abs(Frame::cosTheta(bRec.wi))));
/* Sample M, the microsurface normal */
const Normal m = sampleD(sample, sampleAlpha);
const Normal m = m_distribution.sampleD(sample, sampleAlpha);
if (sampleExactFresnelTerm) {
Float sampleF = fresnel(dot(bRec.wi, m), m_extIOR, m_intIOR);

14
src/libcore/spectrum.cpp
View File

@ -96,6 +96,8 @@ Float Spectrum::m_wavelengths[SPECTRUM_SAMPLES + 1];
void Spectrum::staticInitialization() {
#if SPECTRUM_SAMPLES != 3
std::ostringstream oss;
oss << std::fixed;
oss.precision(2);
Float stepSize = SPECTRUM_RANGE / (Float) SPECTRUM_SAMPLES;
for (int i=0; i<SPECTRUM_SAMPLES + 1; i++) {
Float value = SPECTRUM_MIN_WAVELENGTH + stepSize * i;
@ -406,12 +408,16 @@ void Spectrum::fromRGBE(const uint8_t rgbe[4], EConversionIntent intent) {
std::string Spectrum::toString() const {
std::ostringstream oss;
oss << "[";
oss << std::fixed;
for (int i=0; i<SPECTRUM_SAMPLES; i++) {
#if SPECTRUM_SAMPLES == 3
oss << s[i];
#else
oss.precision(1);
oss << m_wavelengths[i] << "-"
<< m_wavelengths[i+1] << "nm => " << s[i];
<< m_wavelengths[i+1] << "nm => ";
oss.precision(3);
oss << s[i];
#endif
if (i < SPECTRUM_SAMPLES - 1)
oss << ", ";
@ -607,9 +613,13 @@ Float InterpolatedSpectrum::eval(Float lambda) const {
std::string InterpolatedSpectrum::toString() const {
std::ostringstream oss;
oss << std::fixed;
oss << "InterpolatedSpectrum[" << endl;
for (size_t i=0; i<m_wavelengths.size(); ++i) {
oss << " " << m_wavelengths[i] << " nm => " << m_values[i];
oss.precision(1);
oss << " " << m_wavelengths[i] << " nm => ";
oss.precision(3);
oss << m_values[i];
if (i+1 < m_wavelengths.size())
oss << ",";
oss << endl;

12
src/libcore/util.cpp
View File

@ -687,16 +687,16 @@ Float fresnelDielectric(Float cosThetaI, Float cosThetaT,
return (Rs * Rs + Rp * Rp) / 2.0f;
}
Spectrum fresnelConductor(Float cosTheta, const Spectrum &eta, const Spectrum &k) {
Spectrum tmp = (eta*eta + k*k) * (cosTheta * cosTheta);
Spectrum fresnelConductor(Float cosThetaI, const Spectrum &eta, const Spectrum &k) {
Spectrum tmp = (eta*eta + k*k) * (cosThetaI * cosThetaI);
Spectrum rParl2 = (tmp - (eta * (2.0f * cosTheta)) + Spectrum(1.0f))
/ (tmp + (eta * (2.0f * cosTheta)) + Spectrum(1.0f));
Spectrum rParl2 = (tmp - (eta * (2.0f * cosThetaI)) + Spectrum(1.0f))
/ (tmp + (eta * (2.0f * cosThetaI)) + Spectrum(1.0f));
Spectrum tmpF = eta*eta + k*k;
Spectrum rPerp2 = (tmpF - (eta * (2.0f * cosTheta)) + Spectrum(cosTheta*cosTheta)) /
(tmpF + (eta * (2.0f * cosTheta)) + Spectrum(cosTheta*cosTheta));
Spectrum rPerp2 = (tmpF - (eta * (2.0f * cosThetaI)) + Spectrum(cosThetaI*cosThetaI)) /
(tmpF + (eta * (2.0f * cosThetaI)) + Spectrum(cosThetaI*cosThetaI));
return (rParl2 + rPerp2) / 2.0f;
}