BSDF.h File Reference

Abstract representation of a BSDF defined at a single point on a surface in 3-space. More...

#include <core/SurfacePoint.h>
#include <utils/SpectralSampleSet.h>
#include <stats/Sampler.h>
#include <shapes/Shape.h>
#include <common/image/Image.h>

Go to the source code of this file.

Classes
class	BSDF
	Abstract representation of a BSDF defined at a single point on a surface in 3-space. More...

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Detailed Description

Abstract representation of a BSDF defined at a single point on a surface in 3-space.

Author:

Travis Fischer (fisch0920@gmail.com)

Matthew Jacobs (jacobs.mh@gmail.com)

Date:

Fall 2008

A BSDF (or Bidirectional Scattering Distribution Function) is a function defining the fraction of light propagated after hitting a surface in a given exitent direction, wo, from a given incident direction, wi. It represents the observed radiance leaving in direction wo, per unit of irradiance arriving from wi. A BSDF is commonly denoted by the notation fs(wi->wo). It is much more common in computer graphics to hear one speak about BRDFs (or Bidirectional Reflectance Distribution Functions), the difference being that BSDFs are defined over the entire sphere of solid angles and therefore include transmission (transparency), whereas BRDFs are defined only on the positive hemisphere at a surface point with respect to its local geometric normal. BRDFs represent a subset of allowable BSDFs, and they suffice in simulating the majority of real world materials. The added complexity / generality of BSDFs, however, is important to any physically based rendering engine such as Milton. A BRDF is commonly denoted by fr(wi->wo).

Physically valid BRDFs have several basic properties or consraints, namely reciprocity and conservation of energy. Reciprocity means that BRDFs are symmetric: fr(wi->wo) = fr(wo->wi). For this reason, it is common to make the symmetric explicit in the notation by instead writing fr(wi<->wo) in the case of BRDFs or fs(wi<->wo) in the case of BSDFs. Conservation of energy states that a surface should not reflect more energy than it receives. Formally this can be stated as the integral of fr(wi->wo) over the positive hemisphere at any point with respect to a projected solid angle measure has to be less than or equal to one for all possible incident vectors, wi.

Example usage:

      SurfacePoint pt;
      const real_t t = m_scene->getIntersection(ray, pt);
      
      // lazily initialize SurfacePoint and return if no intersection
      if (!pt.init(ray, t))
         return; // ray didn't hit anything (t == INFINITY)
      
      // sample the BSDF for an exitant direction
      const Event &event = pt.bsdf->sample();
      const Vector3 &wo  = event;
      
      if (wo == Vector3::zero())
         return; // invalid exitant direction
      
      // evaluate BSDF in the given exitant direction and divide by probability
      // with which we sampled that direction
      const real_t pdf = pt.bsdf->getPdf(event);
      const SpectralSampleSet &fs = pt.bsdf->getBSDF(wo) / pdf;
      
      // ... trace another ray in direction 'wo' ...
   

Definition in file BSDF.h.