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Distribution Ray Tracing: Theory and

Practice

Peter Shirley

Changyaw Wang

Computer Science Department

Indiana University

Proceedings of the Third Eurographics Workshop on Rendering

1 Intro duction

Distribution ray tracing uses Monte Carlo integration to solve the rendering

equation. This technique was introduced by Cook et. al, and was notable

because of its simplicity and its ability to simulate areal luminaires, camera

lens eects, motion blur, and imp erfect specular reection[5]. Distribution

ray tracing has been extended and modied by many researchers, most no-

tably by Ka jiya who added true indirect illumination[12]. Distribution ray

tracing has also b een used as the viewing comp onent of radiosity systems

(e.g [37, 3]). In this paper we examine some of the central issues of distribu-

tion ray tracing that have been overlooked in the literature but are still of

importance.

Our interest in distribution ray tracing arises for three basic reasons.

The rst reason is that we b elieve any rendering system that has imp erfect

specular reection (e.g. brushed steel) will use distribution ray tracing as a

viewing method. Second, distribution ray tracing is a natural way to render

outdoor scenes, where the eects of single and double reection dominate

color, and where the geometry is extremely complex. Third, it is p ossible to

run ray tracing on large distributed memory multiprocessors[25].

Although the implementation of a simple distribution ray tracer is usually

implied to be straightforward, there are several important implementational

issues that have not been discussed in the literature, and the relationship be-

tween distribution ray tracing code and distribution ray tracing theory has

never b een completely stated. In this pap er, we present some implementa-

tional and mathematical details that we have found to be important in the

design of our software. In Section 2, we discuss the basics of Monte Carlo In-

tegration and Quasi-Monte Carlo integration. In Section 3, we apply Monte

Carlo integration to pixel ltering and use this as an example of how the

mathematics inuence the design of distribution ray tracing co de. Section 4,

we discuss the illumination calculations in a distribution ray tracer. This sec-

tion argues that illumination calculation is not well understo od and discusses

some problems that need further research. Section 5 discusses the need for

perception based display of the output of a distribution ray tracer. Section 6

discusses several implementational considerations we feel are non-obvious and

have recently forced us to redesign our software. Finally, Section 7 summa-

rizes our results and current plan of research.

2 Monte Carlo Integration and Quasi-Monte

Carlo Integration

In Monte Carlo integration, random points with some distribution are used

to nd an approximate value for the integral. For an integral

of a function

over some space

, we can generate an estimate of

using some set of

random points



through



, where each



is distributed according to a

probability density function

(

)

d



(



)

(



)

(1)

Although distribution ray tracing is usually phrased as an application of

Equation 1, many researchers replace the



with more evenly distributed

(quasi-random) samples (e.g. [4, 19 ]). This approach can b e shown to be

sound by analyzing decreasing error in terms of some discrepancy measure[44,

43, 19, 28] rather than in terms of variance. However, it is often convenient

to develop a sampling strategy using variance analysis on random samples,

and to instead use non-random, but equidistributed samples in an implemen-

tation. This approach is almost certainly correct, but its justication and

implications have yet to be explained.

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