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Ray Tracing from the Ground Up by Kevin Suffern

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Chapter 7

Mapping Samples to a Hemisphere

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Objectives

By the end of this chapter you should:

  • understand how to map sample points from a square to a hemisphere with a cosine power density distribution;
  • have the sampling tools available to model a number of direct and indirect illumination effects.

A number of shading applications in later chapters require sample points distributed over the surface of a unit hemisphere. These samples need to have a density that varies as a cosine power of the polar angle measured from the top of the hemisphere. The reason is a cosine factor in the rendering equation (Chapter 13) and because some of the BRDFs ...

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