Ray Tracing from the Ground Up

Chapter 7

Mapping Samples to a Hemisphere

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 ...