Copyright by Eric Lengyel

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Chapter 11. Curves and Surfaces

Curved geometry has become commonplace in 3D graphics engines due to modern hardware’s ability to render the high number of vertices and faces needed to convincingly render smoothly varying surfaces. In addition to geometrical modeling, curves may be employed as paths along which certain objects travel. This chapter examines several classes of three-dimensional cubic curves and then discusses how they can be used to produce bicubic parametric surfaces.

Cubic Curves

Due to the balance that they possess between simplicity and flexibility, curves defined by cubic polynomials have earned widespread use by computer graphics applications. In the sections that follow, we examine several classes of cubic curves and compare ...

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