Graphics Gems V (IBM Version)

IV.5

Fast Generation of Ellipsoids

Ahn Jaewoo,     Systems Engineering Research Institute, KIST Yusong, Daejon, South Korea

Introduction

Among the many methods for generating a polygonal approximation to an ellipse in standard position (of the form x²/a² + y²/b² = 1) (Anton 1984), the one shown in Figure 1 is simple and common. The idea is to subdivide the angles in plane around the center of the unit circle equally, forming a polygonal approximation to the unit circle, which is then scaled by a in the x axis, and by b in the y axis.

Figure 1 A polygonal approximation to an ellipse (n = 7). (a) (cos θ, sin θ), θ = i/n · π/2, i = 0, 1, …, ...