3D Math Primer for Graphics and Game Development, 2nd Edition

Chapter 13

Curves in 3D

I didn’t discover curves; I only uncovered them.

— Mae West (1892–1980)

This chapter talks about how to represent curves mathematically in 3D. Recreating a curve from its mathematical definition is relatively easy; the tricky part is obtaining a curve with desired properties, or alternatively, making a tool that designers can use to draw such curves. Our goal in this chapter is to provide a graceful and intuitive introduction to the mathematics of curves. In comparison with most of the other books on the subject, our aim is to hit the most important points, without stopping every other paragraph to prove that what we are saying is true. (We will, however, stop periodically to discuss correct pronunciation, which is probably ...