Geometry for Programmers

8 Nonlinear transformations and surfaces

This chapter covers

• Performing polynomial transformations in multidimensional space
• Understanding how a multidimensional transformation is the same as a surface
• Using spatial interpolation to build a deformation field

Before this chapter, we barely spoke about 3D space. That’s because the math behind linear equations and projective transformations doesn’t change much when you go from 2D to 3D. And because things are usually easier to understand in 2D, there was no good reason to add a new dimension—until now. This chapter is about building and manipulating 3D objects.

To get there, we’ll once again start with a 2D transformation, but this time, it’ll be nonlinear. In chapter 4, we used a linear transformation ...