Fundamentals of Computer Graphics, 4th Edition

Chapter 22

Implicit Modeling

Brian Wyvill

Implicit modeling (also known as implicit surfaces) in computer graphics covers many different methods for defining models. These include skeletal implicit modeling, offset surfaces, level sets, variational surfaces, and algebraic surfaces. In this chapter, we briefly touch on these methods and describe how to build skeletal implicit models in more detail. Curves can be defined by implicit equations of the form

$f\left(x,y\right)=0.$

If we consider a closed curve, such as a circle, with radius r, then the implicit equation can be written as

$f\left(x,y\right)=x^2+y^2-r^2=0.\text{ (22.1)}$

The value of f(x, y) can be positive (outside the circle), negative (inside the circle), or zero for points precisely on the circle. The equivalent ...