Surface self-intersection is of interest in many applications, such as numerical control machining. For practical applications, it is desirable to incorporate an algorithm capable of supplying the solutions to the self-intersection of general parametric surfaces as it becomes cumbersome to handle different surface types as special cases. It is very important in many applications to have a robust surface self-intersection algorithm available to detect inappropriate solutions when they arise. In the case of numerical control machining, the cost of inappropriate tool selection resulting in surface gouging is extremely high.

The need for a surface self-intersection algorithm capable of handling general parametric surfaces is motivated by examining the description of self-intersection problems, the properties of a widely used complex parametric surface (an offset surface), and the algorithm requirements for an interactive computer graphics program within an engineering environment.