Fundamental Geometric Algorithms

Abstract

In this chapter we present five tools which are fundamental in the implementation of B-spline curves and surfaces; these are knot insertion, knot refinement, knot removal, degree elevation, and degree reduction. We devote a section to each topic, and the layout of each section is roughly:

• a statement of the problem (for curves);

• a list of applications;

• clarification of the problem and solution approaches (curves);

• a list of references where more rigorous derivations and proofs can be found;

• the solution formulas (curves);

• worked examples (curves);

• computer algorithms;

• examples of applications;

• the solution for surfaces, and outlines of the surface algorithms.