Handbook of Computer Aided Geometric Design

Chapter 8

Geometric Continuity

Jörg Peters

This chapter covers geometric continuity with emphasis on a constructive definition for piecewise parametrized surfaces. section 8.1 gives examples that show the need for a notion of continuity different from matching of Taylor expansions as in the case of functions. section 8.2 defines geometric continuity for parametric curves, and for surfaces, first along edges, then around points, and finally for a whole complex of patches which is called a G^k free-form surface spline. Here G^k characterizes a relation between specific maps while C^k continuity is a property of the resulting surface. The composition constraint on reparametrizations and the vertex-enclosure constraints are highlighted. section 8.3 ...