Handbook of Computer Aided Geometric Design

Chapter 9

Splines on Surfaces

Marian Neamtu

This chapter addresses the area of spline theory concerned with the construction of functions defined on manifolds in three-dimensional Euclidean space. For the most part, the mathematical aspects of this discipline are in their infancy and therefore the presentation will have an exploratory character.

9.1 INTRODUCTION

Thus far in this book we have mostly encountered spline curves and surfaces whose parameter domains are subsets of the real line or the Euclidean plane. In particular, in several chapters of this book we became accustomed to the idea that a spline surface is the graph of a bivariate real-valued function or, alternatively, a parametric surface, which is the image of a planar domain ...