Introduction: Foundations
We begin with some background material that will be assumed throughout the remainder of this book. Although we shall discuss several generic types of curve and surface representations, our main focus here is on the ambient mathematical spaces in which these shapes reside. We will also review barycentric coordinates, a topic that is central to the construction of conventional triangular surface patches.
1.1 Ambient Spaces
Four different kinds of mathematical spaces support the representation and analysis of free-form curves and surfaces: vector spaces, affine spaces, Grassmann spaces, and projective spaces. When first reading this chapter, you should focus your attention on vector spaces and affine spaces. ...
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