ABSTRACT
The purpose of this study is, as with curves, to investigate shape properties of parametric surfaces. From a given point on a curve, it is possible to move in only the positive or negative direction along the curve. However, it is possible to move in any of https://www.w3.org/1998/Math/MathML"> 2 π https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064289/fc4a4622-76a5-4c96-97e4-82b5015d6fd6/content/eq5371.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> direction from a given point on a curve. We shall present differential properties of surfaces and some wellknown operators on them, and how these properties can be used to gain information about the shape of a surface. As in the case of curves, we shall try to understand more complex surfaces in terms of simpler ones, namely linear surfaces, i.e., planes, and quadric surfaces. We can also try to understand certain properties of surfaces by looking at classes of curves which lie in the surfaces. We address two major conceptual issues. One is to learn as much as possible about a surface by computing its differential characteristics. The other is to determine which of these characteristics is invariant under surface reparameterization. That is, we seek to determine which characteristics are intrinsic to the surface rather than being based on a particular parametric representation.
