Chapter 3

Geometries for CAGD

Helmut Pottmann and Stefan Leopoldseder

Chapter 2 describes the fundamental geometric setting for 3D modeling and addresses Euclidean, affine and projective geometry, as well as differential geometry. In the present chapter, the discussions will be continued with a focus on geometric concepts which are less widely known. These are projective differential geometric methods, sphere geometries, line geometry, and non-Euclidean geometries. In all cases, we outline and illustrate applications of the respective geometries in geometric modeling.

Special emphasis is put on a general important principle, namely the simplification of a geometric problem by application of an appropriate geometric transformation. For example, ...

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