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Handbook of Computer Aided Geometric Design by M.-S. Kim, J. Hoschek, G. Farin

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Chapter 2

Geometric Fundamentals

Wolfgang Boehm and Hartmut Prautzsch

The following recalls the facts and terminology mostly used in Geometry. It may serve also as a first introduction to geometric tools, for more detailed and founded descriptions see the list of references, in particular [7]. Without additional effort most of the discussed topics can be presented in spaces of any dimension.

2.1 AFFINE FUNDAMENTALS

Many properties of computational geometry and its applications do not need the distance of points but only the concepts of parallelism and ratio.

2.1.1 Points and vectors

In general a point in n-space is fixed by its coordinates with respect to some Cartesian system1. Nevertheless, we start our observations with affine aspects. ...

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