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

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Chapter 31

Modeling and Processing with Quadric Surfaces

Wenping Wang

Quadric surfaces, or quadrics, are surfaces defined by algebraic equations of degree two. We will discuss mainly quadrics in 3D space, though quadrics in higher dimensions are also of certain interest to CAGD. In this chapter the following topics concerning quadrics will be discussed.

1. Definition and Classifications

2. Parametric Representation

3. Fitting, Blending, and Offsetting

4. Intersection and Interference

31.1 DEFINITION AND CLASSIFICATIONS

In this section we will define quadrics and discuss their classifications under different groups of transformations, i.e., Euclidean, affine, and projective transformations [41].

31.1.1 Definition

A quadric is defined by ...

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