Curves and Surfaces for Computer-Aided Geometric Design. A by Gerald Farin

By Gerald Farin

A number one professional in CAGD, Gerald Farin covers the illustration, manipulation, and evaluate of geometric shapes during this the 3rd version of Curves and Surfaces for machine Aided Geometric layout. The e-book bargains an advent to the sector that emphasizes Bernstein-Bezier equipment and offers topics in a casual, readable kind, making this an excellent textual content for an introductory path on the complex undergraduate or graduate level.
The 3rd variation incorporates a new bankruptcy on Topology, deals new workouts and sections inside so much chapters, combines the cloth on Geometric Continuity into one bankruptcy, and updates current fabrics and references. Implementation suggestions are addressed for practitioners through the inclusion of latest C courses for plenty of of the basic algorithms. The C courses can be found on a disk integrated with the text.
method Requirements:
IBM computer or compatibles, DOS model 2.0 or higher.

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* Covers illustration, manipulation, and overview of geometric shapes
* Emphasizes Bernstein-Bezier methods
* Written in a casual, easy-to-read style

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Additional resources for Curves and Surfaces for Computer-Aided Geometric Design. A Practical Guide

Sample text

2 Properties of Bézier Curves Many of the properties in this section have already appeared in the previous chapter. They were derived using geometric arguments. We shall now rederive several of them, using algebraic arguments. If the same heading is used here as in Chapter 3, the reader should look there for a complete description of the property in question. Affine invariance. Barycentric combinations are invariant under affine maps. 5) gives the algebraic verification of this property. We note again that this does not imply invariance under perspective maps!

We will infer these properties from the geometry underlying the algorithm. In the next chapter, we will show how they can also be derived analytically. Affine invariance. 2. They are in the tool kit of every CAD system: objects must be repositioned, scaled, and so on. An important property of Bézier curves is that they are invariant under affine maps, which means that the following two procedures yield the same result: (1) first, compute the point hn(t) and then apply an affine map to it; (2) first, apply an affine map to the control polygon and then evaluate the mapped polygon at parameter value t.

The possibility for a quick decision of no interference is extremely important, since in practice one often has to check one object against thousands of others, most of which can be labeled as "no interference" by the minmax box test. 3 Endpoint interpolation. The Bézier curve passes through bo and b n : we have b n (0) = bo, b n ( l ) = b n . This is easily verified by writing down the scheme of Eq. 3) for the cases t = 0 and t = 1. In a design situation, the endpoints of a curve are certainly two very important points.

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