By Gerald Farin
A number one professional in CAGD, Gerald Farin covers the illustration, manipulation, and review of geometric shapes during this the 3rd variation of Curves and Surfaces for machine Aided Geometric layout. The e-book bargains an creation to the sphere that emphasizes Bernstein-Bezier tools and provides matters in a casual, readable sort, making this a fantastic textual content for an introductory direction on the complicated undergraduate or graduate level.
The 3rd version encompasses a new bankruptcy on Topology, deals new routines and sections inside of so much chapters, combines the fabric on Geometric Continuity into one bankruptcy, and updates present fabrics and references. Implementation concepts are addressed for practitioners through the inclusion of latest C courses for lots of of the basic algorithms. The C courses can be found on a disk incorporated with the text.
IBM computer or compatibles, DOS model 2.0 or higher.
* Covers illustration, manipulation, and overview of geometric shapes
* Emphasizes Bernstein-Bezier methods
* Written in a casual, easy-to-read style
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Extra resources for Curves and Surfaces for Computer-Aided Geometric Design. A Practical Guide
Then we always have c r o s s e c < cross c. 13) This property follows from a simple observation: consider two points b*, bi+χ. The straight line segment through them can cross a given plane at one point at most, while the curve segment from c that connects them may cross the 24 CHAPTER 2. 6: The variation diminishing property: a piecewise linear interpolant to a curve has no more intersections with any plane than the curve itself. same plane in many arbitrary points. 6. 5 Menelaos' Theorem We use the concept of piecewise linear interpolation to prove one of the most important geometric theorems for the theory of CAGD: Menelaos' theorem.
12), it follows that the control vertices of the part corresponding to [c, 1] are given by the b™~J. 2, we see the two subpolygons defining the arcs from b n (0) to b n (c) and from b n (c) to b n ( l ) . 6. 5: Generalized subdivision: evaluation of a quadratic at two parameter values c and d subdivides it into three segments. Its Bézier points are shown in blossom notation. 5 shows the blossom notation if we subdivide at two parameter values c and d simultaneously. Instead of subdividing a Bézier curve, we may also extrapolate it: in that case, we might be interested in the Bézier points d^ corresponding to an interval [l,d].
4, it is clear that it does not matter if the Bézier points are labeled bo, b i , . . , b n or b n , b n _ i , . . , bo- The curves that correspond to the two different orderings look the same; they differ only in the direction in which they are traversed. Written as a formula: £ bjB^t) = £ b n - ^ l - *). 1). We say that Bernstein polynomials are symmetric with respect to t and 1 — t. Invariance under barycentric combinations. The process of forming the Bézier curve from the Bézier polygon leaves barycentric combinations invariant.
Curves and Surfaces for Computer-Aided Geometric Design. A Practical Guide by Gerald Farin