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An urnful of blinding functionsThere is a fundamental connection between the mathematical theory of discrete probability distributions and the parametric curves and surfaces of computer-aided geometric design. It is no accident that the blending functions of Bezier curves and surfaces have an obvious probabilistic interpretation, nor is it a coincidence that the normalized uniform B-spline basis functions also model a simple stochastic process. The link between probability and geometry, and how to exploit simple probabilistic arguments to derive many of the classical geometric properties of the parametric curves and surfaces currently in vogue in computer-aided geometric design is discussed. This probabilistic approach is also used to introduce many new types of curves and surfaces, and it is demonstrated how probability theory can be used to simplify, unify, and generalize many well-known results.
Document ID
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Goldman, R. N.
(Control Data Corp. Minneapolis, MN, United States)
Date Acquired
August 12, 2013
Publication Date
March 1, 1984
Publication Information
Publication: NASA. Langley Research Center Computer-Aided Geometry Modeling
Subject Category
Numerical Analysis
Accession Number
Distribution Limits
Work of the US Gov. Public Use Permitted.
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