Bezier Splines and Patches
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by: Blake Fasching, undergraduate student
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from: Rice University
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when: Monday, November 24, 2003, Noon to 1:00 PM
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where: 427 Herman Brown Hall, Rice University, 6100 Main Street, Houston, Texas
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abstract: Bezier cubics are typically used to describe shapes in geometric modeling.  To model a curved shape, for example, we divide the curve into some number of smaller segments, and then use a Bezier cubic to match each smaller segment as closely as possible.  The result is a Bezier spline.  A simple system allowing a user to input some number of control points describing the shape of the curve desired, and outputting the corresponding Bezier spline curve, helps one get a visual idea of how B-Splines do their job.  Now what do we do when we just have a bunch of curves, why we make surfaces out of them.  The method for making curved surfaces out of Bezier Splines, particularly quadratic Bezier patches, is quite interesting and powerful.  When dealing with CAGD, this technique generalized, allows us to transform surfaces to a different number of polygons allowing us to make smoother or rougher surfaces giving higher or lower rendering time respectively.