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Scientific Visualization and Animation using Bezier Surfaces
An Introduction


Prof. David Bernstein
James Madison University

Computer Science Department
bernstdh@jmu.edu

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Mathematical Representation
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  • Control Points:
    • Let \(p_{ij}\) denote control point \((i,j)\)
    • The patch will be in the convex hull of the control points
  • Blending Polynomials:
    • We have one array of blending polynomials for each parameter
  • The Bezier Patch:
    • \(p(u,v) = \sum_{i=0}^{n} \sum_{j=0}^{m} b_{i}(u) b_{j}(v) p_{ij}\)
Bezier Surfaces in OpenGL
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  • Evaluators:
    • Are used in the same way as for Bezier curves (i.e., to compute the values for the Bernstein polynomials)
  • For Uniform Meshes:
    • glMapGrid2f())
    • glEvalMesh2()
Bezier Surfaces in OpenGL (cont.)
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Using an Evaluator
svaexamples/surfaces/edit.c (Fragment: mesh)
 
Bezier Surfaces in OpenGL (cont.)
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Initialization
svaexamples/surfaces/edit.c (Fragment: setup)
 
A Simple Surface Editing Program
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svaexamples/surfaces/edit.c
 
Adding Lighting and Shading
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Using the Evaluator to Fill
svaexamples/surfaces/shade.c (Fragment: surface)
 
Adding Lighting and Shading (cont.)
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Initialization
svaexamples/surfaces/shade.c (Fragment: setup)
 
There's Always More to Learn
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