Angel: Interactive Computer Graphics 4E Addison-Wesley 2005
Curves and Surfaces in OpenGL
Ed Angel
Professor of Computer Science, Electrical and Computer Engineering, and Media Arts
University of New Mexico
Objectives
Introduce OpenGL evaluators
Learn to render polynomial curves and surfaces
Discuss quadrics in OpenGL
GLUT Quadrics
GLU Quadrics
What Does OpenGL Support
Evaluators: a general mechanism for working with the Bernstein polynomials
Can use any degree polynomials
Can use in 1-4 dimensions
Automatic generation of normals and texture coordinates
NURBS supported in GLU
Quadrics
GLU and GLUT contain polynomial approximations of quadrics
One-Dimensional Evaluators
Evaluate a Bernstein polynomial of any degree at a set of specified values
Can evaluate a variety of variables
Points along a 2, 3 or 4 dimensional curve
Colors
Normals
Texture Coordinates
We can set up multiple evaluators that are all evaluated for the same value
Setting Up an Evaluator
glMap1f(type,u_min,u_max,stride,
order, pointer_to_array)
what we want to evaluate
max and min of u
1+degree of polynomial
pointer to control data
separation between
data points
Each type must be enabled by glEnable(type)
Example
Consider an evaluator for a cubic Bezier curve over (0,1)
point data[ ]={…………..}; * /3d data /*
glMap1f(GL_MAP_VERTEX_3,0.0,1.0,3,4,data);

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