AngelCG39山东university软件学院图形学教材.ppt

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 Example Evaluating The function glEvalCoord1f(u) causes all enabled evaluators to be evaluated for the specified u Can replace glVertex, glNormal, glTexCoord The values of u need not be equally spaced Example Equally Spaced Points Rather than use a loop, we can set up an equally spaced mesh (grid) and then evaluate it with one function call Bezier Surfaces Similar procedure to 1D but use 2D evaluators in u and v Set up with glMap2f(type, u_min, umax, u_stride, u_order, v_min, v_max, v_stride, v_order, pointer_to_data) Evaluate with glEvalCoord2f(u,v) Example Rendering with Lines Rendering with Quadrilaterals Uniform Meshes We can form a 2D mesh (grid) in a similar manner to 1D for uniform spacing glMapGrid2(u_num, u_min, u_max, v_num, v_min, v_max) Can evaluate as before with lines or if want filled polygons glEvalMesh2( GL_FILL, u_start, u_num, v_start, v_num) Rendering with Lighting If we use filled polygons, we have to shade or we will see solid color uniform rendering Can specify lights and materials but we