OpenGL Programming Guide

Chapter 11
Evaluators and NURBS

Chapter Objectives

Advanced

After reading this chapter, you'll be able to do the following:

• Use OpenGL's evaluator commands to draw basic curves and surfaces
  
  

• Use the GLU's higher-level NURBS facility to draw more complex curves and surfaces

Note that this chapter presumes a number of prerequisites; they're listed in "Prerequisites" .

At the lowest level, graphics hardware draws points, line segments, and polygons, which are usually triangles and quadrilaterals. Smooth curves and surfaces are drawn by approximating them with large numbers of small line segments or polygons. However, many useful curves and surfaces can be described mathematically by a small number of parameters such as a few control points. Saving the sixteen control points for a surface requires much less storage than saving 1000 triangles together with the normal vector information at each vertex. In addition, the 1000 triangles only approximate the true surface, but the control points can accurately describe the real surface.

Evaluators provide a way to specify points on a curve or surface (or part of one) using only the control points. The curve or surface can then be rendered at any precision. In addition, normal vectors can be calculated for surfaces automatically. You can use the points generated by an evaluator in many ways - to draw dots where the surface would be, to draw a wireframe version of the surface, or to draw a fully lighted and shaded version.

You can use evaluators to describe any polynomial or rational polynomial splines or surfaces of any degree. These include almost all splines and spline surfaces in use today, including B-splines, NURBS (Non-Uniform Rational B-Spline) surfaces, Bézier curves and surfaces, and Hermite splines. Since evaluators provide only a low-level description of the points on a curve or surface, however, they're typically used underneath utility libraries that provide a higher-level interface to the programmer. The GLU's NURBS facility is such a higher-level interface - the NURBS routines encapsulate lots of complicated code, but the final rendering is done with evaluators.

This chapter contains the following major sections:

• "Prerequisites" discusses what knowledge is assumed for this chapter. It also gives several references where you can obtain this information.
  
  

• "Evaluators" explains how evaluators work and how to control them using the appropriate OpenGL commands.
  
  

• "The GLU NURBS Interface" describes the GLU routines for creating NURBS surfaces.

Prerequisites
Evaluators
The GLU NURBS Interface

OpenGL Programming Guide