Overview

To use NURBS curves and surfaces in an Inventor program, you need to develop an intuitive feel for a number of basic concepts. This section defines these key concepts and shows how they pertain to the various Inventor NURBS-related classes. For a more rigorous mathematical description of a NURBS, see Suggestions for Further Reading at the end of this chapter.

Classes Used with NURBS Shapes

This chapter describes use of the following classes:

SoNurbsCurve	represents a NURBS curve. (This is where the knot sequence is specified.)
SoNurbsSurface	represents a NURBS surface. (This is where the knot sequence is specified.)
SoNurbsProfile	trims regions from a NURBS surface using a NURBS curve.
SoLinearProfile	trims regions from a NURBS surface using connected line segments.
SoProfileCoordinate2	specifies 2D coordinates for trim curves.
SoProfileCoordinate3	specifies rational 2D coordinates for trim curves.
SoCoordinate3	specifies the control points of a NURBS surface or curve.
SoCoordinate4	specifies rational control points of a NURBS surface or curve.

Parametric Curves

For simplicity, this discussion first explains the important NURBS concepts in terms of curves, which are lines in 3D space, such as a helix. Once you understand how to define a NURBS curve, defining a NURBS surface is a simple extension of your knowledge (see NURBS Surfaces).

A NURBS curve or surface is parametric*—that is, the equations that describe it depend on variables (or *parameters) that are not explicitly part of the geometry. A NURBS curve is described in terms of one parameter, u. The following three functions map this single parameter into x-*y*-*z* space:

x = f(u)
y = g(u)
z = h(u)

By sweeping through different values of u (that is, through parameter space), it is possible to evaluate the equations and determine the x, y, and z values for points on the curve in object space. Mapping a Parametric Curve to Object Space represents this mapping of parameter space to object space.

Mapping a Parametric Curve to Object Space