Error Bounded Approximate Reparametrization Of Non-Uniform Rational B-Spline Curves

In designing free-form curves and surfaces, the user of a geometric modeler generally wishes to concentrate on shape. Geometric constructions using parametrically defined representations, however, often lead to unwanted or surprising effects due to curve and surface parametrizations. Reparametrizing curve or surface representations is an important approach to minimizing these effects. Reparametrization also can be viewed as a means for transforming curves and surfaces into representations that are better suited to establishing important properties or exploring the design space. This research explores the use of curve reparametrization in modeling tools for NURBS (Non-Uniform Rational B-Spline) based CAD systems. There are many practical applications of such tools including establishing and exploring correspondence in geometry, creating related speed profiles along motion curves for animation, specifying speeds along tool paths, and identifying geometrically equivalent, or nearly equiv..