Modifying the shape of NURBS surfaces with geometric constraints

NURBS surfaces are among the most commonly used parametric surfaces in CAGD and Computer Graphics. This paper investigates shape modification of NURBS surfaces with geometric constraints, such as point, normal vector, and cur ve constraints. Two new methods are presented by constrained optimization a nd energy minimization. The former is based on minimizing changes in contro l net of surfaces, whereas the latter is based on strain energy minimizatio n. By these two methods, we change control points and weights of an origina l surface, such that the modified surface satisfies the given constraints. Comparison results and practical examples are also given. (C) 2001 Elsevier Science Ltd. All rights reserved.