Automatic construction of nurbs surfaces from unorganized points

Abstract

Modeling with Non Uniform Rational B-Splines (NURBS) surfaces has become a standard in CAD/CAM systems due to its stability, flexibility, and local modification properties. The advantage of fitting with NURBS surfaces is well known, but it is also known that NURBS surfaces have several deficiencies. A NURBS surface cannot be fitted over an unorganized and scattered set of points and the representation of sharp features like edges, corners, and high curvatures is poor. This paper presents a new method for fitting a NURBS surface over an unorganized and scattered cloud of points, preserving its sharp features. In contrast with other methods, ours does not need either to construct a network of NURBS patches or polygon meshes. By reducing the dimensionality of the point cloud using ISOMAP algorithms, our method detects both regions with lacking points, and regions where the cloud is too dense. Then, the cloud is regularized by inserting and removing points, and it is approximated by a NURBS surface. An evolutionary strategy obtains the weights of the NURBS surface in order to improve the representation of sharp features.