Simple Method for Constructing NURBS Surfaces from Unorganized Points

In this paper, a new method for constructing NURBS surfaces from scattered and unorganized points is presented. The method is easy to implement and allows fitting a NURBS surface to a scattered point cloud without constructing either NURBS patches networks or polygon meshes. Based on the projection of the points onto the regression plane of the cloud, the method detects both regions where the cloud lacks points, and regions where the cloud is too dense. Then, by inserting and removing points, the point cloud is regularized and approximated by a NURBS surface. In order to reduce the approximation error, an evolutionary strategy obtains the weights of the NURBS surface so that the distance between the point cloud and the NURBS is minimal. Finally, the points inserted outside the bounds of the point cloud are removed by trimming the NURBS surface. Numerical and graphical results are provided, demonstrating that the method produces valid surfaces with low fitting error.