ABSTRACT
This chapter reviews non-uniform rational B-spline (NURBS) and T-spline. The NURBS surfaces are widely used in aircraft, shipbuilding and automobile industry. In Reverse Engineering (RE), the NURBS data are generated from points cloud or computer aided design systems, and they are usually very dense. Most existing simplification methods were designed for polygonal surfaces, and very little research was conducted on NURBS simplification. The chapter discusses several volumetric T-spline modeling techniques, including converting any quad/hex meshes to standard and rational T-splines, polycube-based parametric mapping, feature preservation using eigenfunctions, Boolean operations and skeletons, truncated hierarchical Catmull—Clark subdivision (THCCS), weighted T-splines, and conformal T-spline modeling. The THCCS incorporates extraordinary nodes and supports local refinement using a similar hierarchical structure as in truncated hierarchical B-splines. The Catmull—Clark subdivision basis functions are generalized to work for elements with more than one extraordinary node.
