Watertight trimmed NURBS

This paper addresses the long-standing problem of the unavoidable gaps that arise when expressing the intersection of two NURBS surfaces using conventional trimmed-NURBS representation. The solution converts each trimmed NURBS into an untrimmed T-Spline, and then merges the untrimmed T-Splines into a single, watertight model. The solution enables watertight fillets of NURBS models, as well as arbitrary feature curves that do not have to follow iso-parameter curves. The resulting T-Spline representation can be exported without error as a collection of NURBS surfaces.

[1]  Eugene Fiume,et al.  Wires: a geometric deformation technique , 1998, SIGGRAPH.

[2]  J. Navarro-Pedreño Numerical Methods for Least Squares Problems , 1996 .

[3]  Henry P. Moreton,et al.  Watertight tessellation using forward differencing , 2001, HWWS '01.

[4]  Henning Biermann,et al.  Approximate Boolean operations on free-form solids , 2001, SIGGRAPH.

[5]  Dinesh Manocha,et al.  Efficient representations and techniques for computing B-rep's of CSG models with NURBS primitives , 1996 .

[6]  Jos Stam,et al.  Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values , 1998, SIGGRAPH.

[7]  Kenneth Steiglitz,et al.  Operations on Images Using Quad Trees , 1979, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[8]  Helmut Pottmann,et al.  Fitting B-spline curves to point clouds by curvature-based squared distance minimization , 2006, TOGS.

[9]  Dinesh Manocha,et al.  An efficient surface intersection algorithm based on lower-dimensional formulation , 1997, TOGS.

[10]  Jianzhong Wang,et al.  Generating Gn parametric blending surfaces based on partial reparameterization of base surfaces , 2007, Comput. Aided Des..

[11]  Tom Lyche,et al.  T-spline simplification and local refinement , 2004, ACM Trans. Graph..

[12]  Jörg Peters,et al.  Patching Catmull-Clark meshes , 2000, SIGGRAPH.

[13]  Ahmad H. Nasri,et al.  T-splines and T-NURCCs , 2003, ACM Trans. Graph..

[14]  Malcolm A. Sabin,et al.  Non-uniform recursive subdivision surfaces , 1998, SIGGRAPH.

[15]  Charles T. Loop Second order smoothness over extraordinary vertices , 2004, SGP '04.

[16]  Theodosios Pavlidis,et al.  A Hierarchical Syntactic Shape Analyzer , 1979, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[17]  Nicholas M. Patrikalakis,et al.  Intersection Problems , 2002, Handbook of Computer Aided Geometric Design.

[18]  Rida T. Farouki,et al.  Linear perturbation methods for topologically consistent representations of free-form surface intersections , 2004, Comput. Aided Geom. Des..

[19]  Hanan Samet,et al.  The Quadtree and Related Hierarchical Data Structures , 1984, CSUR.

[20]  Dinesh Manocha,et al.  Interactive rendering of parametric spline surfaces , 1996 .

[21]  Dieter W. Fellner,et al.  Extended subdivision surfaces: Building a bridge between NURBS and Catmull-Clark surfaces , 2006, TOGS.

[22]  Dinesh Manocha,et al.  BOOLE: A Boundary Evaluation System for Boolean Combinations of Sculptured Solids , 2001, Int. J. Comput. Geom. Appl..

[23]  Rida T. Farouki,et al.  Topologically consistent trimmed surface approximations based on triangular patches , 2004, Comput. Aided Geom. Des..

[24]  Tony DeRose,et al.  Subdivision surfaces in character animation , 1998, SIGGRAPH.

[25]  Ron Goldman,et al.  Implicit representation of parametric curves and surfaces , 1984, Comput. Vis. Graph. Image Process..

[26]  Thomas W. Sederberg,et al.  Genus of the intersection curve of two rational surface patches , 1988, Comput. Aided Geom. Des..

[27]  William Buxton,et al.  Ten CAD challenges , 2005, IEEE Computer Graphics and Applications.