Skeleton Based Parametric Solid Models: Ball B-Spline Surfaces

This paper proposes a new skeleton based parametric representation of freeform shell-like solid objects - Ball B-Spline Surfaces (BBSSs) and their fundamental properties and algorithms. BBSSs are generalizations of ball B-Spline curve from one parameter variable to two parameter variables. BBSSs directly define objects in B- Spline form, unlike a procedure method like sweeping. BBSSs describe not only every point inside 3D solid objects, but also provides their center surface (skeleton). So the representation is more flexible for modeling, manipulation and deformation.

[1]  Helmut Pottmann,et al.  Computing Rational Parametrizations of Canal Surfaces , 1997, J. Symb. Comput..

[2]  Helmut Pottmann,et al.  Pipe surfaces with rational spine curve are rational , 1996, Comput. Aided Geom. Des..

[3]  Germain E. Randriambelosoa.  Space curves approximation using G1 ball-spline curves , 2004 .

[4]  Willem F. Bronsvoort,et al.  A method for converting the surface of a generalized cylinder into a B-spline surface , 1992, Comput. Graph..

[5]  Jovan Popovic,et al.  Progressive simplicial complexes , 1997, SIGGRAPH.

[6]  Robert J. Holt,et al.  Hierarchical multiresolution reconstruction of shell surfaces , 2002, Comput. Aided Geom. Des..

[7]  Jon G. Rokne,et al.  Disk Bézier curves , 1998, Comput. Aided Geom. Des..

[8]  Nicholas M. Patrikalakis,et al.  Analysis and applications of pipe surfaces , 1998, Comput. Aided Geom. Des..

[9]  Paul A. Yushkevich,et al.  Continuous medial representations for geometric object modeling in 2D and 3D , 2003, Image Vis. Comput..

[10]  Seah Hock Soon,et al.  Skeleton Based Parametric Solid Models: Ball B-Spline Curves , 2007, 2007 10th IEEE International Conference on Computer-Aided Design and Computer Graphics.

[11]  Chandrajit L. Bajaj,et al.  Smooth Shell Construction with Mixed Prism Fat Surfaces , 1999, Geometric Modelling.

[12]  Rida T. Farouki,et al.  Approximation by interval Bezier curves , 1992, IEEE Computer Graphics and Applications.

[13]  Envelopes – Computational Theory and Applications Category : survey , 2022 .

[14]  Ramakant Nevatia,et al.  Three-Dimensional Descriptions Based on the Analysis of the Invariant and Quasi-Invariant Properties of Some Curved-Axis Generalized Cylinders , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[15]  L. Piegl,et al.  The NURBS Book , 1995, Monographs in Visual Communications.

[16]  Samuel Hornus,et al.  Subdivision-curve primitives: a new solution for interactive implicit modeling , 2001, Proceedings International Conference on Shape Modeling and Applications.

[17]  Dana H. Ballard,et al.  Splines as embeddings for generalized cylinders , 1982 .