Biquintic G2 surfaces via functionals

Recently, it was shown that a bi-cubic patch complex with n-sided holes can be completed into a curvature-continuous ( G 2 ) surface by n-sided caps of degree bi-5 that offer good and flexible shape (Karciauskas and Peters, 2013). This paper further explores the space of n-sided caps of degree bi-5 but focuses on functionals to set degrees of freedom and to optimally propagate and average out curvature from the bi-cubic complex. Multi-sided holes in a bicubic patch complex are filled by a curvature-continuous cap.The cap is of degree bi-5 and has good and flexible shape.The space of n-sided G 2 caps of degree bi-5 is explored via functionals.

[1]  U. Reif.  TURBS—Topologically Unrestricted Rational B-Splines , 1998 .

[2]  G. Farin.  Curves and Surfaces for Cagd: A Practical Guide , 2001 .

[3]  Jörg Peters,et al.  C2 free-form surfaces of degree (3, 5) , 2002, Comput. Aided Geom. Des..

[4]  Josep Cotrina Navau,et al.  Modelling surfaces from planar irregular meshes , 2000, Comput. Aided Geom. Des..

[5]  Charles T. Loop,et al.  G2 Tensor Product Splines over Extraordinary Vertices , 2008, Comput. Graph. Forum.

[6]  E. Catmull,et al.  Recursively generated B-spline surfaces on arbitrary topological meshes , 1978 .

[7]  Hans-Peter Seidel,et al.  Modeling of surfaces with fair reflection line pattern , 1999, Proceedings Shape Modeling International '99. International Conference on Shape Modeling and Applications.

[8]  Hartmut Prautzsch,et al.  Freeform splines , 1997, Computer Aided Geometric Design.

[9]  Xiuzi Ye,et al.  Curvature continuous interpolation of curve meshes , 1997, Comput. Aided Geom. Des..

[10]  Jörg Peters,et al.  On the complexity of smooth spline surfaces from quad meshes , 2009, Comput. Aided Geom. Des..

[11]  Gerald Farin,et al.  Curves and surfaces for computer aided geometric design , 1990 .

[12]  Adi Levin.  Modified subdivision surfaces with continuous curvature , 2006, ACM Trans. Graph..

[13]  Günther Greiner.  Curvature approximation with application to surface modeling , 1996, Advanced Course on FAIRSHAPE.

[14]  Tony DeRose,et al.  Efficient, fair interpolation using Catmull-Clark surfaces , 1993, SIGGRAPH.

[15]  Jörg Peters,et al.  Biquintic G 2 surfaces , 2013 .

[16]  Horst Nowacki,et al.  Construction of fair surfaces over irregular meshes , 2001, SMA '01.

[17]  Ramon F. Sarraga,et al.  A variational method to model G1 surfaces over triangular meshes of arbitrary topology in R3 , 2000, TOGS.

[18]  John A. Gregory,et al.  A C2 polygonal surface patch , 1989, Comput. Aided Geom. Des..

[19]  W. Boehm,et al.  Bezier and B-Spline Techniques , 2002 .

[20]  Jörg Peters,et al.  Guided spline surfaces , 2009, Comput. Aided Geom. Des..

[21]  John A. Gregory,et al.  Irregular C2 surface construction using bi-polynomial rectangular patches , 1999, Comput. Aided Geom. Des..

[22]  Lexing Ying,et al.  A simple manifold-based construction of surfaces of arbitrary smoothness , 2004, ACM Trans. Graph..

[23]  Przemyslaw Kiciak,et al.  Spline surfaces of arbitrary topology with continuous curvature and optimized shape , 2013, Comput. Aided Des..

[24]  John F. Hughes,et al.  Modeling surfaces of arbitrary topology using manifolds , 1995, SIGGRAPH.

[25]  Jörg Peters,et al.  Shape characterization of subdivision surfaces--case studies , 2004, Comput. Aided Geom. Des..

[26]  Günther Greiner,et al.  Variational Design and Fairing of Spline Surfaces , 1994, Comput. Graph. Forum.

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