Determination of free parameters in algebraic surface blending

In the paper we propose a method to determine parameters that appear in algebraic surface blending. By minimizing the surface energy and adding some point restrictions, we can select the free parameters such that a blending surface with reasonable shape is constructed. The method seems to be extensible for other surface blending problems, although we concentrate on algebraic surface blending.

[1]  Chandrajit L. Bajaj,et al.  C1 modeling with A-patches from rational trivariate functions , 2001, Comput. Aided Geom. Des..

[2]  J. Hopcroft,et al.  The Potential Method for Blending Surfaces and Corners , 1985 .

[3]  Alan E. Middleditch,et al.  Blend surfaces for set theoretic volume modelling systems , 1985, SIGGRAPH '85.

[4]  Thomas W. Sederberg Piecewise algebraic surface patches , 1985, Comput. Aided Geom. Des..

[5]  Joe D. Warren,et al.  Blending algebraic surfaces , 1989, TOGS.

[6]  Josef Hoschek,et al.  Gn∗-functional splines for interpolation and approximation of curves, surfaces and solids , 1990, Comput. Aided Geom. Des..

[7]  J. Hopcroft,et al.  Quadratic blending surfaces , 1985 .

[8]  Falai Chen,et al.  CONSTRUCTING PIECEWISE ALGEBRAIC BLENDING SURFACES , 2004 .

[9]  Seth Allen,et al.  Supercyclides and blending , 1997, Comput. Aided Geom. Des..

[10]  Wolfgang Dahmen,et al.  Cubicoids: modeling and visualization , 1993, Comput. Aided Geom. Des..

[11]  Donal O'Shea,et al.  Ideals, varieties, and algorithms - an introduction to computational algebraic geometry and commutative algebra (2. ed.) , 1997, Undergraduate texts in mathematics.

[12]  Falai Chen,et al.  Blending Quadric Surfaces with Piecewise Algebraic Surfaces , 2001, Graph. Model..

[13]  A. Requicha,et al.  CONSTANT-RADIUS BLENDING IN SOLID MODELLING , 1984 .

[14]  Yun-shi Zhou,et al.  On blending of several quadratic algebraic surfaces , 2000, Comput. Aided Geom. Des..

[15]  Joe D. Warren,et al.  Geometric continuity , 1991, Comput. Aided Geom. Des..

[16]  Insung Ihm,et al.  Smoothing polyhedra using implicit algebraic splines , 1992, SIGGRAPH.

[17]  Michael J. Pratt,et al.  Quartic supercyclides I: Basic theory , 1997, Comput. Aided Geom. Des..

[18]  Falai Chen,et al.  G/sup 2/ blending of corners with piecewise algebraic surfaces , 2003, 11th Pacific Conference onComputer Graphics and Applications, 2003. Proceedings..

[19]  Chen Fa Blending Pipe Surfaces with Piecewise Algebraic Surfaces , 2000 .