Maximum norm optimization of quasi-isometric mappings

A reliable method for maximum norm optimization of spatial mappings is suggested. It is applied to the problem of optimal flattening of surfaces and to precisely controlled surface morphing. Robustness and grid independence of the method are demonstrated on real-life tests. Copyright © 2002 John Wiley & Sons, Ltd.

[1]  R. Tyrrell Rockafellar,et al.  Convex Analysis , 1970, Princeton Landmarks in Mathematics and Physics.

[2]  Michael S. Floater,et al.  Parametrization and smooth approximation of surface triangulations , 1997, Comput. Aided Geom. Des..

[3]  V. A. Garanzha.  Barrier method for quasi-isometric grid generation , 2000 .

[4]  V. A. Garanzha,et al.  Barrier variational generation of quasi‐isometric grids , 2001, Numer. Linear Algebra Appl..

[5]  C. Gotsman,et al.  How to morph tilings injectively , 1999 .

[6]  V. A. Garanzha,et al.  Regularization of the barrier variational method of grid generation , 1999 .

[7]  W. T. Tutte.  How to Draw a Graph , 1963 .

[8]  J. Ball.  Convexity conditions and existence theorems in nonlinear elasticity , 1976 .

[9]  Valmor F. De Almeida,et al.  Domain Deformation Mapping: Application to Variational Mesh Generation , 1999, SIAM J. Sci. Comput..

[10]  In-kyeong Choi.  On straight line representations of random planar graphs , 1992 .

[11]  J. Brackbill,et al.  Adaptive zoning for singular problems in two dimensions , 1982 .

[12]  K. Hormann,et al.  MIPS: An Efficient Global Parametrization Method , 2000 .

[13]  C. D. Boor,et al.  Good approximation by splines with variable knots. II , 1974 .

[14]  W. T. Tutte.  Convex Representations of Graphs , 1960 .

[15]  V. D. Liseikin.  The construction of regular grids on n -dimensional surfaces , 1991 .

[16]  Yu. G. Reshetnyak.  Mappings with bounded deformation as extremals of Dirichlet type integrals , 1968 .

[17]  V. Gol'dshtein,et al.  Quasiconformal mappings and spaces of functions with generalized first derivatives , 1976 .

[18]  Olivier-Pierre Jacquotte,et al.  A mechanical model for a new grid generation method in computational fluid dynamics , 1988 .