On the 'most normal' normal

Given a set of normals in ℛ3, two algorithms are presented to compute the ‘most normal’ normal. The ‘most normal’ normal is the normal that minimizes the maximal angle with the given set of normals. A direct application is provided supposing a surface triangulation is available. The set of normals may represent either the face normals of the faces surrounding a point or the point normals of the points surrounding a point. The first algorithm is iterative and straightforward, and is inspired by the one proposed by Pirzadeh (AIAA Paper 94-0417, 1994). The second gives more insight into the complete problem as it provides the unique solution explicitly. It would correspond to the general extension of the algorithm presented by Kallinderis (AIAA-92-2721, 1992). Copyright © 2007 John Wiley & Sons, Ltd.

[1]  Nimrod Megiddo,et al.  Linear-time algorithms for linear programming in R3 and related problems , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[2]  S. Connell,et al.  Semistructured mesh generation for three-dimensional Navier-Stokes calculations , 1995 .

[3]  Paul-Louis George,et al.  Surface mesh enhancement with geometric singularities identification , 2005 .

[4]  Yasushi Yamaguchi,et al.  Bezier normal vector surface and its applications , 1997, Proceedings of 1997 International Conference on Shape Modeling and Applications.

[5]  R. Löhner.  Regridding Surface Triangulations , 1996 .

[6]  Deok-Soo Kim,et al.  Tangent, normal, and visibility cones on Bézier surfaces , 1995, Comput. Aided Geom. Des..

[7]  Philip M. Gresho,et al.  The implementation of normal and/or tangential boundary conditions in finite element codes for incompressible fluid flow , 1982 .

[8]  D. Hearn,et al.  The Minimum Covering Sphere Problem , 1972 .

[9]  Gabriel Taubin,et al.  A signal processing approach to fair surface design , 1995, SIGGRAPH.

[10]  F. Guibault,et al.  A Parameterization Transporting Surface Offset Construction Method Based on the Eikonal Equation , 2005 .

[11]  D. Hearn,et al.  Geometrical Solutions for Some Minimax Location Problems , 1972 .

[12]  R. Löhner,et al.  Generation of viscous grids with ridges and corners , 2007 .

[13]  Y. Kallinderis,et al.  Prismatic grid generation with an efficient algebraic method for aircraft configurations , 1992 .

[14]  Kazuhiro Nakahashi,et al.  Direct Surface Triangulation Using Stereolithography Data , 2002 .

[15]  I. Papadopoulos,et al.  Critical plane approaches in high-cycle fatigue : On the definition of the amplitude and mean value of the shear stress acting on the critical plane , 1998 .

[16]  Shahyar Pirzadeh,et al.  Viscous unstructured three-dimensional grids by the advancing-layers method , 1994 .

[17]  Rainald Loehner,et al.  Matching semi-structured and unstructured grids for Navier-Stokes calculations , 1993 .