Computer Science ›› 2018, Vol. 45 ›› Issue (3): 67-68.doi: 10.11896/j.issn.1002-137X.2018.03.011

Previous Articles     Next Articles

Birational Trilinear Mapping on Convex Hexahedrons

YE Jin-yun, WANG Xu-hui and QIAN Yi-jia   

  • Online:2018-03-15 Published:2018-11-13

Abstract: Based on the knowledge of three dimensional generalized barycentric coordinates,the results of birational trilinear mapping on planar quadrilateral were generalized to three dimensional convex hexahedron,namely,by assigning a suitable weight to every vertex of convex hexahedron,a three dimensional birational mapping was achieved.In addition,an example was given to illustrate the correctness of this method.

Key words: Barycentric coordinates,Birational mapping,Convex hexahedron,Weight

[1] SEDERBERG T W,GOLDMAN R N.Birational 2D Free-Form Deformation of degree 1×n[J].Computer Aided Geometric Design,2016,44:1-9.
[2] HUDSON H P.Cremona Transformations in Plane and Space[M].Cambridge:Cambridge University Press,1927.
[3] SEDERBERG T W,ZHENG J.Birational quadrilateral maps[J].Computer Aided Geometric Design,2015,32:1-4.
[4] FLOATER M S.The inverse of a rational bilinear mapping[J].Computer Aided Geometric Design,2015,33:46-50.
[5] LEE S Y,CHWA K Y.SHIN S Y.Image metamorphosis using snakes and free-form deformations[C]∥Proceeding of the 22nd Annual Conference on Computer Graphics and Interactive Techniques.1995:59-69.
[6] MANZONI A,QUARTERONI A,ROZZA G.Shape optimization for viscous flows by reduced basis methods and free-form deformations[J].International Journal for Numerical Methods in Fluids,2012,70(5):646-670.
[7] FRANGI A F,NIESSEN W J,VIERGEVER M A.Three-dimensional modeling for functional analysis of cardiac images,a review[J].IEEE Transactions on Medical Imaging,2001,20(1):2-5.
[8] HUANG X,PARAGIOS N,METAXAS D N.Shape registration in implicit spaces using information theory and free form deformations[J].IEEE Transactions on Medical Imaging,2006,28(8):1303-1318.
[9] WARREN J,SCHAEFER S,et al.Barycentric coordinates for convex sets[J].Advances in Computatioanl Mathematics,2007,27(3):319-338.
[10] WARREN J.Barycentric coordinates for convex polytopes[J].Advances in Computational Mathematics,1996,6(1):97-108.

No related articles found!
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!