Geodesic
Conservative interpolation method between non-matching surface meshes
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2014), pp. 64-75

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In this paper, we consider a problem of conservative interpolation data between non-matching surface meshes. We develop a new interpolation method based on voxel representation of the mesh followed by the evaluation of intersection area of each voxel with mesh cells. The mass of cells of the resulting mesh is represented through a linear combination of the known mass of parent cells. The method allows us to consider the problem of interpolation on curved surfaces when it is impossible to define the grid cells geometric intersection. The method was validated by numerical simulation of data interpolation based on various functions for the non-matching meshes describing plane and curved surfaces. The method of voxel interpolation was compared to the interpolation algorithm based on radial basis functions of different smoothness degree.
Mots-clés : conservative interpolation
Keywords: voxel mesh, non-matching surface mesh. 
@article{VUU_2014_4_a4,
     author = {A. S. Karavaev and S. P. Kopysov and I. M. Kuz'min},
     title = {Conservative interpolation method between non-matching surface meshes},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {64--75},
     publisher = {mathdoc},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2014_4_a4/}
}
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A. S. Karavaev; S. P. Kopysov; I. M. Kuz'min. Conservative interpolation method between non-matching surface meshes. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2014), pp. 64-75. http://geodesic.mathdoc.fr/item/VUU_2014_4_a4/