Development of fundamental technologies for next-generation CAD system using subdivision schemes

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Volume subdivision which is an extension of surface subdivision scheme generates a smooth parameterization (cells) for the initial object (volume mesh). Thus, there are relatively no tiny elements in the subdivided volume mesh. This is a useful property for the FEM analysis, because a large difference of volumes between two adjacent cells causes a large error of the FEM analysis. However, previous works did not mention this usefulness, because (we guess) the subdivided volume mesh has planar cells (at the limit, there are completely planar cells). Planar cells make the FEM analysis impossible.Such planar cells are generated by volume subdivisions near boundary. Thus, we proposed new boundary stencils for a volumetric subdivision in order not to generate planar cells.