A performance study of tetrahedral and hexahedral elements in 3-D finite element structural analysis
Finite Elements in Analysis and Design
GI '04 Proceedings of the 2004 Graphics Interface Conference
Pyramid Coordinates for Morphing and Deformation
3DPVT '04 Proceedings of the 3D Data Processing, Visualization, and Transmission, 2nd International Symposium
Journal of Computational and Applied Mathematics
ACM SIGGRAPH 2008 papers
Interactive physically-based shape editing
Computer Aided Geometric Design
Comprehensive biomechanical modeling and simulation of the upper body
ACM Transactions on Graphics (TOG)
An efficient multigrid method for the simulation of high-resolution elastic solids
ACM Transactions on Graphics (TOG)
Interactive deformable models with quadratic bases in Bernstein–Bézier-form
The Visual Computer: International Journal of Computer Graphics - CGI'2011 Conference
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In this paper we present a novel approach to efficiently simulate the deformation of highly detailed meshes using higher order finite elements (FE). An efficient algorithm based on non-linear optimization is proposed in order to find the closest point in the curved computational FE mesh for each surface vertex. In order to extrapolate deformations to surface points outside the FE mesh, we introduce a mapping scheme that generates smooth surface deformations and preserves local shape even for low-resolution computational meshes. The mapping is constructed by representing each surface vertex in terms of points on the computational mesh and its distance to the FE mesh in normal direction. A numerical analysis shows that the mapping can be robustly constructed using the proposed non-linear optimization technique. Furthermore it is demonstrated that the numerical complexity of the mapping scheme is linear in the number of surface nodes and independent of the size of the coarse computational mesh.