Anisotropic polygonal remeshing
ACM SIGGRAPH 2003 Papers
Variational shape approximation
ACM SIGGRAPH 2004 Papers
Effect of finite element mesh orientation on solution accuracy for torsional problems
Finite Elements in Analysis and Design
Periodic global parameterization
ACM Transactions on Graphics (TOG)
Automatic and interactive mesh to T-spline conversion
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Extracting lines of curvature from noisy point clouds
Computer-Aided Design
Effect of finite element mesh orientation on solution accuracy for torsional problems
Finite Elements in Analysis and Design
Exact asymptotics of the uniform error of interpolation by multilinear splines
Journal of Approximation Theory
Finite Elements in Analysis and Design
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This paper compares the theoretical effectiveness of bilinear approximation over quadrilaterals with linear approximation over triangles. Anisotropic mesh transformation is used to generate asymptotically optimally efficient meshes for piecewise linear interpolation over triangles and bilinear interpolation over quadrilaterals. For approximating a convex function, although bilinear quadrilaterals are more efficient, linear triangles are more accurate and may be preferred in finite element computations; whereas for saddle-shaped functions, quadrilaterals may offer a higher-order approximation on a well-designed mesh. A surprising finding is different grid orientations may yield an order of magnitude improvement in approximation accuracy