Harmonic coordinates for character articulation

Joshi, Prasad; Meyer, Mark; DeRose, Tony; Green, Brian; Sanocki, Tom

doi:10.1145/1275808.1276466

Cited by 237 publications

(263 citation statements)

References 21 publications

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“…We also compared to harmonic coordinates [21] and maximum entropy coordinates [19], but found that the choice of the shape function does not make a significant difference. We solve the linear system (3) using the sparse Cholesky factorization of CHOLMOD [6].…”

Section: Resultsmentioning

confidence: 99%

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Optimizing Voronoi Diagrams for Polygonal Finite Element Computations

Sieger

Alliez

Botsch

2010

Proceedings of the 19th International Meshing Roundtable

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Summary. We present a 2D mesh improvement technique that optimizes Voronoi diagrams for their use in polygonal finite element computations. Starting from a centroidal Voronoi tessellation of the simulation domain we optimize the mesh by minimizing a carefully designed energy functional that effectively removes the major reason for numerical instabilities-short edges in the Voronoi diagram. We evaluate our method on a 2D Poisson problem and demonstrate that our simple but effective optimization achieves a significant improvement of the stiffness matrix condition number.

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Section: Resultsmentioning

confidence: 99%

“…Examples of generalized barycentric coordinates are Wachspress coordinates [42], mean value coordinates [12,13,18,43], Laplace interpolants [17], harmonic coordinates [21,25], and maximum entropy coordinates [31,19].…”

Section: Introductionmentioning

confidence: 99%

Optimizing Voronoi Diagrams for Polygonal Finite Element Computations

Sieger

Alliez

Botsch

2010

Proceedings of the 19th International Meshing Roundtable

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“…Ju et al [18] generalize the mean value coordinates [19] from surfaces to volumes to get a smooth volumetric interpolation for cage-based deformation. Joshi et al [20] present harmonic coordinates with nonnegative weights for volumetric interpolation and deformation in concave regions. Martin et al [14] parameterize volumetric model with trivial topology to a cylinder using the finite element method, and later generalize the algorithm [15] to more complicated models with medial surfaces.…”

Section: Volumetric Mappingmentioning

confidence: 99%

“…Linear precision property is desirable in describing shape deformation [20]. For example, when the boundary surface transforms rigidly, it will be natural to see the interior region also transforms in the same rigid manner.…”

Section: Linear Precision Propertymentioning

confidence: 99%

“…Suppose is a harmonic function, i.e., it is a solution to Laplace's equation: r 2 ðxÞ ¼ 0; x 2 , and satisfies the boundary condition ðv i Þ ¼ rðv i Þ; v i 2 @ , where rðxÞ is a linear function. Then, since and r satisfy the same boundary conditions and are both solutions to Laplace's equation (the linear function r is also a harmonic function), by the uniqueness of solutions to Laplace's equation, they must be the same function r. So the harmonic mapping keeps the linear precision property [36].…”

Section: Linear Precision Propertymentioning

confidence: 99%

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Biharmonic Volumetric Mapping Using Fundamental Solutions

et al. 2013

IEEE Trans. Visual. Comput. Graphics

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Abstract-We propose a biharmonic model for cross-object volumetric mapping. This new computational model aims to facilitate the mapping of solid models with complicated geometry or heterogeneous inner structures. In order to solve cross-shape mapping between such models through divide and conquer, solid models can be decomposed into subparts upon which mappings is computed individually. The biharmonic volumetric mapping can be performed in each subregion separately. Unlike the widely used harmonic mapping which only allows C 0 continuity along the segmentation boundary interfaces, this biharmonic model can provide C 1 smoothness. We demonstrate the efficacy of our mapping framework on various geometric models with complex geometry (which are decomposed into subparts with simpler and solvable geometry) or heterogeneous interior structures (whose different material layers can be segmented and processed separately).

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Detail‐aware spatial deformation transfer

Yoshiyasu

Yamazaki

2012

Computer Animation & Virtual

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In this paper, we propose a deformation transfer method that is applicable to multi-component objects and is able to transfer fine-scale deformations. To accomplish our goal, we combine surface-based and space-based deformation transfers. Our system enhances the result of space deformation transfer, which is applicable to multi-component objects but loses details, by using surface-based deformation transfer to add fine-scale deformations. Self-collisions are handled by approximating spatial relationships between surfaces, from the result of space deformation. Experimental results show that our method can transfer fine-scale deformations such as motions of a skirt and muscle bulging.

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Harmonic coordinates for character articulation

Cited by 237 publications

References 21 publications

Optimizing Voronoi Diagrams for Polygonal Finite Element Computations

Optimizing Voronoi Diagrams for Polygonal Finite Element Computations

Biharmonic Volumetric Mapping Using Fundamental Solutions

Detail‐aware spatial deformation transfer

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