Generalized PolyCube Trivariate Splines

Li, Bo; Li, Xin; Wang, Kexiang; Qin, Hong

doi:10.1109/smi.2010.40

Cited by 40 publications

(14 citation statements)

References 16 publications

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“…In recent years, volumetric mapping have gained great interest due to its rich applications in many fields such as computer-aided manufacturing [8], meshing [9], [10], shape registration [11], [12], [13], and trivariate spline construction [14], [15], [16]. Wang et al [12] discretize the volumetric harmonic energy on the tetrahedral mesh using the finite element method, parameterized volumetric shapes over solid spheres by a variational algorithm.…”

Section: Volumetric Mappingmentioning

confidence: 99%

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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Section: Volumetric Mappingmentioning

confidence: 99%

Biharmonic Volumetric Mapping Using Fundamental Solutions

et al. 2013

IEEE Trans. Visual. Comput. Graphics

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“…The method can be generalized to other trivariate representations with more complex topologies by segmenting the volume into trivial parts, ensuring coherence between volumetric patches [16]. A generalized polycube representation can manage non-trivial topologies such as volumetric Möbius bands and identified cube borders [17].…”

Section: Related Workmentioning

confidence: 99%

As-conformal-as-possible discrete volumetric mapping

Paillé

Poulin

2012

Computers & Graphics

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In this paper, we tackle the problem of generalizing conformal maps to volumetric meshes. Current methods seek for harmonicity but unfortunately, no computational methods optimize conformality in the volumetric context. As it is proven that conformal maps do not exist for general volume transformations, we seek to optimize shape preservation with a generalization of the CauchyRiemann equations. Our algorithm is fast and easily adaptable to existing harmonic mapping methods. Compared to harmonic maps, results show improvements on both angular and volumetric energy measures at a cost below 1% of total computations. The method extends well in any dimension and several research areas could benefit from our derivations of volumetric conformal optimization.

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“…Additional term is added to the objective function in order to improve the quality where needed. The use of harmonic mapping is a common characteristic of several works dealing with 2D and 3D parameterization methods [20,21,22].…”

Section: Introductionmentioning

confidence: 99%

A new method for T-spline parameterization of complex 2D geometries

Brovka

López

Escobar

et al. 2013

Engineering with Computers

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We present a new strategy, based on the idea of the meccano method and a novel T-mesh optimization procedure, to construct a T-spline parameterization of 2D geometries for the application of isogeometric analysis. The proposed method only demands a boundary representation of the geometry as input data. The algorithm obtains, as a result, high quality parametric transformation between 2D objects and the parametric domain, the unit square. First, we define a parametric mapping between the input boundary of the object and the boundary of the parametric domain. Then, we build a T-mesh adapted to the geometric singularities of the domain in order to preserve the features of the object boundary with a desired tolerance. The key of the method lies in defining an isomorphic transformation between the parametric and physical T-mesh finding the optimal position of the interior nodes by applying a new T-mesh untangling and smoothing procedure. Bivariate T-spline representation is calculated by imposing the interpolation conditions on points sited both on the interior and on the boundary of the geometry. The efficiency of the proposed technique is shown in several examples. Also we present some results of the application of isogeometric analysis in a geometry parameterized with this technique.

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Generalized PolyCube Trivariate Splines

Cited by 40 publications

References 16 publications

Biharmonic Volumetric Mapping Using Fundamental Solutions

Biharmonic Volumetric Mapping Using Fundamental Solutions

As-conformal-as-possible discrete volumetric mapping

A new method for T-spline parameterization of complex 2D geometries

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