Twofold adaptive partition of unity implicits

Góis, João Paulo; Polizelli-Junior, V.; Etiene, Tiago; Tejada, Eduardo; Castelo, A.; Nonato, Luís Gustavo; Ertl, Thomas

doi:10.1007/s00371-008-0297-x

Cited by 12 publications

(17 citation statements)

References 13 publications

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“…After using signed distance field in [7] to reconstruct mesh surface from point clouds, implicit functions have gained a lot of attention in surface reconstruction because of its ability to handle topological change and fill holes. Example approaches include RBF-based methods [1], [2], [4], [8]- [16], Poisson surface reconstructions [17], [18], smooth signed distance method [19], moving least-squares based methods [20]- [25], wavelets based method [26], and Partition-Of-Unity (POU) based methods [27], [28]. The methods based on RBF implicits are popular for their capability of handling sparse point clouds.…”

Section: Related Workmentioning

confidence: 99%

A closed-form formulation of HRBF-based surface reconstruction by approximate solution

Liu

Wang

Brunnett

et al. 2016

Computer-Aided Design

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Section: Related Workmentioning

confidence: 99%

A closed-form formulation of HRBF-based surface reconstruction by approximate solution

Liu

Wang

Brunnett

et al. 2016

Computer-Aided Design

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“…Recently, point‐based representations of surfaces have been the focus of increased attention [GGG08, GNNB08, GPJE*08]. Again, the natural way to deform a point‐based surface is to move the point set according to the specified deformation, and thus resampling is necessary to ensure that the density of points remains quasi‐uniform and guarantee a good representation [WSS08, AK04].…”

Section: Introductionmentioning

confidence: 99%

Resampling Strategies for Deforming MLS Surfaces

Góis

Buscaglia

2010

Computer Graphics Forum

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Moving-least-squares (MLS) surfaces undergoing large deformations need periodic regeneration of the point set (point-set resampling) so as to keep the point-set density quasi-uniform. Previous work by the authors dealt with algebraic MLS surfaces, and proposed a resampling strategy based on defining the new points at the intersections of the MLS surface with a suitable set of rays. That strategy has very low memory requirements and is easy to parallelize. In this article new resampling strategies with reduced CPU-time cost are explored. The basic idea is to choose as set of rays the lines of a regular, Cartesian grid, and to fully exploit this grid: as data structure for search queries, as spatial structure for traversing the surface in a continuation-like algorithm, and also as approximation grid for an interpolated version of the MLS surface. It is shown that in this way a very simple and compact resampling technique is obtained, which cuts the resampling cost by half with affordable memory requirements.

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“…normal clustering), or even statistical inference to select points belonging to the same sheet before evaluating the implicit function [8], [9]. In this aspect, HRBF implicits are most similar to methods which build into the interpolation/approximation scheme a capability of identifying and handling close sheets without the need of additional information [2], [4], [5], [7].…”

Section: Introductionmentioning

confidence: 99%

Hermite Interpolation of Implicit Surfaces with Radial Basis Functions

Macêdo

Góis

Velho

2009

2009 XXII Brazilian Symposium on Computer Graphics and Image Processing

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Abstract-We present the Hermite radial basis function (HRBF) implicits method to compute a global implicit function which interpolates scattered multivariate Hermite data (unstructured points and their corresponding normals). Differently from previous radial basis functions (RBF) approaches, HRBF implicits do not depend on offset points to ensure existence and uniqueness of its interpolant. Intrinsic properties of this method allow the computation of implicit surfaces rich in details, with irregularly spaced points even in the presence of close sheets. Comparisons to previous works show the effectiveness of our approach. Further, the theoretical background of HRBF implicits relies on results from generalized interpolation theory with RBFs, making possible powerful new variants of this method and establishing connections with previous efforts based on statistical learning theory.

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Twofold adaptive partition of unity implicits

Cited by 12 publications

References 13 publications

A closed-form formulation of HRBF-based surface reconstruction by approximate solution

A closed-form formulation of HRBF-based surface reconstruction by approximate solution

Resampling Strategies for Deforming MLS Surfaces

Hermite Interpolation of Implicit Surfaces with Radial Basis Functions

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