Multi-level partition of unity implicits

Ohtake, Yutaka; Belyaev, Alexander; Alexa, Marc; Turk, Greg; Seidel, Hans‐Peter

doi:10.1145/1198555.1198649

Cited by 349 publications

(317 citation statements)

References 49 publications

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“…Surface reconstruction from unorganized point clouds has been intensively studied; see [3], [12], [13], [16], [27], [40] and references therein. Despite the increased availability of commodity parallel platforms, there has been very little work on parallel algorithms for surface reconstruction.…”

Section: Surface Reconstructionmentioning

confidence: 99%

“…E is given as a percentage of the length of the main diagonal of the bounding box (see e.g., [12], [27]), and it represents an upper bound for the true average distance from the data points to the reconstructed surface. Accordingly, at octree depths D = 10, 11, our method attains reconstruction errors comparable to those in [12], [27].…”

Section: Surface Reconstructionmentioning

confidence: 99%

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Fast Sparse Level Sets on Graphics Hardware

Jalba

Laan

Roerdink

2013

IEEE Trans. Visual. Comput. Graphics

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Abstract-The level set method is one of the most popular techniques for capturing and tracking deformable interfaces. Although level sets have demonstrated great potential in visualization and computer graphics applications, such as surface editing and physically-based modeling, their use for interactive simulations has been limited due to the high computational demands involved. In this paper we address this computational challenge by leveraging the increased computing power of graphics processors, to achieve fast simulations based on level sets. Our efficient, sparse GPU level set method is substantially faster than other state-of-the-art, parallel approaches on both CPU and GPU hardware. We further investigate its performance through a method for surface reconstruction, based on GPU level sets. Our novel multi-resolution method for surface reconstruction from unorganized point clouds compares favorably with recent, existing techniques and other parallel implementations. Finally, we point out that both level set computations and rendering of level-set surfaces can be performed at interactive rates, even on large volumetric grids. Therefore, many applications based on level sets can benefit from our sparse level set method.

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Section: Surface Reconstructionmentioning

confidence: 99%

Section: Surface Reconstructionmentioning

confidence: 99%

Fast Sparse Level Sets on Graphics Hardware

Jalba

Laan

Roerdink

2013

IEEE Trans. Visual. Comput. Graphics

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“…An adaptive octree-based subdivision method introduced by Ohtake et al [18] is used in our space partition. We define the local support radius R=α d i for the cubic cells which are generated during the subdivision, d i is the length of the main diagonal of the cell.…”

Section: Adaptive Space Subdivisionmentioning

confidence: 99%

Implicit Surface Reconstruction from Scattered Point Data with Noise

Yang

Wang

Zhu

et al. 2007

Computational Science – ICCS 2007

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Abstract. This paper addresses the problem of reconstructing implicit function from point clouds with noise and outliers acquired with 3D scanners. We introduce a filtering operator based on mean shift scheme, which shift each point to local maximum of kernel density function, resulting in suppression of noise with different amplitudes and removal of outliers. The "clean" data points are then divided into subdomains using an adaptive octree subdivision method, and a local radial basis function is constructed at each octree leaf cell. Finally, we blend these local shape functions together with partition of unity to approximate the entire global domain. Numerical experiments demonstrate robust and high quality performance of the proposed method in processing a great variety of 3D reconstruction from point clouds containing noise and outliers.

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“…In the third approach, users can obtain approximated implicit form of existing polygonal shape models. Although implicit form typically assumes smoothness of the surfaces, some methods enables implicit expression of sharp edges and corners [21,22].…”

Section: Introductionmentioning

confidence: 99%

Moving particle semi-implicit method for fluid simulation with implicitly defined deforming obstacles

Kanetsuki

Nakata

2015

JASSE

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Abstract. In this paper, we present a particle-based fluid simulation method with deforming obstacles. For defining the geometric information of time-varying obstacles, we employ the implicit function form that varies along the time axis. Our fluid simulation is based on the Moving Particle Semi-implicit (MPS) method, one of the typical particle-based methods for incompressible flow, and we add a new formulation for implicitly defined deforming obstacles. Although many of the particle-based algorithms require a set of particles on the obstacles, our method works without generating particles on the obstacles. We define the particle motion at the vicinity of the obstacles and generate a new algorithm specific to the implicit deforming obstacles by incorporating approximations in the processes of determining particle forces affected by the obstacles.

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Multi-level partition of unity implicits

Cited by 349 publications

References 49 publications

Fast Sparse Level Sets on Graphics Hardware

Fast Sparse Level Sets on Graphics Hardware

Implicit Surface Reconstruction from Scattered Point Data with Noise

Moving particle semi-implicit method for fluid simulation with implicitly defined deforming obstacles

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