Multi-level partition of unity implicits

By Yutaka Ohtake, Alexander G. Belyaev, Marc Alexa, Greg Turk, Hans-Peter Seidel. ACM Transactions on Graphics, 2003

827 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design

View Paper: https://www.semanticscholar.org/paper/a340178b5b99bb9df60bab0816635f346c5dc9d7

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In Computational Mechanics

In Computer Graphics and Computer-Aided Design

Citations in the corpus

Point Cloud Skeletons via Laplacian Based Contraction (2010, neutral): “State-of-the-art surface reconstruction techniques ([19], [20], [21], [22]) can provide high quality results when the underlying surface is sufficiently well-sampled.”
Local Deep Implicit Functions for 3D Shape (2019, background): “Traditional structured representations include scene graphs [11], CSG trees [11], and partition of unity implicits [26], all of which represent complex shapes as the composition of simpler ones.”
A Survey of Surface Reconstruction from Point Clouds (2017, neutral): “In the multi-level partition of unity (MPU) method [OBA ∗ 03], an octree-based partitioning is constructed top down: given a cell, the points inside and nearby the cell are approximated by either a bivariate quadratic polynomial or an algebraic trivariate quadric if the set of orientations spanned…”
Shape Completion from a Single RGBD Image (2017, methodology): “We ﬁrst use the method of [38] to generate a signed distance ﬁeld for the template, which uses piecewise quadratic functions to capture the local shape of the surface and a set of weighting functions to blend together these local shape functions.”
ABC: A Big CAD Model Dataset for Geometric Deep Learning (2018, background): “One important generalization is the (robust) detection of sharp edges and corners, where more than one normal should be assigned to a point [43, 16].”
Robust repair of polygonal models (2004, background): “(Note that another problem related to volumetric model repair considers surface reconstruction from scattered points via an intermediate volume [Hoppe et al. 1992; Ohtake et al. 2003].”
Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstruction (2020, methodology): “One possible solution is to choose w as partition of unity [39] basis functions with local support to combine the decoded SDF values.”
1 An End-to-End Framework for Evaluating Surface Reconstruction (2011, methodology): “2008], to locally fitting functions and moving least squares methods [Alexa et al. 2001; Ohtake et al. 2003; Ohtake et al. 2005b; Fleishman et al. 2005].”
Interpolating and approximating implicit surfaces from polygon soup (2004, methodology): “If we follow the general approach described in [Turk and O’Brien, 1999] and [Ohtake et al., 2003a] of constraining the function to be zero at input points or polygons, supplying appropriate normal constraints, and extracting the iso-surface f ( x ) = 0, then all the input polygons will be parts of…”
Simulating water and smoke with an octree data structure (2004, background): “The representation of implicit surfaces on octree data structures has a long history in the marching cubes community, see the recent papers of [Ju et al. 2002; Ohtake et al. 2003] and the references therein.”