Defining point-set surfaces

By Nina Amenta, Yong Joo Kil. ACM Transactions on Graphics, 2004

396 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/1f193d385806a07d82bd029d176a6e997f4fa61a

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In Computational Mechanics

In Computer Graphics and Computer-Aided Design

Citations in the corpus

Physics-aware Difference Graph Networks for Sparsely-Observed Dynamics (2020, background): “It is unsuitable to directly use continuous differential operators to provide local behaviors because it is hard to approximate the continuous derivatives precisely with the sparse points (Shewchuk, 2002; Amenta & Kil, 2004; Luo et al., 2009).”
Curve skeleton extraction from incomplete point cloud (2009, methodology): “…orientation for shape inference has been a common practice in several other contexts, such as neighborhood identiﬁ-cation via Mahalanobis distance [Amenta and Kil 2004; Lehtinen et al. 2008] and surface reconstruction with the assistance of point normals [Carr et al. 2001; Kazhdan et al. 2006].”
Evolutionary morphing (2005, background): “This approach is a variant of the extremal surface construction, which was developed for extracting surfaces from noisy tensor fields [13] and used recently for point-set surfaces [3].”
A Survey of Surface Reconstruction from Point Clouds (2017, methodology): “Authors rapidly observed that Levin’s method can be signiﬁcantly simpliﬁed by omitting the polynomial ﬁtting step [AK04].”
Point-based multiscale surface representation (2006, methodology): “Smoothing operators based on diffusion or the least squares projection operation are only approximate low-pass filters. Since no global, distortion-free parameterization exists for manifolds in general, applying these filters can lead to deformations such as volume shrinkage. Another issue is that t”
Voronoi-Based Curvature and Feature Estimation from Point Clouds (2011, background): “Yang and Qian [15] derive analytic expressions for computing principal curvatures based on the implicit definition of the moving least squares surface by Amenta and Kil [16].”
A survey of point-based techniques in computer graphics (2004, methodology): “In contrast to the algorithmic construction of MLS surfaces using the projection operator, Amenta and Kil [29] give an explicit definition of MLS surfaces in terms of critical points of the energy function EMLS along lines determined by a vector field.”
A review of algorithms for filtering the 3D point cloud (2017, neutral): “Amenta and Kil [63] presented an explicit version of MLS surface definition in terms of the critical points of an energy function e 𝑀𝐿𝑆 on lines determined by a vector field 𝒏 ( 𝑥 ) = argmin 𝑒 𝑀𝐿𝑆 and gave a simple procedure that produced a point of the MLS surface, which was not…”
Reassembling fractured objects by geometric matching (2006, methodology): “In a second step we fill any holes using a modified method of [Amenta and Kil 2004] such that the virtual fragment is a single closed surface.”