A simple algorithm for homeomorphic surface reconstruction

By Nina Amenta, Sunghee Choi, Tamal K. Dey, Naveen Leekha. SCG '00, 2000

616 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/30218b830158fcf97981ed6b16278b4d35186c79

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In Computational Mechanics

In Computer Graphics and Computer-Aided Design

Citations in the corpus

1 An End-to-End Framework for Evaluating Surface Reconstruction (2011, methodology): “Extensive research efforts have been devoted to this model, producing the Cocone [Amenta et al. 2002] and Power Crust [Amenta et al. 2001] algorithms.”
The power crust, unions of balls, and the medial axis transform (2001, background): “[2] gave a similar, but simpler algorithm, with a much simpler proof, and also showed that the output surface is homeomorphic to the original object surface.”
Provably good sampling and meshing of surfaces (2005, background): “This condition is similar in spirit to other sampling conditions [3, 4, 22].”
Restricted delaunay triangulations and normal cycle (2003, neutral): “F(D −E) ≤ M(C) + M(h♯([0, 1]× ∂D)) Also : M(C) ≤ M(D)sup|f − Id|sup||Df || M(h♯([0, 1]× ∂D)) ≤ M(∂D)sup|f − Id|sup||Df || 2”
On the Geometry of Adversarial Examples (2018, methodology): “Soon after algorithms were developed for surface reconstruction in R 3 , both in the noise-free setting (Amenta and Bern (1999); Amenta et al. (2002)) and in the presence of noise (Dey and Goswami (2004)).”
Estimating surface normals in noisy point cloud data (2003, methodology): “Many current surface reconstruction algorithms [2, 4, 8] can either compute the normal as part of the reconstruction, or the normal can be trivially computed once the surface has been reconstructed.”
Provable surface reconstruction from noisy samples (2004, methodology): “Some of these algorithms, following the work of Amenta and Bern [1], provide theoretical guarantees [2, 3, 6, 13].”
Direct visibility of point sets (2007, methodology): “…proposed, such as representations by implicit functions [Hoppe et al. 1992; Carr et al. 2001; Ohtake et al. 2003], by Moving Least Squares [Alexa et al. 2003; Fleishman et al. 2005], employing Voronoi/Delaunay techniques [Amenta et al. 2002; Amenta et al. 2001; Mederos et al. 2005], and others.”
Delaunay Triangulation Based Surface Reconstruction: Ideas and Algorithms (2004, background): “[ACDL00] as a successor and improvement of the Crust algorithm.”