scholarly journals Smooth surface reconstruction via natural neighbour interpolation of distance functions

2000 ◽  
Author(s):  
Jean-Daniel Boissonnat ◽  
Frédéric Cazals
Keyword(s):  
Surface Reconstruction ◽  
Smooth Surface ◽  
Distance Functions

A surface-lofting approach for smooth-surface reconstruction from 3D measurement data

1997 ◽  
Vol 34 (1) ◽  
pp. 73-85 ◽  
Author(s):  
Chih-Young Lin ◽  
Chung-Shan Liou ◽  
Jiing-Yih Lai
Keyword(s):  
Surface Reconstruction ◽  
Smooth Surface ◽  
Measurement Data ◽  
3D Measurement

Mesh simplification with smooth surface reconstruction

1998 ◽  
Vol 30 (11) ◽  
pp. 875-882 ◽  
Author(s):  
O Volpin ◽  
A Sheffer ◽  
M Bercovier ◽  
L Joskowicz
Keyword(s):  
Surface Reconstruction ◽  
Smooth Surface ◽  
Mesh Simplification

scholarly journals Smooth surface reconstruction from noisy clouds

2004 ◽  
Vol 9 (3) ◽  
pp. 52-66 ◽  
Author(s):  
Boris Mederos ◽  
Luiz Velho ◽  
Luiz Henrique de Figueiredo
Keyword(s):  
Surface Reconstruction ◽  
Smooth Surface

scholarly journals Adaptive Metrics for Adaptive Samples

Algorithms ◽  
2020 ◽  
Vol 13 (8) ◽  
pp. 200
Author(s):  
Nicholas J. Cavanna ◽  
Donald R. Sheehy
Keyword(s):  
Euclidean Space ◽  
Surface Reconstruction ◽  
Critical Points ◽  
Adaptive Sampling ◽  
Local Feature ◽  
Distance Functions ◽  
Feature Size ◽  
Homology Inference ◽  
Definition Of ◽  
Local Feature Size

We generalize the local-feature size definition of adaptive sampling used in surface reconstruction to relate it to an alternative metric on Euclidean space. In the new metric, adaptive samples become uniform samples, making it simpler both to give adaptive sampling versions of homological inference results and to prove topological guarantees using the critical points theory of distance functions. This ultimately leads to an algorithm for homology inference from samples whose spacing depends on their distance to a discrete representation of the complement space.

CRITICAL POINTS OF DISTANCE TO AN ε-SAMPLING OF A SURFACE AND FLOW-COMPLEX-BASED SURFACE RECONSTRUCTION

2008 ◽  
Vol 18 (01n02) ◽  
pp. 29-61 ◽  
Author(s):  
TAMAL K. DEY ◽  
JOACHIM GIESEN ◽  
EDGAR A. RAMOS ◽  
BARDIA SADRI
Keyword(s):  
Surface Reconstruction ◽  
Distance Function ◽  
Critical Points ◽  
Geometric Modeling ◽  
Medial Axis ◽  
Reconstruction Algorithm ◽  
Three Dimensions ◽  
Distance Functions ◽  
Curve Reconstruction ◽  
Discrete Sample

The distance function to surfaces in three dimensions plays a key role in many geometric modeling applications such as medial axis approximations, surface reconstructions, offset computations and feature extractions among others. In many cases, the distance function induced by the surface can be approximated by the distance function induced by a discrete sample of the surface. The critical points of the distance functions are known to be closely related to the topology of the sets inducing them. However, no earlier theoretical result has found a link between topological properties of a geometric object and critical points of the distance to a discrete sample of it. We provide this link by showing that the critical points of the distance function induced by a discrete sample of a surface fall into two disjoint classes: those that lie very close to the surface and those that are near its medial axis. This closeness is precisely quantified and is shown to depend on the sampling density. It turns out that critical points near the medial axis can be used to extract topological information about the sampled surface. Based on this, we provide a new flow-complex-based surface reconstruction algorithm that, given a tight ε-sample of a surface, approximates the surface geometrically, both in distance and normals, and captures its topology. Furthermore, we show that the same algorithm can be used for curve reconstruction.

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