Multi-scale reconstruction of implicit surfaces with attributes from large unorganized point sets

Abstract

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Meshless Time-Domain Method with Modified RPIM-Based Shape Functions for Electromagnetic Wave Propagation Simulation in Complex Shaped Domain

“…Note that the shape functions φ E j (x) and φ H j (x) in (4)- (6) are similarly determined. Hence, in this section, we do not use E and H as superscripts.…”

Implicit Surface Reconstruction from Scattered Point Data with Noise

“…Moving least square (MLS) [3][4][5][6] and radial basis function (RBF) [7][8][9][10][11][12][13][14][15] are two popular 3D implicit surface reconstruction methods.…”

“…Using this technique, an implicit surface is constructed by calculating the weights of a set of radial basis functions such they interpolate the given data points. From the pioneering work [7,8] to recent researches, such as compactly-supported RBF [9,10], fast RBF [11][12][13] and multi-scale RBF [14,15], the established algorithms can generate more and more faithful models of real objects in last twenty years, unfortunately, most of them are not feasible for the approximations of unorganized point clouds containing noise and outliers.…”

Implicit Surface Modeling Suitable for Inside/Outside Tests with Radial Basis Functions

“…However, it is hard to implement. The second way is to divide a large point set into a number of small subdomains and the final function is obtained by blending intermediate implicit functions [6,15]. The third means uses compactly supported RBFs (CSRBF) to make the linear system sparse.…”