Adaptive Slicing of Moving Least Squares Surfaces: Toward Direct Manufacturing of Point Set Surfaces

2008 ◽  
Vol 8 (3) ◽  
Author(s):  
Pinghai Yang ◽  
Xiaoping Qian
Keyword(s):  
Least Squares ◽  
Point Cloud ◽  
Moving Least Squares ◽  
Point Sets ◽  
New Approach ◽  
Adaptive Slicing ◽  
3D Sensing ◽  
Point Set ◽  
Point Set Surfaces ◽  
Model Conversion

Rapid advancement of 3D sensing techniques has led to dense and accurate point cloud of an object to be readily available. The growing use of such scanned point sets in product design, analysis, and manufacturing necessitates research on direct processing of point set surfaces. In this paper, we present an approach that enables the direct layered manufacturing of point set surfaces. This new approach is based on adaptive slicing of moving least squares (MLS) surfaces. Salient features of this new approach include the following: (1) It bypasses the laborious surface reconstruction and avoids model conversion induced accuracy loss. (2) The resulting layer thickness and layer contours are adaptive to local curvatures, and thus it leads to better surface quality and more efficient fabrication. (3) The curvatures are computed from a set of closed formula based on the MLS surface. The MLS surface naturally smoothes the point cloud and allows upsampling and downsampling, and thus it is robust even for noisy or sparse point sets. Experimental results on both synthetic and scanned point sets are presented.

Adaptive Slicing of Moving Least Squares Surfaces: Toward Direct Manufacturing of Point Set Surfaces

2007 ◽  
Author(s):  
Pinghai Yang ◽  
Xiaoping Qian
Keyword(s):  
Least Squares ◽  
Point Cloud ◽  
Moving Least Squares ◽  
Point Sets ◽  
New Approach ◽  
Adaptive Slicing ◽  
3D Sensing ◽  
Point Set ◽  
Point Set Surfaces ◽  
Model Conversion

Rapid advancement of 3D sensing techniques has lead to dense and accurate point cloud of an object to be readily available. The growing use of such scanned point sets in product design, analysis and manufacturing necessitates research on direct processing of point set surfaces. In this paper, we present an approach that enables the direct layered manufacturing of point set surfaces. This new approach is based on adaptive slicing of moving least squares (MLS) surfaces. Salient features of this new approach include: 1) it bypasses the laborious surface reconstruction and avoids model conversion induced accuracy loss; 2) the resulting layer thickness and layer contours are adaptive to local curvature and thus it leads to better surface quality and more efficient fabrication; 3) the MLS surface naturally smoothes the point cloud and allows up-sampling and down-sampling, and thus it is robust even for noisy or sparse point sets. Experimental results of the slicing algorithm on both synthetic and scanned point sets are presented.

scholarly journals POINT CLOUD SMOOTH SAMPLING AND SURFACE RECONSTRUCTION BASED ON MOVING LEAST SQUARES

2020 ◽  
Vol XLII-3/W10 ◽  
pp. 145-151 ◽  
Author(s):  
C. L. Kang ◽  
T. N. Lu ◽  
M. M. Zong ◽  
F. Wang ◽  
Y. Cheng
Keyword(s):  
Least Squares ◽  
Surface Reconstruction ◽  
Point Cloud ◽  
Least Squares Method ◽  
Moving Least Squares ◽  
Cloud Data ◽  
Grid Sampling ◽  
Moving Least Squares Method ◽  
Feature Information ◽  
Voxel Grid

Abstract. In point cloud data processing, smooth sampling and surface reconstruction are important aspects of point cloud data processing. In view of the current point cloud sampling method, the point cloud distribution is not uniform, the point cloud feature information is incomplete, and the reconstructed model surface is not smooth. This paper proposes a method of smoothing sampling processing and surface reconstruction using point cloud using moving least squares method. This paper first introduces the traditional moving least squares method in detail, and then proposes an improved moving least squares method for point cloud smooth sampling and surface reconstruction. In this paper, the algorithm is designed for the proposed theory, combined with C++ and point cloud library PCL programming, using voxel grid sampling and uniform sampling and moving least squares smooth sampling comparison, after sampling, using greedy triangulation algorithm surface reconstruction. The experimental results show that the improved moving least squares method performs point cloud smooth sampling more uniformly than the voxel grid sampling and the feature information is more prominent. The surface reconstructed by the moving least squares method is smooth, the surface reconstructed by the voxel grid sampling and the uniformly sampled data surface is rough, and the surface has a rough triangular surface. Point cloud smooth sampling and surface reconstruction based on moving least squares method can better maintain point cloud feature information and smooth model smoothness. The superiority and effectiveness of the method are demonstrated, which provides a reference for the subsequent study of point cloud sampling and surface reconstruction.

Adaptive Moving Least-Squares Surfaces for Multiple Point Clouds Registration

2011 ◽  
Author(s):  
Yunbao Huang ◽  
Linchi Zhang ◽  
Zhihui Tan ◽  
Qifu Wang ◽  
Liping Chen
Keyword(s):  
Least Squares ◽  
Point Cloud ◽  
Synthetic Data ◽  
Point Clouds ◽  
Integral Invariant ◽  
Gaussian Kernel ◽  
Moving Least Squares ◽  
Multiple Point ◽  
Surface Model ◽  
Core Idea

In this paper, we propose an Adaptive Moving Least-Squares (AMLS) surface based approach for multi-view or multi-sensor point cloud ICP registration. The core idea of this approach is to reconstruct a smooth and accurate surface, e. s. AMLS surface, from a point cloud, without data segmentation and surface model selection, resulting in an accurate point-to-AMLS surface ICP registration. The major difference between AMLS and traditional MLS is that the width of Gaussian kernel is adaptively scaled with the principle curvature, which is defined through local integral invariant analysis. Experimental results of both synthetic data and scanned data from a mechanical part show that the presented approach is more accurate and robust on sensor noise and sample density.

Almost empty polygons

2003 ◽  
Vol 40 (3) ◽  
pp. 269-286 ◽  
Author(s):  
H. Nyklová
Keyword(s):  
Exact Results ◽  
Point Sets ◽  
Planar Point ◽  
Convex Position ◽  
Vertex Set ◽  
Point Set ◽  
Empty Polygons

In this paper we study a problem related to the classical Erdos--Szekeres Theorem on finding points in convex position in planar point sets. We study for which n and k there exists a number h(n,k) such that in every planar point set X of size h(n,k) or larger, no three points on a line, we can find n points forming a vertex set of a convex n-gon with at most k points of X in its interior. Recall that h(n,0) does not exist for n = 7 by a result of Horton. In this paper we prove the following results. First, using Horton's construction with no empty 7-gon we obtain that h(n,k) does not exist for k = 2(n+6)/4-n-3. Then we give some exact results for convex hexagons: every point set containing a convex hexagon contains a convex hexagon with at most seven points inside it, and any such set of at least 19 points contains a convex hexagon with at most five points inside it.

Modelling the characteristics of turbocompressors for fuel cell systems using hybrid method based on moving least squares

2009 ◽  
Vol 86 (7-8) ◽  
pp. 1283-1289 ◽  
Author(s):  
R. Tirnovan ◽  
S. Giurgea ◽  
A. Miraoui ◽  
M. Cirrincione
Keyword(s):  
Fuel Cell ◽  
Least Squares ◽  
Hybrid Method ◽  
Moving Least Squares ◽  
Cell Systems
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