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Research Papers

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

[+] Author and Article Information
Pinghai Yang

Department Of Mechanical, Materials and Aerospace Engineering, Illinois Institute of Technology, Chicago, IL, 60616

Xiaoping Qian1

Department Of Mechanical, Materials and Aerospace Engineering, Illinois Institute of Technology, Chicago, IL, 60616qian@iit.edu

1

Corresponding author.

J. Comput. Inf. Sci. Eng 8(3), 031003 (Aug 19, 2008) (11 pages) doi:10.1115/1.2955481 History: Received May 18, 2007; Revised February 28, 2008; Published August 19, 2008

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.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Approaches for geometric processing of scanned point cloud data for LM

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Figure 2

Comparison of the current projection based and our MLS based slicing approaches. (a) Isoview of the rabbit data with slicing planes. (b) In the projection based approach, larger Δd leads to more points on the slicing plane and potential projection error. (c) In the projection based approach, smaller Δd leads to fewer points projected on the slicing plane and potential truncation error. (d) The resulting points of our MLS based approach.

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Figure 3

Flowchart for our adaptive direct slicing algorithm

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Figure 4

Illustration of the projection process of a projection MLS

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Figure 5

Illustration of adaptive 2D contour generation

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Figure 6

Calculation of the step length Δp

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Figure 7

Four cases in determining the layer thickness d with excess deposition: (a) p in the upper semicircle, k>0; (b) p in the upper semicircle, k<0; (c) p in the lower semicircle, k>0; (d) p in the lower semicircle, k<0

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Figure 8

Validation of the curvature formula for MLS surfaces. (a) Needle plot of curvatures of three planar curves. (b) Color map of the curvature deviation. (c) Comparison of the curvature deviation with different sampling densities of the input point set.

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Figure 9

Slicing of the can data with three horizontal planes. (a) Isoview of the can data with resulting 2D contours on three slicing planes. (b) Top view of the slice at z=1.2. (c) Top view of the slice at z=1.5. (d) Top view of the slice at z=1.8.

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Figure 10

Rendered models of synthetic can data with different standard deviations of noise: (a) σ=0.01, (b) σ=0.02, and (c) σ=0.03

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Figure 11

Illustration of the maximum error between the nominal can surface and the sliced data with different noise levels and sample densities

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Figure 12

Illustration of adaptive layer generation. (a) Front view of the wine glass data with slicing planes in black. (b) Comparison of d, θ, and k as a function of z coordinate.

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