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Research Papers

Surface Reconstruction Using Dexel Data From Three Sets of Orthogonal Rays

[+] Author and Article Information
Weihan Zhang1

Department of Mechanical and Aerospace Engineering, Missouri University of Science and Technology, Rolla, MO 65409wzxq6@mst.edu

Ming C. Leu

Department of Mechanical and Aerospace Engineering, Missouri University of Science and Technology, Rolla, MO 65409mleu@mst.edu

1

Corresponding author,

J. Comput. Inf. Sci. Eng 9(1), 011008 (Mar 06, 2009) (12 pages) doi:10.1115/1.3086034 History: Received November 23, 2007; Revised May 29, 2008; Published March 06, 2009

Triple-dexel modeling is a geometric representation method, which depicts the intersection of a solid with rays cast in three orthogonal directions. Due to its fast Boolean operations, simple data structure, and easy implementation, triple-dexel modeling is highly suitable for real-time graphics-based simulation applications such as numerical control (NC) machining verification and virtual sculpting. This paper presents a novel surface reconstruction method from triple-dexel data by first converting the triple-dexel data into contours on three sets of orthogonal slices and then generating the solid’s boundary surface in triangular facets from these contours. The developed method is faster than the voxel-based method, and the reconstructed surface model is more accurate than the surface reconstructed from voxel representation using the marching cube algorithm. Examples are given to demonstrate the ability of surface reconstruction from the triple-dexel model in virtual sculpting.

Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Illustration of (a) the ray-casting process and (b) the single-dexel representation

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Figure 2

Construction of a triple-dexel model by casting rays in x, y, and z directions

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Figure 3

Proposed method of surface reconstruction from triple-dexel data

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Figure 4

Contour generation from single-dexel data

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Figure 5

(a) xy contours, (b) yx contours, and (c) the combined contours

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Figure 6

Locations of the first and the last associated points of contour Bj for points ai,k and ai,k+1: (a) ai,k and ai,k+1 on the same ray and (b) ai,k and ai,k+1 on adjacent rays

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Figure 7

Illustration of the solution to the case CA4 in Table 1

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Figure 8

Contour combination process: (a) two generated contours from the contour generation process and (b) the combined contour

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Figure 9

Contour combination process: (a) original contour, (b) two generated contours from the contour generation process and (c) the combined contour

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Figure 10

A case study of the contour combination process: (a) the input contour with x-dexel and y-dexel data, (b) contour generated from the x-dexel data, (c) contours generated from the y-dexel data, (d) the input contour with an increase of rays in y direction, (e) contours generated from y-dexel data in (d), and (f) combined contour from (b) and (e)

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Figure 11

A case study of the contour combination process: (a) the input contour with x- and y-dexel data, (b) contours generated from the x-dexel data and y-dexel data, (c) the dexel points after increasing the number of rays in x and y directions, (d) contours generated from x-dexel data in (c), (e) contours generated from y-dexel data in (c), and (f) combined contour from (d) and (e)

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Figure 12

(a) Identification of boundary subvolumes and (b) generation of surface patches within two boundary subvolumes

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Figure 13

Illustrative example of the contour combination algorithm: (a) input object model, (b) contour generated from x-dexel data, (c) contour generated from y-dexel data, and (d) combined contour from (b) and (c)

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Figure 14

A bunny model and the reconstructed surface of the bunny

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Figure 15

Comparisons between the surfaces reconstructed from single-dexel data in (a) and (c) and from triple-dexel data in (b) and (d)

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Figure 16

A cat model generated using the virtual sculpting system and viewed from two different directions

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Figure 17

Two test cases: impeller and bunny

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Figure 18

Surface reconstruction time versus number of divisions from the voxel data and the triple-dexel data for the impeller

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Figure 19

Surface reconstruction time versus the number of divisions from the voxel data and the triple-dexel data for the bunny

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