A Novel Contour Generation Algorithm for Surface Reconstruction From Dexel Data

[+] Author and Article Information
Weihan Zhang

Department of Mechanical and Aerospace Engineering, University of Missouri-Rolla, Rolla, Missouri 65409wzxq6@umr.edu

Xiaobo Peng

Mechanical Engineering Department, Prairie View A&M University, Prairie View, TX 77446xipeng@pvamu.edu

Ming C. Leu1

Department of Mechanical and Aerospace Engineering, University of Missouri-Rolla, Rolla, Missouri 65409mleu@umr.edu

Wei Zhang

Department of Industrial Engineering, Tsinghua University, Beijing 100084, People’s Republic of Chinazhangwei@tsinghua.edu.cn


Corresponding author.

J. Comput. Inf. Sci. Eng 7(3), 203-210 (Mar 09, 2007) (8 pages) doi:10.1115/1.2752817 History: Received February 24, 2006; Revised March 09, 2007

This paper presents a method of reconstructing a triangular surface patch from dexel data generated by ray casting to represent solid models for applications, such as virtual sculpting and numerically controlled (NC) machining simulation. A novel contour generation algorithm is developed to convert dexel data into a series of planar contours on parallel slices. The algorithm categorizes the dexels on two adjacent rays into different groups by using a “grouping” criterion. The dexel points in the same group are connected using a set of rules to form subboundaries. After checking the connections among all the dexel points on one slice, a connection table is created and used to obtain the points of connection in a counterclockwise sequence for every contour. Finally, the contours on all the parallel slices are tiled to obtain triangular facets of the boundary surface of the 3D object. Computational costs and memory requirements are analyzed, and the computational complexity analysis is verified by numerical experiments. Example applications are given to demonstrate the described method.

Copyright © 2007 by American Society of Mechanical Engineers
Topics: Algorithms
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Figure 1

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

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Figure 2

Example of the contour generation algorithm: (a) 3D model and (b) one slice of the 3D model on XZ plane

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Figure 3

Grouping process

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Figure 4

Contouring algorithm

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Figure 5

Special cases: Ri=0 (left) and Ri+1=0 (right)

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Figure 6

Traversing the connection table to separate contours

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Figure 7

Example of contour generation process

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Figure 8

Discussion on the validation of the observations

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Figure 9

The skull models used in the tests: (a) B1 model, (b) B3 model, (c) B5 model, and (d) the generated contour from B1

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Figure 10

Contour generation time T versus average number of dexels per ray (α)

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Figure 11

Contour generation time T versus number of rays (β)

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Figure 12

Virtual sculpting system configuration

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Figure 13

(a) Shows an imported cat model created from a CAD system, (b) shows the eyes and tails created by virtual sculpting, and (c) and (d) show the modified cat model in different viewing directions

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Figure 14

(a) Shows a mouse in the midst of NC machining simulation, and (b) and (c) show the generated mouse viewed from two different directions after performing surface reconstruction during the machining simulation




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