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Research Papers

A Morphological Approach to the Design of Complex Objects

[+] Author and Article Information
R. Sarabia

Department of Computer Science Technology and Computation, University of Alicante, Apartado Correos 99, 03080 Alicante, Spainrsp1@alu.ua.es

A. Jimeno-Morenilla

Department of Computer Science Technology and Computation, University of Alicante, Apartado Correos 99, 03080 Alicante, Spainjimeno@dtic.ua.es

R. Molina-Carmona

Department of Computer Science and Artificial Intelligence, University of Alicante, Apartado Correos 99, 03080 Alicante, Spainrmolina@dccia.ua.es

J. Manuf. Sci. Eng 132(5), 051003 (Sep 10, 2010) (7 pages) doi:10.1115/1.4002193 History: Received December 02, 2008; Revised July 02, 2010; Published September 10, 2010; Online September 10, 2010

The surface-trajectory model gives a solution to some of the problems presented by the general geometric models where the design of an object is separated from its manufacture. In fact, in this model, the internal representation of objects is made up of machining trajectories. As the display systems usually need triangles to represent the objects, a process of triangulation is needed to visualize them. In other words, a secondary surface model is needed to display the objects. The following is a geometric model that, maintaining the philosophy of the surface-trajectory model, encapsulates the calculation of the machining process from the formal framework that provides the set theory and the mathematical morphology. The model addresses the process of designing objects by assimilation of a machining process by giving solutions to the design of complex objects and an arithmetic to support the generation of trajectories of manufacturing. The design process is similar to the craft work of sculptors designing their pieces by hand with their tools. It also gives a direct solution to the problems of the trajectory generation since they are already defined at the design phase. The model is generic and robust as there are no special cases or complex objects in which the model does not provide a correct solution. It also naturally incorporates the realistic display of the machined objects in a quickly and accurately way.

Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Example of a complex model

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Figure 2

Geometric description of an instant basic dilation. (a) Initial position. (b) X transformation. (c) Distance computing.

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Figure 3

Example of a morphologic erosion

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Figure 4

Example of machining a piece with a circular tool following an open trajectory

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Figure 5

Partial morphological erosion as a subset of the complete erosion

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Figure 6

Dilation of simple line in two dimensions

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Figure 7

Dilated erosion trajectory

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Figure 8

Two-dimensional and three-dimensional views of the result of the regularized partial erosion of a trajectory

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Figure 9

Dilation of erosion path from the parallel

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Figure 10

Angular sweep for calculating the two-dimensional dilation

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Figure 11

Example of regularized partial erosion in two dimensions. (a) Trajectory to be eroded. (b) Dilation of the trajectory. (c) Frontier of the regularized partial erosion.

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Figure 12

Examples of regularized partial erosions in two dimensions with discontinuities. (a) Trajectories to be eroded. (b) Dilation of the trajectory. (c) Frontiers of the regularized partial erosions.

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Figure 13

Dilation of a three-dimensional trajectory

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Figure 14

Dilation surface in form of arches as obtained from the algorithm

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Figure 16

Details of erosion trajectories

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Figure 17

Examples of regularized partial erosions in three dimensions

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Figure 18

Examples of regularized partial erosions in three dimensions

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Figure 19

Execution time for a simple erosion (Fig. 1)

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