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Deterministic mathematical morphology for CAD/CAM

Rubén Sarabia-Pérez (Department of Computer Technology, University of Alicante, Alicante, Spain)
Antonio Jimeno-Morenilla (Department of Computer Technology, University of Alicante, Alicante, Spain)
Rafael Molina-Carmona (Department of Computer Science and Artificial Intelligence, University of Alicante, Alicante, Spain)

Engineering Computations

ISSN: 0264-4401

Article publication date: 30 September 2014

122

Abstract

Purpose

The purpose of this paper is to present a new geometric model based on the mathematical morphology paradigm, specialized to provide determinism to the classic morphological operations. The determinism is needed to model dynamic processes that require an order of application, as is the case for designing and manufacturing objects in CAD/CAM environments.

Design/methodology/approach

The basic trajectory-based operation is the basis of the proposed morphological specialization. This operation allows the definition of morphological operators that obtain sequentially ordered sets of points from the boundary of the target objects, inexistent determinism in the classical morphological paradigm. From this basic operation, the complete set of morphological operators is redefined, incorporating the concept of boundary and determinism: trajectory-based erosion and dilation, and other morphological filtering operations.

Findings

This new morphological framework allows the definition of complex three-dimensional objects, providing arithmetical support to generating machining trajectories, one of the most complex problems currently occurring in CAD/CAM.

Originality/value

The model proposes the integration of the processes of design and manufacture, so that it avoids the problems of accuracy and integrity that present other classic geometric models that divide these processes in two phases. Furthermore, the morphological operative is based on points sets, so the geometric data structures and the operations are intrinsically simple and efficient. Another important value that no excessive computational resources are needed, because only the points in the boundary are processed.

Keywords

Citation

Sarabia-Pérez, R., Jimeno-Morenilla, A. and Molina-Carmona, R. (2014), "Deterministic mathematical morphology for CAD/CAM", Engineering Computations, Vol. 31 No. 7, pp. 1221-1241. https://doi.org/10.1108/EC-02-2013-0056

Publisher

:

Emerald Group Publishing Limited

Copyright © 2014, Emerald Group Publishing Limited

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