Figure 16 - uploaded by Antonio Jimeno-Morenilla
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Source publication
Background. The Surface-Trajectory model gives 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...
Contexts in source publication
Context 1
... a consequence, the method is very quickly and accurate, due to the lack of extra calculations for the erosion trajectories visualization. The process of display of the object machining has a low temporal cost, as can be seen in the chart in figure 21. It shows the execution time for a simple object like the one in figure 16. The platform ...
Citations
... The specialization is based on a trajectory function, which uses The model has been defined to support the needs of CAD/CAM processes. Its validity was demonstrated by Sarabia et al. (2010), who presents a computer system for designing three-dimensional objects by trajectory, based on the morphological model presented (Figure 11). The computer system develops an environment of pieces modeled by trajectory using the deterministic morphological framework, providing solutions for designing complex objects and arithmetical support to generate machining trajectories, one of the most complex problems currently occurring in computer-aided design and manufacturing environments. ...
Mathematical morphology addresses the problem of describing shapes in an n-dimensional space using the concepts of set theory. A series of standardized morphological operations are defined, and they are applied to the shapes to transform them using another shape called the structuring element.
In an industrial environment, the process of manufacturing a piece is based on the manipulation of a primitive object via contact with a tool that transforms the object progressively to obtain the desired design. The analogy with the morphological operation of erosion is obvious. Nevertheless, few references about the relation between the morphological operations and the process of design and manufacturing can be found. The non-deterministic nature of classic mathematical morphology makes it very difficult to adapt their basic operations to the dynamics of concepts such as the ordered trajectory.
A new geometric model is presented, inspired by the classic morphological paradigm, which can define objects and apply morphological operations that transform these objects. The model specializes in classic morphological operations, providing them with the determinism inherent in dynamic processes that require an order of application, as is the case for designing and manufacturing objects in professional computer-aided design and manufacturing (CAD/CAM) environments. The operators are boundary-based so that only the points in the frontier are handled. As a consequence, the process is more efficient and more suitable for use in CAD/CAM systems.
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.
