On the design of optimisers for surface reconstruction

Abstract

In many industrial applications the need for an efficient and high-quality reconstruction of free-form surfaces does exist. Surface Reconstruction -the generation of CAD models from physical objects -has become an independent area of research. The supplementary modification and the automated manufacturing of workpieces represent typical fields of application. Small tolerances in the desired properties result in a very high number of scan points needed. Thus, modern approaches have to be capable of processing, analysing and modelling these amounts of data.There are several studies that use evolutionary algorithms (EA) for surface reconstruction tasks. Until now, these studies only describe the general ability of EA to successfully optimise surfaces. Aspects like runtime as well as comparability to other optimisation techniques have not been considered. Since these aspects are of great importance for integration in applicable software tools, in this paper the ability of a state-of-the-art multi-objective EA to be successfully integrated in surface reconstruction software is analysed. Major drawbacks are disclosed and necessary add-on modules are presented.

On the Use of Problem-Specific Candidate Generators for the Hybrid Optimization of Multi-Objective Production Engineering Problems

“…For each sensor point, the point p i,j in P having the minimal squared distance can then be determined. An efficient method for this task was presented by Wagner et al (2007b). Weinert et al (2001) combined NURBS with constructive solid geometry (Hoffmann, 1989) by using a hybrid evolutionary algorithm with additional genetic programming operators.…”

“…The x-and y-coordinates were then varied in the second phase of fine-tuning the solution obtained in the first phase. Wagner et al (2007b) analyzed the effect of both distance functions on the performance of a single-objective genetic algorithm (GA). By means of a simple workpiece, they pointed out that in cases where the initial solution is far from the point set, the GA gets often trapped in undesirable local optima, which results in effectively no decision space diversity in the population.…”

“…Nevertheless, this aggregation approach only results in a single solution. Wagner et al (2007b) were the first to take a multi-objective perspective on the problem of surface reconstruction. In their study, the exact calculation and the discrete approximation of the distance between the scan points and the surface were used as objectives.…”

“…The numerical approaches (Wagner et al, 2007b;Pottmann et al, 2005) can provide initial solutions optimized with respect to the first objective f 1 or a given aggregation of both objectives. Wagner et al (2007b) have shown that the solutions provided by these approaches often dominate the whole approximation set generated by a MOEA which is initialized with a surface far from the point set.…”

“…Wagner et al (2007b) have shown that the solutions provided by these approaches often dominate the whole approximation set generated by a MOEA which is initialized with a surface far from the point set. Thus, the use of these solutions can significantly improve the optimization results.…”