Gábor Renner

Genetic algorithms in computer aided design

Abstract Design is a complex engineering activity, in which computers are more and more involved. The design task can often be seen as an optimization problem in which the parameters or the structure describing the best quality design are sought. Genetic algorithms constitute a class of search algorithms especially suited to solving complex optimization problems. In addition to parameter optimization, genetic algorithms are also suggested for solving problems in creative design, such as combining components in a novel, creative way. Genetic algorithms transpose the notions of evolution in Nature to computers and imitate natural evolution. Basically, they find solution(s) to a problem by maintaining a population of possible solutions according to the ‘survival of the fittest’ principle. We present here the main features of genetic algorithms and several ways in which they can solve difficult design problems. We briefly introduce the basic notions of genetic algorithms, namely, representation, genetic operators, fitness evaluation, and selection. We discuss several advanced genetic algorithms that have proved to be efficient in solving difficult design problems. We then give an overview of applications of genetic algorithms to different domains of engineering design.

Advanced surface fitting techniques

Abstract In spite of extensive research on fitting parametric surfaces, the published ‘standard’ solutions often fail, when data points are irregularly distributed over topologically irregular domains, high accuracy is required and the free quantities of least squares fitting—such as the number and placement of knots, the weights of the smoothing functionals and the best parametrisation of the data points—must be set without user assistance. Further difficulties arise when the fitted surface needs to be extended in a natural way and hole loops without underlying point data need to be covered smoothly. This paper attempts to analyse the above difficulties and provide practical solutions to overcome these. Main results include algorithms to compute a good initial parametrisation, a fitting strategy to maintain tight tolerances and smoothness simultaneously, to handle weakly defined control points and a shape dependent knot refinement procedure. A few examples and suggestions for future work conclude the paper.

Exact and approximate computation of B-spline curves on surfaces

Abstract Curves on surfaces are important elements in computer aided geometric design. After presenting a method to explicitly compute these curves in three-dimensions, practical algorithmic issues are discussed concerning the efficiency of the implementation. Good approximations are important because of the quite high degree of exact curves on surfaces. We present two approximate solutions to the problem. The first is derived from the exact representation, while the second extends conventional least-squares approximation by incorporating the geometry of the surface as well. The efficiency and behaviour of the algorithms are evaluated by means of examples.

Method of shape description for mechanical engineering practice

Abstract A new method for curve representation is presented which takes the special features of engineering practice into consideration. The resulting curve may contain straight and free form sections, with tangent vector continuity to their surroundings. The interpolation is local and the parameter which describes the curve is approximately equal to the arc length of the curve.

Spline interpolation with genetic algorithms

A general framework is set up for the application of genetic algorithms in curve design. Then, within this scheme, the problem of spline interpolation-a frequently used method for representing complex geometrical shapes in CAD/CAM systems-is dealt with. While the method itself is simple and robust, it suffers from the drawback that some parameters must be given that are needed for the mathematical description but are not closely related to the geometrical input data of the object. The authors suggest taking a genetic approach to define the above parameters. The resulting curve minimizes a nonlinear functional which simulates the shape of an elastic bar.

Segmentation and Surface Fitting in Reverse Engineering

After a general overview on reverse engineering, various techniques to segment point clouds, which represent ‘regular’ or ‘free-form’ objects are described. More details are given on the so-called functional decomposition approach, which is based on the logical separation of primary surfaces and feature elements.

Techniques for the calculation of medial surfaces of solids

The Medial Axis Transform (MAT) surface, or simply Medial Surface (MS), offers the possibility of mathematically-based volumetric reasoning about geometric models using global shape and proximity information. The MAT surface is an important tool which can be used for several applications, such as designing manufacturing applications, robot path planning and offsetting, but has the disadvantage that it is computationally intensive. This paper describes two techniques which have been developed to improve the efficiency of the calculation process of the MAT of planar polyhedral objects. The first is a thorough analysis of the cases which can arise when calculating the vertex positions of the MAT of an object as combinations of points, lines and planes. The second technique, presented here, is a divide-and-conquer method, which makes use of some properties of the MAT structure to subdivide the problem. The power of the algorithms is illustrated by some examples, which show the MAT of solid objects with complicated shape and structure.

Note on the RBG-patch concept

Abstract The paper suggests a simplication in the method for smooth connection of RBG patches of Chiyokura et al. which results in the reduction of the degree of the patches.

Quality Control and Refinement of Car-Body Surfaces

The quality of the car-body surfaces is evaluated in the design phase. For that purpose, sensitive methods were developed; these are mainly the evaluation of the shape and distribution of reflection lines or highlight lines. In the paper, we propose a method to semi-automatically evaluate and improve the quality of the highlight line structures. Following the selection of the defective highlight line segments, the correction is carried out in two steps. First, sequences of evaluation points are computed to quantify the error in terms of distance and angle functions. Next, the corrected highlight points are calculated, and based on these points the corrected highlight line segments are constructed. The correspondence between the shape of the highlight lines and the surface parameters is highly complicated and strongly nonlinear. In the paper, a genetic process is proposed for the computation of the parameters of the surfaces, that corresponds to the corrected highlight line structure. Application of the method is demonstrated by correction of the highlight line structure and the shape of several car-body surfaces.

Correction of Highlight Line Structures

Class A surfaces are external surfaces of industrial objects, to which aesthetic appeal is attributed. Their design involves beyond functional criteria also subjective ones related to style and appearance. The design criteria include appropriate highlight line structures of the surfaces. Correction of highlight lines is usually performed interactively by the designer, which is time consuming, tedious and inaccurate.