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.

Technical objects which are typically described by free-form surfaces, usually also contain conventional elements (planes, cylinders, cones). Consequently, methods and systems for defining free-form shapes are advantageously complemented by description of simple geometrical elements. In the paper, known methods of computational geometry are examined from the point of view of describing curves containing straight line sections. Moreover an analysis of the accuracy of approximating a circle by these methods i s given.

A new method for interpolation is presented which starts from a given set of data pints. The resulting curve consisting of a set of polynomials has tangent vector continuity in the nodes, and can have straight line sections incorporated in it, with preserved continuity properties. The interpolation is local in the sense, that the shape of the curve at a certain data pint is influenced by five data points in its neighbourhood. First the construction of tangent vectors, then the determination Of the parameter intervals are dealt with. These are selected in such a way that a quasi-natural parametrization is held along the whole curve.