Efficient construction algorithms of finite circles and their applications to 2D layout optimization

In order to explore the efficiency of finite circle method (FCM) and to reduce the circle number as much as possible, three new methods, i.e. the bisection algorithm, the three-step algorithm and the improved three-step algorithm with gap are proposed for the automatic generation of circles in this paper. The first one is to generate the circle for each borderline segment of the component by considering the segment length and the prescribed tolerance value. If this is not the case, the borderline segment will be equally divided into halves until the obtained circle satisfies the tolerance value over the whole borderlines of the component. The basic idea of the last two algorithms aims at covering the domain occupied by the component as much as possible. The circle generation is carried out sequentially from salient angle to the sector formed by the salient angle till the uncovered borderline segments of the component. Particularly, the three-step algorithm with gap allows that the generated circles are distributed with gap along the component contour. Lots of numerical examples are finally tested. It is shown that the three-step algorithm and the improved three-step algorithm with gap can approximate the component with fewer circles. Thus, they can improve considerably the efficiency of multi-components packing and layout optimization.