Genetic B-spline approximation on combined B-reps

We present a genetic algorithm for approximating densely sampled curves with uniform cubic B-Splines suitable for Combined B-reps. A feature of this representation is altering the continuity property of the B-Spline at any knot, allowing combining freeform curves and polygonal parts within one representation. Naturally there is a trade-off between different approximation properties like accuracy and the number of control points needed. Our algorithm creates very accurate B-Splines with few control points, as shown in Fig. 1. Since the approximation problem is highly nonlinear, we approach it with genetic methods, leading to better results compared to classical gradient based methods. Parallelization and adapted evolution strategies are used to create results very fast