Computational morphogenesis method for freeform structures generated by translating B-spline curves

Recently freeform structures have become more and more popular, but how to create flexible surfaces by considering both designer's preference and structural rationality is still an unsolved problem. In this paper, a computational morphogenesis method for translational surfaces is put forward by combining the geometrical modeling technique and the structural optimal method. To meet the freeform requirements, B-spline functions controlled by some geometrical key parameters are adopted to describe the generatrix and directrix. The structural strain energy is taken as the criterion for assessing the mechanical performance. A link between the differential of structural strain energy and the geometrical key parameters of B-spline curves are weaved based on the gradient method. By adjusting the shapes of generatrix and directrix, a series of freeform surfaces with minimum structural strain energy can be obtained. Due to the process of computational morphogenesis starting from the generatrix and directrix rather than the whole surface, this method can maintain the constant relationships between curves on surface during the process of creation, which can bring convenience for grid structure manufacturing. Some examples are shown to verify the efficiency of this method.