A graph-based method for calculating draping strategies for the application of fiber-reinforced materials on arbitrary surfaces

This paper is focused on a method for calculating the optimal drape origin on arbitrary surfaces considering a minimal shear-deformation of the applied fiber-reinforced material. The presented method is based on the mesh from a triangulated surface and therefore not restricted by the assumption of a mathematical differentiable surface description. It is shown how the information of the mesh can be used to calculate the point-wise Gaussian-curvature on the given surface. It is further shown how this curvature information can be used to construct a directed planar graph and how this graph can help calculating the optimal drape sequence in order to minimize the shear-deformation of the applied fabric. The paper is concluded by a demonstration of the developed method for different example surfaces.