Tiling surfaces with straight strips

We present an algorithm computing geodesic curves partitioning an open mesh into segments which can be approximated using long, trimmed strips of material possessing a prescribed width. We call this straight strip tiling of a curved surface, with applications such as the surfacing of curved roofs. Our strips are straight since they conform to being rectangular, in contrast to possibly highly curved strip segments studied for developable surface decomposition. Starting from a geodesic curve defined by a user-specified starting point and direction we compute recursively neighbouring geodesics which respect the constraints and lead to optimal material usage. Our algorithm is exact with respect to the polyhedral geometry of the mesh and runs on a variety of surfaces with modest time complexity of O(n1.5), where n is the mesh size. We extend the algorithm by relaxing the constraint that geodesics span the mesh allowing application to meshes with greater undulation.