Computing ruled surfaces using weighted graph

Ruled surfaces play an extremely important role in computer aided design and computer graphics. Based on the idea of boundary bridge triangulation, we transfer the problem of seeking various ruled surface to the computation of the shortest path for a weighted graph, and the well known Dijkstra algorithm can be used to achieve the solution. We devise some new optimal objective functions for the boundary bridge triangulation to satisfy practical purpose. We also present some hybrid schemes which combine several advantages of different types of ruled surfaces. Considering the aesthetic requirements, we propose a shape parameter to avoid the skinny triangle in our triangulation. Experiments and examples shown in the last demonstrate the advantage of hybrid ruled surface, the effect of the shape parameter in controlling the shape of triangles and the applications of our methods.