Ruled Surface Extraction from Mesh Model

We have proposed a novel method to extract ruled surface from mesh model. Based on retrieving and approximating the ruling line sets, our method first selects a trusted ruling line according to sorted error weights. Then neighboring ruling lines are found using the local frame, and the searching of next ruling lines is performed by relocating the local frame until the boundary of an open mesh or the beginning of a cycled searching is reached. A projection method is used to smooth out start and end points of the ruling line sets. With predefined Euclidean 6 space distances, the problem of ruled surface approximation from line sets in Euclidean 3 space can be converted into a least square B-spline curve fitting issue in Euclidean 6 space. For smooth surface approximation, we also add energy function term into the curve fitting process. Compared with other algorithms, examples show that our method can retrieve line sets more robustly and accurately, and can more effectively and rationally fit smooth ruled.