부산대학교 도서관

T-splines are a generalization of tensor-product B-splines which allow T-junctions in the control meshes and thus allow local refinement. However, the famous de~Boor algorithm to evaluate a tensor-product B-spline surface can't be extended to general T-spline surfaces. In this paper, the authors prove a sufficient and necessary condition under which the de~Boor algorithm can be applied to evaluate points on a T-spline surface. An algorithm is developed to search in a T-mesh for the appropriate control points and blend them using the de~Boor algorithm to compute the corresponding point on the T-spline surface. This is the first de~Boor--like algorithm to evaluate T-spline surfaces, and the results are a significant contribution to T-spline theory and will be useful for applications.