| Popis: |
In this paper we propose a new subdivision scheme based on uniform Powell-Sabin spline subdivision. For each vertex we have a control triangle tangent to the surface instead of a control point. The main advantage of this scheme is that we can choose the values of the tangent vectors in the initial vertices, which gives more design possibilities. Strictly speaking it is an approximating scheme, the control points for the vertices change each iteration. However, the point where the control triangle is tangent to the surface remains the same. Therefore in practice it is an interpolating scheme. In the regular regions we use the uniform Powell-Sabin rules and we develop subdivision rules for the new vertices in the neighbourhood of extraordinary vertices. The scheme yields C1 continuous surfaces. We also do the convergence analysis based on the eigenproperties of the subdivision matrix and the properties of the characteristic map. ispartof: TW Reports nrpages: 15 status: published |
