An algorithm for multi-resolution analysis of NURBS surfaces

A new algorithm is proposed for the multi-resolution representation of NURBS (Non-Uniform Rational B-Spline) surfaces with boundary consistency constraints. The kernel idea is to employ T-meshes (T-spline control meshes) to construct the multi-resolution representation for surfaces. To this end, the original B-mesh (B-spline control mesh) is first divided into a boundary part and an inner one; then, the multi-resolution representation of the inner part is achieved by wavelet transform; at last, the topology of the boundary part is added onto the obtained multi-resolution meshes to construct the final T-spline based multi-resolution representation result. The boundary shapes keep unchanged in the whole process of the treatment, because the boundary consistency constraints are always contained in the boundary part. This advantage of the new algorithm is demonstrated by three examples.