A practical construction of G1 smooth biquintic B-spline surfaces over arbitrary topology
The motivation of this paper is to develop a local scheme of constructing G1 smooth B-spline surfaces with single interior knots over arbitrary topology. In this paper, we obtain the conditions of G1 continuity between two adjacent biquintic B-spline surfaces with interior single knots. These conditions are directly represented by the relevant control points of the two B-spline surfaces. By utilizing these G1 conditions, we develop the first local scheme of constructing G1 smooth biquintic B-spline surfaces with interior single knots for arbitrary topological type. The high complexity of deriving the local G1 scheme is well overwhelmed. The biquintic is the lowest degree for which there exists a local scheme of constructing G1 smooth B-spline surfaces with interior single knots over arbitrary topology.
g1 smooth biquintic b-spline surface arbitrary topology local scheme discrete b-spline