Curve network interpolation by $C^1$ quadratic B-spline surfaces
For geometric modeling applications requiring smooth surface interpolation from curve networks, this provides a provably unique solution with a practical algorithm.
The paper presents a method for interpolating a B-spline curve network using C^1 quadratic B-spline surfaces on criss-cross triangulations, proving existence and uniqueness with a constructive algorithm. Numerical results show the method's effectiveness.
In this paper we investigate the problem of interpolating a B-spline curve network, in order to create a surface satisfying such a constraint and defined by blending functions spanning the space of bivariate $C^1$ quadratic splines on criss-cross triangulations. We prove the existence and uniqueness of the surface, providing a constructive algorithm for its generation. We also present numerical and graphical results and comparisons with other methods.