Efficient Construction of B-Spline Curves with Minimal Internal Energy

In this paper, we propose an efficient method to construct energy-minimizing B-spline curves by using discrete mask method. The linear relations between control points are firstly derived for different energy-minimization problems, then the construction of B-spline curve with minimal internal energy can be addressed by solving a sparse linear system. The existence and uniqueness of the solution for the linear system are also proved. Experimental results show the efficiency of the proposed approach, and its application in G1 blending curve construction is also presented.