Explicit G2-constrained degree reduction of Bézier curves by quadratic optimization

摘要

In this paper, we revisit G2-constrained degree reduction of Bézier curves which has been solved in our previous work by using iterative methods. We propose an explicit and effective method for G1-constrained degree reduction and C1G2-constrained degree reduction. Our main idea is to express the distance function defined in the L2-norm as a strictly convex quadratic function of two variables, which becomes a quadratic optimization problem. We can explicitly obtain the unique solution by solving two linear equations such that the distance function is minimized. The existence of the unique solution is also proved.