Explicit G~2-constrained degree reduction of Bézier curves by quadratic optimization

摘要

In this paper, we revisit G~2-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 G~1-constrained degree reduction and C~1G~2- constrained degree reduction. Our main idea is to express the distance function defined in the L~2-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.