Explicit Multi-degree Reduction of Said-Bézier Generalized Ball Curves with Endpoints Constraints ?

Theoretical study shows that Said-Bézier generalized Ball curves (SBGB curves) are distinctly superior to Bézier curves in evaluation, degree elevation and reduction. However in practical engineering, there is no effective algorithm for explicit multi-degree reduction of SBGB curves with endpoints constraints in the world. It is going against designing and applying generalized Ball curves. In order to shrug off this trouble, this paper deduces the matrices for both degree elevation and derived vectors at endpoints, of SBGB curves, and then applying the theory about generalized inverse matrices and partitioned matrices, deduces the explicit algorithm for multi-degree reduction of SBGB curves with constraints of arbitrary order continuity at the endpoints. Finally, the error analysis for degree-reduced approximation is given. Many numerical examples show the rationality and validity of this algorithm.