document: Optimal multi-degree reduction of Bezier curves with constraints of endpoints continuity Given a Bezier curve of degree n , the problem of optimal multi-degree reduction -LRB- degree reduction of more than one degree -RRB- by a Bezier curve of degree m -LRB- m < n-1 -RRB- with constraints of endpoint continuity is investigated . With respect to L/sub 2 / norm , this paper presents an approximate method -LRB- MDR by L/sub 2 / -RRB- that gives an explicit solution to deal with it . The method has good properties of endpoint interpolation : continuity of any r , s -LRB- r , s > or = 0 -RRB- orders can be preserved at two endpoints respectively . The method in the paper performs multi-degree reduction at one time and does not need stepwise computing . When applied to multi-degree reduction with endpoint continuity of any order , the MDR by L/sub 2 / obtains the best least squares approximation . Comparison with another method of multi-degree reduction -LRB- MDR by L/sub infinity / -RRB- , which achieves the nearly best uniform approximation with respect to L/sub infinity / norm , is also given . The approximate effect of the MDR by L/sub 2 / is better than that of the MDR by L/sub infinity / . Explicit approximate error analysis of the multi-degree reduction methods is presented
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