The product calculation of linear polynomial and B-spline curve

In this paper, we mainly discuss how to calculate the product of linear polynomial function and B-spline curve with arbitrary degree k and generally structured knot. This product calculation involves two questions, the one is how to calculate the product of parameter t and B-spline curve; the other is degree elevation of B-spline curve. Firstly, by making use of the conversion matrix between k-th B-spline bases and (k+1)-th B-spline bases, we present an approach for calculating the product of parameter t and B-spline curve. Meanwhile, we put forward a simple method for the degree elevation of B-spline curve. Further, we obtain the formula for calculating the product of linear polynomial function and a B-spline curve. At the end, we give the examples with k = 3, namely the product of linear polynomial function and cubic B-spline curve, which also show that the product calculation method in this paper easily implements.