The deduction of coefficient matrix for cubic non-uniform B-Spline curves

The cubic B-Spline curves have many engineering applications, such as graphic matching, materials cutting and layout arrangement. The existing mathematical representations, usually defined as polynomial function, its coefficient matrix of non-uniform B-Spline curves are complicated, difficult to understand, and require sophisticated algorithm in programming implementation. This paper aims at presenting a procedure based on the de Boor-Cox recursion formula, the coefficient matrixes of non-uniform B-Spline curves could be deducted. The application of this approach has been successfully used in shoe manufacturing process for material cutting control system.