Title: A matrix Method for Computing the Derivatives of Interval Uniform BSpline Curves  
Author(s): O. Ismail  
Pages: 15  Paper ID:1557029393IJVIPNSIJENS  Published: April, 2015 
Abstract: The matrix forms for curves and surfaces were largely promoted in CAD. These formulations are very compact to write, simple to program, and clear to understand. They manifest the desired basis as a matrix transformation of the common power basis. Furthermore, this implementation can be made extremely fast if appropriate matrix facilities are available in either hardware or software. Derivatives are very important in computation in engineering practice on graphics structures. Bspline functions are defined recursive, so direct computation is very difficult. A method for obtaining the matrix representations of uniform Bsplines and Bezier curves of arbitrary degrees have been presented in this paper. By means of the basis matrix, the matrix representations of uniform Bsplines and Bezier curves are unified by a recursive formula. The four fixed uniform Kharitonov's polynomials (four fixed uniform Bspline curves) associated with the original interval uniform Bspline curve are obtained in matrix form. The fixed control points of the r^th derivatives of the four fixed uniform Kharitonov's polynomials (four fixed uniform Bspline curves) are found. Finally the interval control points of the r^th derivative of the interval Bspline curve is computed from the fixed control points of the r^th derivatives of the four fixed uniform Kharitonov's polynomials (four fixed uniform Bspline curves). A numerical example is included in order to demonstrate the effectiveness of the proposed method.


Keywords: Recursive matrix representations, interval Bspline curve, CAD, derivatives of Bspline curve, CAGD.  
Full Text (.pdf)  393 KB 