Abstract—By introducing the inner-product matrix of two vector functions and using conversion matrix, explicit formulas for the dual basis functions of Wang-Said type generalized Ball bases (WSGB) with respect to the Jacobi weight function are given. The dual basis functions with and without boundary constraints are also considered. As a result, the paper includes the weighted dual basis functions of Bernstein basis, Wang-Ball basis and some intermediate bases. These results are useful for the application of generalized Ball curves of Wang-Said type and their popularization in Computer Aided Geometric Design.

Index Terms—Weighted dual function, WSGB, inner-product matrix, bernstein basis.

Davood Bakhshesh was with Department of Mathematical Sciences, Sharif Univeristy of Technology, Tehran, Iran (e-mail:dbakhshesh@gmail.com).
Mohammad Reza Samiee is with Department of Computer Engineering,Payame Noor University (PNU), Khorasan Shomali, Iran (e-mail:samiee.reza@gmail.com).

Cite: Davood Bakhshesh and Mohammad Reza Samiee, "The Weighted Dual Functions for Wang-Said Type Generalized Ball Bases With and Without Boundary Constraints," International Journal of Computer and Electrical Engineering vol. 4, no. 4, pp. 572-576, 2012.