By introducing the homogenous coordinates, degree elevation formulas and combinatorial identities, also by using multiplication of Bernstein polynomials and identity transformation on equations, this paper presents so...By introducing the homogenous coordinates, degree elevation formulas and combinatorial identities, also by using multiplication of Bernstein polynomials and identity transformation on equations, this paper presents some explicit formulas of the first and second derivatives of rational triangular Bézier surface with respect to each variable (including the mixed derivative) and derives some estimations of bound both on the direction and magnitude of the corresponding derivatives. All the results above have value not only in surface theory but also in practice.展开更多
We implemented accurate FFD in terms of triangular Bezier surfaces as matrix multiplications in CUDA and rendered them via OpenGL. Experimental results show that the proposed algorithm is more efficient than the previ...We implemented accurate FFD in terms of triangular Bezier surfaces as matrix multiplications in CUDA and rendered them via OpenGL. Experimental results show that the proposed algorithm is more efficient than the previous GPU acceleration algorithm and tessel- lation shader algorithms.展开更多
A family of Said-Bézier type generalized Ball （SBGB） bases and surfaces with a parameter H over triangular domain is introduced,which unifies Bézier surface and Said-Ball surface and includes several inter...A family of Said-Bézier type generalized Ball （SBGB） bases and surfaces with a parameter H over triangular domain is introduced,which unifies Bézier surface and Said-Ball surface and includes several intermediate surfaces. To convert different bases and surfaces,the dual functionals of bases are presented. As an application of dual functionals,the subdivision formulas for surfaces are established.展开更多
基金Project supported by the National Natural Science Foundation of China (Nos. 60373033 & 60333010), the National Natural Science Foundation for Innovative Research Groups (No. 60021201), and the National Basic Research Program (973) of China (No. 2002CB312101)
文摘By introducing the homogenous coordinates, degree elevation formulas and combinatorial identities, also by using multiplication of Bernstein polynomials and identity transformation on equations, this paper presents some explicit formulas of the first and second derivatives of rational triangular Bézier surface with respect to each variable (including the mixed derivative) and derives some estimations of bound both on the direction and magnitude of the corresponding derivatives. All the results above have value not only in surface theory but also in practice.
基金Supported by the National Natural Science Foundation of China(61170138 and 61472349)
文摘We implemented accurate FFD in terms of triangular Bezier surfaces as matrix multiplications in CUDA and rendered them via OpenGL. Experimental results show that the proposed algorithm is more efficient than the previous GPU acceleration algorithm and tessel- lation shader algorithms.
文摘A family of Said-Bézier type generalized Ball （SBGB） bases and surfaces with a parameter H over triangular domain is introduced,which unifies Bézier surface and Said-Ball surface and includes several intermediate surfaces. To convert different bases and surfaces,the dual functionals of bases are presented. As an application of dual functionals,the subdivision formulas for surfaces are established.
