Real-time rendering of algebraic B-spline surfaces via Bzier point insertion

This paper presents a GPU-based real-time raycasting algorithm for piecewise algebraic surfaces in terms of tensor product B-splines. 3DDDA and depth peeling algorithms are employed to traverse the piecewise surface patches along each ray. The intersection between the ray and the patch is reduced to the root-finding problem of the univariate Bernstein polynomial. The polynomial is obtained via Chebyshev sampling points interpolation. An iterative and unconditionally convergent algorithm called B′ezier point insertion is proposed to find the roots of the univariate polynomials. The B′ezier point insertion is robust and suitable for the SIMD architecture of GPU. Experimental results show that the proposed root-finding algorithm performs better than other root-finding algorithms, such as B′ezier clipping and B-spline knot insertion. Our rendering algorithm can display thousands of piecewise algebraic patches of degrees 6–9 in real time and can achieve the semi-transparent rendering interactively.