Traditional generating algorithms for B Spline curves and surfaces require approximation methods where how to increment the parameter to get the best approximation is problematic; or they take the pixel-based method needing matrix transformation from B Spline representation to Bezier form. Here, a fast, direct point-by-point generating algorithm for B Spline curves and surfaces is presented. The algorithm does not need matrix transformation, can be used for uniform or nonuniform B Spline curves and surfaces of any degree, and has high generating speed and good rendering accuracy.