Rendering and anti-aliasing drawing hyperbola based on residuals

In order to improve the efficiency of generating algorithms for hyperbola, a novel algorithm is proposed. In the algorithm, redefined residuals are employed to construct iteration relations. Because of monotonicity between decision parameter and residual, float residuals may be eliminated and a pure integral algorithm can be gained. Furthermore, the residuals may be directly used to decide the distances from real curve to candidate pixels, and then integral anti-aliasing drawing algorithm is derived. Analyses and experiments show that the efficiency of our algorithm increases by about 12% contrast to that of some proposed algorithms, and the property of the generated curve is also well, and its derivation is simple and easy to be understood.