Algorithms for Rendering Cubic Curves
Benjamin A. Watson, Larry F. Hodges · 1992
We present two integer-only algorithms to be used in tandem for rendering cubic functions and parametric cubic curves with rational coefficients. We then show how to take advantage of curve shape to improve algorithm performance. Analysis of execution speed of existing algorithms shows that our algorithms will match or outperform other current algorithms. Furthermore, while other existing algorithms can only handle curves shaped by rational coefficients by introducing some approximation error, our algorithms always choose the best approximation. When plotting parametric curves, our algorithms may require more bits of representation for some integer variables than other existing algorithms. Categories and Subject Descriptors: G.1.1 [Numerical Analysis]: Interpolation ---- spline and piecewise polynomial interpolation; G.1.2 [Numerical Analysis]: Approximation ---- spline and piecewise polynomial approximation; I.3.3 [Computer Graphics]: Picture/Image Generation ---- display algorithms; ...