In order to improve speed of circles drawing, some multi-step or run-length slice algorithms are proposed. Based on careful analysis of the characteristics of raster-scan circles, a simple and fast method to calculate lengths of slices is presented in this paper. In the new algorithm, double-step control is mainly used for larger horizontal run-slices, and mixed single-step and double-step control is adopted for complicated pattern and run-slices with 45° angle, furthermore, each horizontal run-slice is output at once, only about 2.9 times basic operations are needed for once stepping on average. Experiments and analysis shows that the new algorithm is significantly faster than previously published ones, and its' derivation can be gained in a simple manner. Furthermore, it can be implemented with hardware since no complex operations are involved, and can be developed to draw other conic curves.%为了提高直线和曲线的光栅转换速度而产生了多步算法和行程算法.论文分析了光栅圆弧的特性,利用对中点法的结构和决策参数的重新构造,提出了一种简单、快速的行程计算方法.该方法以2点步进为主进行行程计算,并可以容易地结合局部模式分析以处理复杂的光栅模式.实验和分析表明,所形成的新算法综合利用了2点步进和行程方法的优势,有效地减少了计算量和I/O次数,其圆弧绘制速度明显优于现有其它算法,且理论推导简单,不含乘法、开方等复杂运算,硬件实现容易,并可以推广到其他圆锥曲线的绘制.
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