差分迭代椭圆算法

DIFFERENCE ITERATION ALGORITHM FOR GENERATING ELLIPSE

在一般光栅象素的椭圆生成算法中,其主循环中均带有乘法和开方等运算,因而其计算量较大。本文介绍的差分迭代椭圆算法,利用椭圆的某一参数方程可表示成两个圆参数方程的组合,而采用圆的差分迭代算法。因此,使其在主循环中仅有加、减法和移位运算,极大地降低了计算量,并易于硬件集成。本文还对椭圆弧的生成作进一步讨论,并举例就其误差与中点椭圆算法作了比较。

In the general ellipse - generating algorithm for raster - pixel, there are always multiplication and square root operating in the main iteration loop, so the calculating cost is more expensive. In this paper, the difference iteration algorithm for ellipse is developed. It uses the difference iteration for circles, because one of the parametric representations of ellipse can be described as two - circle parametric representations. After this, there are only addition,subtraction and shift operations in the main loop.So the calculating cost is reduced and it is best suited for hardware implementation. Generating ellipse arc is also discussed in this paper. Some examples are developed for compare between the central - point algorithm and difference iteration algorithm in calculating cost and error.