生成圆弧的等距线约束方法及其应用

栅格圆弧的生成算法在计算机图形学和图像处理中有着大量的应用．一条曲线一定位于该线两侧的两条到该线距离足够小的等距线之间，或认为该曲线受其两侧的两条等距线的约束．本文从真实圆弧曲线受其两侧的等距圆的约束出发，提出一种生成栅格圆弧的等距线约束算法，并分析了该算法的精度．其优点是可单方向连续生成圆弧，且生成的两个相邻栅格圆之间不会有空隙或重叠，因此可直接用于圆域有关的图形生成和栅格点扩散搜索．本文最后研究了该方法在栅格圆环、圆盘及球面、球等生成及Euclid距离变换中的应用．

AN ISO-DISTANCE CONSTRAINT ALGORITHM FOR CIRCLE GENERATION AND ITS APPLICATIONS

Generation algorithms of raster circles have been applied to some as-pects of computer graphics and image processing. In this paper, a new method forgenerating circles on raster grids is proposed,which is deduced from the constraintof iso-distance curves, since a curve is always located between its iso-distancecurves on both sides or is considered as being constrained by its two iso-distancecurves. In this paper, the iso-distance is chosen as 1/2, for rings between Radius l1/2 (Radius = 0, 1, 2, 3, ..' ) circles can cover whole two dimensional space withoutgap or overlapping. The accuracy of the algorithm is constantly the iso-distance, 1/2, which is not as bood as that of the best approximation methods. But the newmethod has the advantages of producing circles continuously and rasterizing rings,disks, etc. continuously and without gap or overlapping, which make the rasterizedcircular propagation (nearest point searching, area searching, area filling,digital el-evation model interpolation, Euclidean distance transformation,etc.) correct, easyand efficient. The method can also be extended to perform in three dimensionalspace for integer sphere generation, spherical searching, spherical propagation,etc. without gap or overlapping. Finally, applications of the method for ring anddisk generation, sphere generation, and Euclidean distance transformation are de-scribed to demonstrate its effectiveness.