| This paper researches the basic algorithms of Computer Graphics including the algorithm for implementing Boolean operation between regions and the pixel-level algorithm for generating parametric curves by dividing the segments.Boolean operations of regions include intersecting, subtracting and joining, which are widely used in practice. And we cannot find these functions in most popular and common used software products. In this paper, an efficient algorithm for implementing Boolean operations between regions is presented, which can deal with the regions involving several polygons with holes in them. The algorithm has many advantages such as the input format and output format being uniformed, high efficient, wide application, etc. It has abroad market values in many domains, such as the weather character demonstration, computing and the demonstration of anomalous graphics, etc. We know that curves can be approached by mini line-segments, so the Boolean operations between almost all regions can be implemented by this algorithm.With the widely use of raster display, pixel-level algorithm becomes a research hotspot of fundamental algorithms of Computer Graphics now. For the pixel-level generation of parametric curves, we find that the point densities chosen by the existing algorithms are not even along the curves. By analyzing the existing algorithms, we present a new pixel-level algorithm for generating parametric curves by dividing the segments. We notice that each subsection has different step length and we divide the curve by its power. It is proved that the step length got by subsection is more than or equal to that of not subsection. So the points calculated are less than or equal to those of not subsection. Thus the problem of uneven densities in generating curves is radically solved, and the algorithm is speeded up. It is also proved that the step length after subsection is less than or equal to one pixel unit, so the curves drawn are equally smooth.
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