Abstract: The speed of graphics processing and analysis is affected by the inefficiency, high memory occupancy rate and other issues of the vector circular cutting in existing algorithms. Therefore, an algorithm with linear complexity for vector circular cutting against arbitrary polygon window is proposed. Firstly, using the projection method for linear mapping of vector circles, a linear function of radiation is constructed to detect the intersection of circles and polygons quickly and accurately. Meanwhile, through the line truncation method, the real intersection points between circles and the polygon are obtained by using the linear equation. Then, the intersection points are sorted according to the prescribed direction based on the cross product between three points. Finally, the midpoint detection method is used to determine the visibility of arcs or circles drawn to the memory, and the drawn image and the statistical pattern complexity are output. The experimental results indicate that the proposed algorithm can effectively avoid the generation of virtual intersections, reduce the time and space complexity of the clipping process, and improve the accuracy of vector circles clipping.