两个凸多边形的交集 [英] Intersection of two convex polygons

问题描述

我有两个凸多边形.多边形被实现为其顶点的循环列表.如何找到这两个多边形的交点?

I have two convex polygons. Polygons are implemented as cyclic lists of their vertices. How to find an intersection of this two polygons?

推荐答案

For each edge V1-V2 in the first polygon,
    Let H := Half-plane tangenting V1-V2, with the remaining
        vertices on the "inside".
    Let C := New empty polygon.
    For each edge V3-V4 in the second polygon,
        Let X := The intersection between V3-V4 and H.
        If V3 inside H, and V4 is outside H then,
            Add V3 to C.
            Add X to C.
        Else if both V3 and V4 lies outside H then,
            Skip.
        Else if V3 outside H, and V4 is inside H then,
            Add X to C.
        Else
            Add V3 to C.
    Replace the second polygon with C.

这对于简单的使用应该足够了；10-20 个顶点，而不是每帧都重新计算.—O(n²)

This should suffice for simple usage; 10-20 vertices and not recalculating every frame. — O(n²)

这里有几个链接:

• 计算机图形学多边形裁剪和填充 (pdf)
• rosettacode.org –Sutherland-Hodgman 多边形裁剪

• Computer Graphics I – Polygon Clipping and Filling (pdf)
• rosettacode.org – Sutherland-Hodgman polygon clipping

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