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定义1 对于平面图形内的任意两点A、B,线段AB上的所有点都在形内,这样的平面图形叫做凸形。显然,平面几何中研究的线段,三角形、凸多边形等都是凸形。定义2 对于平面上的有限个点所组成的平面点集,存在一个凸多边形,它包含这整个点集,且其顶点与这集的点重合。这样的凸多边形称为已知点集的凸包。特殊地,当平面上的点在一直线上时,凸包为线段。平面上有限点集的凸包的存在性从直观上看是显然的。在给定的有限个点的每个点插上大头针,用一根线圈上这些针,拉紧后构成的图形就是凸包。自然,这个直观的考虑不是凸包存在性的严格证明,
Definition 1 For any two points A and B in a plane figure, all the points on the line segment AB are within the shape. Such a plane figure is called a convex shape. Obviously, the line segments studied in plane geometry, such as triangles and convex polygons, are all convex. Definition 2 For a set of planar points consisting of a finite number of points on a plane, there is a convex polygon which contains the entire set of points and whose vertices coincide with the points of this set. Such a convex polygon is called a convex set of a known point set. In particular, when the point on the plane is in a straight line, the convex hull is a line segment. The existence of the convex hulls of the finite set on the plane is intuitively obvious. Insert a pin at each point of a given limited number of points, and use a needle on the coil. The pattern that is formed after the tension is the convex hull. Naturally, this intuitive consideration is not a rigorous proof of the existence of convex hulls.