Python库:SciPy.spatial.ConvexHull
顶点定义法：有限点集中有限个极点Exteme Point构成的凸对象Convex Object
【极点】
极点是不能由凸多胞体内其他点的凸组合Convex Combination表出的点
$$ a_1x_1+...+a_kx_k,a_i\ge0,a_1+...+a_k=1. $$
一条线段：端点的所有凸组合
半空间Half Space交定义法：一个凸多胞体表示成有限个半空间相交的封闭Closed空间(有边界)
超平面，把$R^n$空间分成两半的平面
$$ \Gamma:a_1x_1+a_2x_2+...+a_nx_n=b.\\ Half\_Space:a_1x_x+a_2x_2+...+a_nx_n\le b. $$
面facet：凸多胞体$P$的面$F:P \cap \{x:a\cdot x = b\}$
岭Ridge：一个面的边界，两个面的邻接Adjacency部分
欧拉公式：三维空间$V-E+F=2$，多面体的顶点数，边数，面数
Some formal definitions and approaches.
A set is convex: $x\in S,y\in S\to xy\subset S$ segment.
segment $xy:\alpha x+\beta y,\alpha,\beta\ge0,\alpha+\beta =1$. to Convex Combination to barycentric coordinates.
Convex Hull of a set of $S$ is the set of all convex combinations of points of $S$. $conv S,\mathcal{H} (S)$.
all convex combinations of S → of $\le d+1$ of $S$ by Caratheodory’s Theorem, Lay 1982.
is the intersection of all convex sets that contains $S$.
is the intersection of all halfspaces that contains $S$ & closed.
convex hell of a finite set of points $S$ is the smallest convex polygon $P$ that encloses $S$.[subset nesting]
is the enclosed convex polygon $P$ with smalest area.
is the enclosed convex polygon $P$ with smalest perimeter.
is the union of all the triangles determined by points in $S$
Graham扫描算法(Graham,1972)。无法拓展至高维。$O(n \log h)$$n$点集元素个数，$h$凸包顶点个数.
凸包算法(convex hull)_convexhull_mjiansun的博客-CSDN博客
Ronald L Graham. "An efficient algorithm for determining the convex hull of a finite planar set." Information processing letters, vol.1, no.4, pp.132-133, 1972.