# Math

# computational geometry

平面的一个子集 S 被称为是"凸"的，当且仅当对于任意两点 $p,q\in S$ ，线段 pq 都完全属于 $S$ 。集合 $S$ 的凸包 $CH(S)$ ，就是包含 $S$ 的最小凸集 ⎯⎯ 更准确地说，它是所有包含 $S$ 的所有凸集的交

A face of the subdivision is a maximal connected subset of the plane that doesn’t contain a point on an edge or a vertex. Thus a face is an open polygonal region whose boundary is formed by edges and vertices from the subdivision.

If a vertex is the endpoint of an edge, then we say that the vertex and the edge are incident.
Similarly, a face and an edge on its boundary are incident,

# how do we know whether a cycle is an outer boundaryor the boundary of a hole in a face

This can be decided by looking at the leftmost vertex v of the cycle, or, in case of ties, at the lowest of the left most ones
we can compute the angle these two half-edges make inside the incident face
If this angle is smaller than $180^{\circ}$ then the cycle is an outer boundary,and otherwise it is the boundary of a hole.

# 判断点落在有向线段的左边还是右边

# 其他

条件概率表示为 $P(A|B)$ ，读作" $A$ 在 $B$ 发生的条件下发生的概率"。

$P(x|z) = \frac{P(z|x)P(x)}{P(z)} \propto P(z|x)P(x)$
$\propto$ 表示正比于

后验概率 $P(x|z)$

似然 $P(z|x)$

先验概率 $P(x)$

# what is arg max

$exp(x) == e^x$

反对称矩阵（或称斜对称矩阵）指转置矩阵 (opens new window)和自身的加法逆元 (opens new window)相等的方形矩阵 (opens new window)

\begin{bmatrix}0 & 2 & -1 \\ -2 & 0 & -4 \\1 & 4 & 0 \end{bmatrix}

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