本文学习总结自:How to use the ACM SIGGRAPH / TOG LaTeX template
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首先解压 “my paper” 中的文件,并用Latex打开mypaper.tex
.
多行连等公式
\begin{equation}
表示编号公式,\[ \]
表示无编号公式
- 无编号
实现结果:\begin{align*}\Delta\left(v\right) &= \sum_{p\in planes(v)}{\left(v^Tp\right)\left(p^Tv\right)} \\&= \sum_{p\in planes(v)}{v^T\left(p^Tp\right)v} \\&= v^T\left(\sum_{p\in planes(v)}{K_p}\right)v \end{align*}
Δ ( v ) = ∑ p ∈ p l a n e s ( v ) ( v T p ) ( p T v ) = ∑ p ∈ p l a n e s ( v ) v T ( p T p ) v = v T ( ∑ p ∈ p l a n e s ( v ) K p ) v \begin{align*} \Delta\left(v\right) &= \sum_{p\in planes(v)}{\left(v^Tp\right)\left(p^Tv\right)} \\ &= \sum_{p\in planes(v)}{v^T\left(p^Tp\right)v} \\ &= v^T\left(\sum_{p\in planes(v)}{K_p}\right)v \end{align*} Δ(v)=p∈planes(v)∑(vTp)(pTv)=p∈planes(v)∑vT(pTp)v=vT p∈planes(v)∑Kp v - 有编号
- 共同编号
实现结果(其中aligned表示为多行公式,split表示整体为一个公式):\begin{equation}\begin{aligned} %也可使用\begin{split}\Delta\left(v\right) &= \sum_{p\in planes(v)}{\left(v^Tp\right)\left(p^Tv\right)} \\&= \sum_{p\in planes(v)}{v^T\left(p^Tp\right)v} \\&= v^T\left(\sum_{p\in planes(v)}{K_p}\right)v\end{aligned} %\end{split} \end{equation}
Δ ( v ) = ∑ p ∈ p l a n e s ( v ) ( v T p ) ( p T v ) = ∑ p ∈ p l a n e s ( v ) v T ( p T p ) v = v T ( ∑ p ∈ p l a n e s ( v ) K p ) v \begin{equation} \begin{aligned} \Delta\left(v\right) &= \sum_{p\in planes(v)}{\left(v^Tp\right)\left(p^Tv\right)} \\ &= \sum_{p\in planes(v)}{v^T\left(p^Tp\right)v} \\ &= v^T\left(\sum_{p\in planes(v)}{K_p}\right)v \end{aligned} \end{equation} Δ(v)=p∈planes(v)∑(vTp)(pTv)=p∈planes(v)∑vT(pTp)v=vT p∈planes(v)∑Kp v - 单独编号
实现结果(其中加入\begin{align}\Delta\left(v\right) &= \sum_{p\in planes(v)}{\left(v^Tp\right)\left(p^Tv\right)} \\&= \sum_{p\in planes(v)}{v^T\left(p^Tp\right)v} \\&= v^T\left(\sum_{p\in planes(v)}{K_p}\right)v \end{align}
\nonumber
会使本行不编号):
Δ ( v ) = ∑ p ∈ p l a n e s ( v ) ( v T p ) ( p T v ) = ∑ p ∈ p l a n e s ( v ) v T ( p T p ) v = v T ( ∑ p ∈ p l a n e s ( v ) K p ) v \begin{align} \Delta\left(v\right) &= \sum_{p\in planes(v)}{\left(v^Tp\right)\left(p^Tv\right)} \\ &= \sum_{p\in planes(v)}{v^T\left(p^Tp\right)v} \nonumber\\ &= v^T\left(\sum_{p\in planes(v)}{K_p}\right)v \end{align} Δ(v)=p∈planes(v)∑(vTp)(pTv)=p∈planes(v)∑vT(pTp)v=vT p∈planes(v)∑Kp v
- 共同编号
矩阵
\cdots
表示横向多点 ⋯ \cdots ⋯,\vdots
表示竖向多点 ⋮ \vdots ⋮,\ddots
表示斜向多点 ⋱ \ddots ⋱
- 矩阵表示
实现结果(其中\[K_p=pp^T=\left[\begin{array}{cccc}a^2 & ab & ac & ad \\ab & b^2 & bc & bd \\ac & bc & c^2 & cd \\ad & db & dc & d^2 \\\end{array}\right] \]
{cccc}
代表有4列,若为方阵可直接使用\begin{matrix}
):
K p = p p T = [ a 2 a b a c a d a b b 2 b c b d a c b c c 2 c d a d d b d c d 2 ] K_p=pp^T= \left[ \begin{array}{cccc} a^2 & ab & ac & ad \\ ab & b^2 & bc & bd \\ ac & bc & c^2 & cd \\ ad & db & dc & d^2 \\ \end{array} \right] Kp=ppT= a2abacadabb2bcdbacbcc2dcadbdcdd2 - 矩阵连乘
实现结果:\begin{equation}\left[\begin{array}{c}\varphi \\\theta \\\psi\end{array}\right]=\left[\begin{array}{ccc}a_{11} & a_{12} & a_{13} \\a_{21} & a_{22} & a_{23} \\a_{31} & a_{32} & a_{33}\end{array}\right]\left[\begin{array}{c}b_{1} \\ b_{2} \\b_{3}\end{array}\right] \end{equation}
[ φ θ ψ ] = [ a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 ] [ b 1 b 2 b 3 ] \begin{equation} \left[ \begin{array}{c} \varphi \\ \theta \\ \psi \end{array} \right] = \left[ \begin{array}{ccc} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{array} \right] \left[ \begin{array}{c} b_{1} \\ b_{2} \\ b_{3} \end{array} \right] \end{equation} φθψ = a11a21a31a12a22a32a13a23a33 b1b2b3
列表
-
有序列表
\begin{enumerate}\item $(v_1, v_2)$ is an edge, or\item $\lVert v_1 - v_2 \rVert < t$, where $t$ is a threshold parameter \end{enumerate}
实现效果(默认为
()
,通过\item[1.]
修改格式):
-
无序列表
\begin{itemize}\item $(v_1, v_2)$ is an edge, or\item $\lVert v_1 - v_2 \rVert < t$, where $t$ is a threshold parameter \end{itemize}
实现效果(默认为
·
,通过\item[-]
修改格式):
引用公式
需要在某个公式后添加\label{}
标签
\ref{eq1}