# Latex排版SIGGRAPH总结（持续总结中…）

## 多行连等公式

begin{equation}表示编号公式，[ ]表示无编号公式

1. 无编号

begin{align*}
Deltaleft(vright)
&= sum_{pin planes(v)}{left(v^Tpright)left(p^Tvright)}
&= sum_{pin planes(v)}{v^Tleft(p^Tpright)v}
&= v^Tleft(sum_{pin planes(v)}{K_p}right)v
end{align*}


实现结果：

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begin{align*} Deltaleft(vright) &= sum_{pin planes(v)}{left(v^Tpright)left(p^Tvright)} \ &= sum_{pin planes(v)}{v^Tleft(p^Tpright)v} \ &= v^Tleft(sum_{pin planes(v)}{K_p}right)v end{align*}

Δ(v)=pplanes(v)(vTp)(pTv)=pplanes(v)vT(pTp)v=vT

pplanes(v)Kp

v

2. 有编号

• 共同编号
begin{equation}
begin{aligned} %也可使用begin{split}
Deltaleft(vright)
&= sum_{pin planes(v)}{left(v^Tpright)left(p^Tvright)}
&= sum_{pin planes(v)}{v^Tleft(p^Tpright)v}
&= v^Tleft(sum_{pin planes(v)}{K_p}right)v
end{aligned} %end{split}
end{equation}


实现结果（其中aligned表示为多行公式，split表示整体为一个公式）：

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begin{equation} begin{aligned} Deltaleft(vright) &= sum_{pin planes(v)}{left(v^Tpright)left(p^Tvright)} \ &= sum_{pin planes(v)}{v^Tleft(p^Tpright)v} \ &= v^Tleft(sum_{pin planes(v)}{K_p}right)v end{aligned} end{equation}

Δ(v)=pplanes(v)(vTp)(pTv)=pplanes(v)vT(pTp)v=vT

pplanes(v)Kp

v

• 单独编号
begin{align}
Deltaleft(vright)
&= sum_{pin planes(v)}{left(v^Tpright)left(p^Tvright)}
&= sum_{pin planes(v)}{v^Tleft(p^Tpright)v}
&= v^Tleft(sum_{pin planes(v)}{K_p}right)v
end{align}


实现结果（其中加入nonumber会使本行不编号）：

Δ

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begin{align} Deltaleft(vright) &= sum_{pin planes(v)}{left(v^Tpright)left(p^Tvright)} \ &= sum_{pin planes(v)}{v^Tleft(p^Tpright)v} nonumber\ &= v^Tleft(sum_{pin planes(v)}{K_p}right)v end{align}

Δ(v)=pplanes(v)(vTp)(pTv)=pplanes(v)vT(pTp)v=vT

pplanes(v)Kp

v

## 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

1. 矩阵表示

[
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]
]


实现结果（其中{cccc}代表有4列，若为方阵可直接使用begin{matrix}）：

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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=

2. 矩阵连乘

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}


实现结果：

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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

1. 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）：

2. 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

ref{eq1}


THE END

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