Latex排版SIGGRAPH总结（持续总结中...）

本文学习总结自：How to use the ACM SIGGRAPH / TOG LaTeX template
相关文件：百度网盘

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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

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：
   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*} 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)​=p∈planes(v)∑​(vTp)(pTv)=p∈planes(v)∑​vT(pTp)v=vT ​p∈planes(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）：
     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} 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)​=p∈planes(v)∑​(vTp)(pTv)=p∈planes(v)∑​vT(pTp)v=vT ​p∈planes(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 ( 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} 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)​=p∈planes(v)∑​(vTp)(pTv)=p∈planes(v)∑​vT(pTp)v=vT ​p∈planes(v)∑​Kp​ ​v​​

矩阵

cdots表示横向多点$\cdots$，vdots表示竖向多点 $⋮$，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}）：
   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= ​a2abacad​abb2bcdb​acbcc2dc​adbdcdd2​ ​
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：
   [ 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​ ​= ​a11​a21​a31​​a12​a22​a32​​a13​a23​a33​​ ​ ​b1​b2​b3​​ ​​​

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

需要在某个公式后添加label{}标签

ref{eq1}