math.tex

\documentclass[12pt,a4paper]{article}
\usepackage{xeCJK}
\usepackage{amsmath}
\usepackage{geometry}

\geometry{left=2.5cm,right=2.5cm,top=2.5cm,bottom=2.5cm}
\xeCJKDeclareSubCJKBlock{JP}
{"0800 -> "4E00}
\xeCJKDeclareSubCJKBlock{KO}
{"1100 -> "11FF , "3130 -> "318F , "AC00 -> "D7AF , "A960 -> "A97F , "D7B0 -> "D7FF}

\setmainfont{Times New Roman}
\setCJKmainfont[KO=Nanum Gothic, JP=YuGothic]{苹方-简}

\title{插值计算式推导}
\author{Yeonji}

\begin{document}

\maketitle

\section{一维立方插值 Cubic Interpolation}

\begin{equation}
f(x) = ax^3 + bx^2 + cx + d
\end{equation}


\begin{equation}
\left\{
\begin{aligned}
f(-3) &= -27a + 9b -3c + d\\
f(-1) &= -a + b - c + d\\
f(1) &= a + b + c + d\\
f(3) &= 27a + 9b + 3c + d
\end{aligned}
\right.
\end{equation}

\begin{equation}
f(0) = -0.0625f(-3) + 0.5625f(-1) + 0.5625f(1) -0.0625f(-3)
\end{equation}

\section{二维立方插值 Bicubic Interpolation}

\begin{equation}
\begin{aligned}
f(x,y) &= \sum_{i=0}^3 \sum_{j=0}^3 a_{ij} x^i y^j\\
&= a_{00} + a_{01}y + a_{02}y^2 + a_{03}y^3\\
&+ a_{10}x + a_{11}xy + a_{12}xy^2 + a_{13}xy^3\\
&+ a_{20}x^2 + a_{21}x^2y + a_{22}x^2y^2 + a_{23}x^2y^3\\
&+ a_{30}x^3 + a_{31}x^3y + a_{32}x^3y^2 + a_{33}x^3y^3\\
\end{aligned}
\end{equation}

\end{document}