双线性插值优点云主机优点

用f(x1,y1)f(x_1,y_1)f(x1​,y1​)表示位置(x1,y1)(x_1,y_1)(x1​,y1​)处的值，相当于一共三个维度，固定一个维度，根据另外两个维度的两个点确定一条直线，两个蓝色点(x,y1)(x,y_1)(x,y1​)和(x,y2)(x,y_2)(x,y2​)分别在line1color{blue}line_1line1​和line2color{blue}line_2line2​，红色点(x,y)(x,y)(x,y)在line3color{red}line_3line3​上，也就是插值位置，最后求f(x,y)color{red}oxed{fleft(x,y ight)}f(x,y)​

固定yyy，根据两个上顶点和两个下顶点：{(x1,f(x1,y1))(x2,f(x2,y1))→line1(x1,f(x1,y2))(x2,f(x2,y2))→line2left{(x1,f(x1,y1))(x2,f(x2,y1))→line1(x1,f(x1,y2))(x2,f(x2,y2))→line2(x1,f(x1,y1))(x2,f(x2,y1))→line1(x1,f(x1,y2))(x2,f(x2,y2))→line2egin{aligned}left(x_1,f(x_1,y_1) ight);;;left(x_2,f(x_2,y_1) ight) oline_1\left(x_1,f(x_1,y_2) ight);;;left(x_2,f(x_2,y_2) ight) oline_2end{aligned} ight.{(x1​,f(x1​,y1​))(x2​,f(x2​,y1​))→line1​(x1​,f(x1​,y2​))(x2​,f(x2​,y2​))→line2​​固定xxx，根据两个蓝色交点：(y1,f(x,y1))、(y2,f(x,y2))→line3left(y_1,f(x,y_1) ight)、left(y_2,f(x,y_2) ight) oline_3(y1​,f(x,y1​))、(y2​,f(x,y2​))→line3​

推导整理三条直线得到：f(x,y1)≈x2−xx2−x1f(x1,y1) x−x1x2−x1f(x2,y1)line1f(x,y2)≈x2−xx2−x1f(x1,y2) x−x1x2−x1f(x2,y2)line2f(x,y)≈y2−yy2−y1f(x,y1) y−y1y2−y1f(x,y2)line3⇓f(x,y)≈f(x1,y1)(x2−x1)(y2−y1)(x2−x)(y2−y) f(x2,y1)(x2−x1)(y2−y1)(x−x1)(y2−y) f(x1,y2)(x2−x1)(y2−y1)(x2−x)(y−y1) f(x2,y2)(x2−x1)(y2−y1)(x−x1)(y−y1)egin{aligned}