4个点对角线交点的公式麻烦给个公式

Question

4个点对角线交点的公式
麻烦给个公式

Answer 1

假设4个点是A1(x1,y1),A2(x2,y2),A3(x3,y3),A4(x4,y4),A1A3是一条对角线,A2A4是另一条对角线,根据两点式列出这两条直线的方程,求其交点.A1A3:(y-y1)/(x-x1)=(y3-y1)/(x3-x1),A2A4:(y-y2)/(x-x2)=(y4-y2)/(x4-x2),解得x=-(-x2 x3 y1 + x3 x4 y1 + x1 x4 y2 - x3 x4 y2 + x1 x2 y3 - x1 x4 y3 - x1
x2 y4 + x2 x3 y4)/(x2 y1 - x4 y1 - x1 y2 + x3 y2 - x2 y3 + x4 y3 +
x1 y4 - x3 y4),y=-(-(-x3 y1 + x1 y3) (y2 - y4) + (y1 - y3) (-x4 y2 + x2 y4))/((-x2 + x4) (y1 - y3) - (-x1 + x3) (y2 - y4))