有5个点,您可以找到圆锥截面的一般公式(此处为椭圆形),该矩阵的扩展行列式(用点坐标替换xi,yi
):
(图片taken here)
Simple example to begin with
使用my answer for inverse problem
//calc implicit ellipse equation
//semiaxes rx,ry; rotated at fi radians; centered at (cx,cy)
//note: implicit form Ax^2+Bxy+Cy^2+Dx+Ey+F=0 (not 2B,2D,2E)
// in Pascal notation Sqr is squared
B := Sin(2 * Fi) * (ry * ry - rx * rx);
A := Sqr(ry * Cos(fi)) + Sqr(rx * Sin(fi));
C := Sqr(rx * Cos(fi)) + Sqr(ry * Sin(fi));
D := -B * cy - 2 * A * cx;
E := -2 * C * cy - B * cx;
F := C * cy * cy + A * cx * cx + B * cx * cy - rx * rx * ry * ry;
我们可以看到
Fi = 0.5 * atan2(B,A-C)
然后
ry^2+rx^2 = A + C
ry^2-rx^2 = B / Sin(2*Fi)
如此
ry = Sqrt((A + C + B / Sin(2*Fi))/2)
rx = Sqrt((A + C - B / Sin(2*Fi))/2)
(Fi = 0情况除外,我们可以直接从A和C提取半轴)
然后从D / E方程系统中找到cx,cy
也请查看Wiki formulas中的相同问题
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