两个旋转多项式的交点

Question

我目前正在尝试找到两个旋转多项式第二度的交点（也称为抛物线）。 我能够计算没有旋转的交点，但不能用一个。

我目前的代码基于Code or formula for intersection of two parabolas in any rotation

syms t1 t2 
% a1 b1 c1 are coefficients of the first polynomial
% a2 b2 c2 of the second one

% First polynomial equation
fax = a1*t1.^2 + b1*t1 + c1;
fay = t1;

fax1 = fax*cos(w1) - sin(w1)*fay;
fay1 = +fax*sin(w1) + cos(w1)*fay;

% Second polynomial equation
fbx = a2*t2.^2 + b2*t2+ c2;
fby = t2;

fbx1 = fbx*cos(w2) - sin(w2)*fby;
fby1 = fbx*sin(w2) + cos(w2)*fby;

[solT1 solT2]  = solve([fbx1-fax1,fby1-fay1],[t1 t2],'MaxDegree', 4);

double(solT1)
double(solT2)

但是求解函数不会返回x / y方程的相等值。有人可以帮助我，我在哪里失败？

输出：

>> double(solT1)
ans =
          -35970.3949972882 +                     0i
          -547.958594347212 +                     0i
           45277.2230289302 +      73433.2725463157i
           45277.2230289302 -      73433.2725463157i
>> double(solT2)
ans =
          -43312.4016357418 +                     0i
          -123.972586439179 +                     0i
           87780.3324792941 -      89532.7369678429i
           87780.3324792941 +      89532.7369678429i