High order equation Solving

Question

Jack_111 2013-10-11

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https://ww2.mathworks.cn/matlabcentral/answers/89898-high-order-equation-solving

评论： Walter Roberson 2013-10-14

I am doing ray tracing and I have to make intersection between the ray and polynomial so I got the following equation and I have to solve it for t.

A(21).*(Y.^5) + (A(20).*(Y.^4)).*X + A(19).*(Y.^4) + (A(18).*(Y.^3)).*(X.^2) + (A(17).*(Y.^3)).*X + A(16).*(Y.^3) + (A(15).*(Y.^2)).*(X.^3) + (A(14).*(Y.^2)).*(X.^2) + (A(13).*(Y.^2)).*X + A(12).*(Y.^2) + (A(11).*(Y)).*(X.^4) + (A(10).*Y).*(X.^3) + (A(9).*Y).*(X.^2) + (A(8).*Y).*(X) + (A(7).*Y) + A(6).*(X.^5) + A(5).*(X.^4) + A(4).*(X.^3) + A(3).*(X.^2) + A(2).*X + A(1) - Z = 0;*

While:

    X = (px +t*dx);
    Y = (py +t*dy);
    Z = (pz +t*dz);

so I want to get t in respect to the other variables. ( I have all the other variables but I don't know how to calculate it )

Please support Many thanks in advance

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Answer 1

sixwwwwww 2013-10-12

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Dear Yaman, Here is the solution of your problem in symbolic form:

syms X Y Z p x y z t dx dy dz
A = sym('A%d', [1 21]);
X = p * x + t * dx;
Y = p * y + t * dy;
Z = p * z + t * dz;
equation = A(21) * Y^5 + (A(20) * Y^4) * X + A(19)* Y^4 + (A(18) * Y^3) * X^2 + (A(17) * Y^3) * X + A(16) * Y^3 + (A(15) * Y^2) * X^3 + ...
    (A(14) * Y^2) * X^2 + (A(13) * Y^2) * X + A(12) * Y^2 + (A(11) * Y) * X^4 + (A(10) * Y) * X^3 + (A(9) * Y) * X^2 + (A(8) * Y) *X + A(7) * Y +...
    A(6) * X^5 + A(5) * X^4 + A(4) * X^3 + A(3) * X^2 + A(2) * X + A(1) - Z;
Solution = solve(equation == 0, t);