Optimizing this script without using symbolic toolbox

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Kasper 2011-4-28

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/6426-optimizing-this-script-without-using-symbolic-toolbox

采纳的回答： Andrew Newell

Hi guys, this is the script which takes up all the time

function [t_sol,xi,yi] = solveIntersection(px,py,rx,ry,r)

syms t

x = px + t*rx;

y = py + t*ry;

c = x^2+y^2-r^2;

t_sol = max(double(solve(c)));

xi = double(subs(x,'t',t_sol));

yi = double(subs(y,'t',t_sol));

This script calculates the intersection of a circle and a given vektor. How do i calculate the intersection without using the symbolic toolbox? Or just how can I optimize this function?

The vector starts in (px,py) and has a direction (rx,ry). r is the radius of the circle.

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采纳的回答

Andrew Newell 2011-4-28

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/6426-optimizing-this-script-without-using-symbolic-toolbox#answer_8877

在 MATLAB Online 中打开

If you run this code

syms t px py rx ry r
x = px + t*rx;
y = py + t*ry;
c = expand(x^2+y^2-r^2);
c = collect(c,t)
solve(c,t)

you'll get explicit equations for the two solutions for t. These can be put in the function:

function [t,xi,yi] = solveIntersectionNum(px,py,rx,ry,r)
    t = [-(px*rx + py*ry + (- px^2*ry^2 + 2*px*py*rx*ry - py^2*rx^2 + r^2*rx^2 + r^2*ry^2)^(1/2))/(rx^2 + ry^2)
    -(px*rx + py*ry - (- px^2*ry^2 + 2*px*py*rx*ry - py^2*rx^2 + r^2*rx^2 + r^2*ry^2)^(1/2))/(rx^2 + ry^2)];
    xi = px + t*rx;
    yi = py + t*ry;

It's about 100 times faster.