Optimizing this script without using symbolic toolbox

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.

Answer 1

[Andrew Newell]

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.

[Kasper]

Is there anyway to do it without the copypaste of the long expression:)?

Thanks anyway I think I will use it unless something better comes up.

[Walter Roberson]

Apply matlabFunction() to the symbolic expression.

[Andrew Newell]

Why don't you want to copy and paste? Do you have more general problems in mind?

[Kasper]

Yes what if I want to analyze an ellipse instead. But I could make 2 different functions. One for ellipsis and one for circles.

[Andrew Newell]

A circle is a special case of an ellipse ...