MATLAB: Find intersection between line and circle

circle line intersection particlefsolveMATLABSymbolic Math Toolbox

Hi I currently work with a small project regarding particle behaviour in closed domains.
I want to create a function which takes start point, and start direction for a point. The domain is a circle. How do I calculate the two intersections with the circle?
I know how to do the calculations but I have trouble with the implementation.
px = -0.5; % start x-coordinate of point
py = -0.5; % start y-coordinate of point
rx = 1; % x-direction of vector with the above startcoordinates
ry = 2; % y ------ || ---------
I tried using symbolic toolbox but I can't convert it back to normal variables.
fsolve won't help because the representation of a circle is not a function. What to do?
Thanks in advance
Regards

Best Answer

You're pretty close. Except you don't want to solve
'x^2 + y^2 = 0'
You want to solve 'x^2 + y^2 = R^2'
-------------------------------
Try this:
R = sym('R');
x = sym('px + t*rx');
y = sym('py + t*ry');
c = x^2+y^2-R^2;
t_sol = solve(c);
x_sol = subs(x,'t',t_sol)
y_sol = subs(y,'t',t_sol)
Then x_sol gives you the x values, and y_sol has the y values of the solution.
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