how to detect collision

how can i detect whether a point in 2D will collide with a circle when going to another.suppose i have to go from x1,y1 to x2,y2 and there is a circle with radius r centered at cx,cy. how can i check whether the straight line path from x1,y1 will touch the circle

Answer 1

[Ameer Hamza]

Based on the condition given here, you can write following statement to check whether the line touch the circle or not

C = [2 5];
r = 3;
X1 = [1 0];
X2 = [5 4];

coff = polyfit([X1(1), X2(1)], [X1(2), X2(2)], 1);
doesTouch = abs(coff(1)*C(1) + coff(2) - C(2))/norm([1 coff(1)]) < r;

Answer 2

[Nicola Bombace]

You could create a line between the points (x1,y1) and (x2,y2) in the form y = ax + b with polyfit and work out the slope and the intercept of the path. Then use the function linecirc and check the output. If the output is Nan, the path does not intersect the circle.

% input: x1 y1--> point 1  
%        x2 y2 --> point 2
%        cx,cy,r --> coordinates center and radius of the circle 

coefficients = polyfit([x1, x2], [y1, y2], 1);
a = coefficients (1);
b = coefficients (2);
[xout,yout] = linecirc(a,b,cx,cy,r);
if any(isnan(xout))
  disp('The line does not intercept the circle')
else
  disp('The line intercepts the circle')
end