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c#mathmathematical-optimization

I need Method that takes a vector and a circle and looks if they intersect

I have a vector in 2d space that starts at A and ends at B. I also have a circle in 2d space with the Position C and has a radius of r

I need to know if the vector AB does intersect with the circle(center:C,radius:r)

what would be the most efficient way to do this calculation?

Solution

  • Given A and B are endpoints of a line. It can be represented as a vector with direction from A to B with a magnitude as the distance of AB.

    The line AB doesn't intersect with the circle when the distance between the center of the circle C and the line AB perpendicular to the direction of the line is greater than the radius r of the circle.
    Refer to the image below for visualization.

    enter image description here

    Calculating the distance between the line and the center of the circle:

    Step 1: Get the line equation of AB from the formula below.
    Here x1 = A.x, x2 = B.x, y1 = A.y, y2 = B.y.

    enter image description here
    Solving, a line equation of the form ax + by + c = 0 is obtained.

    Step 2: Calculate the distance d from the formula below.
    Here x0 = C.x and y0 = C.y.

    enter image description here

    Finally, check whether the distance between the line and the center of the circle d is greater than the radius of the circle r or not. If yes, then the line lies outside the circle.