How to check intersection between a line and a rectangle?

Question

The title says it all, Ive been searching around and couldnt find anything that was straight and to the point. How would I take a line with points (x1,y1) & (x2, y2) and check its intersection between a rectangle (xR,yR)? I saw in the Line2D package that there were some intersection methods but not sure how to set it all up. Can someone show me a correct way of setting it up to check for an intersection (collision)?

Answer 1

A rectangle is 4 lines. You could compute the intersect between your line and the 4 lines of the rectangle.

given the equations of two lines, they would intersect when x and y are equal.

y = m1x + b1 y = m2x + b2

solving the equation you should get:

x = b2 - b1 / (m1 - m2);

Note that if m1 == m2, the lines are parallel and will never intersect, watch out for the divided by 0 in this case.

Then, since you are dealing with segments ratter than infinite lines, check if the intersect falls off within your segments (check if both X and Y are within each segment's boundaries).

Answer 2

Using the available classes from the 2D Graphics API.

Rectangle r1 = new Rectangle(100, 100, 100, 100);
Line2D l1 = new Line2D.Float(0, 200, 200, 0);
System.out.println("l1.intsects(r1) = " + l1.intersects(r1));

What this doesn't tell you, is where...

Answer 3

Returns null if lines do not intersect. Modified some c code from another response to similar question to make it Java. Haven't bothered to look into how/why it works, but does the job I needed it to.

static Point get_line_intersection(Line2D.Double pLine1, Line2D.Double pLine2)
{
    Point
        result = null;

    double
        s1_x = pLine1.x2 - pLine1.x1,
        s1_y = pLine1.y2 - pLine1.y1,

        s2_x = pLine2.x2 - pLine2.x1,
        s2_y = pLine2.y2 - pLine2.y1,

        s = (-s1_y * (pLine1.x1 - pLine2.x1) + s1_x * (pLine1.y1 - pLine2.y1)) / (-s2_x * s1_y + s1_x * s2_y),
        t = ( s2_x * (pLine1.y1 - pLine2.y1) - s2_y * (pLine1.x1 - pLine2.x1)) / (-s2_x * s1_y + s1_x * s2_y);

    if (s >= 0 && s <= 1 && t >= 0 && t <= 1)
    {
        // Collision detected
        result = new Point(
            (int) (pLine1.x1 + (t * s1_x)),
            (int) (pLine1.y1 + (t * s1_y)));
    }   // end if

    return result;
}