2D运动物体碰撞

Question

I 'm creating a two 2D simulation and I need to determine if 2 moving objects A and B will cross paths . A moves with a constant speed Va and B with Vb .

I'm able to determine the point where the the object's path intersect but I can't figure out if will they actually collide.

I calculated the point of collision using

This formula

and the same for y

Answer 1

Let's consider case of two axis-aligned rectangles. They do intersect, if projections of both to X-axis intersect, and projections of both to Y-axis intersect.

First rectangle coordinates (Ax1,Ay1),(Ax2,Ay2), velocity vector (VAx,VAy)
Second rectangle coordinates (Bx1,By1),(Bx2,By2), velocity vector (VBx,VBy)

Time interval when X-projections intersect:

Ax2+VAx*t1=Bx1+VBx*t1
t1=(Bx1-Ax2)/(VAx-VBx)
t2=(Bx2-Ax1)/(VAx-VBx)

Interval is Ix=(t1,t2) (or (t2,t1) if t2 < t1)

For Y-projections

u1=(By1-Ay2)/(VAy-VBy)
u2=(By2-Ay1)/(VAy-VBy)

Interval is Iy=(u1,u2) (or (u2,u1) if u2 < u1)

Check if these two time ranges Ix and Iy intersect. If they do, objects collide.

Answer 2

This is how I have it setup in my code, although it probably won't work to simply add this to your code, hopefully this will help you make sense of the math:

rectangleIntersect() will return true if the two objects have intersected.

public static boolean intersectRange(int min, int max, int min2, int max2){
    return Math.max(min, max) >= Math.min(min2, max2) && 
           Math.min(min, max) <= Math.max(min2, max2);
}

public static boolean intersectRange(float min, float max, float min2, float max2){
    return Math.max(min, max) >= Math.min(min2, max2) && 
           Math.min(min, max) <= Math.max(min2, max2);
}

public static boolean rectangleIntersect(Rectangle rect, Rectangle rect2){
    return intersectRange(rect.getX(), rect.getX() + rect.getWidth(), rect2.getX(), rect2.getX() + rect2.getWidth()) &&
            intersectRange(rect.getY(), rect.getY() + rect.getHeight(), rect2.getY(), rect2.getY() + rect2.getHeight());
}