XNA, C# - Check if a Vector2 path crosses another Vector2 path

Question

I have an XNA question for those with more experience in these matters than myself (maths).

Background: I have a game that implements a boundary class, this simply hosts 2 Vector2 objects, a start and an end point. The current implementation crudely handles collision detection by assuming boundaries are always vertical or horizontal, i.e. if start.x and end.x are the same check I am not trying to pass x etc.

Ideally what I would like to implement is a method that accepts two Vector2 parameters. The first being a current location, the second being a requested location (where I would like to move it to assuming no objections). The method would also accept a boundary object. What the method should then do is tell me if I am going to cross the boundry in this move. this could be a bool or ideally something representing how far I can actually move.

This empty method might explain better than I can in words.

        /// <summary>
    /// Checks the move.
    /// </summary>
    /// <param name="current">The current.</param>
    /// <param name="requested">The requested.</param>
    /// <param name="boundry">The boundry.</param>
    /// <returns></returns>
    public bool CheckMove(Vector2 current, Vector2 requested, Boundry boundry)
    { 
        //return a bool that indicated if the suggested move will cross the boundry.
        return true;
    }

Is this "boundary" a rectangle, line, line segment, or something else? — John McDonald
Hi John, The boundary is a line (ops! just noticed my awful spelling). For clarification the simple way of solving this problem would be to store every Vector2 that was a boundary in a collection then as an object is moving check said collection to make sure we have not hit a Vector2 in that collection. This is however a real pain for level development and pretty expensive on the old processing time. Hence since pretty much every boundary is a line it made sense to only store the start and end vector2 objects and mathematically calculate on the fly if it has been hit/crossed. Hope this helps — Nick

Tipx Tipx · Accepted Answer · 2010-12-22T14:52:38

I suggested an answer already, but here is another one, similar, yet different :

I would use a variant of the Point-Line Distance, as taken from Wolfram once again! http://mathworld.wolfram.com/Point-LineDistance2-Dimensional.html

If you take equation 14, but take off the absolute ( | | ) in the numerator, you get a signed distance. I never heard about a signed distance concept so don't expect this term to be accurate though. Ok, so if the signed distance of the origin and the destination are different, it means that the origin and the destination are on opposite sides of the line :

public bool CheckMove(Vector2 current, Vector2 requested, Boundry boundry)
{
    // Assuming you got 2 points in boundry.
    float signedDistanceCurrent = GetSignedDistance(current, boundry.Vector1, boundry.Vector2);
    float signedDistanceRequested = GetSignedDistance(current, boundry.Vector1, boundry.Vector2);

    return signedDistanceRequested * signedDistanceCurrent < 0;
}

public float GetSignedDistance(Vector2 point0, Vector2 point1, Vector2 point2)
{
    // Equation 14 without the |s.
    return ((point2.X-point1.X)*(point1.Y-point0.Y)-(point2.X-point0.X)*(point2.Y-point1.Y))/((point2.X-point1.X)^2+(point2.Y-point1.Y)^2)^(0.5F);
}

Btw, I prefer this answer to my previous one, but it's up to you.

Edit: Btw, with that method, you can also know when the collision happened : If you do this :

float timeFractionToCollision = -signedDistanceCurrent / (signedDistanceRequested - signedDistanceCurrent);

You'll get the fraction of the period fraction of the time period the collision happened in.

XNA, C# - Check if a Vector2 path crosses another Vector2 path

5 Answers