What is going on in this SAT/vector projection code?
- by ssb
I'm looking at the example XNA SAT collision code presented here:
http://www.xnadevelopment.com/tutorials/rotatedrectanglecollisions/rotatedrectanglecollisions.shtml
See the following code:
private int GenerateScalar(Vector2 theRectangleCorner, Vector2 theAxis)
{
//Using the formula for Vector projection. Take the corner being passed in
//and project it onto the given Axis
float aNumerator = (theRectangleCorner.X * theAxis.X) + (theRectangleCorner.Y * theAxis.Y);
float aDenominator = (theAxis.X * theAxis.X) + (theAxis.Y * theAxis.Y);
float aDivisionResult = aNumerator / aDenominator;
Vector2 aCornerProjected = new Vector2(aDivisionResult * theAxis.X, aDivisionResult * theAxis.Y);
//Now that we have our projected Vector, calculate a scalar of that projection
//that can be used to more easily do comparisons
float aScalar = (theAxis.X * aCornerProjected.X) + (theAxis.Y * aCornerProjected.Y);
return (int)aScalar;
}
I think the problems I'm having with this come mostly from translating physics concepts into data structures. For example, earlier in the code there is a calculation of the axes to be used, and these are stored as Vector2, and they are found by subtracting one point from another, however these points are also stored as Vector2s. So are the axes being stored as slopes in a single Vector2?
Next, what exactly does the Vector2 produced by the vector projection code represent? That is, I know it represents the projected vector, but as it pertains to a Vector2, what does this represent? A point on a line?
Finally, what does the scalar at the end actually represent? It's fine to tell me that you're getting a scalar value of the projected vector, but none of the information I can find online seems to tell me about a scalar of a vector as it's used in this context. I don't see angles or magnitudes with these vectors so I'm a little disoriented when it comes to thinking in terms of physics. If this final scalar calculation is just a dot product, how is that directly applicable to SAT from here on? Is this what I use to calculate maximum/minimum values for overlap? I guess I'm just having trouble figuring out exactly what the dot product is representing in this particular context.
Clearly I'm not quite up to date on my elementary physics, but any explanations would be greatly appreciated.
