math & physics
dega512 at February 1st, 2010 22:24 — #1
I'm working on some 2D non-axis-aligned rectangle collisions using the separating axis theorem (following this tutorial). My implementation kind of works. Kind of. Here is a link to a video showing how it is working right now (SWF file). Screenshots too just in case:
For whatever reason when one of the rectangles enters the upper-left area of the other it automatically assumes it is a collision (as shown in the video, or the bottom right area will cause a false collision if the other rectangle is moving, as shown in the screen shots).
I'm sitting here banging my head trying to figure out where I might be going wrong. So, with that said, I'm looking for pointers on where I could be going wrong!
Not that I'm expecting anyone to, but if somebody really wants to look at the code here it is. Like I said though, I'm looking for a nudge in the right direction so I can figure it out :lol: .
smokingrope at February 2nd, 2010 07:29 — #2
The part of your code starting with th comment
// Find "values" for each of the projected points (square magnitude)
Should actually be a dot product between each of the projections and the axis
dega512 at February 2nd, 2010 16:54 — #3
Thanks a ton for taking a look at my code and pointing that out! That was a good find but that didn't fix it 100%; it now seems that one of my axes is off and I'm trying to find it (I think it is my 2nd axis: RectA.UR - RectA.LR). I figured it could have been because I wasn't normalizing each axis but that didn't do it either. I'll keep working on it though. Thanks again!
oisyn at February 2nd, 2010 17:55 — #4
Rather than posting a zip containing your entire project, could you just post the relevant piece of the algorithm (including a definition of the used types)?
dega512 at February 2nd, 2010 20:55 — #5
The first "building block" of my project is an object called 'CollisionRectangle' that has four points: UL (upper left), UR (upper right), LL (lower left), and LR (lower right). You build it by passing a center x/y, a width/height, and a rotation and these four points are generated.
| -y |
| (0,0) |
| +y |
My collision starts off like the following (pseudocode):
function RectanglesAreColliding(CollisionRectangle a, CollisionRectangle b)
// calculate the axes
var axis1 = a.UR - a.UL;
var axis2 = a.UR - a.LR;
var axis3 = b.UL - b.LL;
var axis4 = b.UL - b.UR;
return CheckAxis(a, b, axis1) &&
CheckAxis(a, b, axis2) &&
CheckAxis(a, b, axis3) &&
CheckAxis(a, b, axis4);
This is where I was talking about how I thought that I might be getting incorrect results because I wasn't normalizing these axes, but normalizing them made no difference. Also, if I don't check 'axis2' here I get the same results which is leading me to believe that I'm not using the right axis.
My 'CheckAxis' is as follows (again, pseudocode, it's shorter):
function CheckAxis(CollisionRectangle a, CollisionRectangle b, Vector2 axis)
var a_proj_ul = Project(a.UL, axis);
var b_proj_ul = Project(b.UL, axis);
/* so on and so forth, project each of the 4 corners of each rectangle
onto the axis */
// find "values" for each of the projected points (used to use
// square magnitude)
// thanks to SmokingRope for pointing out I need to use the
// dot product between the projection and axis here instead!
var a_ul = Dot(a_proj_ul, axis);
var b_ul = Dot(b_proj_ul, axis);
/* so on and so forth for each projection... */
// find the min and max "value" for each rect
var a_min = Math.Min(Math.Min(a_ul, a_ur), Math.Min(a_ll, a_lr));
var a_max = Math.Max(Math.Max(a_ul, a_ur), Math.Max(a_ll, a_lr));
var b_min = Math.Min(Math.Min(b_ul, b_ur), Math.Min(b_ll, b_lr));
var b_max = Math.Max(Math.Max(b_ul, b_ur), Math.Max(b_ll, b_lr));
// check for overlap on this axis
return b_min <= a_max || b_max <= a_min;
smokingrope at February 2nd, 2010 22:58 — #6
I think your overlap checking is off. I use the following to check for overlap in my own code.
return a_max >= b_min && a_min <= b_max;
What you've got returns true in the following scenario:
dega512 at February 2nd, 2010 23:06 — #7
Doh! You're right - that fixed it. Thank you for your help!