计算包含旋转的框的边界

Question

I am working on collision system for my game that uses custom colliders. I used this to create bounding box for collisions.

I am getting problem for the boxes where right and forward values have been used to create box. Otherwise its working fine. Anybody has any idea how to include right and forward vectors in calculating 8 points for the cube.

Below is my code for calculating points:

 public static void GetBoundsPointsNoAlloc(BoxRegion bx, Matrix4x4 colliderBox4x4,Vector3[] points, Matrix4x4 mx) {
 Transform tr = Utils.FromMatrix4x4(ref DebugCollisionTestSphere.trans,mx);

 Vector3 v3Center = bx.center;
 Vector3 v3ext = bx.GetExtents();
 Vector3 right = bx.right;
 Vector3 forw = bx.forward;

   //Quaternion qua =Quaternion.LookRotation(bx.forward,Vector3.Cross     (bx.forward, bx.right));

   //tr.TransformDirection (bx.forward);
   //tr.localRotation = qua;
   tr.forward = bx.forward;
   tr.right =   bx.right;
   //tr.rotation = qua;

 points [0] = tr.TransformPoint (new Vector3 (v3Center.x - v3ext.x, v3Center.y + v3ext.y, v3Center.z - v3ext.z));  // Front top left corner
 points [1] = tr.TransformPoint (new Vector3 (v3Center.x + v3ext.x, v3Center.y + v3ext.y, v3Center.z - v3ext.z));  // Front top right corner
 points [2] = tr.TransformPoint (new Vector3 (v3Center.x - v3ext.x, v3Center.y - v3ext.y, v3Center.z - v3ext.z));  // Front bottom left corner
 points [3] = tr.TransformPoint (new Vector3 (v3Center.x + v3ext.x, v3Center.y - v3ext.y, v3Center.z - v3ext.z));  // Front bottom right corner
 points [4] = tr.TransformPoint (new Vector3 (v3Center.x - v3ext.x, v3Center.y + v3ext.y, v3Center.z + v3ext.z));  // Back top left corner
 points [5] = tr.TransformPoint (new Vector3 (v3Center.x + v3ext.x, v3Center.y + v3ext.y, v3Center.z + v3ext.z));  // Back top right corner
 points [6] = tr.TransformPoint (new Vector3 (v3Center.x - v3ext.x, v3Center.y - v3ext.y, v3Center.z + v3ext.z));  // Back bottom left corner
 points [7] = tr.TransformPoint (new Vector3 (v3Center.x + v3ext.x, v3Center.y - v3ext.y, v3Center.z + v3ext.z));  // Back bottom right corner
 }

Box is changing its position when i apply quaternion to transform

Answer 1

You'd need to concatenate the box's orientation (stored as Right and Forward) to the world transform. Something like this should probably work:

Vector3 fwd=bx.forward.normalized(), rt=br.right.normalized(), up=fwd.Cross(rt);
Quaternion qbox; qbox.SetLookRotation(fwd,up);
tr.rotation = tr.rotation*qbox;

(since Unity is annoyingly left-handed, you might have to fiddle with signs and the concatenation order a bit, or perhaps use rt instead of fwd in SetLookRotation)

Update: following a discussion in chat, this seems to be the final working version.

Quaternion quat = Quaternion.identity; 
quat.SetLookRotation(bx.forward, Vector3.Cross(bx.forward,bx.right)); 
points[0] = mx.MultiplyPoint3x4(quat * new Vector3(-bx.width/2,+bx.height/2,-bx.depth/2)+bx.center); 
...
points[7] = mx.MultiplyPoint3x4(quat * new Vector3(+bx.width/2,-bx.height/2,+bx.depth/2)+bx.center);

Answer 2

Let's redefine this problem in terms of classes that are available natively within Unity3D's framework. If you understand the math well enough, you can take that and adapt it to these other classes that you're using.

If all you need is an axis-aligned bounding box (or AABB), then you can easily get that from any Renderer or Collider through their respective bounds properties. That's a quick solution that will suffice in many cases.

Some other bounding boxes are expressed in local space -- for example, a Mesh has a bounds property that's in local space. For whatever reason, you will sometimes have a box that is some size up, right, and forward, and you may need to transform the points of that box into world space.

Let's say our box looks like this:

       size.x
   .+------+
 .' |    .'|
+---+--+'  | size.y      (all around some point 'center')
|   |  |   |
|  ,+--+---+
|.'    | .' size.z 
+------+'   

Suppose we have a unit cube centered at zero:

Vector3 center = Vector3.zero;
Vector3 size = Vector3.one;

The box's extents are half of its size:

Vector3 extents = size * 0.5f;

That makes it easy enough to calculate the eight points around the box:

Vector3[] points = new Vector3[8];
points[0] = center + new Vector3( extents.x,  extents.y,  extents.z);
points[1] = center + new Vector3( extents.x,  extents.y, -extents.z);
points[2] = center + new Vector3( extents.x, -extents.y,  extents.z);
points[3] = center + new Vector3( extents.x, -extents.y, -extents.z);
points[4] = center + new Vector3(-extents.x,  extents.y,  extents.z);
points[5] = center + new Vector3(-extents.x,  extents.y, -extents.z);
points[6] = center + new Vector3(-extents.x, -extents.y,  extents.z);
points[7] = center + new Vector3(-extents.x, -extents.y, -extents.z);

These points are all in local space, still. We just need a transform component to convert them into world space:

for (int i=0; i<8; i++) {
    points[i] = transform.TransformPoint(points[i]);
}