# plane bounding box intersection

I am developing a visualization where I have already calculated the best fit plane from points and have a bounding box (from the voxel structure). The plane is defined by its normal and the centroid and the bounding box by center and the size. I have to specify the end points of the plane. Is there any easy way to find out the bounds of the best-fit plane?

-
So you're after the corners of the rectangle resulting from intersecting the plane $(c, \vec{n})$ with the bounding box $(p_1,$ $p_2,$ $p_3,$ $p_4,$ $p_5,$ $p_6,$ $p_7,$ $p_8),$ right? Now let $\{ p_1, p_2, p_3, p_4 \}$ be the upper corner points of the bounding box. I'm a bit confused, but here's an idea not necessarily the easiest: project $\{ p_1, p_2, p_3, p_4 \}$ onto the plane. Doesn't this give you the corners of the intersection rectangle? (edit: Ops, I've just noticed that your (axis-aligned) bounding box is not defined in terms of its corner points.) – user2468 Aug 19 '12 at 2:13
Thanks for your response. Yeah the bounding box is defined as (center, size). But I can think about it. – shunyo Aug 19 '12 at 4:43

## 1 Answer

The intersection of the plane and the bounding box is going to be a polygon that has between three and six sides (I'm ignoring some special cases that are probably not interesting).

It's not clear what you mean by the "bounds" of the plane.

One interpretation would be that the "bounds" of the plane are just the edges of the polygon mentioned above. You can find these edges by intersecting the plane with each of the faces of the bounding box.

If you want a simpler bounding shape, you can construct this from the aforementioned polygon.

-