# 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