Contents
How to define the orientation of a bounding box?
One popular way to define them is to specify a (center) point C and orthonormal set of basis vectors {ˆu, ˆv, ˆw}, which determines location and orientation, and three scalars representing the half-width, half-height, and half-depth, as shown in Figure 11.65.
How is the size of an object determined by its axis aligned bounding box?
The extent of an object o can be roughly characterized by its axis-aligned bounding box (AABB). This, however, is not a precise measure, since the size of the AABB depends on the orientation of an object. After rotation, a different measure is obtained, although the object itself has still the same size.
How to calculate the distance from a point to an OBB?
In this section we address the problem of computing the distance from a point to an oriented bounding box (OBB). An OBB is defined as a centerpoint C; three unit vectors Û, ˆv, and ˆw forming a right-handed orthornormal basis; and three scalars hu, hv, and hw representing half the dimension in each of the u, v, and w directions.
How is the oriented bounding box computed in PCA?
The oriented bounding box is computed by a principal component analysis (PCA) of the pointset P forming the lines. The center of gravity is subtracted from all points pi resulting in a new pointset Pnorm. Based on this pointset, the covariance matrix A is determined.
How is the OBB an axis-aligned box?
Observe that, relative to that frame, the OBB is an axis-aligned box centered at the origin, whose sides lie in one of the XY, XZ, or YZ planes. If we compute the position of a point P in this frame, then we can exploit this axis-aligned, origin-centered nature of the OBB and compute the closest point, and the distance to it, quite trivially.
How to find the arbitrarily oriented minimum bounding box?
The rectangle can also have floating coordinates and be rotated in any angle and further shrunk… Not just X, Y, Width and Height! I already know how to find the smallest polygon or not rotated rectangle, but it’s not what I need…I wish to know how to find the arbitrarily oriented minimum bounding box.