An oriented box is a
3D object that is defined by a center
C,three
orthonormal axes
Ui that form a
right handed coordinate system and three positive non zero extents
ei for
i = 0, 1, 2. All points
X within the box or on the surface of the box are defined by the equation:
X = C + RY
where the
matrix R = [
U0,
U1,
U2] and
Y = (
y0,
y1,
y2) with |
yi| ≤
ei.
A special case of the oriented box is the axis-aligned box. In such a box the axes Ui are all parallel to one of the coordinate system axes.
Ex. The properties of an axis-aligned cube with the side 1 centered at the origin:
C = (0, 0, 0)
U0 = (1, 0, 0)
U1 = (0, 1, 0)
U2 = (0, 0, 1)
ei = 0.5, i = 0, 1, 2
Rerence:
3D Game Engine Design: A Practical Approach to Real-Time Computer Graphics by David H. Eberly