the intersection of the SWIP with the given plane can be
obtained by coordinate transformation.
The given plane can be specified by its normal N and
the shortest distance to the plane from the origin of the
global system, d. We can set a new reference system Oxyz
with the x axis coincident with the normal of the plane, and
with the origin coincident with the origin of the old system
as shown in Fig. 4.7. The axis y is set to be perpendicular
to both the axis X of the old system and the normal. Let n,
r, and s now be unit vectors on the three new axes of x, y
and z, respectively. The unit vector n is given as
n = (nx, ny, nz)T
Then
i
r = ix n = 1
nx
i
s = nx r = nx
0
j k
0 0 = (0, -n,, ny)T
ny n"
k
n, = (ny2 + nz2, -nxny, -nxnz)T
ny
The transformation matrix from the new system to the
old one can be written as