(x',y',z') such that the plane (x',y') coincides with the ground 
plane, origin being in the nadir point. Wwe restrict the 
derivation here to the flat Earth approximation, assuming that it 
can be easily generalized. 
3.2 Lookpoint model 
The attitude of the platform can be best described by the set of 
Euler angles: roll, pitch and yaw. The lookpoint, that is the 
point on the ground, imaged by a detector element (pixel), is the 
point of intersection of the light ray, emanating from the pixel 
and coming through the focal point, with the ground plane. For 
the nine arrays the vector, colinear with such a ray has compo- 
nents: 
= ET 
r (Xp? Yp» £3 
where: 
Xp? Yp define the pixel position; 
f is the focal length of the instrument. 
The platform attitude in the ground reference frame after an 
arbitrary rotation is most easily defined by a set of Euler 
matrixes: 
1 0 0 cos(o) 0 -sin(w) 
M(6)={0 cos( 9$) sin(s) M(w)= 0 1 0 
0 -sin(o) cos(4$) sin(w) 0 cos(w) 
Cos(X) . sin(X) 0 
(3.2.13 MCX)2] -sinCX) cos(X) 0 
0 0 1 
where: 
X 
is roll angle; 
w is pitch angle; 
is yaw angle. 
The combination of three Euler rotations is determined by the 
matrix product M(?,w,X)=M(?)M(w)M(X), so that the components of r 
in the ground reference frame are defined as: 
(3.2.2) rt(xt,y*,z!)MrGooy.z). 
Now, from the similarity of the triangles, the ground coordinates 
Of the lookpoint P(Xg,Yc) are easily obtained: