186 5 “Sphere to tangential plane”: polar (normal) aspect
N
S
r max
r max
P r
P l
p r
p l
O
Q lr
Φ r
Φ r
H
O
∗
D
Fig. 5.18. Line-of-sight, normal perspective mapping of the sphere to the tangential plane at the South Pole,
projection plane at maximal distance.
For later reference, Box 5.14 outlines the corresponding data for the line-of-sight and the line-ofcontact: compare with Figs. 5.18 and 5.19. Note that the special case where the projection plane is
placed in the center O of the sphere S
2
R is discussed at the end of this section.
p r
p l
r max
r max
Q lr
P r
P l
Φ r
Φ r
N
S
O
∗
H
D
Fig. 5.19. Line-of-sight, normal perspective mapping of the sphere to the tangential plane at the North Pole,
projection plane at minimal distance.
N
S
r max
r max
P r
P l
p r
p l
O
Q lr
Φ r
Φ r
H
O
∗
D
Fig. 5.18. Line-of-sight, normal perspective mapping of the sphere to the tangential plane at the South Pole,
projection plane at maximal distance.
For later reference, Box 5.14 outlines the corresponding data for the line-of-sight and the line-ofcontact: compare with Figs. 5.18 and 5.19. Note that the special case where the projection plane is
placed in the center O of the sphere S
2
R is discussed at the end of this section.
p r
p l
r max
r max
Q lr
P r
P l
Φ r
Φ r
N
S
O
∗
H
D
Fig. 5.19. Line-of-sight, normal perspective mapping of the sphere to the tangential plane at the North Pole,
projection plane at minimal distance.