Geography Reference
In-Depth Information
Fig. 1.30.
Left angular shear
l
:=
Ψ
l
−
Ψ
r
, left Gauss frame, left Cartan frame, left Darboux frame, angular
shear parameter
Ψ
l
.
image curve is generated by mapping the original curve
C
(
S
)
∈
M
l
⊂
M
l
to
c
(
s
)
∈
M
r
⊂
M
r
.
Box
1.53
summarizes the related reference frames, namely
Gauss reference frame (3-leg):
{
G
1
,
G
2
,
G
3
|
U, V
}
,
{
g
1
,
g
2
,
g
3
|
u, v
}
;
(1.319)
Cartan reference frame (3-leg, orthonormal, repere mobile):
{
C
1
,
C
2
,
C
3
|
U, V
}
,
{
c
1
,
c
2
,
c
3
|
u,v
}
;
(1.320)
Darboux reference frame (3-leg, orthonormal):
{
D
1
,
D
2
,
D
3
|
U
(
S
)
,V
(
S
)
}
,
{
d
1
,
d
2
,
d
3
|
u
(
s
)
,v
(
s
)
}
.
(1.321)
Fig. 1.31.
Right angular shear
r
:=
Ψ
r
− Ψ
l
, right Gauss frame, right Cartan frame, right Darboux frame,
angular shear parameter
Ψ
r
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