Biomedical Engineering Reference
In-Depth Information
Fig. 1 (a) Showing two artificial surfaces in contact and illustration of how the normal vector and
the principal curvatures are located in the contact region of
S
a
. The X, Y and
Z
are the global
coordinate system. (b) The tangent plane is perpendicular to the normal
ve
ctor
n
a
. The
red/dark
grey zone S
c
is the region where
S
a
and
S
b
ar
e
in contact. The
p
a
and
p
a
are the maximal and
minimal principal directions respectively and
v
is
the
d
irection along which we computed the
normal curvature. Angle
is the angle between
p
a
and
v
a
2.1 Congruity Formulation
R
3
as shown in Fig.
1
a and we would like
to estimate their congruity. Let
S
c
and
S
c
be the regions of
S
a
and
S
b
that are in close
proximity. Let
X
,
Y
, and
Z
be the axis of a coordinate system.
The normal vectors (first order features) at
S
c
and
S
c
are denoted as
n
a
and
n
b
.
The second order features are the curvatures. The principal curvatures of t
he
surfa
ce
S
c
are denoted as
k
1
and
k
2
and corresponding principal directions are
p
a
and
p
a
(Fig.
1
b).
R
3
and
S
b
∈
Consider two surfaces
S
a
∈
