Spacetrack Directory Name | MOVE-IIb |
Alternative name | 2019-038N |
Orbit launches | 2019-07-05 |
Starting point | VOSTO (Vostochny Cosmodrome) |
WWW | Here |
Categories | |
Perigee | 510 km/h |
Apogee | 544 km |
Height MOVE-IIb | 317.22 km |
In geometry, the Minkowski sum (also known as dilation) of two sets of position vectors A and B in Euclidean space is formed by adding each vector in A to each vector in B, i.e., the set
A
+
B
=
{
a
+
b
|
a
?
A
,
b
?
B
}
.
{\displaystyle A+B=\{\mathbf {a} +\mathbf {b} \,|\,\mathbf {a} \in A,\ \mathbf {b} \in B\}.}
Analogously, the Minkowski difference (or geometric difference) is defined using the complement operation as
A
?
B
=
(
A
c
+
B
)
c
{\displaystyle A-B=(A^{c}+B)^{c}}
In general
A
?
B
?
A
+
(
?
B
)
{\displaystyle A-B\neq A+(-B)}
. For instance, in a one-dimensional case
A
=
[
?
2
,
2
]
{\displaystyle A=[-2,2]}
and
B
=
[
?
1
,
1
]
{\displaystyle B=[-1,1]}
the Minkowski difference
A
?
B
=
[
?
1
,
1
]
{\displaystyle A-B=[-1,1]}
, whereas
A
+
(
?
B
)
=
A
+
B
=
[
?
3
,
3
]
.
{\displaystyle A+(-B)=A+B=[-3,3].}
In a two-dimensional case, Minkowski difference is closely related to erosion (morphology) in image processing.
The concept is named for Hermann Minkowski.