Minkowski Sums
The Minkowski sum (also known as the vector sum) of two
sets P and Q in R^{2}
is the set {p+q  p in P, q in Q} .
Application Areas
 robot motion planning
 computeraided design and manufacturing (CAD/CAM)
On the right there is a screenshot of the Example
for Minkowski sum and difference. The polygons are shown in
red and green, the Minkowski sum in black, and the Minkowski difference
in blue.


Example for Minkowski
sum and difference
The functions
GEN_POLYGON MINKOWSKI_SUM(const POLYGON& P, const POLYGON& R)
GEN_POLYGON MINKOWSKI_SUM(const GEN_POLYGON& P, const POLYGON& R)
compute the Minkowski sum of P and R , and the
functions
GEN_POLYGON MINKOWSKI_DIFF(const POLYGON& P, const POLYGON& R)
GEN_POLYGON MINKOWSKI_DIFF(const GEN_POLYGON& P, const POLYGON& R)
compute the Minkowski difference, i.e., the Minkowski sum of P
and R.reflect(point(0,0)) .
We use the notation POINT (POLYGON, GEN_POLYGON) to indicate
that the algorithm works both for points (polygons
, gen_polygons ) and rat_points (rat_polygons
, rat_gen_polygons ). See also Writing
Kernel Independent Code.

See also:
Data Types for 2D Geometry
Writing Kernel Independent Code
Geometry Algorithms
Geometry
Graphs and Related Data Types
GeoWin
Number Types
Manual Entries
Manual
Page of Geometry Algorithms
