Version 5.0 The LEDA User Manual

edge CONVEX COMPONENTS(const gen polygon& GP,
GRAPH & G,
list& inner edges, list& boundary edges,
list& hole edges)
if GP is a bounded and non-trivial generalized polygon, its interior is
decomposed into convex parts. All inner edges of the constructed decomposition
are returned in inner edges. boundary edges contains the edges
of every counter-clockwise oriented boundary cycle of GP, and hole edges
contains the edges of every clockwise oriented boundary cycle of GP.
Note that the reversals of boundary and hole edges will be stored in
inner edges. The function returns an edge of the convex hull if GP is a
bounded and non-trivial and nil otherwise. Precondition: GP must be
simple.
list TRIANGLE COMPONENTS(const gen polygon& GP)
triangulates the interior of generalized polygon GP and returns the result
of the triangulation as a list of polygons.
list CONVEX COMPONENTS(const gen polygon& GP)
if GPis a bounded and non-trivial generalized polygon, its interior is
decomposed into convex parts. The function returns a list of polygons
that form the convex decomposition of GPs interior.
• Minkowski Sums
Please note that the Minkowski sums only work reliable for the rational kernel.
gen polygon MINKOWSKI SUM(const polygon& P, const polygon& R)
computes the Minkowski sum of P and R.
gen polygon MINKOWSKI DIFF(const polygon& P, const polygon& R)
computes the Minkowski difference of P and R, i.e. the Minkowski sum
of P and R.reflect(point(0, 0)).
gen polygon MINKOWSKI SUM(const gen polygon& P, const polygon& R)
computes the Minkowski sum of P and R.
gen polygon MINKOWSKI DIFF(const gen polygon& P, const polygon& R)
computes the Minkowski difference of P and R, i.e. the Minkowski sum
of P and R.reflect(point(0, 0)).
The following variants of the MINKOWSKI functions take two additional call-back function
arguments conv partition and conv unite which are used by the algorithm to partition
the input polygons into convex parts and for computing the union of a list of convex polygons,
respectively (instead of using the default methods).