As of October, 2016, Embarcadero is offering a free release
of Delphi (Delphi
10.1 Berlin Starter Edition ). There
are a few restrictions, but it is a welcome step toward making
more programmers aware of the joys of Delphi. They do say
"Offer may be withdrawn at any time", so don't delay if you want
to check it out. Please use the
link to let me know if the link stops working.
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The question is: "What is the largest rectangle that can be inscribed in an
arbitrary given simple polygon"?
Background & Techniques
This is an exploration of techniques for finding the maximum area rectangle
that can be inscribed in arbitrary concave or convex simple polygons.
Polygons can be defined by clicking vertex points on the image area or loaded
from a text file. All coordinates in this version are pixel locations on
an 500 x 500 pixel image area.
Once a polygon has been defined or loaded, the search strategy is based on
finding the maximum area polygon from a given center point. A trial and
error loop successively creates rectangles with a range of major axis angles
(typically 0 to 180 degrees) and a range of Width/Height ratios (typically
1 to 5). Parameters can be set controlling angle and ratio step size
and the max ratio to be tested.
Several strategies are available for searching for rectangles. The
"Strategies" options create trial rectangle centers which are then passed to the
rectangle creation procedure, looking for new maximum area examples.
Load and Save buttons do what they say, preserving and restoring polygon
vertices and maximal rectangle information if a search has been performed.
There are additional options to ignore best rectangle for a particular polygon
to aid in evaluating specific strategies, and one to restrict rectangles to
squares (Width/Height ratio set to 1.0) .
Note: This is not a finished project - there are several known rough spots to be
polished as time permits.
A small book could be written describing the code written so far, however
because of the exploratory nature of the program, the geometry involved, and
time constraints it is probably best to delay better documentation until
the code has evolved to a more permanent form. Much of the code was
developed while "in the zone" which is not conducive to tidy organization so
cleanup is needed.
It is still fun to play with though, watching various strategies
improve results, sometimes quickly, sometimes slowly.
The UGeometry library unit has been modified to add a TPolygon type and to
override the PolygonArea function to return the Centroid (center of mass) point
as well as the Area of a polygon. The modified version has been
included with the source download here and will be added to our DFFLib zip file
with the next update.
Running/Exploring the Program
Suggestions for Further Explorations
||Automate successive strategy application to find
the best rectangle.
||.Make searches "smarter" to
stop when there is no chance that a better solution will be found with current
|Original: December 23, 2015
February 18, 2016