Polyhedral Moving Region Algebra (PMRegion)
===========================================

based on the paper "A polyhedra-based model for moving regions in databases"
https://www.tandfonline.com/eprint/MNTtxvte8V9XsR4xYgcv/full

Author: Florian Heinz <fh@sysv.de> - Ralf Hartmut Güting <rhg@fernuni-hagen.de>



Prerequisites: CGAL Library (with dependencies gmp/mpfr/boost)
==============

Debian/Ubuntu: sudo apt install libcgal-dev

CentOS/Redhat: sudo yum install CGAL-devel




In the directory "pmregion" the source code for the libpmregion library can be
found, which is integrated in secondo. There is also a command line program
"pmregcli", which allows stand-alone usage of some important operations using
textfiles as input/output.

Three example objects can be found in pmregion/examples:

pmreg1, pmreg2 - polyhedral moving regions
mpoint - a moving point



Example: Performing some operations on polyhedral moving regions
========


# First, restore the objects into a (already opened) database

restore pmreg1 from '<HOME>/secondo/Algebras/PMRegion/pmregion/examples/pmreg1'
restore pmreg2 from '<HOME>/secondo/Algebras/PMRegion/pmregion/examples/pmreg2'
restore mpoint from '<HOME>/secondo/Algebras/PMRegion/pmregion/examples/mpoint'

# Build the union, intersection and differences of the two polyhedral moving
# regions

let pmreg3 = pmreg1 union pmreg2
let pmreg4 = intersection(pmreg1, pmreg2)
let pmreg5 = pmreg1 minus pmreg2
let pmreg6 = pmreg2 minus pmreg1

# Query the unified moving regions for two instants

query pmreg3 atinstant instant("1970-01-04-00:00:00")
query pmreg3 atinstant instant("1970-01-05-00:00:00")

# Query the times, where an mpoint is inside the unified moving regions

query mpoint inside pmreg3

# Query the intervals, during which the two moving regions intersect

query pmreg1 intersects pmreg2

# query the perimeter and area of the unified moving regions

query perimeter(pmreg3)
query area(pmreg3)

# Determine the traversed area of the unified moving regions

query traversedarea(pmreg3)

# Translate the moving region by (300, 1000) and one day (86400000 ms)

query pmreg3 translate [300.0, 1000.0, 86400000.0]

# Convert the unified polyhedral moving region into a unit-based moving
# region

query pmreg2mreg(pmreg3)