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datovky
ds2-notes
Commits
32e95fcf
Commit
32e95fcf
authored
6 years ago
by
Martin Mareš
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Geometric: Introduction
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07-geom/Makefile
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07-geom/geom.tex
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=
..
include
../Makerules
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07-geom/geom.tex
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\ifx\chapter\undefined
\input
adsmac.tex
\singlechapter
{
7
}
\fi
\chapter
[geom]
{
Geometric data structures
}
There is a~rich landscape of data structures for handling geometric objects.
Let us perform a~small survey. First, there are different objects which can
be stored in the structure: points in~
$
\R
^
d
$
, lines in~
$
\R
^
d
$
, or even more
complex shapes like polygons, conic sections or splines.
Queries are asked about all objects which lie within a~given
\em
{
region
}
(or intersect its boundary). Usually, the region is one of:
\tightlist
{
o
}
\:\em
{
a~single object
}
--- test if the given object is stored in the structure
\:\em
{
a~range
}
--- a~
$
d
$
-dimensional ``box''
$
[
a
_
1
,b
_
1
]
\times
[
a
_
2
,b
_
2
]
\times
\ldots
\times
[
a
_
d,b
_
d
]
$
;
some of the intervals can extend to infinity
\:\em
{
partial match
}
--- some parameters of the object are specified precisely,
the remaining ones can be arbitrary. E.g., report all points in~
$
\R
^
3
$
for which
$
x
=
3
$
and
$
z
=
5
$
. This is a~special case of a~range, where
each interval is either a~single point or the whole~
$
\R
$
.
Partial match queries frequently occur in database indices,
even in otherwise non-geometric situations.
\:\em
{
a~polygon
}
\endlist
We might want to
\em
{
enumerate
}
all objects within the region,
or just
\em
{
count
}
them enumerating all of them.
enumerating all of them. If there is a~value associated with each
object, we can ask for a~sum or a~maximum of values of all objects
within the range --- this is generally called an
\em
{
aggregation
}
query.
In this chapter, we will consider the simple case of range queries
on points in~
$
\R
^
d
$
\section
{
Range queries in one dimension
}
TODO
\section
{
Multi-dimensional search trees (k-d trees)
}
TODO
\section
{
Multi-dimensional range trees
}
TODO
\endchapter
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