Slideshow:
Definition: Bounding Box (BB)
Example:
Definition: Minimum Bounding Box (MBB)
Example:
How to define/represent rectangle (minimum) bounding boxes
Intro to Region-trees (R-trees)
The sub-tree
indexed by the
Bounding Box BB1
contains
only objects
that lies inside BB1
The sub-tree
indexed by the
Bounding Box BB2
contains
only objects
that lies inside BB2
The sub-tree
indexed by the
Bounding Box BB3
contains
only objects
that lies inside BB3
And so on.
Structure of an internal node
of the R-tree
Structure of an internal node
of the R-tree
Structure of an internal node
of the R-tree
Structure of a leaf node
of the R-tree
R-tree index -
Example
The locations on these 7 objects on the map:
R-tree index -
Example
R-tree index -
Example
R-tree index -
Example
Data records:
R-tree:
Note: The mbb field for different objects are different - see coordinate map for mmb values
R-tree index -
Important note
Bounding boxes used to index the objects:
R-tree:
Note: The bounding boxes can overlap !!
- Bounding Box:
- Bounding Box = a rectangle that contains a group of objects
- Example:
- A group of
objects:
- A Bounding Box for this
group of
objects:
- A group of
objects:
- Minimum Bounding Box:
- Minimum Bounding Box = the smallest rectangle that contains a group of objects
- Example:
- A group of
objects:
- The Minimum Bounding Box for this
group of
objects:
- A group of
objects:
- Note:
- A rectangle
can be represented as
follows:
Rectangle: coordinate of the lower left corner coordinate of the upper right cornerExample:
- A rectangle
can be represented as
follows:
- R-tree: (Region-tree)
- R-tree =
an index tree-structure
derived from
the B-tree
that
uses
bounding boxes
as search keys
Example:
- The internal nodes contains
a number of
index entries of the
following format:
- The leaf nodes contains
a number of entries of the
follwoing format:
- R-tree =
an index tree-structure
derived from
the B-tree
that
uses
bounding boxes
as search keys
- Search property
of a R-tree:
- The sub-tree
indexed by an internal node
of the R-tree
has the following
structure:
I.e.:
- The subtree
indexed by
the bounding box will
contain:
- Only objects that is contained within the given bounding box !!!
- The subtree
indexed by
the bounding box will
contain:
- The sub-tree
indexed by an internal node
of the R-tree
has the following
structure:
- Important note:
- Bounding boxes in
a R-tree node can
overlap !!!
Example:
- Bounding boxes in
a R-tree node can
overlap !!!
- Example: R-tree
- Objects that we want to
represent:
There are 7 objects:
- school, pop (point of presence), house1, house2, road1 road2, pipeline
- The 3 objects:
- house1, road1 and road2
are completely enclosed by the bounding box ((0,0),(60,50):
- The objects:
- school, pop , house2 and pipeline
are completely enclosed by the bounding box ((20,20),(100,80):
- Here is a R-tree that uses
the bounding boxes above:
Note:
- For brevity sake:
- I used mbb in each object to denote its minimum bounding box
-
Warning:
- The
mbb
field for
different objects are
different
I don't want to add these details for brevity (save me time and you won't learn anything from the mbb info) !!!
(You can see the location of the objects in the figure and find the mbb (min. bounding box) yourself !!!)
- The
mbb
field for
different objects are
different
- For brevity sake:
- Objects that we want to
represent:
- Notice that:
- The bounding boxes used in the internal R-tree nodes can overlap !!!
Example:
You can see the overlap clearly in this pitcure: