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Smallest rectangle which encloses some planar set of points
In computational geometry, the minimum bounding rectangle (MBR), also known as bounding box (BBOX) or envelope, is an expression of the maximum extents
Minimum_bounding_rectangle
Smallest box which encloses some set of points
called the minimum bounding rectangle. The axis-aligned minimum bounding box (or AABB) for a given point set is its minimum bounding box subject to the
Minimum_bounding_box
Closed volume that completely contains the union of a set of objects
bounding volume (or bounding region) for a set of objects is a closed region that completely contains the union of the objects in the set. Bounding volumes
Bounding_volume
Algorithms in computational geometry
problem is that of finding the oriented minimum bounding box enclosing a set of points. It is a type of bounding volume. "Smallest" may refer to volume
Minimum bounding box algorithms
Minimum_bounding_box_algorithms
Data structures used in spatial indexing
their minimum bounding rectangle in the next higher level of the tree; the "R" in R-tree is for rectangle. Since all objects lie within this bounding rectangle
R-tree
empty sphere Minimum bounding box, Minimum bounding rectangle A. Naamad, D. T. Lee and W.-L. Hsu (1984). "On the Maximum Empty Rectangle Problem". Discrete
Largest_empty_rectangle
Generalization of a rectangle for higher dimensions
Its plane cross selections in all pairs of axes are rhombi. Minimum bounding rectangle Cuboid Hilbert cube N.W. Johnson: Geometries and Transformations
Hyperrectangle
R-tree variant and index for multidimensional objects
should group "similar" data rectangles together, to minimize the area and perimeter of the resulting minimum bounding rectangles (MBRs). Packed Hilbert R-trees
Hilbert_R-tree
Polygon in which all angles are right
axis-aligned rectangle - a rectangle with 2 sides parallel to the x axis and 2 sides parallel to the y axis. See also: Minimum bounding rectangle. A golygon
Rectilinear_polygon
Geospatial vector data format
int32 little Shape type (see reference below) 36–67 double little Minimum bounding rectangle (MBR) of all shapes contained within the dataset; four doubles
Shapefile
N-dimensional bounding volume (called Minimum Bounding Rectangles – MBR) as a point in N-dimensions, represented by the ordered pair of the rectangles. The term
Priority_R-tree
Database of data representing objects in geometric space
data. Objects (shapes, lines and points) are grouped using the minimum bounding rectangle (MBR). Objects are added to an MBR within the index that will
Spatial_database
Graphics structure
of the tree, are wrapped in bounding volumes. These nodes are then grouped as small sets and enclosed within larger bounding volumes. These, in turn, are
Bounding_volume_hierarchy
Largest and smallest value taken by a function at a given point
In mathematical analysis, the maximum and minimum of a function are, respectively, the greatest and least value taken by the function. Known generically
Maximum_and_minimum
Optimization problem in mathematics
larger rectangle with width W {\displaystyle W} and height H {\displaystyle H} , the integer program looks as follows: Objective minimizing bounding-box-netlength
Rectangle_packing
List of topics in geography
Landscape ecology Linear Reference System Map Military geography Minimum bounding rectangle Muslim world Nunatak hypothesis Palaeogeography Pedology Philosophy
Index_of_geography_articles
Topics referred to by the same term
register Minimum bounding rectangle Minimum bit rate Membrane bioreactor, in waste disposal Microwave background radiation, in cosmology Minimum bend radius
MBR
Blinn–Phong reflection model Bloom (shader effect) Bounding interval hierarchy Bounding sphere Bounding volume Bounding volume hierarchy Bresenham's line algorithm
List of computer graphics and descriptive geometry topics
List_of_computer_graphics_and_descriptive_geometry_topics
Index tree structure in computer science
supernodes. The data nodes of the X-tree contain rectilinear minimum bounding rectangles (MBRs) together with pointers to the actual data objects, and
X-tree
Integral constructed using Darboux sums
integral must exist as well. Regulated integral Lebesgue integration Minimum bounding rectangle David J. Foulis; Mustafa A. Munem (1989). After Calculus: Analysis
Darboux_integral
Standard for representing locations on Earth's surface in databases
or spatial extents in a more flexible manner than a standard minimum bounding rectangle, and to support "lightweight", text-based spatial querying; it
C-squares
for a region is the ratio between the length and width of the minimum bounding rectangle of the region. It is considered a feature of the region. It can
Elongatedness
Area for playing association football
touchline is still on the field of play, and a foul committed over the line bounding the penalty area results in a penalty. Therefore, a ball has to completely
Football_pitch
Discrete mathematics decomposition
decomposition of a rectangle into finitely many interior-disjoint rectangles. The size of a rectangulation describes the number of rectangles used in the decomposition
Rectangulations
Cuboid with all right angles and equal opposite faces
three different lengths. Hyperrectangle — generalization of a rectangle; Minimum bounding box — a measurement of a cuboid in which all points exist; Padovan
Rectangular_cuboid
Unrelated vertices in graphs
largest independent set α ( G ) {\displaystyle \alpha (G)} and the size of a minimum vertex cover β ( G ) {\displaystyle \beta (G)} is equal to the number of
Independent set (graph theory)
Independent_set_(graph_theory)
diagram Minimum bounding box (Smallest enclosing box, Smallest bounding box) 2-D case: Smallest bounding rectangle (Smallest enclosing rectangle) There
List of combinatorial computational geometry topics
List_of_combinatorial_computational_geometry_topics
Set of edges without common vertices
perfect matching is also a minimum-size edge cover. Thus, the size of a maximum matching is no larger than the size of a minimum edge cover: ν ( G ) ≤
Matching_(graph_theory)
Shape that blocks all lines of sight
from the minimum-perimeter bounding box of the input, consisting of a polygonal chain stretched around the polygon from one corner of the bounding box to
Opaque_set
Two-dimensional packing problem
half-integer vertex coordinates. Circle packing in a square Squaring the square Rectangle packing Moving sofa problem Brass, Peter; Moser, William; Pach, János
Square_packing
Subset of a graph's vertices, including at least one endpoint of every edge
every edge of the graph. In computer science, the problem of finding a minimum vertex cover is a classical optimization problem. It is NP-hard, so it
Vertex_cover
Examples are axis-aligned rectangles (or hyperrectangles), the ones with edges parallel to the coordinate axes. Minimum bounding boxes are often implicitly
Axis-aligned_object
Multidimensional search tree for points in k dimensional space
coordinate of the search rectangle. If the median is less than the xlow coordinate of the search rectangle, then no rectangle in the left branch can ever
K-d_tree
Set of basic shapes which assemble into a polygon
partition of a polygon is a set of primitive units (e.g., triangles, rectangles, etc.), which do not overlap and whose union equals the polygon. A polygon
Polygon_partition
Classical problem in combinatorics
by the intersection of the universe and geometric shapes (e.g., disks, rectangles). Set packing is the problem of selecting the maximum number of sets that
Set_cover_problem
A collection of (region, child) pairs containing a description of the bounding region along with a pointer to the child page corresponding to that region
K-D-B-tree
Process of partitioning a rectilinear polygon
the area of the produced rectangles or their value, or minimize the waste or the number of required sheets. In the minimum edge-length rectangular-partition
Guillotine_partition
Theorem on polygon dissections
is a rectangle of sides a · x and a · (1/x) and Q is a square of side length a, then Px and Q are equidecomposable for every x > 0. An upper bound for
Wallace–Bolyai–Gerwien theorem
Wallace–Bolyai–Gerwien_theorem
Unsolved geometry problem about planar regions
area of a convex set containing a segment, a triangle, and a rectangle to show a lower bound of 0.232239 for a convex cover. In the 1970s, John Wetzel conjectured
Moser's_worm_problem
Distance estimation problems in computational geometry
Smallest enclosing rectangle: unlike the bounding box problem mentioned above, the rectangle may be of any orientation Largest empty rectangle Geometric spanner
Proximity_problems
Problem in computer science
{\mathcal {U}}} . These sets may overlap. The optimization version finds the minimum number of such sets. The maximum set packing need not cover every possible
Set_packing
Concept in computational geometry
intersects at least one rectangle (hence m ≤ n). Each rectangle is intersected by exactly one line. Since the height of all rectangles is H, it is not possible
Maximum_disjoint_set
Mathematical and computational problem
guillotine cutting problem, both the items and the "bins" are two-dimensional rectangles rather than one-dimensional numbers, and the items have to be cut from
Bin_packing_problem
Concept in economics
Because the rectangle OP1EQ1 is the total revenue actually obtained by the manufacturer, that is, A + B, and the trapezoid OPMEQ. The minimum total profit
Economic_surplus
Field of geometry closely arranging circles on a plane
Circle packing in a circle Circle packing in a square Circle packing in a rectangle Circle packing in an equilateral triangle Circle packing in an isosceles
Circle_packing
Mathematical concept
of the area between this curve and the axes, and the area in the rectangle bounded by the lines x = 0 , x = a , y = 0 , y = b , {\displaystyle x=0,x=a
Young's inequality for products
Young's_inequality_for_products
Operations research problem of packing items into the largest number of bins
covering, the bin sizes are bounded from below and the goal is to maximize their number; in bin packing, the bin sizes are bounded from above and the goal
Bin_covering_problem
Basic integral in elementary calculus
finite sums of areas of vertical rectangles. For suitable functions, including every continuous function on a closed bounded interval, these Riemann sums
Riemann_integral
Non-orientable surface with one edge
of four-dimensional Euclidean space. The minimum-energy shape of a smooth Möbius strip glued from a rectangle does not have a known analytic description
Möbius_strip
Geometric fractal-like pattern
All of the bounded regions surrounded by toothpicks in the pattern, but not themselves crossed by toothpicks, must be squares or rectangles. It has been
Toothpick_sequence
Three linked but pairwise separated rings
ellipses, or (using the vertices of a regular icosahedron) by linked golden rectangles. It is impossible to realize them using circles in three-dimensional space
Borromean_rings
Arithmetic mean is greater than or equal to geometric mean
perimeter of a rectangle with sides of length x1 and x2. Similarly, 4√x1x2 is the perimeter of a square with the same area, x1x2, as that rectangle. Thus for
AM–GM_inequality
Axis-aligned bounding box (sometimes called "axis oriented"), a bounding box stored in world coordinates; one of the simplest bounding volumes. Additive
Glossary_of_computer_graphics
Intersection graph of a chord diagram
case the routing area is a rectangle, all nets are two-terminal, and the terminals are placed on the perimeter of the rectangle. It is easily seen that the
Circle_graph
All numbers between two given numbers
{\displaystyle n} finite intervals. For n = 2 {\displaystyle n=2} this is a rectangle; for n = 3 {\displaystyle n=3} this is a rectangular cuboid (also called
Interval_(mathematics)
theory, that deals with balancing geometric sets, such as intervals or rectangles. The general research question in this field is: given a set of points
Geometric_discrepancy
Number of occurrences in an experiment or study
to the frequency of the observations in the interval. The height of a rectangle is also equal to the frequency density of the interval, i.e., the frequency
Frequency_(statistics)
American mathematician (1923–2013)
Fan Chung, Ron Graham, and Jack van Lint on partitions of rectangles into smaller rectangles.[CGG] Author biography from Borst, S. C.; Coffman, E. G.;
Edgar_Gilbert
Generalization of a magic square
existence of magic n-dimensional rectangles, Discrete Mathematics 207 (1999), 53-63. Thomas R. Hagedorn, Magic rectangles revisited, Discrete Mathematics
Magic_hypercube
Method to solve optimization problems
function is a convex function, which implies that every local minimum is a global minimum; similarly, a linear function is a concave function, which implies
Linear_programming
Machine learning algorithm
problem: given a picture, decide whether it contains faces, and construct bounding boxes for the faces. To make the task more manageable, the Viola–Jones
Viola–Jones object detection framework
Viola–Jones_object_detection_framework
Type of mathematical sequence
points are chosen as x i = i / N {\displaystyle x_{i}=i/N} , this is the rectangle rule. If the points are chosen to be randomly (or pseudorandomly) distributed
Low-discrepancy_sequence
Type of computational problem
prove the following for the special case in which the conflict-graph has bounded arboricity: If the geometric cover problem is fixed-parameter tractable
Covering_problems
Methodological basis for 3D CAD/CAM solid modeling and image rendering
the number of primitive solids/surfaces in the composition. By using minimum bounding boxes around the solids in the composition tree, the exhaustive search
Ray_casting
Operation in mathematical calculus
century, who thought of the area under a curve as an infinite sum of rectangles of infinitesimal width. Bernhard Riemann later gave a rigorous definition
Integral
points in the plane with as few additional points as possible to avoid rectangles with only two points on their boundary. As typically formulated, the online
Geometry of binary search trees
Geometry_of_binary_search_trees
Problem in geometric probability
square, or regular hexagon (or their affine transformations, including the rectangles and parallelograms), the probabilities are respectively 2 3 ≈ 0.6667 {\displaystyle
Sylvester's four point problem
Sylvester's_four_point_problem
Triangulation method
For four or more points on the same circle (e.g., the vertices of a rectangle) the Delaunay triangulation is not unique: each of the two possible triangulations
Delaunay_triangulation
Natural number
see Ramsey's theorem. Either 16 or 18 unit squares can be formed into rectangles with perimeter equal to the area; and there are no other natural numbers
17_(number)
5th-century fortress in Bukhara, Uzbekistan
northwestern part of contemporary Bukhara. In layout, it resembles a modified rectangle, a little elongated from the west to the east. The perimeter of the external
Ark_of_Bukhara
Branch of computer science
Bentley–Ottmann algorithm Shamos–Hoey algorithm Minimum bounding box algorithms: find the oriented minimum bounding box enclosing a set of points Nearest neighbor
Computational_geometry
Characteristic of human females
Hourglass, Spoon, Rectangle, Diamond, Oval, Triangle, Inverted Triangle}", 2002 Connell's "Body Shape Assessment Scale: {Hourglass, Pear, Rectangle, Inverted
Female_body_shape
Shape containing unit line segments in all directions
much as possible. In the worst case, these two regions are two 1 by ε rectangles perpendicular to each other so that they overlap at an area of only ε2
Kakeya_set
Edge-colored graph matching where all edges have distinct colors
matching? Drisko studied this question using the terminology of Latin rectangles. He proved that, for any n ≤ k, in the complete bipartite graph Kn,k,
Rainbow_matching
High-area shapes can shift to hold many grid points
any lower dimensional subspace, are separated from each other by some minimum distance, and can be combined by adding or subtracting their coordinates
Blichfeldt's_theorem
Smallest dimension where a graph can be represented as an intersection graph of boxes
representation of this graph as an intersection graph of six axis-parallel rectangles (two-dimensional boxes) on the Euclidean plane. This graph cannot be represented
Boxicity
Mathematical problem in operations research
The guillotine problem is another 2-D problem of cutting sheets into rectangles of specified sizes, however only cuts that continue all the way across
Cutting_stock_problem
and the escape path to a rectangle in the plane. In this variation, the goal is to find a path from the top side of the rectangle to the bottom side that
Barrier_resilience
On tangency patterns of circles
circular rectangle, the region R {\displaystyle R} bounded by a cycle of four tangent circles (which may be given the symmetries of a rectangle by a Möbius
Circle_packing_theorem
Computational physics simulation algorithm
never exceed the minimum of the non-committed new event times. Next particle to be examined by the algorithm has the current minimum of new event times
Lubachevsky–Stillinger algorithm
Lubachevsky–Stillinger_algorithm
Collection of open sets used to define a topology
Euclidean topology on the plane admits as a base the set of all open rectangles with horizontal and vertical sides, and a nonempty intersection of two
Base_(topology)
Method for solving quadratic equations
congruent rectangles with sides x {\displaystyle x} and b 2 a {\displaystyle {\tfrac {b}{2a}}} . To this square and pair of rectangles, one more
Completing_the_square
Complexity of sending information in a distributed algorithm
is the binary logarithm of the rectangle covering number of the matrix: the minimum number of combinatorial 1-rectangles required to cover all 1-entries
Communication_complexity
Question in geometric probability
F(φ), let's first look at the case for the horizontal edges of the bounding rectangle. The total side length is a and the midpoint must not be within l/2
Buffon's_needle_problem
Sony PlayStation budget range
the original box art shrunk slightly, with a grey border, and a yellow rectangle on top of it, with Platinum The Best of PlayStation 3 written on it. PlayStation
Essentials_(PlayStation)
this context, reconstruction is the formation of a graph from its deck. rectangle A simple cycle consisting of exactly four edges and four vertices. regular
Glossary_of_graph_theory
French mathematician (1875–1941)
to a plane, the area of skew polygons, surface integrals of minimum area with a given bound, and the final note gave the definition of Lebesgue integration
Henri_Lebesgue
Standard sizes of paper
doubled. The international business card has the size of the smallest rectangle containing a credit card rounded to full millimetres, but in Western Europe
Paper_size
Fourth standardized moment in statistics
for clarity as a rectangle in both images), excess kurtosis = −1.2. Note that in these cases the platykurtic densities have bounded support, whereas the
Kurtosis
2D geometric minimization problem
of axis-aligned rectangles and a strip of bounded width and infinite height, determine an overlapping-free packing of the rectangles into the strip, minimizing
Strip_packing_problem
Municipality of Rio Grande do Sul, Brazil
green and white in normal tones, it features a blue and red triangle-rectangle and a quadrilateral green that ascends between the two triangles with
Quaraí
Non-Euclidean geometry
u and −u / ‖u‖2, and taking the distance from v to this pair to be the minimum of the distances from v to each of these two points. Because spherical
Elliptic_geometry
Covering by shapes without overlaps or gaps
each vertex is the same. The fundamental region is a shape such as a rectangle that is repeated to form the tessellation. For example, a regular tessellation
Tessellation
Circle that passes through the vertices of a triangle
The useful minimum bounding circle of three points is defined either by the circumcircle (where three points are on the minimum bounding circle) or by
Circumcircle
District in Rajasthan, India
and in the west and north by Pakistan. The district is located within a rectangle lying between 26°.4’ –28°.23' north parallel and 69°.20'-72°.42' east
Jaisalmer_district
Non-crossing graph with vertices on outer face
outerplanar graph can be represented as an intersection graph of axis-aligned rectangles in the plane, so outerplanar graphs have boxicity at most two. Every outerplanar
Outerplanar_graph
Solitaire card game
facedown at the upper left of the layout. The four foundations (light rectangles in the upper right of the figure) are built up by suit from Ace (low in
Klondike_(solitaire)
distractions the seats were removed and the area was painted black. A rectangle on either side of home plate in which the batter must be standing for
Glossary_of_baseball_terms
River in India
144,591 square kilometres (55,827 sq mi). The drainage area resembles a rectangle up to the junction of the Parvathi and Banas Rivers with the Chambal flowing
Chambal_River
Korean sword-based martial art
and using bamboo swords. The competition court is typically a square or rectangle measuring between 9 and 11 meters per side, with an additional margin
Kumdo
MINIMUM BOUNDING-RECTANGLE
MINIMUM BOUNDING-RECTANGLE
Girl/Female
English, Hindu, Indian, Marathi
Small Daughter
Surname or Lastname
English and German
English and German : patronymic from Bold as a personal name.Danish : habitational name from a place so named in Jutland.
Surname or Lastname
English
English : variant of Blanton.
Male
Chinese
righteous sounding.
Girl/Female
Christian, Gujarati, Hindu, Indian, Kannada, Marathi, Sindhi, Telugu
Wished-for Child
Boy/Male
Arabic
Wounding; Cutter
Surname or Lastname
English
English : from the late Old English personal name Golding.
Female
Chinese
simple sounding.
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Tamil, Telugu
Love; Bonding
Boy/Male
Arabic
Wounding; Cutter
Boy/Male
Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Physical Bonding
Girl/Female
Gujarati, Hindu, Indian
Bonding; Love
Girl/Female
Arabic
Pounding; Generous
Boy/Male
Hindu
Sweet sounding
Surname or Lastname
English
English : nickname from some fancied resemblance to the songbird (Emberiza spp.).German : patronymic from an unexplained Frisian-Lower Saxon personal name, or a derivative of Bunt- (see Bunten).Sarah Bunting (1686–1762), born in Matlock, Derbyshire, became a noted Quaker minister in Cross Wicks, NJ. It is believed but not certain that other members of her family, including her father, John Bunting, came with her to NJ sometime before 1704, when her marriage to William Murfin is recorded.
Surname or Lastname
English (Suffolk)
English (Suffolk) : variant of Browning.
Boy/Male
Tamil
Physical bonding
Surname or Lastname
English
English : variant of Boulding, a patronymic from the Germanic personal name Baldo, a short form of any of the various compound names with the first element bald ‘bold’.
Boy/Male
British, English
Free
Boy/Male
Tamil
Madhughosh | மதà¯à®•à¯‹à®·
Sweet sounding
MINIMUM BOUNDING-RECTANGLE
MINIMUM BOUNDING-RECTANGLE
Surname or Lastname
French
French : from Old French denier, originally the name of a copper coin, later a term for money in general, hence probably a metonymic occupational name for a moneyer or minter.English : variant spelling of Denyer, cognate with 1.
Girl/Female
Indian, Punjabi, Sikh
Pretty; Glory
Male
Portuguese
Galician-Portuguese form of Latin Albertus, ALBERTE means "bright nobility."
Boy/Male
Greek
Virgin.
Girl/Female
Tamil
Way of offering prayer to God
Girl/Female
Tamil
Sarunati | ஸரà¯à®¨à®¾à®¤à¯€
Nobleminded
Girl/Female
Muslim/Islamic
Poetress
Female
Turkish
Turkish name BILGE means "wise."
Surname or Lastname
English (Bath)
English (Bath) : unexplained.
Boy/Male
Anglo, Arabic, British, English, German, Indian, Muslim, Parsi, Swedish
Decree; Edict; Command; Order; Traveller Merchant; Royal Patent
MINIMUM BOUNDING-RECTANGLE
MINIMUM BOUNDING-RECTANGLE
MINIMUM BOUNDING-RECTANGLE
MINIMUM BOUNDING-RECTANGLE
MINIMUM BOUNDING-RECTANGLE
a.
Pompous; noisy; ostentatious; as, high-sounding words or titles.
n.
The least quantity assignable, admissible, or possible, in a given case; hence, a thing of small consequence; -- opposed to maximum.
n.
That by which anything is prepared for use, or set off to advantage; equipment; embellishment; setting; as, the mounting of a sword or diamond.
n.
measurement by sounding; also, the depth so ascertained.
a.
Making blind or as if blind; depriving of sight or of understanding; obscuring; as, blinding tears; blinding snow.
n.
In a curve referred to polar coordinates, any point for which the radius vector is a maximum or minimum.
a.
Making or emitting sound; hence, sonorous; as, sounding words.
pl.
of Minimum
a.
Greatest in quantity or highest in degree attainable or attained; as, a maximum consumption of fuel; maximum pressure; maximum heat.
n.
Anything very minute; as, the minims of existence; -- applied to animalcula; and the like.
n.
Any place or part of the ocean, or other water, where a sounding line will reach the bottom; -- usually in the plural.
pl.
of Minimus
n.
See Sound boarding, under Sound, a noise.
n.
The sand, shells, or the like, that are brought up by the sounding lead when it has touched bottom.
n.
Minimum.
n.
A self-registering thermometer, especially one that registers the maximum and minimum during long periods.
n.
The greatest quantity or value attainable in a given case; or, the greatest value attained by a quantity which first increases and then begins to decrease; the highest point or degree; -- opposed to minimum.
p. p & a.
Made obligatory; imposed as a duty; binding.
n.
A minim.