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Polygon in which all angles are right
rectilinear polygon is a polygon all of whose sides meet at right angles. Thus the interior angle at each vertex is either 90° or 270°. Rectilinear polygons
Rectilinear_polygon
Topics referred to by the same term
animal locomotion Rectilinear polygon, a polygon whose edges meet at right angles Rectilinear propagation, a property of waves Rectilinear Research Corporation
Rectilinear
Set of primitive shapes whose union equals a polygon
problems, depending on the type of polygon being covered. An example polygon covering problem is: given a rectilinear polygon, find a smallest set of squares
Polygon_covering
Set of basic shapes which assemble into a polygon
length. An important sub-family of polygon partition problems arises when the large polygon is a rectilinear polygon, and the goal is to partition it into
Polygon_partition
Process of partitioning a rectilinear polygon
Guillotine partition is the process of partitioning a rectilinear polygon, possibly containing some holes, into rectangles, using only guillotine-cuts
Guillotine_partition
Optimization problem in mathematics
of size (137,95) in a big rectangle of size (1600,1230). Given a rectilinear polygon (whose sides meet at right angles) R in the plane, a set S of points
Rectangle_packing
Mathematical problem
visible regions in a scene. Covering a rectilinear polygon with star polygons Star-shaped polygon, a class of polygon for which the art gallery problem can
Art_gallery_problem
Quadrilateral with four right angles
In Euclidean plane geometry, a rectangle is a rectilinear convex polygon or a quadrilateral with four right angles. It can also be defined as: an equiangular
Rectangle
Plane figure bounded by line segments
equilateral. A non-convex regular polygon is called a regular star polygon. Rectilinear: the polygon's sides meet at right angles, i.e. all its interior angles
Polygon
Flat-sided three-dimensional shape
three-dimensional analogs of two-dimensional orthogonal polygons, also known as rectilinear polygons. Orthogonal polyhedra are used in computational geometry
Polyhedron
axis-aligned. A more general case is rectilinear polygons, the ones with all sides parallel to coordinate axes or rectilinear polyhedra. Many problems in computational
Axis-aligned_object
Visualisation method for hierchical data
Orthoconvex treemaps can be used. There, all regions are orthoconvex rectilinear polygons with aspect ratio at most 64; and the leaves are either rectangles
Treemapping
point at infinity). The most well-known example of isothetic polygons are rectilinear polygons, and the former term is commonly used as a synonym for the
Isothetic_polygon
Shape with four equal sides and angles
given number of unit squares can fit into an orthogonally convex rectilinear polygon with half-integer vertex coordinates is NP-complete. Squaring the
Square
Polygon with right angles and consecutive lengths
or more generally a serial isogon of 90°, is any polygon with all right angles (a rectilinear polygon) whose sides are consecutive integer lengths. Golygons
Golygon
Value determined from a polyhedron
some other dissection puzzles, including the problem of dissecting rectilinear polygons into each other by axis-parallel cuts and translations. In two dimensions
Dehn_invariant
Natural number
straight, though they showed some tendencies to making the digit more rectilinear. The eastern Arab peoples developed the digit from a form that looked
7
Process of producing small rectangular items of fixed dimensions
that the original sheet might not be rectangular - it can be any rectilinear polygon. In particular, it might contain holes (representing defects in the
Guillotine_cutting
Smallest convex set containing a given set
geodesic between any two of its points. The orthogonal convex hull or rectilinear convex hull is the intersection of all orthogonally convex and connected
Convex_hull
Minimal superset that intersects each axis-parallel line in an interval
intersection with K. The orthogonal convex hull is also known as the rectilinear convex hull, or, in two dimensions, the x-y convex hull. The figure shows
Orthogonal_convex_hull
Problem of sorting pairs of numbers by their sum
points in sorted order by their distances, and testing whether one rectilinear polygon can be translated to fit within another. The problem of testing whether
X_+_Y_sorting
Boolean satisfiability problem restricted to a planar incidence graph
as possible. When the figure is a rectilinear polygon and it should be partitioned into rectangles, and the polygon is hole-free, then the problem is
Planar_SAT
Typographical symbol
POINTED PINWHEEL STAR U+2737 ✷ EIGHT POINTED RECTILINEAR BLACK STAR U+2738 ✸ HEAVY EIGHT POINTED RECTILINEAR BLACK STAR U+2742 ❂ CIRCLED OPEN CENTRE EIGHT
Star_(grapheme)
Finnish-Swedish mathematician and astronomer (1740–1784)
simple polygons in two articles "On solving rectilinear polygons". Lexell discussed two separate groups of problems: the first had the polygon defined
Anders_Johan_Lexell
Graph in which every two vertices are adjacent
7234 crossings. Further values are collected by the Rectilinear Crossing Number project. Rectilinear Crossing numbers for Kn are 0, 0, 0, 0, 1, 3, 9, 19
Complete_graph
Method for recursively subdividing a space into two subsets using hyperplanes
environment could be used to accelerate polygon ordering. The technique made use of depth coherence, which states that a polygon on the far side of the plane cannot
Binary_space_partitioning
Five coplanar points have a subset forming a convex quadrilateral
on 2013-07-02 Scheinerman, Edward R.; Wilf, Herbert S. (1994), "The rectilinear crossing number of a complete graph and Sylvester's "four point problem"
Happy_ending_problem
On short connecting nets with added points
Further well-known variants are the Euclidean Steiner tree problem and the rectilinear minimum Steiner tree problem. The Steiner tree problem in graphs can
Steiner_tree_problem
Family of problems in computational geometry
the point in polygon problem, in which one needs to determine whether a point is inside, outside, or on the boundary of a single polygon. Other special
Point_location
Natural number
1016/S0012-365X(96)00327-5. Sloane, N. J. A. (ed.). "Sequence A014540 (Rectilinear crossing number of complete graph on n nodes)". The On-Line Encyclopedia
229_(number)
Area interpreted positively or negatively
construction for a parallelogram of the same area as any "rectilinear figure" (simple polygon) by splitting it into triangles. Greek geometers often compared
Signed_area
proof; rectilinear polygons; guards that can patrol a line segment rather than a single point; special classes of polygons including star-shaped polygons, spiral
Art Gallery Theorems and Algorithms
Art_Gallery_Theorems_and_Algorithms
Problem of computing shortest paths around geometric obstacles
Preparata, F. P. (1984), "Euclidean shortest paths in the presence of rectilinear barriers", Networks, 14 (3): 393–410, doi:10.1002/net.3230140304. Li
Euclidean_shortest_path
, that which makes it what it is: e.g., a triangle is a three-sided rectilinear figure. Genus is that part of the essence which is also predicable of
Predicable
Public park in Abuja, Nigeria
administrative buildings of the city. A river crosses the Park in its main rectilinear axis, dividing it into two parts. One side on the Park is dedicated to
Millennium_Park_(Abuja)
Scientific visualization software
back-end. Handles structured (uniform rectilinear, non-uniform rectilinear, and curvilinear grids), unstructured, polygonal, image, multi-block and AMR data
ParaView
Optical instrument to view patterns due to repeated reflection
are placed parallel to each other (see Fig. 5 of patent illustration), rectilinear patterns are shown Brewster also imagined another application for the
Kaleidoscope
Fortification in Melilla, Spain
to Cabrerizas. It is a neo-medieval style fort, with a polygonal plan with three rectilinear fronts interrupted by two pentagonal bastions, located opposite
Fuerte_de_Cabrerizas_Altas
Problem of constructing equal-area shapes
parallelogram is found equal to any rectilinear figure, it is worthy of investigation whether one can prove that rectilinear figures are equal to figures bound
Squaring_the_circle
5-sided star shaped polygon
Pentagramma mirificum (Latin for "miraculous pentagram") is a star polygon on a sphere, composed of five great circle arcs, all of whose internal angles
Pentagramma_mirificum
Polygon through a set of points
polygon with the given points as its vertices. A polygonalization may also be called a polygonization, simple polygonalization, Hamiltonian polygon,
Polygonalization
Space with one dimension
curve. In physical space, a 1D subspace is called a "linear dimension" (rectilinear or curvilinear), with units of length (e.g., metre). In algebraic geometry
One-dimensional_space
transformation consists of a polygon mesh (usually triangles). The transformation is executed by texture mapping from the rectilinear mesh of the input image
Image_geometry_correction
Catastrophic earthquake that primarily affected Lisbon, Portugal
ordered city, the king commissioned the construction of big squares, rectilinear, large avenues and widened streets – the new mottos of Lisbon. The Pombaline
1755_Lisbon_earthquake
k-sets and halving lines For each arrangement of points in which the rectilinear crossing number is minimized, is the number of halving lines maximized
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Processes of altering images
distortion that results from photographs being taken at an oblique angle to a rectilinear subject. Care is needed while performing this task, as the image is reprocessed
Image_editing
French optical physicist (1788–1827)
straight edges, including the first satisfactory wave-based explanation of rectilinear propagation. By further supposing that light waves are purely transverse
Augustin-Jean_Fresnel
NP-hard problem in combinatorial optimization
cities is the Euclidean distance between the corresponding points. In the rectilinear TSP, the distance between two cities is the sum of the absolute values
Travelling_salesman_problem
Street in Minnesota, United States
comparatively more modern style also took root on Summit Avenue, the Rectilinear Style. In this style, the architectural form moves away from previous
Summit_Avenue_(St._Paul)
Architectural style of Medieval Europe
presents an elegant square base and is adorned with marble decorations in rectilinear compartments. The transept crossing in Italian cathedrals is generally
Gothic_architecture
Distance-transitive cubic graph with 20 nodes and 30 edges
correspond to pseudorotations of the ligands. The Desargues graph has rectilinear crossing number 6, and is the smallest cubic graph with that crossing
Desargues_graph
1890–1911 European style of art and architecture
Deco, which rejected organic surfaces altogether in preference for a rectilinear style derived from the contemporary artistic avant-garde. Art Nouveau
Art_Nouveau
Historic house in Oak Park, Illinois
version of the traditional Queen Anne style design. The houses incorporate rectilinear features which would later become hallmarks of Wright's fully mature
Thomas_H._Gale_House
Number of edge slopes in graph drawing
1007/978-3-540-31843-9_14. Eades, Peter; Hong, Seok-Hee; Poon, Sheung-Hung (2010), "On rectilinear drawing of graphs", in Eppstein, David; Gansner, Emden R. (eds.), Graph
Slope_number
Subset of a graph's vertices, including at least one endpoint of every edge
Retrieved 2010-03-05. Garey, Michael R.; Johnson, David S. (1977). "The rectilinear Steiner tree problem is NP-complete". SIAM Journal on Applied Mathematics
Vertex_cover
Type of textile
often more complicated. Rectilinear patterns tend to be bolder and more angular. Floral patterns can be woven in rectilinear design, but they tend to
Oriental_rug
Stage of electronic circuit design
The task of all routers is the same. They are given some pre-existing polygons consisting of pins (also called terminals) on cells, some obstacles where
Routing (electronic design automation)
Routing_(electronic_design_automation)
Robot that can rearrange its own parts
slinky-like, snake-like: concertina in a gopher hole, inchworm gaits, rectilinear undulation and sidewinding gaits, rolling like a tread at up to 1.4 m/s
Self-reconfiguring modular robot
Self-reconfiguring_modular_robot
Historical fortification around the city of Braga, Portugal
3rd century. Recent information points to polygonal plan, defined by rectilinear lines that crossed the structure, with an area between 40 and 50 hectares
Castle_of_Braga
Multi-dimensional object whose lengths in each dimension are similar
this GeoGebra page for a demonstration. On the other hand, consider a rectilinear 'snake' with width 1/b and length b, that is entirely folded within
Fat_object_(geometry)
k = 1, 2, 3. Another well researched graph parameter is the following. Rectilinear crossing number: The minimum number of crossing points over all straight-line
Topological_graph
Computational human phantoms are models of the human body
advanced mathematics, such as non-uniform rational B-spline (NURBS) and polygon meshes, which allow for 4-D phantoms where simulations can take place not
Computational_human_phantom
Least-weight tree connecting graph vertices
plane (or space). The rectilinear minimum spanning tree is a spanning tree of a graph with edge weights corresponding to the rectilinear distance between vertices
Minimum_spanning_tree
Dutch mathematician and physicist (1629–1695)
Fresnel adapted Huygens's principle to give a complete explanation of the rectilinear propagation and diffraction effects of light in 1821. Today this principle
Christiaan_Huygens
Interdisciplinary branch of science concerned with presenting scientific data visually
shapefile containing a polygonal description of the building footprints was read in and then the polygons were resampled onto a rectilinear grid, which was extruded
Scientific_visualization
building which permits ventilation of the building. Vierendeel truss A rectilinear truss usually fabricated of steel or concrete with horizontal top and
Glossary_of_architecture
Stone tool
worked, but not cut); or cut, with a rounded (polygonal), flat or pointed end. Edges—convex, rectilinear or concave, and more or less even. Edges on some
Hand_axe
Physical object which does not deform when forces or moments are exerted on it
meaning of the term "line": "linear" (= along a straight or curved line), "rectilinear" (= along a straight line, from Latin rectus = straight, and linere =
Rigid_body
Creation of buildings, structures, and sculpture using stone
Formwork stone is distinct from cyclopean concrete in that the former uses rectilinear tiles, while the latter uses boulders and/or cobblestone. Massive precut
Stonemasonry
Sharpest angle between edges at a vertex
Tamassia, Roberto (1995), "On the computational complexity of upward and rectilinear planarity testing", in Tamassia, Roberto; Tollis, Ioannis (eds.), Graph
Angular resolution (graph drawing)
Angular_resolution_(graph_drawing)
Quantified formulas with real-number variables
determine whether there exists a drawing achieving a given bound on the rectilinear crossing number (the minimum number of pairs of edges that cross in any
Existential theory of the reals
Existential_theory_of_the_reals
Method to draw shadows in computer graphic images
ist.psu.edu/viewdoc/download?doi=10.1.1.59.3376&rep=rep1&type=pdf RTW "Rectilinear" http://www.cspaul.com/wiki/doku.php?id=publications:rosen.2012.i3d RMSM
Shadow_mapping
Church in Aube, France
of similar height. The two patterns are unified by the framework of rectilinear wall sections and the grid of vertical and horizontal elements. The building
Basilique Saint-Urbain de Troyes
Basilique_Saint-Urbain_de_Troyes
Mathematical set with some added structure
distinguishes continuous from discontinuous, but does not distinguish rectilinear from curvilinear. Intuition tells us that the Euclidean structure cannot
Space_(mathematics)
Portuguese medieval castle
protruding. On top of the building is a belfrey. On the ground floor is a rectilinear slot in slate, and the second by two rectangular windows (one over the
Castle_of_Aguiar_da_Beira
Italian mathematician (1499–1557)
Nova Scientia, Tartaglia proposes to find the length of that initial rectilinear path for a projectile fired at an elevation of 45°, engaging in a Euclidean-style
Nicolo_Tartaglia
consisted of a central forum with city services, surrounded by a compact, rectilinear grid of streets, and wrapped in a wall for defense. To reduce travel
Ancient_Roman_architecture
Railway viaduct in Landore, Wales
beneath the viaduct's deck. Both the viaduct's abutments and the five rectilinear-plan piers located to the west of the river, each featuring two round-arch
Landore_Viaduct
Historic house in New York, United States
included, at that time, portions of the Catskills across the river. The rectilinear forms of the Federal and Greek Revival styles established their authority
Montgomery_Place
American architect (1918–2008)
and bold asymmetrical arcs and polygons suggests such influences as analytical cubism, biomorphism, and the rectilinear geometry of Mondrian's paintings
Robert_Royston
Church in England
deeply curved and bottom partly curved. The raised inscription plaque is rectilinear, and sits on a square-edged stepped shelf supported by curved brackets
St Andrew and St Mary's Church, Stoke Rochford
St_Andrew_and_St_Mary's_Church,_Stoke_Rochford
St. Vitus church is one of the best-preserved churches in Württemberg
cornice in the process; the support and sound lid were removed. The new rectilinear staircase has an unadorned iron railing. On the south side of the choir
St._Vitus_church_(Gärtringen)
Church in Vagharshapat, Armenia
that sought to reconcile the circularity of a central dome within a rectilinear ground plan." Adriano Alpago-Novello noted that the type is "significant
Saint_Hripsime_Church
Mathematics of Ancient Greece and the Mediterranean, 5th BC to 6th AD
acquaintance with mathematics: Antiphon claimed to be able to construct a rectilinear figure with the same area as a given circle, while Hippias is credited
Ancient_Greek_mathematics
Type of geometry
Grassmann" (English translation of book) E. Kummer, "General theory of rectilinear ray systems" (English translation) M. Pasch, "On the focal surfaces of
Projective_geometry
United States historic place
structure built on a raised basement. Its basic form is compact and rectilinear. It rises three floors above an exposed basement and features an asymmetrical
Argyle_Flats
Port in Italy
port by the prevailing winds. It was built from 1888 to 1900, has a rectilinear structure, a length of 490 meters and the direction of 105° - 285°. The
Port_of_Livorno
Term commonly used to denote rugs woven in Anatolia
patterns (the "Caucasian" type) or more floral patterns, stylized in rectilinear design (the "Turkish" type). They use typical Western Anatolian colour
Anatolian_rug
District of Genoa, Italy
in the Foce district. At the time of its opening, the street, wide, rectilinear and flanked by buildings of unusual height for the times and with high
Portoria
Wall surrounding the Civitas Turonorum
limits the effects of Loire floods. The southern face of the castrum is rectilinear, except for the southern half-ellipse of the amphitheater, which forms
Gallo-Roman enclosure of Tours
Gallo-Roman_enclosure_of_Tours
Prehistoric stone tool
advantage, over indirect percussion with pointer, of producing much more rectilinear pieces, as was the case with the other method. The extraction of leaves
Hammerstone
Shortest network connecting points
spanning tree. For instance, for the vertices of a regular polygon, removing any edge of the polygon produces a minimum spanning tree. Publications on the
Euclidean minimum spanning tree
Euclidean_minimum_spanning_tree
Heritage-listed building in Tasmania
removed and the tower elongated above the level of the circular drum in a rectilinear shape, with no banding, surmounted at the top by a drum and hemispherical
General Post Office, Launceston
General_Post_Office,_Launceston
Italian architect, priest, mathematician and writer (1624–1683)
tall, oval cylinder, which is joined by sweeping counter-curves to the rectilinear end bays of the wings. Two great staircases wind around the central oval
Guarino_Guarini
Church in Lincolnshire, England
further piscina with a seven-cusped arch surround with spandrels within a rectilinear frame, this sitting on a projecting ledge, with above, an entablature
St_James'_Church,_Aslackby
Priory in France
supports a ceiling made of large slabs. Access to the polygonal tower is via a door framed by a rectilinear lintel. This entrance is set within a forebay aedicula
Louroux_Priory
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