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Polygon intersected up to twice by lines orthogonal to a given line
In geometry, a polygon P in the plane is called monotone with respect to a straight line L, if every line orthogonal to L intersects the boundary of P
Monotone_polygon
Partition of a simple polygon into triangles
be split into two monotone chains. A polygon that is monotone with respect to the y-axis is called y-monotone. A monotone polygon with n vertices can
Polygon_triangulation
Connected series of line segments
between a polygonal area and a polygonal chain. A space closed polygonal chain is also known as a skew "polygon". A polygonal chain is called monotone if there
Polygonal_chain
Shape bounded by non-intersecting line segments
These polygons include as special cases the convex polygons, star-shaped polygons, and monotone polygons. The sum of external angles of a simple polygon is
Simple_polygon
Topics referred to by the same term
and bargaining systems. Monotone class theorem, in measure theory Monotone convergence theorem, in mathematics Monotone polygon, a property of a geometric
Monotone
Polygon through a set of points
every non-collinear set of points has a polygonalization that is a monotone polygon. This means that, with respect to some straight line (which may be
Polygonalization
Polygon in which all angles are right
convex. See Orthogonally convex rectilinear polygon . A monotone rectilinear polygon is a monotone polygon which is also rectilinear. A T-square is a fractal
Rectilinear_polygon
Plane figure bounded by line segments
regular star polygon. Rectilinear: the polygon's sides meet at right angles, i.e. all its interior angles are 90 or 270 degrees. Monotone with respect
Polygon
Determining where a point is in relation to a coplanar polygon
available for some special polygons. Simpler algorithms are possible for monotone polygons, star-shaped polygons, convex polygons and triangles. The triangle
Point_in_polygon
Mathematical problem
vertex guards in two special sub-classes of simple polygons, viz. monotone polygons and polygons weakly visible from an edge. Krohn & Nilsson (2013)
Art_gallery_problem
Method in geometry for representing a polygon by a topological skeleton
position. A monotone polygon with respect to a line L is a polygon with the property that every line orthogonal to L intersects the polygon in a single
Straight_skeleton
Polygon visible from one of its points
of polygons, a faster method is possible: Lee & Preparata (1979) presented an algorithm to construct the kernel in linear time. Monotone polygon Franco
Star-shaped_polygon
Set of basic shapes which assemble into a polygon
been studied, including: spiral shapes, star polygons and monotone polygons. See for a survey. Polygon covering – a related problem in which the pieces
Polygon_partition
NP-hard problem in combinatorial optimization
accepted. The bitonic tour of a set of points is the minimum-perimeter monotone polygon that has the points as its vertices; it can be computed efficiently
Travelling_salesman_problem
Type of geometry processing
for Boolean operations on polygons can be found in References below. Boolean operations on convex polygons and monotone polygons of the same direction may
Boolean operations on polygons
Boolean_operations_on_polygons
Family of problems in computational geometry
A (vertical) monotone chain is a path such that the y-coordinate never increases along the path. A simple polygon is (vertical) monotone if it is formed
Point_location
polygons including star-shaped polygons, spiral polygons, and monotone polygons; non-simple polygons; prison yard problems, in which the guards must view
Art Gallery Theorems and Algorithms
Art_Gallery_Theorems_and_Algorithms
Combinatorial algorithm
finding the minimum value in each row of an implicitly defined totally monotone matrix. It is named after the initials of its five inventors, Peter Shor
SMAWK_algorithm
is a generalization of the two-dimensional geometric object, the monotone polygonal chain. As the name may suggest, a major application area of polyhedral
Polyhedral_terrain
Class of algorithms in computational geometry
polygon's boundary, is described later in a separate subsection. If not all points are on the same line, then their convex hull is a convex polygon whose
Convex_hull_algorithms
2026 film score by Ludwig Göransson
Göransson adds a lovely monotone layer of woodwinds or a keening chorus that sounds like the oldest song on Earth." Jake Kleinman of Polygon called it "a masterful
The_Odyssey_(soundtrack)
Sums vector sets A and B by adding each vector in A to each vector in B
11003. Oks, Eduard; Sharir, Micha (2006), "Minkowski Sums of Monotone and General Simple Polygons", Discrete & Computational Geometry, 35 (2): 223–240, doi:10
Minkowski_addition
Unsolved problem about inscribing a square in a Jordan curve
parallel to n ( p ) {\displaystyle n(p)} . Locally monotone curves include all types of polygons, all closed convex curves, and all piecewise C 1 {\displaystyle
Inscribed_square_problem
Straight path on a curved surface or a Riemannian manifold
surfaces an eikonal-equation solver originally formulated on regular grids: a monotone upwind finite-difference scheme builds the distance function by sweeping
Geodesic
Complexity class of problems
this function? Monotone dualization: given CNF and DNF formulas for monotone Boolean functions, do they represent the same function? Monotone self-duality:
NP-intermediate
American voice actor
outcast character and noted that portraying him was challenging due to his monotone voice. In March 2024, Le was announced to be the English voice of Sung
Aleks_Le
Boolean satisfiability problem restricted to a planar incidence graph
via a reduction from planar monotone rectilinear 3SAT. This is the problem of partitioning a polygon into simpler polygons such that the total length of
Planar_SAT
Video games by developer/publisher
Archived from the original on 2009-04-08. Retrieved 2011-07-06. "Soul Eater: Monotone Princess". GameSpot. Archived from the original on 2009-01-30. Retrieved
List of Square Enix video games
List_of_Square_Enix_video_games
Measure of similarity between curves
a path from the lower left corner to the upper right corner, which is monotone both in the horizontal and in the vertical direction. In addition to measuring
Fréchet_distance
American animated television series
flat-out resents them, much to their displeasure. He often talks in a monotone and is quite submissive. According to Megan Dong, the creation of Comfortable
Centaurworld
Sufficiently long sequences of numbers have long monotonic subsequences
ISBN 978-0-8176-4841-1 Steele, J. Michael (1995), "Variations on the monotone subsequence theme of Erdős and Szekeres", in Aldous, David; Diaconis, Persi;
Erdős–Szekeres_theorem
both Frank Miller's Sin City and other Japanese and Western comics. This monotone coloring is only broken by blood that comes from attacking and killing
List of commercial failures in video and arcade games
List_of_commercial_failures_in_video_and_arcade_games
Online community of Twitter users
the most official unofficial fan source" that can "take on a corporate monotone on par with many singers' own junket." An artist's fanbase is often attached
Stan_Twitter
Japanese animation studio
Eureka Seven vol. 2: The New Vision (Bandai, May 11, 2006) Soul Eater: Monotone Princess (Square Enix, September 25, 2008) Fullmetal Alchemist: Prince
Bones_(studio)
Graph drawn with all edges intersecting
thrackles drawn in such a way that every edge is an x {\displaystyle x} -monotone curve, crossed at most once by every vertical line. Lovász, Pach & Szegedy
Thrackle
Fictional character in the Overwatch franchise
spheres and prayer to "reload" them. He additionally praised Zenyatta's monotone voice as "excellently chill", feeling that even in moments of failure it
Zenyatta_(Overwatch)
Final Fantasy character
fact that he is never seen blinking or breathing, and his voice is always monotone and calm. In the film, the staff stated that his strength had considerably
Sephiroth_(Final_Fantasy)
Linear interpolation: a method of curve fitting using linear polynomials Monotone cubic interpolation: a variant of cubic interpolation that preserves monotonicity
List_of_algorithms
American adult animated sitcom
red hair and a beard much like his voice actor, and speaks in a deep, monotone voice. Jim is a genius at all things electronic, whether it's electronic
Mission_Hill_(TV_series)
Graph of the vertices and edges of a demihypercube
a hypercube as a spanning subgraph, it inherits from the hypercube all monotone graph properties, such as the property of containing a Hamiltonian cycle
Halved_cube_graph
conjecture is known to be true for x-monotone topological graphs. A topological graph is said to be x-monotone if every vertical line intersects every
Topological_graph
1971 single by Don McLean
narrator who is rejected in favor of another man for the prom, and The Monotones' The Book of Love ("Did you write the book of love"). Many additional
American_Pie_(song)
Fictional character
still criticized his interactions with non-playable characters for its monotone style. GamesRadar enjoyed Ryo's story for its mix of fight scenes similar
Ryo_Hazuki
13, 2007 November 20, 2007 August 28, 2008 August 28, 2008 Soul Eater: Monotone Princess Square Enix Bones Square Enix 2008-09-25JP September 25, 2008
List_of_Wii_games
2021 superhero film by James Gunn
designer Beth Mickle said Gunn wanted the film to be "grey and drab and monotone" until the characters arrive in Corto Maltese, which he wanted to "explode
The_Suicide_Squad_(film)
Mexican-American stand-up comedian and actor (born 1955)
during his tenure as host, the doo-wop hit "The Book of Love" by The Monotones was used as its theme song). El Show de Paul Rodriguez was on Univision
Paul_Rodriguez_(actor)
Degrees of separation from Paul Erdős
alphabetically earlier author to the alphabetically later author and defining the monotone Erdős number of an author to be the length of a longest path from Erdős
Erdős_number
On the existence of hyperplanes separating disjoint convex sets
Golshtein, E. G.; Tretyakov, N.V. (1996). Modified Lagrangians and monotone maps in optimization. New York: Wiley. p. 6. ISBN 0-471-54821-9.{{cite
Hyperplane_separation_theorem
Type of chart
spider web charts, star charts, star plots, cobweb charts, irregular polygons, polar charts, and Kiviat diagrams. It is equivalent to a parallel coordinates
Radar_chart
Subdivision of the plane by lines
set of lines. An arrangement consists of bounded and unbounded convex polygons, the cells of the arrangement, line segments and rays, the edges of the
Arrangement_of_lines
Curve that winds around a central point
Jiachuan; Wang, Kanchang; Wang, Shuchun (2004). "Designing fair curves using monotone curvature pieces". Computer Aided Geometric Design. 21 (5): 515–527. doi:10
Spiral
Number of balls of a given size needed to cover a given space
non-increasing in r and non-decreasing in K. The internal covering number is monotone in r but not necessarily in K. The following properties relate to covering
Covering_number
2011 single by Selena Gomez & the Scene
mixed reviews from music critics, who criticized its lyrics and Gomez's monotone vocals. John Bergstrom of PopMatters expressed a mixed opinion about the
Love_You_like_a_Love_Song
American animated television series
Rodger Bumpass described his character Squidward as "a very nasally, monotone kind of guy." Bumpass found Squidward interesting due to his range of emotions
SpongeBob_SquarePants
Method for speeding related binary searches
location in a monotone subdivision, that is, a partition of the plane into polygons such that any vertical line intersects any polygon in at most two
Fractional_cascading
among 1950s bands (e.g., Dick Dale and the Del-Tones, The Quin-Tones, The Monotones, The Cleftones, and The Harptones). Carpenter said the name is intentionally
List of musician and band name etymologies
List_of_musician_and_band_name_etymologies
Preorder on vectors of real numbers
Cambridge University Press, ISBN 978-0-521-46713-1 Majorization and Matrix Monotone Functions in Wireless Communications (2007) Eduard Jorswieck and Holger
Majorization
Japanese animation studio
Hug Nanda Dialogue+ December 21, 2022 Shirayuki Eve December 23, 2022 Monotone Yoasobi October 1, 2024 Created for Fureru. Co-production with Ijigen Tokyo
CloverWorks
Comic book antihero
in Justice League Unlimited, mimics Rorschach's speaking patterns and monotone voice and his reputation for being crazy by the other heroes. In the episode
Rorschach_(character)
Fictional character
character". Adam's distinctive voice is close to Toufexis's own, using a lower monotone style to both allow easy player identification and as a homage to Deus
Adam_Jensen
1993–1994 American animated television series
Sally uses to hack into Robotnik's technology. Nicole speaks in a female monotone, and exhibits artificial intelligence. It is indicated that Sally received
Sonic the Hedgehog (TV series)
Sonic_the_Hedgehog_(TV_series)
Motion of a curve based on its curvature
by approximating the curve as a polygon and using the finite difference method to calculate the motion of each polygon vertex. Alternative methods include
Curve-shortening_flow
Classical problem in combinatorics
subset of the hypotheses whose effects include all of the observations. Monotone dualization is a computational problem equivalent to either listing all
Set_cover_problem
Video games by developer/publisher
original on 2012-02-07. Retrieved 2013-06-11. "Press Release 20060915 - monotone" (PDF) (in Japanese). Square Enix. Archived (PDF) from the original on
List of Square Enix mobile games
List_of_Square_Enix_mobile_games
Visual presentation on some surface
Pythagorean theorem. In art, "graphics" is often used to distinguish work in a monotone and made up of lines, as opposed to painting. Drawing generally involves
Graphics
Mathematical operator
of a fixed point theorem for J. Consider the one-step operator J of a monotone logic. This is the operator associating any set X of formulas with the
Closure_operator
English affixes added before a word
micro- small microbacillus, microscope mono-, mon- sole, only monogamy, monotone, monosyllabic, monomial, monobrow, monarch multi-, mult- many multicultural
English_prefix
Forgejo Fossil Git Git-annex GNU arch Hgsubversion Kallithea Mercurial Monotone OpenGrok QVCS Revision Control System RhodeCode Source Code Control System
List of free and open-source software packages
List_of_free_and_open-source_software_packages
hypertonia, hypertonic, hypotenuse, hypotonia, hypotonic, isotonic, microtone, monotone, monotonic, monotonous, monotony, neoteny, octatonic, oxytone, paroxytone
List of Greek and Latin roots in English/P–Z
List_of_Greek_and_Latin_roots_in_English/P–Z
Finite collection of distinct objects
amorphous set.) II-finite. Every non-empty ⊆ {\displaystyle \subseteq } -monotone set of subsets of S {\displaystyle S} has a ⊆ {\displaystyle \subseteq
Finite_set
Puella Magi Madoka Magica character
thought Homura would be a "monotone" character like Yuki Nagato from Haruhi Suzumiya. Vee said she wanted to play her "monotone" but after learning about
Homura_Akemi
Type of random mathematical object
inhomogeneous Poisson process can be transformed into a homogeneous by a monotone transformation or mapping, which is achieved with the inverse of Λ {\displaystyle
Poisson_point_process
Japanese video game director (born 1971)
(2015-01-21). "Overworked but happy: The man behind Final Fantasy 15 and Type-0". Polygon. Archived from the original on 2016-03-15. Retrieved 2016-02-12. Sato (April
Hajime_Tabata
special case of cubic Hermite splines without self-intersections or cusps Monotone cubic interpolation Hermite spline Bézier curve De Casteljau's algorithm
List of numerical analysis topics
List_of_numerical_analysis_topics
Value to which an infinite sequence tends
then lim n → ∞ c n = L {\displaystyle \lim _{n\to \infty }c_{n}=L} . (Monotone convergence theorem) If a n {\displaystyle a_{n}} is bounded and monotonic
Limit_of_a_sequence
On tangency patterns of circles
strongly monotone drawings of polyhedral graphs. These are straight-line drawings in which every two vertices are connected by a polygonal path that
Circle_packing_theorem
preparation theorem (singularity theory) Mean value theorem (calculus) Monotone convergence theorem (mathematical analysis) Müntz–Szász theorem (functional
List_of_theorems
Fictional kingdom inhabited by hand puppet characters, created by Mr. Rogers
two-toned purple-colored giant panda from Planet Purple with a robotic, monotone voice. He arrives in the neighborhood by teleporting, which is "The Purple
Neighborhood_of_Make-Believe
Branch of mathematics
behavior can be transferred to the Lebesgue integral. One has theorems like monotone convergence, Fatou's lemma, and the dominated convergence theorem that
Mathematical_analysis
Multidimensional data visualization
The bagplot consists of three nested polygons, called the "bag", the "fence", and the "loop". The inner polygon, called the bag, is constructed on the
Bagplot
Mathematical and computational problem
most 7/4, and an asymptotic worst-case ratio of 1.691 for any concave and monotone cost function. Cohen, Keller, Mirrokni and Zadimoghaddam study a setting
Bin_packing_problem
Church in Victoria, Australia
stencilling of the sanctuary and side chapels was lost in the 1960s to a monotone covering of paint. By the nineties much of the external fabric was dangerously
St Mary Star of the Sea, West Melbourne
St_Mary_Star_of_the_Sea,_West_Melbourne
Hash function that is suitable for use in cryptography
file; several source code management systems, including Git, Mercurial and Monotone, use the sha1sum of various types of content (file content, directory trees
Cryptographic_hash_function
Fictional universe of a video game series
communicating with other species as their speech patterns come across as monotone and difficult to comprehend. The Hanar, an overly polite and philosophically
Universe_of_Mass_Effect
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