Green indicates one intersection, blue indicates two intersections, and red indicates three or more. The top two polygons are monotone with respect to L while the bottom two are not.
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 at most twice.[1]
Similarly, a polygonal chain C is called monotone with respect to a straight line L, if every line orthogonal to L intersects C at most once.
For many practical purposes this definition may be extended to allow cases when some edges of P are orthogonal to L, and a simple polygon may be called monotone if a line segment that connects two points in P and is orthogonal to L lies completely in P.
Following the terminology for monotone functions, the former definition describes polygons strictly monotone with respect to L.
^Preparata, Franco P.; Shamos, Michael Ian (1985), Computational Geometry – An Introduction, Springer-Verlag, ISBN 0-387-96131-3, 1st edition; 2nd printing, corrected and expanded, 1988:; Russian translation, 1989
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...
{n(n+1)...(2n-4)}{(n-2)!}}} , a formula found by Leonhard Euler. A monotonepolygon can be triangulated in linear time with either the algorithm of A....
monotonepolygonal chain is open. In comparison, a monotonepolygon is a polygon (a closed chain) that can be partitioned into exactly two monotone chains...
and bargaining systems. Monotone class theorem, in measure theory Monotone convergence theorem, in mathematics Monotonepolygon, a property of a geometric...
These polygons include as special cases the convex polygons, star-shaped polygons, and monotonepolygons. The sum of external angles of a simple polygon is...
available for some special polygons. Simpler algorithms are possible for monotonepolygons, star-shaped polygons, convex polygons and triangles. The triangle...
convex. See Orthogonally convex rectilinear polygon . A monotone rectilinear polygon is a monotonepolygon which is also rectilinear. A T-square is a fractal...
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...
position. A monotonepolygon with respect to a line L is a polygon with the property that every line orthogonal to L intersects the polygon in a single...
been studied, including: spiral shapes, star polygons and monotonepolygons. See for a survey. Polygon covering – a related problem in which the pieces...
for Boolean operations on polygons can be found in References below. Boolean operations on convex polygons and monotonepolygons of the same direction may...
every non-collinear set of points has a polygonalization that is a monotonepolygon. This means that, with respect to some straight line (which may be...
accepted. The bitonic tour of a set of points is the minimum-perimeter monotonepolygon that has the points as its vertices; it can be computed efficiently...
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...
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...
is a generalization of the two-dimensional geometric object, the monotonepolygonal chain. As the name may suggest, a major application area of polyhedral...
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...
polygons including star-shaped polygons, spiral polygons, and monotonepolygons; non-simple polygons; prison yard problems, in which the guards must view...
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...
internet culture and video games. White's content is characterized by his monotone voice and deadpan comedic style. In addition, White is the co-founder and...
and when it is possible to take limits under the integral sign (via the monotone convergence theorem and dominated convergence theorem). While the Riemann...
Wesker in Resident Evil: Welcome to Raccoon City and said "Wesker lacks his monotone, conniving demeanor that's matched in the games" and "doesn't exude cocky...
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...
flat-out resents them, much to their displeasure. He often talks in a monotone and is quite submissive. Borg also voices a message bird in "The Ballad...
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