|
Orthogonal Polygon
A 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 are a special case of isothetic polygons. In many cases another definition is preferable: a rectilinear polygon is a polygon with sides parallel to the axes of Cartesian coordinates. The distinction becomes crucial when spoken about sets of polygons: the latter definition would imply that sides of all polygons in the set are aligned with the same coordinate axes. Within the framework of the second definition it is natural to speak of horizontal edges and vertical edges of a rectilinear polygon. Rectilinear polygons are also known as orthogonal polygons. Other terms in use are iso-oriented, axis-aligned, and axis-oriented polygons. These adjectives are less confusing when the polygons of this type are rectangles, and the term axis-aligned rectangle is preferred, although orthogonal rectangle and rectilinear rectangle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rectilinear Polygons
Rectilinear means related to a straight line; it may refer to: * Rectilinear grid, a tessellation of the Euclidean plane * Rectilinear lens, a photographic lens * Rectilinear locomotion, a form of animal locomotion * Rectilinear polygon, a polygon whose edges meet at right angles * Rectilinear propagation, a property of waves * Rectilinear Research Corporation, a now defunct manufacturer of high-end loudspeakers * Rectilinear style, the third historical division of English Gothic architecture * Rectilinear motion or linear motion is motion along a straight line * Rectilinear prophecy, where a straight line can be drawn from the prophecy to the fulfillment without any branches as in the case of typological interpretations * Near-rectilinear halo orbit, a highly-elliptical orbit around a Lagrangian point of a moon, that due to the moons orbital movement, will be nearly rectilinear in some frames of reference. See also * Linear (other) The word linear comes from the Latin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simple Rectilinear Polygon With Squares
Simple or SIMPLE may refer to: * Simplicity, the state or quality of being simple Arts and entertainment * ''Simple'' (album), by Andy Yorke, 2008, and its title track * "Simple" (Florida Georgia Line song), 2018 * "Simple", a song by Johnny Mathis from the 1984 album ''A Special Part of Me'' * "Simple", a song by Collective Soul from the 1995 album '' Collective Soul'' * "Simple", a song by Katy Perry from the 2005 soundtrack to '' The Sisterhood of the Traveling Pants'' * "Simple", a song by Khalil from the 2017 album '' Prove It All'' * "Simple", a song by Kreesha Turner from the 2008 album '' Passion'' * "Simple", a song by Ty Dolla Sign from the 2017 album ''Beach House 3'' deluxe version * ''Simple'' (video game series), budget-priced console games Businesses and organisations * Simple (bank), an American direct bank * SIMPLE Group, a consulting conglomeration based in Gibraltar * Simple Shoes, an American footwear brand * Simple Skincare, a British brand of so ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intersection (set Theory)
In set theory, the intersection of two sets A and B, denoted by A \cap B, is the set containing all elements of A that also belong to B or equivalently, all elements of B that also belong to A. Notation and terminology Intersection is written using the symbol "\cap" between the terms; that is, in infix notation. For example: \\cap\=\ \\cap\=\varnothing \Z\cap\N=\N \\cap\N=\ The intersection of more than two sets (generalized intersection) can be written as: \bigcap_^n A_i which is similar to capital-sigma notation. For an explanation of the symbols used in this article, refer to the table of mathematical symbols. Definition The intersection of two sets A and B, denoted by A \cap B, is the set of all objects that are members of both the sets A and B. In symbols: A \cap B = \. That is, x is an element of the intersection A \cap B if and only if x is both an element of A and an element of B. For example: * The intersection of the sets and is . * The number 9 is in t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean Operations On Polygons
Boolean operations on polygons are a set of Boolean operations (AND, OR, NOT, XOR, ...) operating on one or more sets of polygons in computer graphics. These sets of operations are widely used in computer graphics, CAD, and in EDA (in integrated circuit physical design and verification software). Algorithms * Greiner–Hormann clipping algorithm * Vatti clipping algorithm * Sutherland–Hodgman algorithm (special case algorithm) * Weiler–Atherton clipping algorithm (special case algorithm) Uses in software Early algorithms for Boolean operations on polygons were based on the use of bitmaps. Using bitmaps in modeling polygon shapes has many drawbacks. One of the drawbacks is that the memory usage can be very large, since the resolution of polygons is proportional to the number of bits used to represent polygons. The higher the resolution is desired, the more the number of bits is required. Modern implementations for Boolean operations on polygons tend to use plane sweep ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthogonal Convex Hull
In geometry, a set is defined to be orthogonally convex if, for every line that is parallel to one of standard basis vectors, the intersection of with is empty, a point, or a single segment. The term "orthogonal" refers to corresponding Cartesian basis and coordinates in Euclidean space, where different basis vectors are perpendicular, as well as corresponding lines. Unlike ordinary convex sets, an orthogonally convex set is not necessarily connected. The orthogonal convex hull of a set is the intersection of all connected orthogonally convex supersets of . These definitions are made by analogy with the classical theory of convexity, in which is convex if, for every line , the intersection of with is empty, a point, or a single segment. Orthogonal convexity restricts the lines for which this property is required to hold, so every convex set is orthogonally convex but not vice versa. For the same reason, the orthogonal convex hull itself is a subset of the convex hu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthogonal Range Searching
In computer science, the range searching problem consists of processing a set ''S'' of objects, in order to determine which objects from ''S'' intersect with a query object, called the ''range''. For example, if ''S'' is a set of points corresponding to the coordinates of several cities, find the subset of cities within a given range of latitudes and longitudes. The range searching problem and the data structures that solve it are a fundamental topic of computational geometry. Applications of the problem arise in areas such as geographical information systems (GIS), computer-aided design (CAD) and databases. Variations There are several variations of the problem, and different data structures may be necessary for different variations. In order to obtain an efficient solution, several aspects of the problem need to be specified: * Object types: Algorithms depend on whether ''S'' consists of points, lines, line segments, boxes, polygons.... The simplest and most studied ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polyhedron
In geometry, a polyhedron (plural polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is the convex hull of finitely many points, not all on the same plane. Cubes and pyramids are examples of convex polyhedra. A polyhedron is a 3-dimensional example of a polytope, a more general concept in any number of dimensions. Definition Convex polyhedra are well-defined, with several equivalent standard definitions. However, the formal mathematical definition of polyhedra that are not required to be convex has been problematic. Many definitions of "polyhedron" have been given within particular contexts,. some more rigorous than others, and there is not universal agreement over which of these to choose. Some of these definitions exclude shapes that have often been counted as polyhedra (such as the self-crossing polyhedra) or include shapes that are often not considered as valid polyhedr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
T-square (fractal)
In mathematics, the T-square is a two-dimensional fractal. It has a boundary of infinite length bounding a finite area. Its name comes from the drawing instrument known as a T-square.Dale, Nell; Joyce, Daniel T.; and Weems, Chip (2016). ''Object-Oriented Data Structures Using Java'', p.187. Jones & Bartlett Learning. . "Our resulting image is a fractal called a T-square because with it we can see shapes that remind us of the technical drawing instrument of the same name." Algorithmic description It can be generated from using this algorithm: # Image 1: ## Start with a square. (The black square in the image) # Image 2: ## At each convex corner of the previous image, place another square, centered at that corner, with half the side length of the square from the previous image. ## Take the union of the previous image with the collection of smaller squares placed in this way. # Images 3–6: ## Repeat step 2. The method of creation is rather similar to the ones used to cre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monotone Polygon
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. 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''. Properties Assume that ''L'' coincides with the ''x''-axis. Then the leftmost and rightmost vertices of a monotone polygon decompose its boundary into two monotone polygonal chains such that when the vertices of any chain are being traversed in th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthogonally Convex
In geometry, a set is defined to be orthogonally convex if, for every line that is parallel to one of standard basis vectors, the intersection of with is empty, a point, or a single segment. The term "orthogonal" refers to corresponding Cartesian basis and coordinates in Euclidean space, where different basis vectors are perpendicular, as well as corresponding lines. Unlike ordinary convex sets, an orthogonally convex set is not necessarily connected. The orthogonal convex hull of a set is the intersection of all connected orthogonally convex supersets of . These definitions are made by analogy with the classical theory of convexity, in which is convex if, for every line , the intersection of with is empty, a point, or a single segment. Orthogonal convexity restricts the lines for which this property is required to hold, so every convex set is orthogonally convex but not vice versa. For the same reason, the orthogonal convex hull itself is a subset of the convex hull of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Polygon
In geometry, a convex polygon is a polygon that is the boundary of a convex set. This means that the line segment between two points of the polygon is contained in the union of the interior and the boundary of the polygon. In particular, it is a simple polygon (not self-intersecting). Equivalently, a polygon is convex if every line that does not contain any edge intersects the polygon in at most two points. A strictly convex polygon is a convex polygon such that no line contains two of its edges. In a convex polygon, all interior angles are less than or equal to 180 degrees, while in a strictly convex polygon all interior angles are strictly less than 180 degrees. Properties The following properties of a simple polygon are all equivalent to convexity: *Every internal angle is strictly less than 180 degrees. *Every point on every line segment between two points inside or on the boundary of the polygon remains inside or on the boundary. *The polygon is entirely contained in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
