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Rotating Calipers
In computational geometry, the method of rotating calipers is an algorithm design technique that can be used to solve optimization problems including finding the width or diameter (computational geometry), diameter of a set of points. The method is so named because the idea is analogous to rotating a spring-loaded vernier caliper around the outside of a convex polygon. Every time one blade of the caliper lies flat against an edge of the polygon, it forms an antipodal point, antipodal pair with the point or edge touching the opposite blade. The complete "rotation" of the caliper around the polygon detects all antipodal pairs; the set of all pairs, viewed as a graph, forms a thrackle. The method of rotating calipers can be interpreted as the Duality (projective geometry), projective dual of a sweep line algorithm in which the sweep is across slopes of lines rather than across - or -coordinates of points. History The rotating calipers method was first used in the dissertation of M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Rotating Caliper 3x2
Rotation or rotational/rotary motion is the circular movement of an object around a central line, known as an ''axis of rotation''. A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis intersecting anywhere inside or outside the figure at a ''center of rotation''. A solid figure has an infinite number of possible axes and angles of rotation, including chaotic rotation (between arbitrary orientations), in contrast to rotation around a axis. The special case of a rotation with an internal axis passing through the body's own center of mass is known as a spin (or ''autorotation''). In that case, the surface intersection of the internal ''spin axis'' can be called a ''pole''; for example, Earth's rotation defines the geographical poles. A rotation around an axis completely external to the moving body is called a revolution (or ''orbit''), e.g. Earth's orbit around the Sun. The ends of the external ''axis of revolution'' can be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Diameter (computational Geometry)
In computational geometry, the diameter of a finite set of points or of a polygon is its diameter as a set, the largest distance between any two points. The diameter is always attained by two points of the convex hull of the input. A trivial brute-force search can be used to find the diameter of n points in time O(n^2) (assuming constant-time distance evaluations) but faster algorithms are possible for points in low dimensions. Static 2d input In two dimensions, the diameter can be obtained by computing the convex hull and then applying the method of rotating calipers. This involves finding two parallel support lines for the convex hull (for instance vertical lines through the two vertices with minimum and maximum x-coordinate) and then rotating the two lines through a sequence of discrete steps that keep them as parallel lines of support until they have rotated back to their original orientation. The diameter is the maximum distance between any pair of convex hull vertices ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Smallest Enclosing Box
{{disambiguation ...
Small means of insignificant size. Small may also refer to: Science and technology * SMALL, an ALGOL-like programming language * ''Small'' (journal), a nano-science publication * <small>, an HTML element that defines smaller text Arts and entertainment Fictional characters * Small, in the British children's show Big & Small Other uses * Small (surname) * List of people known as the Small * "Small", a song from the album ''The Cosmos Rocks'' by Queen + Paul Rodgers See also * Smal (other) * Smalls (other) Smalls may refer to: * Smalls (surname) * Camp Robert Smalls, a United States Naval training facility * Fort Robert Smalls, a Civil War redoubt * Smalls Creek, a northern tributary of the Parramatta River * Smalls Falls, a waterfall in Maine, USA ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Convex Hull
In geometry, the convex hull, convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined either as the intersection of all convex sets containing a given subset of a Euclidean space, or equivalently as the set of all convex combinations of points in the subset. For a Bounded set, bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around the subset. Convex hulls of open sets are open, and convex hulls of compact sets are compact. Every compact convex set is the convex hull of its extreme points. The convex hull operator is an example of a closure operator, and every antimatroid can be represented by applying this closure operator to finite sets of points. The algorithmic problems of finding the convex hull of a finite set of points in the plane or other low-dimensional Euclidean spaces, and its projective duality, dual problem of intersecting Half-space (geome ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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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. Strictly convex polygon A convex polygon is ''strictly'' convex if no line contains more than two vertices of the polygon. 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 less than or equal to 180 degrees. *Every point on every line segment between two points inside or on the boundary of the polygon remains inside or on the bou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Theory And Applications
A theory is a systematic and rational form of abstract thinking about a phenomenon, or the conclusions derived from such thinking. It involves contemplative and logical reasoning, often supported by processes such as observation, experimentation, and research. Theories can be scientific, falling within the realm of empirical and testable knowledge, or they may belong to non-scientific disciplines, such as philosophy, art, or sociology. In some cases, theories may exist independently of any formal discipline. In modern science, the term "theory" refers to scientific theories, a well-confirmed type of explanation of nature, made in a way consistent with the scientific method, and fulfilling the criteria required by modern science. Such theories are described in such a way that scientific tests should be able to provide empirical support for it, or empirical contradiction ("falsify") of it. Scientific theories are the most reliable, rigorous, and comprehensive form of scientific know ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Critical Support Line
Critical or Critically may refer to: *Critical, or critical but stable, medical states **Critical, or intensive care medicine *Critical juncture, a discontinuous change studied in the social sciences. *Critical Software, a company specializing in mission and business critical information systems *Critical theory, a school of thought that critiques society and culture by applying knowledge from the social sciences and the humanities *Critically endangered, a risk status for wild species *Criticality (status), the condition of sustaining a nuclear chain reaction Art, entertainment, and media * ''Critical'' (novel), a medical thriller written by Robin Cook * ''Critical'' (TV series), a Sky 1 TV series * "Critical" (''Person of Interest''), an episode of the American television drama series ''Person of Interest'' *"Critical", a song by Abhi the Nomad from the album ''Abhi vs the Universe'', 2021 *"Critical", a 1999 single by Zion I from the album ''Mind over Matter'' People *Cr1TiKaL ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |