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# Topic: Convex polygon

###### In the News (Fri 24 May 19)

 Convex Hull of a 2D Point Set or Polygon The convex hull of a geometric object (such as a point set or a polygon) is the smallest convex set containing that object. In this case, the boundary of a compact set is bounded by a polygon in 2D, and a polyhedron in 3D. The lower or upper convex chain is constructed using a stack algorithm almost identical to the one used for the Graham scan. geometryalgorithms.com /Archive/algorithm_0109/algorithm_0109.htm   (0 words)

 CONVEX QUADRILATERALS A polygon is a figure with three or more segments that lie on the same plane that intersect only at endpoints with no two segments colinear. A convex quadrilateral has the property that its diagonals lie within the interior of the quadrilateral and the sum of its four angles is always 360°. We can view the set of convex quadrilaterals in much the same way as we view a family tree showing the various ways in which individuals are related to others. www.gvsu.edu /math/students/bst/CONVEXQUADRILATERALS.htm   (812 words)

 Convex polygon Encyclopedia   (Site not responding. Last check: ) In geometry, a convex polygon is a simple polygon whose interior is a convex set. Every line segment between two vertices of the polygon does not go exterior to the polygon (i.e., it remains inside or on the boundary of the polygon). A concave polygon is often called re-entrant polygon (but in some cases the latter term has a different meaning). www.hallencyclopedia.com /topic/Convex_polygon.html   (297 words)

 Polygon - MSN Encarta These restrictions require that the sides of a polygon not cross each other and that pairs of sides intersect at their endpoints, which are called vertices. All polygons have an equal number of sides and vertices, and the sum of the interior angles of a polygon with n sides is 180° × (n – 2). Every interior angle of a convex polygon is less than 180°, while at least one angle of a concave polygon is greater than 180°. encarta.msn.com /encnet/refpages/RefArticle.aspx?refid=761553849   (282 words)

 Polygon - Wikipedia, the free encyclopedia If a polygon is simple, then its sides (and vertices) constitute the boundary of a polygonal region, and the term polygon sometimes also describes the interior of the polygonal region (the open area that this path encloses) or the union of both the region and its boundary. Polygons are named according to the number of sides, combining a Greek-derived numerical prefix with the suffix -gon, e.g. Equiangular polygon: a polygon whose vertex angles are equal (Williams 1979, p. en.wikipedia.org /wiki/Polygon   (971 words)

 SparkNotes: Polygons: Different Kinds of Polygons For a polygon to be convex, all of its interior angles must be less than 180 degrees. Another way to think of it is this: the diagonals of a convex polygon will all be in the interior of the polygon, whereas certain diagonals of a concave polygon will lie outside the polygon, on its exterior. The center of a regular polygon is the point from which all the vertices of the polygon are equidistant. www.sparknotes.com /math/geometry1/polygons/section2.rhtml   (247 words)

 Convex polygon - Wikipedia, the free encyclopedia In geometry, a convex polygon is a simple polygon whose interior is a convex set. Every line segment between two vertices of the polygon does not go exterior to the polygon (i.e., it remains inside or on the boundary of the polygon). A concave polygon is often called re-entrant polygon (but in some cases the latter term has a different meaning). en.wikipedia.org /wiki/Convex_polygon   (180 words)

 Polygon Summary Polygons are named to indicate the number of their sides or number of noncollinear points present in the polygon. If a polygon is simple, then its sides (and vertices) constitute the boundary of a polygonal region, and the term polygon sometimes also describes the interior of the polygonal region (the open area that this path encloses) or the union of both the region and its boundary. Polygons are named according to the number of sides, combining a Greek-derived numerical prefix with the suffix -gon, e.g. www.bookrags.com /Polygon   (1346 words)

 NOTES - Miscellaneous   (Site not responding. Last check: ) Convex Polygon In geometry, a convex polygon is a simple polygon whose interior is a convex set. to the polygon (i.e., it remains inside or on the boundary of the polygon). Equivalently, a polygon is strictly convex if every line segment between two vertices of the polygon is strictly interior to the polygon except at its endpoints. maxpages.com /mathnotesmodb/Archive_Notes - !http://maxpages.com/mathnotesmodb/Archive_Notes   (731 words)

 convex - Search Results - MSN Encarta Convex, shape of a surface curving outward, or toward the eye. For example, the outer surface of a ball appears convex. Every interior angle of a convex polygon is less than 180°, while at least one angle of a concave polygon is... ca.encarta.msn.com /convex.html   (134 words)

 Polygons Polygons are named according to the number of sides. If a polygon has no reflex angle, then it is said to be a convex polygon. A regular polygon's sides are all of the same length and its angles are the same size. www.mathsteacher.com.au /year7/ch09_polygons/05_polygon/pol.htm   (225 words)

 The Incredible Hull For a set of two-dimensional objects, their convex hull is the convex polygon of least area that completely encloses all of the objects. In the figure below, the three solid-lined objects on the left are enclosed in a dotted-line convex polygon, but that polygon is not their convex hull; on the right the same three objects are enclosed by their convex hull. Determining the convex hull of a set of objects is a fundamental problem in both computer graphics and computational geometry. acm.uva.es /p/v5/596.html   (553 words)

 PlanetMath: regular polygon   (Site not responding. Last check: ) In ordinary usage, a regular polygon is a convex polygon with all its sides equal and all its angles equal, that is, a polygon that is both equilateral and equiangular. Any regular polygon can be inscribed into a circle and a circle can be inscribed within it. This is version 10 of regular polygon, born on 2002-02-19, modified 2006-11-03. planetmath.org /encyclopedia/RegularPolygon.html   (338 words)

 Using Shape Analyses for Placement of Polygon Labels The intersection operation between the polygon layers creates a combination of soils/land use polygons that are inside of a parcel boundary and the boundary of the parcel subdivides the original soils/land use polygons (Figure 1). The term "pseudo-convex type polygon" means a polygon that is suitable to find a label location using algorithms for convex polygons and the result satisfies the objectives of label placement. It is enough to use pseudo-convex type polygon to find a label position for CAUV instead of creating a convex polygon from pseudo-convex type polygon because pseudo-convex type polygon is created from inside buffer so it is located inside the polygon and there is no big difference in label positions in both cases. gis.esri.com /library/userconf/proc01/professional/papers/pap388/p388.htm   (2592 words)

 Polygons   (Site not responding. Last check: ) convex polygon is a polygon that has no side in the interior of the polygon. If the diagonals of a polygon is drawn from one vertex, then the sum of the measures of the angles of the polygon can be calculated. A regular polygon is a polygon that is both equilateral and equiangular. library.thinkquest.org /10030/6poly.htm   (161 words)

 Polygons In other words, the x coordinate of the first polygon vertex is the first element of the x coordinate array, and the y coordinate of the first vertex is the first element of the y coordinate array. Perhaps the most important polygon display function is fg_polyfill(), which displays a filled convex polygon in screen space (the polygon is filled with pixels of the current color). Fastgraph considers a polygon to be convex if any horizontal line drawn through the polygon crosses the left edge exactly once and the right edge exactly once (excluding horizontal and zero-length edge segments). www.fastgraph.com /help/polygons.html   (1110 words)

 Point in Polygon Strategies If a number of points are to be tested against a polygon, it may be worthwhile determining whether the polygon is convex at the start and so be able to use a faster test. Unlike the convex test, where an intersection means that the test is done, all the triangles must be tested against the point for the non-convex test. The bounding box surrounding the polygon is split into a number of horizontal bins and the parts of the edges in a bin are kept in a list, sorted by the minimum X component. www.acm.org /pubs/tog/editors/erich/ptinpoly   (4418 words)

 Search Tuna Report for convex hull   (Site not responding. Last check: ) Problem: Find the smallest convex polygon containing all the points of S. Excerpt from The Algorithm Design Manual: Finding the convex hull of a set of points is the most elementary interesting problem in computational geometry, just as minimum spanning tree is the most elementary interesting problem in graph algorithms. Arbitrary Dimensional Convex Hull, Voronoi Diagram, Delaunay Triangulation.... convex hull The convex hull CH P of a polygon P is the smallest convex polygon that contains P.... www.searchtuna.com /ftlive2/285.html   (2320 words)

 x plus y files - Issue 6 - Convex polygons   (Site not responding. Last check: ) An equilateral triangle is convex, a square is convex, and a bee will always produce a natural hexagon, completely regular and convex, like the other two. What is true for this pentagon, and every concave polygon, is that we can always find two points within the shape, labelled here A and B, such that when we join them together the line passed out of the shape and back in again. It soon became clear that we only got convex polygons when the external angle was a factor of 360°. www.m-a.org.uk /xplusyfiles/home/issue_6/convex_polygons/index.htm   (357 words)

 Convex Hull - Algorithmist Computing the convex hull in Computational Geometry is what Sorting in many problems - it is perhaps the most basic, elementary function on a set of points. A polygon P is convex if and only if, for any two points A and B inside the polygon, the line segment AB is inside P. Any convex hull algorithm have the lower bound of θ(nlogn) through a reduction from Sorting, but it gives rises to Output Sensitive Algorithms, where the Complexity of the algorithm depends on the size of the output. www.algorithmist.com /index.php/Convex_Hull   (466 words)

 CS184 : Discussion Section 3 - Scan Conversion Distillation Convex polygons have the property that intersecting lines cross it either one (crossing a corner), two (crossing an edge, going through the polygon and going out the other edge), or an infinine number of times (if the interesecting line lies on an edge). Triangles are the only polygons which are guaranteed to be convex and planar, and we'll say why this is important later in the course. Concave polygons don't have the nice properties of convex polygons, and are thus more complicated. www.cs.berkeley.edu /~ddgarcia/cs184/r3   (1484 words)

 Computational Geometry For instance if you want to display a polygon on a computer screen, you need to be able to test whether each pixel of the screen corresponds to a point that's inside or outside the polygon, so you can tell what color to draw it. Convex polygons are typically much easier to deal with than non-convex ones. The smallest convex polygon containing a collection of points is known as the convex hull; this can also be defined as the intersection of the (infinitely many) halfspaces (portions of the plane on one side of a line) that contain all the points. www.ics.uci.edu /~eppstein/161/960307.html   (2502 words)

 polygonal labs » Calculating the Moment of Inertia of a non-regular convex Polygon First the polygon is triangulated by fanning around the centroid (center of mass), so that the centroid is part of every triangle. To calculate the ‘mass’ moment of inertia of a polygon you just have to multiply the area with a scalar that represents the density of the polygon, for example 2 [gramm per square meter]. I.e imagine the points A and B in the polygon shown in the article to be missing; the polygon would be concave. lab.polygonal.de /2006/08/17/calculating-the-moment-of-inertia-of-a-convex-polygon   (0 words)

 All Elementary Mathematics - Study Guide - Geometry - Polygon...   (Site not responding. Last check: ) A, angles of polygon; segments AC, AD, BE etc. are diagonals; AB, BC, CD, DE, EF, FA – sides of polygon; a sum of sides lengths AB + BC + … + FA is called a perimeter of polygon and signed as p (sometimes – 2p, then p – a half-perimeter). A hexagon on Fig.17 is a convex one; a pentagon ABCDE on Fig.19 is not a convex polygon, because its diagonal AD lies outside of it. A sum of interior angles in any convex polygon is equal to 180 (n – 2) deg, where n is a number of angles (or sides) of a polygon. www.bymath.com /studyguide/geo/sec/geo6.htm   (207 words)

 Glossary If one constructs a line segment between any two points of a convex object, then every point on the line segment is part of the object. The pentagram is a non-convex polygon; the Kepler-Poinsot solids are non-convex polyhedra. Various authors differ on the fine points of the definition, e.g., whether it is a solid or just the surface, whether it can be infinite, and whether it can have two different vertices that happen to be at the same location. www.georgehart.com /virtual-polyhedra/glossary.html   (0 words)

 Algorithmic Geometry 3-Dimensional VoronoiDiagram (VD), Delunay Triangulation (DT), and Convex Hull (CH) 2-Dimensional Voronoi Diagram, Delunay Triangulation, and Convex Hull -- Randomized incremental trapex of arrangement of polygons in the plane or on the sphere. www.personal.kent.edu /~rmuhamma/Compgeometry/compgeom.html   (827 words)

 How Many Regular Polyhedrons Are There In This or Any Universe? Regular polygons are thus convex polygons whose vertex angles are all equal (or congruent) and whose sides are likewise all congruent. Convex polygons have a very neat property: Take any vertex and draw all possible diagonals within the polygon. Since a triangle's three vertex angles have a sum of 180 degrees, an n-sided convex polygon's n vertices must have an angle sum of 180(n-2) degrees. www.iit.edu /~smile/ma8606.html   (1460 words)

 Convex Polygon Definition - Math Open Reference A convex polygon is defined as a polygon with all its interior angles less than 180°. A convex polygon is the opposite of a concave polygon. The area of a convex polygon can be found by dividing it into triangles and summing the triangle's areas. www.mathopenref.com /polygonconvex.html   (234 words)

 Computational Geometry Project: The Hertel-Mehlhorn Algorithm Polygon partitioning is an important preprocessing step for many geometric algorithms, because most geometric problems are simpler and faster on convex objects than on non-convex ones. Two types of partition of a polygon P may be distinguished: a partition by diagonals or a partition by segments. In some convex partition of a polygon by diagonals, call a diagonal d essential for vertex v if removal of d creates a piece that is non-convex at v. www.bringyou.to /compgeom   (1575 words)

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