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The term '''complex polygon''' can mean two different things:
*In [[computer graphics]], as a [[polygon]] which is neither [[convex polygon|convex]] nor [[concave polygon|concave]].
*In [[geometry]], as a polygon in the [[unitary space|unitary]] plane, which has two [[complex number|complex]] dimensions.
 
==Computer graphics==
[[Image:Complex polygon.svg|160px|right|thumb|A complex (self-intersecting) pentagon]]
 
In the world of computer graphics, a complex polygon is a [[polygon]] which is neither [[convex polygon|convex]] nor concave. This includes any polygon which:
*Intersects itself. These include [[star polygon]]s such as the [[pentagram]]:[[Image:Pentagram green.svg|40px|A star polygon]]
 
*Has a boundary comprising discrete circuits, such as a polygon with a hole in it.
 
Therefore, unlike [[simple polygon]]s, a complex polygon may not always be interpreted as a simple polygonal region. Vertices are only counted at the ends of edges, not where edges intersect in space.
 
A formula relating an integral over a bounded region to a closed [[line integral]] may still apply when the "inside-out" parts of the region are counted negatively.
 
Moving around the polygon, the total amount one "turns" at the vertices can be any integer times 360°, e.g. 720° for a [[pentagram]] and 0° for an angular "eight".
 
See also: [[orbit (dynamics)]], [[Winding number]].
 
==Geometry==
In [[geometry]], a complex polygon is a polygon in the complex [[Hilbert space|Hilbert]] plane, which has two [[complex number|complex]] dimensions.
 
A [[complex number]] may be represented in the form <math>(a + ib)</math>, where <math>a</math> and <math>b</math> are [[real number]]s, and <math>i</math> is the square root of <math>-1</math>. A complex number lies in a [[complex plane]] having one real and one imaginary dimension, which may be represented as an [[Argand diagram]]. So a single complex dimension is really two dimensions, but of different kinds.
 
The [[unitary space|unitary]] plane comprises two such complex planes, which are [[orthogonal]] to each other. Thus it has two real dimensions <math>x</math> and <math>y,</math> and two imaginary dimensions <math>ix</math> and <math>iy</math>.
 
A complex polygon is a two-dimensional example of the more general [[complex polytope]] in higher dimensions.
 
In a ''real'' plane, a visible figure can be constructed as the ''real conjugate'' of some complex polygon.
 
== References ==
* [[Harold Scott MacDonald Coxeter|Coxeter, H. S. M.]], ''Regular Complex Polytopes'', Cambridge University Press, 1974.
 
== See also ==
* [[Simple polygon]]
* [[Convex and concave polygons]]
* [[Star polygon]]
* [[Convex hull]]
* [[Nonconvex uniform polyhedron]]
* [[Nonzero-rule]]
 
== External links ==
* [http://freespace.virgin.net/hugo.elias/graphics/x_polyd.htm Introduction to Polygons]
 
[[Category:Polygons]]
 
{{geometry-stub}}

Revision as of 21:44, 4 March 2014

Not perhaps one of the best-known of Singapore sights, the Spice Garden at Fort Canning Park is a veritable trove of Singapore's natural history, with over a hundred types of crops and timber lining its trails.

Mental property legislation impacts many areas of our lives, straight and not directly. Understanding mental property laws can therefore help us to understand the fundamental processes concerned in coping with intellectual property in its many manifestations. This course is helpful for many who work in varied business and industrial settings. It would also be suitable for these with an interest within the inventive industries. Many Singaporeans have been investing in property throughout the causeway lately, attracted by comparatively low costs. Nevertheless, those who need to exit their investments rapidly are prone to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell.

Search on the status of the current owner to be obtained from the Excessive Court docket by a lawyer Certificates of Statutory Completion (CSC) issued by the constructing authority that the constructing has been competed in accordance with all laws. It also denotes legal completion. Collective sale/en-bloc sale collective sale of plenty of owners of separate items in a non-public residential or business constructing Comparative Market Analysis (CMA) a report on the worth of a home in comparison with others offered on the current property sales market. Fixtures private property that has grow to be attached to the property so as to turn into part of the property itself.

You'll be able to search by postal code, kind, finances and location using TisProperty. Much like ninety nine.co, the app additionally utilises a map view to offer you a greater visual expertise. There are at the moment over 237,000 listings available on TisProperty. For extra information on the concessionary owner-occupier's tax charge, please check with IRAS' web site Every nation has its personal sort of wealth taxes corresponding to property tax, property tax, inheritance tax and capital positive aspects tax. The challenge is to design a wealth tax regime that's equitable, can't be easily prevented, and doesn't impede economic activities. Dear BuyersWe are promoting a unit @ veerasamy roadWe are only looking for Direct consumers (NO AGENT)Pls contact me @ 84252007 Serangoon / Thomson (D19-20) Far East Plaza Shop for rent

Singapore is dedicated to deepening the manpower experience throughout the IP worth chain. The IP Academy of Singapore, established in 2002, supplies professional training across a wide area together with IP administration, IP due diligence and transaction, and know-how transfer. The IP Academy also delivers graduate-level programmes such because the Graduate Certificates in IP Legislation (GCIP) and the MSc in IP Administration to lift the level of experience of IP professionals in Singapore.

Solely Singapore citizens and accepted individuals should purchase Landed 'residential property'as defined within the Residential Properties Act. Foreigners are eligible to purchaseunits in condominiums or apartments which are not landed dwelling homes. Foreignerswho wish to buy landed property in Singapore must first search the approval ofthe Controller of Residential Property. Your Lawyer's Role in a Property Buy SINGAPORE The Vehicle Affiliation of singapore property new (AAS) is buying a 5-storey industrial constructing on the corner of East Coast Highway and Chapel Close for $43 million. Extra element Orchard Road, Singapore 238868 Wing Tai Holdings Ltd Singapore Singapore Property — If the Minister is Fearful, Ought to We Be Too? (at Propwise.sg) Sale and Purchase Agreement

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