American polyconic projection

In the cartography of the United States, the American polyconic projection is a map projection used for maps of the United States and its regions beginning early in the 19th century. It belongs to the polyconic projection class, which consists of map projections whose parallels are non-concentric circular arcs except for the equator, which is straight. Often the American polyconic is simply called the polyconic projection.

The American polyconic projection was probably invented by Swiss-American cartographer Ferdinand Rudolph Hassler around 1825. It was commonly used by many map-making agencies of the United States from the time of its proposal until the middle of the 20th century.^[1] It is not used much these days, having been replaced by conformal projections in the State Plane Coordinate System.

Description

The American polyconic projection can be thought of as "rolling" a cone tangent to the Earth at all parallels of latitude. This generalizes the concept of a conic projection, which uses a single cone to project the globe onto. By using this continuously varying cone, each parallel becomes a circular arc having true scale, contrasting with a conic projection, which can only have one or two parallels at true scale. The scale is also true on the central meridian of the projection.

The projection is defined by:

${\begin{aligned}x&=\cot \varphi \sin \!{\bigl (}[\lambda -\lambda _{0}]\sin \varphi {\bigr )}\\y&=\varphi -\varphi _{0}+\cot \varphi \,{\Bigl (}1-\cos {\bigl (}[\lambda -\lambda _{0}]\sin \varphi {\bigr )}{\Bigr )}\end{aligned}}$

where:

$λ$ is the longitude of the point to be projected;
$φ$ is the latitude of the point to be projected;
$λ 0$ is the longitude of the central meridian;
$φ 0$ is the latitude chosen to be the origin at $λ 0$ .

To avoid division by zero, the formulas above are extended so that if $φ = 0$ , then $x = λ - λ 0$ and $y = - φ 0$ .

References

^ Flattening the Earth: Two Thousand Years of Map Projections, John P. Snyder, 1993, pp. 117-122, ISBN 0-226-76747-7.

External links

Weisstein, Eric W. "American polyconic projection". MathWorld.
Table of examples and properties of all common projections, from radicalcartography.net
An interactive Java Applet to study the metric deformations of the Polyconic Projection.

Map projection

By surface

Cylindrical

Mercator-conformal	Gauss–Krüger Transverse Mercator Oblique Mercator
Equal-area	Balthasart Behrmann Gall–Peters Hobo–Dyer Lambert Smyth equal-surface Trystan Edwards
Cassini Central Equirectangular Gall stereographic Gall isographic Miller Space-oblique Mercator Web Mercator

Pseudocylindrical

Equal-area	Collignon Eckert II Eckert IV Eckert VI Equal Earth Goode homolosine Mollweide Sinusoidal Tobler hyperelliptical
Kavrayskiy VII Wagner VI Winkel I and II

Conical

Pseudoconical

Azimuthal
(planar)

General perspective	Gnomonic Orthographic Stereographic
Equidistant Lambert equal-area

Bonne	Sinusoidal Werner
Bottomley	Sinusoidal Werner
Cylindrical	Balthasart Behrmann Gall–Peters Hobo–Dyer Lambert cylindrical equal-area Smyth equal-surface Trystan Edwards
Tobler hyperelliptical	Collignon Mollweide
Albers Briesemeister Eckert II Eckert IV Eckert VI Equal Earth Goode homolosine Hammer Lambert azimuthal equal-area Quadrilateralized spherical cube Strebe 1995

Equidistant in
some aspect

Gnomonic

Gnomonic

Loxodromic

Retroazimuthal
(Mecca or Qibla)

Planar	Gnomonic Orthographic Stereographic
Central cylindrical

Polyhedral

See also
Interruption (map projection) Latitude Longitude Tissot's indicatrix Map projection of the tri-axial ellipsoid

This cartography or mapping term article is a stub. You can help Wikipedia by expanding it.

Read other articles:

Музей архітектури і побуту «Старе село»

У Вікіпедії є статті про інші значення цього терміна: Старе Село. Музей архітектури і побуту«Старе село» Музей «Державної народної школи» 48°26′01″ пн. ш. 23°43′45″ сх. д. / 48.433730000027772178° пн. ш. 23.72940000002777694° сх. д. / 48.433730000027772178; 23.72940000002777694Координ�...

Ralph Hancock (landscape gardener)

British landscape gardener This article has multiple issues. Please help improve it or discuss these issues on the talk page. (Learn how and when to remove these template messages) This article possibly contains original research. Please improve it by verifying the claims made and adding inline citations. Statements consisting only of original research should be removed. (November 2014) (Learn how and when to remove this template message) This article includes a list of general references, bu...

David Koresh

David KoreshKoresh in 1987LahirVernon Wayne Howell(1959-08-17)17 Agustus 1959Houston, Texas, Amerika Serikat.Meninggal19 April 1993(1993-04-19) (umur 33)Mount Carmel CenterMcLennan County, Waco, Texas, Amerika Serikat.Sebab meninggalLuka tembak di kepalaPenemuan jasadMarkas Ranting DaudMcLennan County, Texas, Amerika Serikat.MakamPemakaman Memorial Park32°21′23″N 95°22′03″W / 32.35640°N 95.36750°W / 32.35640; -95.36750 (Memorial Park Ceme...

Göztepe S.K.

GöztepeNama lengkapGöztepe Spor KulübüJulukanGöz GözBerdiri14 Juni 1925; 98 tahun lalu (1925-06-14)dengan nama Göztepe Gençlik KulübüStadionGürsel Aksel Stadium(Kapasitas: 20,040)KetuaMehmet SepilManajerİlhan PalutLigaTFF 1. Lig2022–2023ke-7Situs webSitus web resmi klub Kostum kandang Kostum tandang Musim ini Göztepe Spor Kulübü atau Göztepe adalah klub sepak bola profesional Turki yang berbasis di daerah Göztepe dan Güzelyalı di kota İzmir. Kesuksesan terbesar...

Qingyuan

Qingyuan 清远市PrefekturDistrik QingchengLocation of Qingyuan in GuangdongQingyuanLocation in ChinaKoordinat (Qingyuan government): 23°40′55″N 113°03′22″E / 23.682°N 113.056°E / 23.682; 113.056Koordinat: 23°40′55″N 113°03′22″E / 23.682°N 113.056°E / 23.682; 113.056NegaraTiongkokProvinsiGuangdongDivisi tingkat County9Divisi tingkat Township53City seatDistrik QingchengLuas • Prefektur19.152,9 km2 (73...

Merkurius

Untuk kegunaan lain, lihat Merkurius (disambiguasi). Merkurius Gambar warna semu Merkurius oleh MESSENGERPenamaanNama alternatifUtarid (عطارد)Kata sifat bahasa InggrisMerkurian, Merkurial[1]Ciri-ciri orbit[4]Epos J2000Aphelion69.816.900 km0,466 697 SAPerihelion46.001.200 km0,307 499 SASumbu semimayor57.909.100 km0,387 098 SAEksentrisitas0,205 630[2]Periode orbit87,969 1 hari(0,240 846 tahun)Periode sinodis115,88 d[2]...

Science fiction convention

Science fiction fan gatherings This article's lead section may be too short to adequately summarize the key points. Please consider expanding the lead to provide an accessible overview of all important aspects of the article. (September 2017) Hugo Award winners at Worldcon 2005 in Glasgow, August 2005. Speculative fiction Alternate history List of alternate history fiction Retrofuturism Sidewise Award Writers Fantasy fiction Anime Fandom Fantasy art Fiction magazines Films Genres History Lege...

Susila (mitologi)

Artikel ini tidak memiliki referensi atau sumber tepercaya sehingga isinya tidak bisa dipastikan. Tolong bantu perbaiki artikel ini dengan menambahkan referensi yang layak. Tulisan tanpa sumber dapat dipertanyakan dan dihapus sewaktu-waktu.Cari sumber: Susila mitologi – berita · surat kabar · buku · cendekiawan · JSTOR Dalam mitologi Hindu, Susila (Dewanagari: सुशीला; ,IAST: Suśīlā, सुशीला) adalah anak Srikandi...

The Bohemian Girl

1843 Irish romantic opera For other uses, see The Bohemian Girl (disambiguation). The Bohemian GirlIrish Romantic opera by Michael William BalfeTitle page of the original librettoLibrettistAlfred BunnLanguageEnglishBased onLa gitanillaby Miguel de CervantesPremiere27 November 1843 (1843-11-27)Drury Lane Theatre, London The Bohemian Girl is an Irish Romantic opera composed by Michael William Balfe with a libretto by Alfred Bunn. The plot is loosely based on a Miguel de Cervantes...

XII Tactical Air Command

XII Tactical Air CommandP-47 Thunderbolts during the occupation of Germany[note 1]Active1942-1947Country United StatesBranch United States Air ForceRoleCommand of tactical unitsEngagementsMediterranean Theater of Operations[1]InsigniaPatch with unofficial XII Tactical Air Command emblem[2]Military unit The XII Tactical Air Command was a formation of the United States Army Air Forces. Its last assignment was with the United States Air Forces in Europe at Bad ...

Organisation des Nations unies pour l'éducation, la science et la culture

UNESCO Organisation des Nations unies pour l'éducation, la science et la culture Logo de l'Unesco Organe de l'ONU Type d'organisation Agence spécialisée de l'ONU Acronymes (en) UNESCO(fr) ONUESC (rare) Directrice générale Audrey Azoulay sous-Chef Xing Qu Statut Active Membres 194 États Siège Paris (7 place de Fontenoy, 75007, France) Budget 1,5 milliard de dollars (2022-2023[1]) Création 16 novembre 1945 Site web unesco.org Organisation parente Organisation des Nations unies...

Force India

Force IndiaSede India Regno UnitoSilverstone CategorieFormula 1 Dati generaliAnni di attivitàdal 2008 al 2018 Fondatore Vijay Mallya Michiel Mol Direttore Otmar Szafnauer Formula 1Anni partecipazioneDal 2008 al 2018 Miglior risultato4º posto (2016, 2017) Gare disputate212[1] Vittorie0 NoteErede della Spyker F1 e sostituita dalla Racing Point La Force India è stata una scuderia indiana di Formula 1 con sede a Silverstone, nel Regno Unito, di proprietà della società ...

James May

English television presenter and journalist For other people named James May, see James May (disambiguation). James MayMay in 2007BornJames Daniel May (1963-01-16) 16 January 1963 (age 61)Bristol, EnglandAlma materLancaster UniversityOccupation(s)Television presenter, author, columnist, journalistYears active1980 (1980)s–presentEmployer Amazon Prime Video Former employers: W. Chump & Sons BBC Channel 4 ITV Sky Autocar The Daily Telegraph Known for Driven (1998) ...

Club Atlético Osasuna

CA Osasuna Généralités Nom complet Club Atlético Osasuna Surnoms Gorritxoak / Los Rojillos (Les petits rouges)[1] Fondation 24 octobre 1920 Couleurs Rouge et bleu Stade Stade El Sadar (23 576 places) Siège Carretera Aranguren Pampelune Championnat actuel LaLiga EA Sports FC Président Luis Sabalza Entraîneur Jagoba Arrasate Joueur le plus capé Francisco Puñal (513) Meilleur buteur Sabino Andonegui (127) Site web osasuna.es Palmarès principal National[2] Championnat de deux...

Hak menentukan nasib sendiri

Protes terhadap perlakuan pemerintahan Presiden Soeharto terhadap Timor Timur di Belanda, 1986. Hak menentukan nasib sendiri (bahasa Inggris: right to self-determination) adalah hak setiap orang untuk ara bebas menentukan kehendaknya sendiri, khususnya dalam hal prinsip mengenai status politik dan kebebasan mengejar kemajuan di bidang ekonomi, sosial, serta budaya. Kepentingan akan menentukan nasib sendiri, oleh sebab itu terletak pada adanya kebebasan dalam membuat pilihan.[1] Na...

土库曼斯坦总统

土库曼斯坦总统土库曼斯坦国徽土库曼斯坦总统旗現任谢尔达尔·别尔德穆哈梅多夫自2022年3月19日官邸阿什哈巴德总统府（Oguzkhan Presidential Palace）機關所在地阿什哈巴德任命者直接选举任期7年，可连选连任首任萨帕尔穆拉特·尼亚佐夫设立1991年10月27日土库曼斯坦土库曼斯坦政府与政治国家政府土库曼斯坦宪法国旗国徽国歌立法機關（英语：National Council of Turkmenistan） ...

Son, Norway

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: Son, Norway – news · newspapers · books · scholar · JSTOR (January 2017) (Learn how and when to remove this message) Town in Akershus, NorwaySonTownSonCoordinates: 59°31′25″N 10°41′15″E / 59.52361°N 10.68750°E / 59.52361; 10....

John Hammill

American politician For the South African tennis player, see John Hammill (tennis). John Hammill24th Governor of IowaIn officeJanuary 15, 1925 – January 15, 1931LieutenantClem F. Kimball Arch W. McFarlanePreceded byNathan E. KendallSucceeded byDaniel Webster TurnerLieutenant Governor of IowaIn officeJanuary 13, 1921 – January 15, 1925GovernorN. E. KendallPreceded byErnest Robert MooreSucceeded byClem F. KimballMember of the Iowa SenateIn office1908–1913 Personal de...

Stasiun Nishi-Kokura

JA 27 JF 02 JI 02 Stasiun Nishi-Kokura西小倉駅 Stasiun Nishi-Kokura pada Maret 2010LokasiKokurakita-ku, KitakyushuJepangKoordinat33°53′19″N 130°52′27″E / 33.888631°N 130.874222°E / 33.888631; 130.874222Operator JR KyushuJalur■ Jalur Utama Kagoshima■ Jalur Utama NippōPenumpangFY20165.361 Lokasi pada petaJA 27 JF 02 JI 02 Stasiun Nishi-KokuraLokasi d...

Dear Zachary: A Letter to a Son About His Father

2008 American documentary film directed by Kurt Kuenne Dear Zachary: A Letter to a Son About His FatherTheatrical release posterDirected byKurt KuenneWritten byKurt KuenneProduced byKurt KuenneCinematographyKurt KuenneEdited byKurt KuenneMusic byKurt KuenneProductioncompanyMSNBC FilmsDistributed byOscilloscope LaboratoriesRelease dates January 2008 (2008-01) (Slamdance Film Festival) October 31, 2008 (2008-10-31) Running time93 minutesCountryUnited StatesLanguageE...

American polyconic projection

Description

See also

References

External links

Read other articles: