This document provides information about map projections and geographic coordinate systems. It discusses different types of geographic coordinate systems including spheroids, datums, and examples of North American datums. It also covers different types of map projections, how they work, and examples including Mercator, UTM, and others. The document provides details on how to perform geographic transformations between different coordinate systems and datums. It provides specifications for many common map projections supported in GIS software.
CIRM in collaboration with the Institute of Water Modelling, Dhaka, Bangladesh published a report on Flood Hazard Model for an Index Based Flood Insurance Products for Sirajganj District, Bangladesh.
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Understanding Coordinate Systems and Projections for ArcGISJohn Schaeffer
Everything you need to know to work with coordinate systems and projecting data in ArcGIS. The presentation starts by explaining the terminology, and then discusses the details you need to know to actually work successfully with coordinate systems, use the proper projections, and geographic transformations. This is a very practical look at a complex subject.
CIRM in collaboration with the Institute of Water Modelling, Dhaka, Bangladesh published a report on Flood Hazard Model for an Index Based Flood Insurance Products for Sirajganj District, Bangladesh.
DuPont Krytox Product Overview, H 58505 5Jim_Bradshaw
This Brochure provides a product overview of Krytox<sup>®</sup> lubricants including Properties, Performance Characteristics and offers a variety of Industrial Applications where this product range has been successfully applied.
Understanding Coordinate Systems and Projections for ArcGISJohn Schaeffer
Everything you need to know to work with coordinate systems and projecting data in ArcGIS. The presentation starts by explaining the terminology, and then discusses the details you need to know to actually work successfully with coordinate systems, use the proper projections, and geographic transformations. This is a very practical look at a complex subject.
To study for my art final, I decided instead of making flashcards and burying my face into a textbook, I would make a helpful powerpoint. While doing this, I realized how much I actually enjoy this subject.
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Spinoff is NASA's annual premier publication featuring successfully commercialized NASA technology. For more than 40 years, NASA has facilitated the transfer of its technology to the private sector, benefiting global competition and the economy.
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Similar to Sistemas de Información Geográfica: Understanding Map Projections (20)
1891 - Primera discusión semicientífica sobre Una Nave Espacial Propulsada po...Champs Elysee Roldan
La primera discusión semicientífica sobre una nave espacial propulsada por cohetes la realizó el alemán Hans Ganswindt, quien abordó los problemas de la propulsión no mediante la fuerza reactiva de los gases expulsados sino mediante la eyección de cartuchos de acero que contenían dinamita. Supuso que la explosión de una carga transferiría energía cinética a la pared de la nave espacial y la impulsaría en la dirección deseada. Supuso que múltiples explosiones proporcionarían suficiente velocidad para alcanzar la órbita y la velocidad de escape.
El 27 de mayo de 1891, pronunció un discurso público en la Filarmónica de Berlín, en el que introdujo su concepto de un vehículo galáctico(Weltenfahrzeug).
Ganswindt también exploró el uso de una estación espacial giratoria para contrarrestar la ingravidez y crear gravedad artificial.
1891 - 14 de Julio - Rohrmann recibió una patente alemana (n° 64.209) para s...Champs Elysee Roldan
El concepto del cohete como plataforma de instrumentación científica de gran altitud tuvo sus precursores inmediatos en el trabajo de un francés y dos Alemanes a finales del siglo XIX.
Ludewig Rohrmann de Drauschwitz Alemania, concibió el cohete como un medio para tomar fotografías desde gran altura. Recibió una patente alemana para su aparato (n° 64.209) el 14 de julio de 1891.
En vista de la complejidad de su aparato fotográfico, es poco probable que su dispositivo haya llegado a desarrollarse con éxito. La cámara debía haber sido accionada por un mecanismo de reloj que accionaría el obturador y también posicionaría y retiraría los porta películas. También debía haber sido suspendido de un paracaídas en una articulación universal. Tanto el paracaídas como la cámara debían ser recuperados mediante un cable atado a ellos y desenganchado de un cabrestante durante el vuelo del cohete. Es difícil imaginar cómo un mecanismo así habría resistido las fuerzas del lanzamiento y la apertura del paracaídas.
1890 –7 de junio - Henry Marmaduke Harris obtuvo una patente británica (Nº 88...Champs Elysee Roldan
El 7 de junio de 1890, por ejemplo, Henry Marmaduke Harris obtuvo una patente británica (Nº 8816) para "Máquinas aéreas con aerostatos" en las que el "coche... en forma de barco" estaba unido a un globo y era "impulsado por la reacción de los gases descargados a través de una boquilla... cuya dirección estaba controlada, relacionada con algún tipo de dispositivo o tecnología de dirección. ".
1886 -1887-El 12 de octubre de 1886 Alexandre Ciurcu recibió la patente franc...Champs Elysee Roldan
El 12 de octubre de 1886, Alexandre Ciurcu (alias Alexandru Churc 1854 - 1922) del Reino de Rumania, recibió la patente francesa nº 179.001 para un “Propulseur a Jtéaction” (“Propulsor de reacción"). En esta invención, había sido Con la ayuda del francés Just Buisson. Ambos consideraron el invento tan importante que también fue patentado en Alemania el 19 de octubre de 1886 (patente n° 39.964), en Inglaterra el 7 de junio de 1887 (n° 8.182) y en Bélgica el 8 de junio de 1887. (Nº 1 10. 77.754), en Italia el 17 de junio de 1887 tNo. 21.863), en Austria-Hungría el 21 de agosto 1887 (n° 41.129), y en Estados Unidos el 23 de julio de 1889 (n° 407.394).
1885 - 25 de Agosto - El Capitán Griffiths obtiene la Patente Británica No 10...Champs Elysee Roldan
1885 – 25 de agosto: El Capitán de Navío Tomas Griffiths obtuvo la Patente Británica No. 10,068 para “Mejora en la Propulsión a Chorro”
Esto es muy interesante por sí mismo; fue uno de los primeros usos del término "propulsión a chorro" aplicado específicamente a máquinas voladoras. Sin embargo, la patente cubre en gran medida las mismas características técnicas y aplicaciones que había presentado en su discurso ante la Real Sociedad Aeronáutica de Gran Bretaña en 1883 (sobre su concepto de "Un motor ligero y económico para la propulsión en el aire"; se concentró en sus ideas para un motor de una máquina voladora potencial, no en el avión en sí, sino que era aplicable a todo tipo de aparatos... ya sean globos o alas"), pero con una alteración extremadamente significativa en la redacción. "El chorro o chorros de vapor combinado de aire y gases", dice, "se entregan desde una boquilla en forma de botella en la atmósfera...".
Por lo tanto, no estaba descartando el vapor; también estaba incluyendo la posibilidad de gases continuos. Luego agrega: "Mi método está especialmente adaptado para el uso de combustible líquido...". Pero, curiosamente, la combustión aún queda fuera, o al menos la combustión directa, ya que menciona un "horno de caldera" para producir el vapor o los gases.
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1883- Konstantin Eduardovich Tsiolkovsky Prepara un manuscrito titulado Free ...Champs Elysee Roldan
El teórico ruso Konstantin E. Tsiolkovsky preparó un manuscrito titulado "Espacio libre" (Free Space), en el que exploraba la posibilidad de utilizar la fuerza reactiva para navegar por el espacio. Analizó el movimiento mecánico en el espacio y elaboró un esquema de una nave espacial, proponiendo el uso de un dispositivo giroscópico para estabilizar el vehículo. Tsiolkovski había sido admitido recientemente en la Sociedad de Física y Química de San Petersburgo tras haber entrado en contacto con el famoso químico ruso Dmitri Ivanovich Mendeleyev..
En resumen, Konstantin Eduardovich Tsiolkovsky, un destacado científico ruso, escribió un manuscrito titulado "Free Space" ("Espacio Libre" en español) en 1883. Este manuscrito es uno de los primeros trabajos de Tsiolkovsky relacionados con la exploración del espacio y la astronautica. En "Free Space", Tsiolkovsky aborda una variedad de temas relacionados con la física y la posibilidad de viajar y explorar el espacio exterior.
Algunos de los temas tratados en "Free Space" incluyen:
1. Propulsión espacial: Tsiolkovsky discute los principios de la propulsión y cómo podrían aplicarse para permitir que los humanos viajen por el espacio.
2. Gravedad y movimiento: Explora las leyes de la gravedad y cómo afectan el movimiento de los objetos en el espacio, así como las posibles formas de superar los desafíos gravitacionales en la exploración espacial.
3. Colonización del espacio: Tsiolkovsky también presenta ideas sobre la colonización del espacio y cómo los humanos podrían establecerse en otros planetas o lunas en el futuro.
4. Visión futurista: En su trabajo, Tsiolkovsky demuestra una visión futurista y especulativa sobre el potencial de la humanidad para explorar y aprovechar los recursos del cosmos.
"Free Space" sentó las bases para muchas de las ideas y teorías que Tsiolkovsky desarrollaría más adelante en su carrera, incluyendo sus conceptos sobre cohetes, propulsión espacial y la exploración humana del espacio. Sus ideas visionarias jugaron un papel crucial en el desarrollo posterior de la astronáutica y la exploración espacial, y Tsiolkovsky es considerado uno de los padres de la cosmonáutica moderna.
1882- 5 de Octubre: Nace el Padre de la Cohetería Moderna Robert Hutchings G...Champs Elysee Roldan
Generalmente reconocido como el "Padre de la Cohetería Moderna", Robert Hutchings Goddard nació en Worcester, Massachusetts. De niño se sintió atraído por la física y las matemáticas y absorbió los escritos de autores de ciencia ficción como Julio Verne y Herbert George Wells. A los 19 años escribió un artículo titulado "La Navegación Espacial" que no fue aceptado para su publicación. Impresionado por el potencial de los propulsores líquidos, Goddard comenzó en 1909 a realizar cálculos detallados sobre motores de cohetes mientras estudiaba en la Universidad Clark de Worcester. En 1911 obtuvo el doctorado y posteriormente se convirtió en profesor de física en Clark.
En 1914 se le concedieron patentes sobre cámaras de combustión, sistemas de suministro de propulsante y cohetes multietapa.
El único cohete estadounidense que salvó vidas con éxito fue el de Patrick
Cunningham, ex ballenero y ex presidente de la American Carrier Rocket Company de New Bedford, Massachusetts.
Patentó su primer modelo en 1882. El cohete Cunningham tenía una característica novedosa: la línea de vida estaba enrollada en un cilindro de acero que formaba la barra estabilizadora del cohete. En total medía 2,2 metros de largo y 8,75 centímetros de diámetro.
Pesaba 20 kilogramos y tenía un alcance de entre 300 metros y 765 metros dependiendo del peso de la línea de vida utilizada. En 1888 se proporcionaron al menos 20 estaciones. Sólo se sabe que todavía existe un espécimen: en el Museo de la Asociación Histórica de Luces Gemelas, Long Branch, Nueva Jersey.
1882 – 1895 - Sergei Sergeevich Nezhdanovsky avanzó por primera vez en la id...Champs Elysee Roldan
CASO DE ESTUDIO: COHETERÍA Y ASTRONÁUTICA: CONCEPTOS, TEORÍAS Y ANÁLISIS DESPUÉS DE 1880 - SOBRE LOS TRABAJOS DE S.S. NEZHDANOVSKY EN EL CAMPO DEL VUELO BASADO EN PRINCIPIOS REACTIVOS, 1880 - 1895
1882 - 1895 – Sergei Sergeevich Nezhdanovsky de nuevo retoma la posibilidad de producir aviones propulsados a reacción, discutiendo diferentes variantes de motores activados por la reacción de ácido carbónico, vapor de agua y aire comprimido.
En 1882, Nezhdanovsky volvió a plantearse la posibilidad de producir aviones a reacción;
aviones propulsados, discutiendo diferentes variantes de motores activados por la reacción de ácido carbónico, vapor de agua y aire comprimido. Expresó las ideas concretas de construir un motor a reacción "según el principio del cargador o de las ametralladoras de dos o tres cañones con el mismo fin de tener la posibilidad de regular la potencia y el “tiempo
del vuelo." Ese mismo año avanzó la idea de construir dos tipos de aviones a reacción más pesados que el aire, con y sin alas. También señaló la posibilidad de utilizar uno de los motores que había propuesto, que funcionaba con la reacción de aire comprimido, para el vuelo horizontal de aviones más ligeros que el aire ("un globo con forma de cigarro").
1879 – Trabajo de Propulsión en Máquinas Voladoras por Enrico ForlaniniChamps Elysee Roldan
En 1879, encontramos a otro pionero que concibió la idea de las máquinas voladoras propulsadas por cohetes. Se trata del talentoso y conocido ingeniero italiano Enrico Forlanini (1848-1930) que, de hecho, llegó a construir y experimentar con una máquina de este tipo utilizando verdaderos cohetes, pero también del tipo de pólvora. El modelo, sin embargo, sólo servía para probar el principio. Ya en 1877, Forlanini construyó y voló con éxito un helicóptero propulsado por vapor que, según el historiador de la aviación Gibbs-Smith, fue la segunda máquina de este tipo que tuvo éxito después del helicóptero propulsado por reacción del inglés William Henry Phillips demostrado en 1842.
1877- Trabajos en Propulsión de Maquínas Voladoras de: - Pennington -Abate- R...Champs Elysee Roldan
James Jackson Pennington (1819-1885) fue un agricultor y comerciante de la pequeña Henryville, en el norte del condado de Lawrence, Tennessee, Estados Unidos. También era inventivo y en 1872 ideó y construyó un prototipo de su máquina voladora "Aerial Bird" que utilizaba un ventilador y un mecanismo de muelle-reloj. Se desconoce si el prototipo era sólo un modelo o una máquina de tamaño real, pero al parecer voló muy brevemente.
El mismo año de la patente de Pennington apareció el folleto de siete páginas La Direzione delle Macchine Aerostatiche per Invenzione de Stanislao Abate (La dirección de la máquina aerostática por invención de Stanislao Abate), publicado privadamente en Salerno, Sicilia, Italia, que incluye interesantes representaciones de su arte.
Sin embargo, en la historia del desarrollo de la aeronáutica hubo sin duda otros pioneros en este aspecto que fueron mucho más sistemáticos y científicos. Uno de ellos fue el inglés Charles Blachford Mansfield (1819-1851), cuya obra de más de 500 páginas, Aerial Navigation, apareció también en 1877 (https://books.google.com.na/books?id=GzkDAAAAQAAJ&printsec=frontcover#v=onepage&q&f=false).
Finalmente, también en 1877, encontramos la patente británica del 15 de octubre de ese año de Charles Ogle Rogers para una "Máquina Militar" en la que proponía "Uno o más globos conectados por una línea o líneas" en los que los globos llevaran bombas explosivas que debían ser descargadas desde el aire contra un enemigo y los globos también "propulsados por los explosivos, o disparando cohetes... ".
También debemos mencionar que en el mismo año, el vicealmirante ruso Nikolai Mikhailovich Sokovnin (1811-1984), presentó sus ideas en el número de diciembre de 1877 de la revista francesa L'Aeronaute.
1876 - 27 de Enero - Patente Británica de John Buchanan -nº 327- también tit...Champs Elysee Roldan
1876 – 27 de Enero: Patente Británica de John Buchanan (nº 327) también titulada "Propulsión y Dirección".
Un ejemplo más auténtico de propulsión por reacción directa en máquinas voladoras se encuentra en la patente británica de John Buchanan (nº 327) de 27 de enero de 1876, también titulada "Propulsión y dirección".
1871 - 9 de Septiembre: Primeros Intentos No Demostrados de Propulsión de Coh...Champs Elysee Roldan
Lo encontramos en un curioso artículo del diario británico The Graphic (Londres) del 9 de septiembre de 1871 bajo el título "Recortes transatlánticos".
"El paracaídas no es un invento nuevo", comienza el artículo, "pero un viejo filósofo de Delaware, ambicioso de fama aeronáutica, perdió recientemente la vida al intentar utilizar este artilugio de una manera un tanto novedosa. Erigió en su jardín un enorme cohete celeste [un cohete pirotécnico propulsado por pólvora], a cuya cabeza ató un paracaídas de tal manera que... mientras el cohete celeste se elevaba hacia arriba, permanecía cerrado, pero se abría como un paraguas al descender y así amortiguaba su caída al suelo. En consecuencia, se ató al extremo inferior del palo, con la espoleta [es decir, la mecha] vuelta hacia él, para que el fuego no le hiriera, aplicó una luz [encendió la espoleta], y se fue zumbando por el aire a una velocidad enorme. Pero, ¡ay! del filósofo y de su ciencia... porque el cohete y su paracaídas fueron vistos girar bruscamente en el aire y caer, mientras que el temerario aeronauta fue encontrado cerca de su laboratorio terriblemente quemado y destrozado".
Abstract
This chapter concludes our historical survey of concepts of reaction-propelled manned aircraft from 1670 to 1900. Part 1, covering 1670-1869, was a paper presented at the 47th History Symposium of the International Academy of Astronautics (IAA) as part of the 64th International Astronautical Federation (1AF) Congress held in Beijing, China during 23-27 September 2013 (IAC-13- E4.2.2.).' The current chapter covers the period 1870 to 1900, and covers later pioneers including Thomas Griffiths, Russell Thayer, Sumter B. Battey, Edmund Pynchon, et al. As with the previous presentation, the present chapter helps fill gaps in the history of the earliest known concepts of manned, rocket-propelled flying craft. However, this survey does not cover reaction aircraft utilizing air-breathing concepts (precursors to jet planes), excluding de Louvrie's 1865 concept covered in Part I, nor the earliest reaction-propelled spacecraft concepts, nor fictional concepts. Rather, the emphasis is upon rocket or near rocket-propelled designs.
Resumen
Este capítulo concluye nuestro estudio histórico de los conceptos de aeronaves tripuladas propulsadas por reacción de 1670 a 1900. La parte 1, que abarca de 1670 a 1869, fue una ponencia presentada en el 47º Simposio de Historia de la Academia Internacional de Astronáutica (IAA) como parte del 64º Congreso de la Federación Astronáutica Internacional (1AF) celebrado en Pekín (China) del 23 al 27 de septiembre de 2013 (IAC-13- E4.2.2.).' El presente capítulo abarca el período comprendido entre 1870 y 1900, y cubre a pioneros posteriores como Thomas Griffiths, Russell Thayer, Sumter B. Battey, Edmund Pynchon, etc. Al igual que la presentación anterior, el presente capítulo ayuda a llenar lagunas en la historia de los primeros conceptos conocidos de naves voladoras tripuladas propulsadas por cohetes. Sin embargo, este estudio no abarca las aeronaves de reacción que utilizan conceptos de respiración aérea (precursores de los aviones a reacción), excluyendo el concepto de de Louvrie de 1865 tratado en la Parte I, ni los primeros conceptos de naves espaciales propulsadas por reacción, ni los conceptos ficticios. En cambio, se hace hincapié en los diseños propulsados por cohetes o casi cohetes.
Sin duda, una de las apariciones más insólitas e históricas de una máquina voladora propulsada por reacción tuvo su origen en el asesinato del zar ruso Alejandro II el 13 de marzo de 1881.
Nikolai Ivanovich Kibalchich (1583-1881), el fabricante de la bomba utilizada en el crimen, fue uno de los detenidos.
1880 – Julio: Sergei Sergeevich Nezhdanovsky avanzó por primera vez en la id...Champs Elysee Roldan
Sergei Sergeevich Nezhdanovsky (1850-1940) fue un científico e inventor soviético bastante conocido por sus investigaciones en el Campo de la Ciencia y la Tecnología Aeronáuticas. Sin embargo, sus investigaciones en el Campo del Vuelo Reactivo apenas se mencionan en la ciencia de la ingeniería, en la literatura científico-ingenieril o histórico-científica hasta la década de 1950.
Nezhdanovski comenzó a estudiar la posibilidad de utilizar el principio propulsión a chorro para para resolver el problema del vuelo humano en los 1880s.
1881 - El Médico Frances Louis Figuier describió el Mal de AlturaChamps Elysee Roldan
El Médico Frances Louis Figuier describió el mal de altura de los aeronautas con cierto detalle, pero la Aeromedicina como base de la Medicina Espacial empezó a desarrollarse en los años 30 con el vuelo de aviones a gran altitud.
Estos estudios y pruebas prácticas, constituyeron, como en el caso de investigaciones similares en los EE.UU. y la URSS, un punto de partida para el crecimiento de la ciencia bioastronáutica.
1872 - El Español Federico Gómez Arias presenta un trabajo sobre la propulsió...Champs Elysee Roldan
Federico Gómez Arias se interesó por la propulsión de máquinas voladoras.
En 1872 presentó un trabajo sobre la propulsión reactiva.
Aunque Gómez no mencionó los vuelos espaciales, su trabajo es importante para la astronáutica porque calculó las características de una nave voladora propulsada por un motor cohete muchos años antes que Kibaltchich, y sugirió la posibilidad de propulsores propuestos más tarde por Tsiolkovsky, y recomendó un sistema de alimentación de propulsante idéntico al descrito por Ganswindt.
Mission Definition:
Ÿ Flight demonstration and evaluation of Test Vehicle sub systems.
Ÿ Flight demonstration and evaluation of Crew Escape System including various
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Ÿ Crew Module characteristics & deceleration systems demonstration at higher
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Welcome to the first live UiPath Community Day Dubai! Join us for this unique occasion to meet our local and global UiPath Community and leaders. You will get a full view of the MEA region's automation landscape and the AI Powered automation technology capabilities of UiPath. Also, hosted by our local partners Marc Ellis, you will enjoy a half-day packed with industry insights and automation peers networking.
📕 Curious on our agenda? Wait no more!
10:00 Welcome note - UiPath Community in Dubai
Lovely Sinha, UiPath Community Chapter Leader, UiPath MVPx3, Hyper-automation Consultant, First Abu Dhabi Bank
10:20 A UiPath cross-region MEA overview
Ashraf El Zarka, VP and Managing Director MEA, UiPath
10:35: Customer Success Journey
Deepthi Deepak, Head of Intelligent Automation CoE, First Abu Dhabi Bank
11:15 The UiPath approach to GenAI with our three principles: improve accuracy, supercharge productivity, and automate more
Boris Krumrey, Global VP, Automation Innovation, UiPath
12:15 To discover how Marc Ellis leverages tech-driven solutions in recruitment and managed services.
Brendan Lingam, Director of Sales and Business Development, Marc Ellis
Elevating Tactical DDD Patterns Through Object CalisthenicsDorra BARTAGUIZ
After immersing yourself in the blue book and its red counterpart, attending DDD-focused conferences, and applying tactical patterns, you're left with a crucial question: How do I ensure my design is effective? Tactical patterns within Domain-Driven Design (DDD) serve as guiding principles for creating clear and manageable domain models. However, achieving success with these patterns requires additional guidance. Interestingly, we've observed that a set of constraints initially designed for training purposes remarkably aligns with effective pattern implementation, offering a more ‘mechanical’ approach. Let's explore together how Object Calisthenics can elevate the design of your tactical DDD patterns, offering concrete help for those venturing into DDD for the first time!
Accelerate your Kubernetes clusters with Varnish CachingThijs Feryn
A presentation about the usage and availability of Varnish on Kubernetes. This talk explores the capabilities of Varnish caching and shows how to use the Varnish Helm chart to deploy it to Kubernetes.
This presentation was delivered at K8SUG Singapore. See https://feryn.eu/presentations/accelerate-your-kubernetes-clusters-with-varnish-caching-k8sug-singapore-28-2024 for more details.
GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...James Anderson
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
Transcript: Selling digital books in 2024: Insights from industry leaders - T...BookNet Canada
The publishing industry has been selling digital audiobooks and ebooks for over a decade and has found its groove. What’s changed? What has stayed the same? Where do we go from here? Join a group of leading sales peers from across the industry for a conversation about the lessons learned since the popularization of digital books, best practices, digital book supply chain management, and more.
Link to video recording: https://bnctechforum.ca/sessions/selling-digital-books-in-2024-insights-from-industry-leaders/
Presented by BookNet Canada on May 28, 2024, with support from the Department of Canadian Heritage.
Enhancing Performance with Globus and the Science DMZGlobus
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Epistemic Interaction - tuning interfaces to provide information for AI supportAlan Dix
Paper presented at SYNERGY workshop at AVI 2024, Genoa, Italy. 3rd June 2024
https://alandix.com/academic/papers/synergy2024-epistemic/
As machine learning integrates deeper into human-computer interactions, the concept of epistemic interaction emerges, aiming to refine these interactions to enhance system adaptability. This approach encourages minor, intentional adjustments in user behaviour to enrich the data available for system learning. This paper introduces epistemic interaction within the context of human-system communication, illustrating how deliberate interaction design can improve system understanding and adaptation. Through concrete examples, we demonstrate the potential of epistemic interaction to significantly advance human-computer interaction by leveraging intuitive human communication strategies to inform system design and functionality, offering a novel pathway for enriching user-system engagements.
zkStudyClub - Reef: Fast Succinct Non-Interactive Zero-Knowledge Regex ProofsAlex Pruden
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Paper: https://eprint.iacr.org/2023/1886
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- Reduction in onboarding time from 5 weeks to 1 day
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https://arxiv.org/abs/2306.08302
2. Microsoft Research's GraphRAG paper and a review paper on various uses of knowledge graphs:
https://www.microsoft.com/en-us/research/blog/graphrag-unlocking-llm-discovery-on-narrative-private-data/
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The latest edition of the OT/ICS and IoT security Threat Landscape Report 2024 also covers:
State of global ICS asset and network exposure
Sectoral targets and attacks as well as the cost of ransom
Global APT activity, AI usage, actor and tactic profiles, and implications
Rise in volumes of AI-powered cyberattacks
Major cyber events in 2024
Malware and malicious payload trends
Cyberattack types and targets
Vulnerability exploit attempts on CVEs
Attacks on counties – USA
Expansion of bot farms – how, where, and why
In-depth analysis of the cyber threat landscape across North America, South America, Europe, APAC, and the Middle East
Why are attacks on smart factories rising?
Cyber risk predictions
Axis of attacks – Europe
Systemic attacks in the Middle East
Download the full report from here:
https://sectrio.com/resources/ot-threat-landscape-reports/sectrio-releases-ot-ics-and-iot-security-threat-landscape-report-2024/
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This talk is aimed at encouraging a more independent approach to using PHP frameworks, moving towards a more flexible and future-proof approach to PHP development.
7. Geographic
1 coordinate
systems
In this chapter you’ll learn about longitude
and latitude.You’ll also learn about the parts
that comprise a geographic coordinate system
including
• Spheres and spheroids
• Datums
• Prime meridians
7
8. G EOGRAPHIC COORDINATE SYSTEMS
A geographic coordinate system (GCS) defines meridians. These lines encompass the globe and
locations on the earth using a three-dimensional form a gridded network called a graticule.
spherical surface. A GCS is often incorrectly called a
datum, but a datum is only one part of a GCS. A The line of latitude midway between the poles, the
GCS includes an angular unit of measure, a prime horizontal axis, is called the equator and defines the
meridian, and a datum (based on a spheroid). line of zero latitude. The vertical axis, which defines
the line of zero longitude, is called the prime
A feature is referenced by its longitude and latitude meridian. For most geographic coordinate systems,
values. Longitude and latitude are angles measured the prime meridian is the longitude that passes
from the earth’s center to a point on the earth’s through Greenwich, England. Other countries use as
surface. The angles are measured in degrees (or in prime meridians longitude lines that pass through
grads). Bern, Bogota, and Paris.
Where the equator and prime meridian intersect
defines the origin (0,0). The globe is then divided
into four geographical quadrants based on compass
bearings from the origin. Above and below the
equator are north and south, and to the left and right
of the prime meridian are west and east.
Latitude and longitude values are traditionally
measured in decimal degrees or in degrees, minutes,
and seconds (DMS). Latitudes are measured relative
to the equator and range from -90° at the South Pole
to +90° at the North Pole. Longitude is measured
relative to the prime meridian positively, up to 180°,
when traveling east and measured negatively up to
-180°, when traveling west. If the prime meridian is
at Greenwich, then Australia, which is south of the
equator and east of Greenwich, has positive
longitude values and negative latitude values.
The world as a globe showing the longitude and latitude values.
Although longitude and latitude can locate exact
In the spherical system, ‘horizontal’ or east–west positions on the surface of the globe, they are not
lines are lines of equal latitude or parallels. ‘Vertical’ uniform units of measure. Only along the equator
or north–south lines are lines of equal longitude or does the distance represented by one degree of
The parallels and meridians that form a graticule.
8 • Understanding Map Projections
9. longitude approximate the distance represented by
one degree of latitude. This is because the equator is
the only parallel as large as a meridian. (Circles with
the same radius as the spherical earth are called
great circles. All meridians and the equator are great
circles.)
Above and below the equator, the circles defining
the parallels of latitude get gradually smaller until
they become a single point at the North and South
Poles where the meridians converge. As the
meridians converge toward the poles, the distance
represented by one degree of longitude decreases to
zero. On the Clarke 1866 spheroid, one degree of
longitude at the equator equals 111.321 km, while at
60° latitude it is only 55.802 km. Since degrees of
latitude and longitude don’t have a standard length,
you can’t measure distances or areas accurately or
display the data easily on a flat map or computer
screen.
Geographic coordinate systems • 9
10. S PHEROIDS AND SPHERES
The shape and size of a geographic coordinate
system’s surface is defined by a sphere or spheroid.
Although the earth is best represented by a spheroid,
the earth is sometimes treated as a sphere to make
mathematical calculations easier. The assumption
that the earth is a sphere is possible for small-scale
maps, those smaller than 1:5,000,000. At this scale,
the difference between a sphere and a spheroid is
not detectable on a map. However, to maintain
accuracy for larger-scale maps (scales of 1:1,000,000
or larger), a spheroid is necessary to represent the
shape of the earth.
The semimajor axis and semiminor axis of a spheroid.
A spheroid is defined by either the semimajor axis,
a, and the semiminor axis, b, or by a and the
flattening. The flattening is the difference in length
between the two axes expressed as a fraction or a
decimal. The flattening, f, is
f = (a - b) / a
The flattening is a small value, so usually the
quantity 1/f is used instead. Sample values are
A sphere is based on a circle, while a spheroid (or a = 6378137.0 meters
ellipsoid) is based on an ellipse. The shape of an 1/f = 298.257223563
ellipse is defined by two radii. The longer radius is The flattening ranges between zero and one. A
called the semimajor axis, and the shorter radius is flattening value of zero means the two axes are
called the semiminor axis. equal, resulting in a sphere. The flattening of the
earth is approximately 0.003353.
Another quantity is the square of the eccentricity, e,
that, like the flattening, describes the shape of a
spheroid.
2 a2 − b2
e =
a2
The major and minor axes of an ellipse.
Rotating the ellipse around the semiminor axis DEFINING DIFFERENT SPHEROIDS FOR
creates a spheroid. ACCURATE MAPPING
The earth has been surveyed many times to better
understand its surface features and their peculiar
irregularities. The surveys have resulted in many
spheroids that represent the earth. Generally, a
spheroid is chosen to fit one country or a particular
area. A spheroid that best fits one region is not
10 • Understanding Map Projections
11. necessarily the same one that fits another region.
Until recently, North American data used a spheroid
determined by Clarke in 1866. The semimajor axis of
the Clarke 1866 spheroid is 6,378,206.4 meters, and
the semiminor axis is 6,356,583.8 meters.
Because of gravitational and surface feature
variations, the earth is neither a perfect sphere nor a
perfect spheroid. Satellite technology has revealed
several elliptical deviations; for example, the South
Pole is closer to the equator than the North Pole.
Satellite-determined spheroids are replacing the older
ground-measured spheroids. For example, the new
standard spheroid for North America is GRS 1980,
whose radii are 6,378,137.0 and 6,356,752.31414
meters.
Because changing a coordinate system’s spheroid
changes all previously measured values, many
organizations don’t switch to newer (and more
accurate) spheroids.
Geographic coordinate systems • 11
12. D ATUMS
While a spheroid approximates the shape of the position on the surface of the earth. This point is
earth, a datum defines the position of the spheroid known as the ‘origin point’ of the datum. The
relative to the center of the earth. A datum provides coordinates of the origin point are fixed, and all
a frame of reference for measuring locations on the other points are calculated from it. The coordinate
surface of the earth. It defines the origin and system origin of a local datum is not at the center of
orientation of latitude and longitude lines. the earth. The center of the spheroid of a local
datum is offset from the earth’s center. The North
Whenever you change the datum, or more correctly, American Datum of 1927 (NAD27) and the European
the geographic coordinate system, the coordinate Datum of 1950 are local datums. NAD27 is designed
values of your data will change. Here’s the to fit North America reasonably well, while ED50
coordinates in DMS of a control point in Redlands was created for use in Europe. A local datum is not
on NAD 1983. suited for use outside the area for which it was
-117 12 57.75961 34 01 43.77884 designed.
Here’s the same point on NAD 1927.
-117 12 54.61539 34 01 43.72995
The longitude value differs by about a second while
the latitude value is around 500th of a second.
In the last 15 years, satellite data has provided
geodesists with new measurements to define the
best earth-fitting spheroid, which relates coordinates
to the earth’s center of mass. An earth-centered, or
geocentric, datum uses the earth’s center of mass as
the origin. The most recently developed and widely
used datum is the World Geodetic System of 1984
(WGS84). It serves as the framework for locational
measurement worldwide.
A local datum aligns its spheroid to closely fit the
earth’s surface in a particular area. A point on the
surface of the spheroid is matched to a particular
12 • Understanding Map Projections
13. N ORTH A MERICAN DATUMS
There are two horizontal datums used almost that were not widely available when the NAD 1983
exclusively in North America. These are the North datum was being developed. This project, known as
American Datum of 1927 (NAD 1927) and the North the High Accuracy Reference Network (HARN), or
American Datum of 1983 (NAD 1983). High Precision GPS Network (HPGN), is a
cooperative project between the National Geodetic
NAD 1927 Survey and the individual states.
The North American Datum of 1927 uses the Clarke
Currently all states have been resurveyed, but not all
1866 spheroid to represent the shape of the earth.
of the data has been released to the public yet.
The origin of this datum is a point on the earth
Thirty-three states are published as of November
referred to as Meades Ranch in Kansas. Many NAD
1999.
1927 control points were calculated from
observations taken in the 1800s. These calculations
were done manually and in sections over many
years. Therefore, errors varied from station to station.
NAD 1983
Many technological advances in surveying and
geodesy since the establishment of NAD 1927—
electronic theodolites, GPS satellites, Very Long
Baseline Interferometry, and Doppler systems—
revealed weaknesses in the existing network of
control points. Differences became particularly
noticeable when linking existing control with newly
established surveys. The establishment of a new
datum would allow for a single datum to cover
consistently North America and surrounding areas.
The North American Datum of 1983 is based upon
both earth and satellite observations, using the
GRS80 spheroid. The origin for this datum is the
earth’s center of mass. This affects the surface
location of all longitude–latitude values enough to
cause locations of previous control points in North
America to shift, sometimes as much as 500 feet. A
10 year multinational effort tied together a network
of control points for the United States, Canada,
Mexico, Greenland, Central America, and the
Caribbean.
Because NAD 1983 is an earth-centered coordinate
system, it is compatible with global positioning
system (GPS) data. The raw GPS data is actually
reported in the World Geodetic System 1984 (WGS
1984) coordinate system.
HARN OR HPGN
There is an ongoing effort at the state level to
readjust the NAD 1983 datum to a higher level of
accuracy using state-of-the-art surveying techniques
Geographic Coordinate Systems • 13
15. 2 Projected
coordinate
systems
Projected coordinate systems are any
coordinate system designed for a flat surface
such as a printed map or a computer screen.
Topics in this chapter include
• Characteristics and types of map projec-
tion
• Different parameter types
• Customizing a map projection through its
parameters
• Common projected coordinate systems
15
16. P ROJECTED COORDINATE SYSTEMS
A projected coordinate system is defined on a flat,
two-dimensional surface. A projected coordinate
system, unlike a geographic one, has the advantage
that lengths, angles, and areas are constant across
the two dimensions. This is not true when working
in a geographic coordinate system. A projected
coordinate system is always based on a geographic
coordinate system that can use a sphere or spheroid.
In a projected coordinate system, locations are
identified by x,y coordinates on a grid, with the
origin at the center of the grid. Each position has
two values referencing it to that central location. One
specifies its horizontal position and the other its
vertical position. The two values are called the
x-coordinate and y-coordinate. Using this notation,
the coordinates at the origin are x = 0 and y = 0.
On a gridded network of equally spaced horizontal
and vertical lines, the horizontal line in the center is
called the x-axis and the central vertical line is called
the y-axis. Units are consistent and equally spaced
across the full range of x and y. Horizontal lines
above the origin and vertical lines to the right of the
origin have positive values; those below or to the left
are negative. The four quadrants represent the four
possible combinations of positive and negative x-
and y-coordinates.
The signs of x- and y-coordinates in a projected coordinate
system.
16 • Understanding Map Projections
17. W HAT IS A MAP PROJECTION ?
Whether you treat the earth as a sphere or as a A map projection uses mathematical formulas to
spheroid, you must transform its three-dimensional relate spherical coordinates on the globe to flat,
surface to create a flat map sheet. This mathematical planar coordinates.
transformation is commonly referred to as a map
projection. One easy way to understand how map (l,j) « (x, y)
projections alter spatial properties is to visualize Different projections cause different types of
shining a light through the earth onto a surface, distortions. Some projections are designed to
called the projection surface. minimize the distortion of one or two of the data’s
A spheroid can’t be flattened to a plane any easier characteristics. A projection could maintain the area
than flattening a piece of orange peel—it will rip. of a feature but alter its shape. In the above graphic,
Representing the earth’s surface in two dimensions data near the poles is stretched. The diagram on the
causes distortion in the shape, area, distance, or next page shows how three-dimensional features are
direction of the data. compressed to fit onto a flat surface.
The graticule of a geographic coordinate system is projected
onto a cylindrical projection surface.
Projected coordinate systems • 17
18. Map projections are designed for specific purposes. Equidistant projections
A map projection might be used for large-scale data
Equidistant maps preserve the distances between
in a limited area, while another is used for a small-
certain points. Scale is not maintained correctly by
scale map of the world. Map projections designed
any projection throughout an entire map; however,
for small-scale data are usually based on spherical
there are, in most cases, one or more lines on a map
rather than spheroidal geographic coordinate
along which scale is maintained correctly. Most
systems.
projections have one or more lines for which the
length of the line on a map is the same length (at
Conformal projections
map scale) as the same line on the globe, regardless
Conformal projections preserve local shape. of whether it is a great or small circle or straight or
Graticule lines on the globe are perpendicular. To curved. Such distances are said to be true. For
preserve individual angles describing the spatial example, in the Sinusoidal projection, the equator
relationships, a conformal projection must show and all parallels are their true lengths. In other
graticule lines intersecting at 90-degree angles on the equidistant projections, the equator and all meridians
map. This is accomplished by maintaining all angles. are true. Still others (e.g., Two-Point Equidistant)
The drawback is that the area enclosed by a series of show true scale between one or two points and
arcs may be greatly distorted in the process. No map every other point on the map. Keep in mind that no
projection can preserve shapes of larger regions. projection is equidistant to and from all points on a
map.
Equal area projections
Equal area projections preserve the area of displayed True-direction projections
features. To do this, the other properties of shape, The shortest route between two points on a curved
angle, and scale are distorted. In equal area surface such as the earth is along the spherical
projections, the meridians and parallels may not equivalent of a straight line on a flat surface. That is
intersect at right angles. In some instances, especially the great circle on which the two points lie. True-
maps of smaller regions, shapes are not obviously direction or azimuthal projections maintain some of
distorted, and distinguishing an equal area projection the great circle arcs, giving the directions or azimuths
from a conformal projection may prove difficult of all points on the map correctly with respect to the
unless documented or measured. center. Some true-direction projections are also
conformal, equal area, or equidistant.
18 • Understanding Map Projections
19. P ROJECTION TYPES
Because maps are flat, some of the simplest
projections are made onto geometric shapes that can
be flattened without stretching their surfaces.
Common examples are cones, cylinders, and planes.
A mathematical expression that systematically
projects locations from the surface of a spheroid to
representative positions on a planar surface is called
a map projection.
The first step in projecting from one surface to
another is to create one or more points of contact.
Each contact is called a point (or line) of tangency.
As illustrated in the section below about ‘Planar
projections’, a planar projection is tangential to the
globe at one point. Tangential cones and cylinders
touch the globe along a line. If the projection surface
intersects the globe instead of merely touching its
surface, the resulting projection is a secant rather
than a tangent case. Whether the contact is tangent
or secant, the contact point or lines are significant
because they define locations of zero distortion.
Lines of true scale are often referred to as standard
lines. In general, distortion increases with the
distance from the point of contact.
Many common map projections are classified
according to the projection surface used: conic,
cylindrical, and planar.
Projected coordinate systems • 19
20. Conic projections by two standard parallels. It is also possible to define
The most simple conic projection is tangent to the a secant projection by one standard parallel and a
globe along a line of latitude. This line is called the scale factor. The distortion pattern for secant
standard parallel. The meridians are projected onto projections is different between the standard
the conical surface, meeting at the apex, or point, of parallels than beyond them. Generally, a secant
the cone. Parallel lines of latitude are projected onto projection has less overall distortion than a tangent
the cone as rings. The cone is then ‘cut’ along any case. On still more complex conic projections, the
meridian to produce the final conic projection, which axis of the cone does not line up with the polar axis
has straight converging lines for meridians and of the globe. These are called oblique.
concentric circular arcs for parallels. The meridian The representation of geographic features depends
opposite the cut line becomes the central meridian. on the spacing of the parallels. When equally
In general, distortion increases away from the spaced, the projection is equidistant in the north–
standard parallel. Thus, cutting off the top of the south direction but neither conformal nor equal area
cone produces a more accurate projection. This is such as the Equidistant Conic projection. For small
accomplished by not using the polar region of the areas, the overall distortion is minimal. On the
projected data. Conic projections are used for mid- Lambert Conic Conformal projection, the central
latitude zones that have an east-to-west orientation. parallels are spaced more closely than the parallels
Somewhat more complex conic projections contact near the border, and small geographic shapes are
the global surface at two locations. These projections maintained for both small-scale and large-scale
are called secant conic projections and are defined maps. Finally, on the Albers Equal Area Conic
20 • Understanding Map Projections
21. projection, the parallels near the northern and
southern edges are closer together than the central
parallels, and the projection displays equivalent
areas.
Projected Coordinate Systems • 21
22. Cylindrical projections of equidistance. Other geographical properties vary
Cylindrical projections can also have tangent or according to the specific projection.
secant cases. The Mercator projection is one of the
most common cylindrical projections, and the
equator is usually its line of tangency. Meridians are
geometrically projected onto the cylindrical surface,
and parallels are mathematically projected,
producing graticular angles of 90 degrees. The
cylinder is ‘cut’ along any meridian to produce the
final cylindrical projection. The meridians are equally
spaced, while the spacing between parallel lines of
latitude increases toward the poles. This projection is
conformal and displays true direction along straight
lines. Rhumb lines, lines of constant bearing, but not
most great circles, are straight lines on a Mercator
projection.
For more complex cylindrical projections the
cylinder is rotated, thus changing the tangent or
secant lines. Transverse cylindrical projections such
as the Transverse Mercator use a meridian as the
tangential contact or lines parallel to meridians as
lines of secancy. The standard lines then run north
and south, along which the scale is true. Oblique
cylinders are rotated around a great circle line
located anywhere between the equator and the
meridians. In these more complex projections, most
meridians and lines of latitude are no longer straight.
In all cylindrical projections, the line of tangency or
lines of secancy have no distortion and thus are lines
22 • Understanding Map Projections
23. Planar projections projections. Perspective points may be the center of
Planar projections project map data onto a flat the earth, a surface point directly opposite from the
surface touching the globe. A planar projection is focus, or a point external to the globe, as if seen
also known as an azimuthal projection or a zenithal from a satellite or another planet.
projection. This type of projection is usually tangent
to the globe at one point but may be secant. The
point of contact may be the North Pole, the South
Pole, a point on the equator, or any point in
between. This point specifies the aspect and is the
focus of the projection. The focus is identified by a
central longitude and a central latitude. Possible
aspects are polar, equatorial, and oblique.
Polar aspects are the simplest form. Parallels of
latitude are concentric circles centered on the pole,
and meridians are straight lines that intersect at the
pole with their true angles of orientation. In other
aspects, planar projections will have graticular angles
of 90 degrees at the focus. Directions from the focus
are accurate.
Great circles passing through the focus are
represented by straight lines; thus the shortest
distance from the center to any other point on the
map is a straight line. Patterns of area and shape
distortion are circular about the focus. For this
reason, azimuthal projections accommodate circular
regions better than rectangular regions. Planar
projections are used most often to map polar
regions.
Some planar projections view surface data from a
specific point in space. The point of view determines
how the spherical data is projected onto the flat
surface. The perspective from which all locations are
viewed varies between the different azimuthal
Projected Coordinate Systems • 23
24. Azimuthal projections are classified in part by the
focus and, if applicable, by the perspective point.
The graphic below compares three planar
projections with polar aspects but different
perspectives. The Gnomonic projection views the
surface data from the center of the earth, whereas
the Stereographic projection views it from pole to
pole. The Orthographic projection views the earth
from an infinite point, as if viewed from deep space.
Note how the differences in perspective determine
the amount of distortion toward the equator.
24 • Understanding Map Projections
25. O THER PROJECTIONS
The projections discussed previously are
conceptually created by projecting from one
geometric shape (a sphere) onto another (a cone,
cylinder, or plane). Many projections are not related
as easily to one of these three surfaces.
Modified projections are altered versions of other
projections (e.g., the Space Oblique Mercator is a
modification of the Mercator projection). These
modifications are made to reduce distortion, often by
including additional standard lines or changing the
distortion pattern.
Pseudo projections have some of the characteristics
of another class of projection. For example, the
Sinusoidal is called a pseudocylindrical projection
because all lines of latitude are straight and parallel
and all meridians are equally spaced. However, it is
not truly a cylindrical projection because all
meridians except the central meridian are curved.
This results in a map of the earth having an oval
shape instead of a rectangular shape.
Other projections are assigned to special groups
such as circular, star, and so on.
Projected coordinate systems • 25
26. Geographic
3 transformations
This chapter discusses the various datum
transformation methods including
• Geographic translation
• Coordinate Frame and Position Vector
• Molodensky and Abridged Molodensky
• NADCON and HARN
• NTv2
27
27. G EOGRAPHIC TRANSFORMATION METHODS
Moving your data between coordinate systems
sometimes includes transforming between the
geographic coordinate systems.
Because the geographic coordinate systems contain
datums that are based on spheroids, a geographic
transformation also changes the underlying spheroid.
There are several methods for transforming between
datums, which have different levels of accuracy and
ranges.
A geographic transformation always converts
geographic (longitude–latitude) coordinates. Some
methods convert the geographic coordinates to
geocentric (X, Y, Z) coordinates, transform the X, Y,
Z coordinates, and convert the new values to
geographic coordinates.
The X, Y, Z coordinate system.
Other methods use a grid of differences and convert
the longitude–latitude values directly.
28 • Understanding Map Projections
28. E QUATION - BASED METHODS
Geocentric translations Without getting into a lot of mathematics, it’s
The simplest datum transformation method is a possible to define the rotation angles as positive
geocentric, or three-parameter, transformation. The either clockwise or counterclockwise as you look
geocentric transformation models the differences toward the origin of the XYZ systems.
between two datums in the X, Y, Z coordinate
system. One datum is defined with its center at 0, 0,
0. The center of the other datum is defined to be at
some distance (DX, DY, DZ) in meters away.
The Coordinate Frame (or Bursa-Wolf) definition of the rotation
values.
The above equation is the way that the United States
and Australia define the equations and is called the
Usually the transformation parameters are defined as
‘Coordinate Frame Rotation’ transformation. The
going ‘from’ a local datum ‘to’ WGS84 or to another
rotations are positive counterclockwise. Europe uses
geocentric datum.
a different convention called the ‘Position Vector’
transformation. Both methods are sometimes referred
X ∆X X to as the Bursa-Wolf method. In the Projection
Engine, the Coordinate Frame and Bursa-Wolf
Y = ∆Y + Y
Z methods are the same. Both Coordinate Frame and
new ∆Z Z original
Position Vector methods are supported, and it is easy
to convert transformation values from one method to
Seven parameter methods
the other simply by changing the signs of the three
A more complex and accurate datum transformation rotation values. For example, the parameters to
is possible by adding four more parameters to a convert from the WGS72 datum to the WGS84 datum
geocentric transformation. The seven parameters are with the Coordinate Frame method are:
three linear shifts (DX, DY, DZ), three angular
rotations around each axis (rx, ry, rz), and a scale (0.0, 0.0, 4.5, 0.0, 0.0, -0.554, 0.227)
factor (s). To use the same parameters with the Position Vector
method, change the sign of the rotation so the new
X ∆X 1 rz − ry X parameters are:
Y = ∆Y + ( 1 + s ) ⋅ − rz 1 rx ⋅ Y (0.0, 0.0, 4.5, 0.0, 0.0, +0.554, 0.227)
Z r 1 Z
new ∆Z
y − rx original Unless explicitly stated, it’s impossible to tell from
the parameters alone which convention is being
The rotation values are given in decimal seconds, used. If you use the wrong method, your results can
while the scale factor is in parts per million (ppm). return inaccurate coordinates. The only way to
The rotations are defined in two different ways. determine how the parameters are defined is by
Geographic transformations • 29
29. checking a control point whose coordinates are The Molodensky method returns in decimal seconds
known in the two systems. the amounts to add to the latitude and longitude.
The amounts are added automatically by the
Molodensky method Projection Engine.
The Molodensky method converts directly between
two geographic coordinate systems without actually Abridged Molodensky method
converting to an X, Y, Z system. The Molodensky The Abridged Molodensky method is a simplified
method requires three shifts (DX, DY, DZ) and the and less accurate version of the Molodensky method.
differences between the semimajor axes (Da) and the
flattenings (Df) of the two spheroids. The Projection M ∆ϕ = − sin ϕ cos λ ∆X − sin ϕ sin λ ∆Y
Engine automatically calculates the spheroid
differences according to the datums involved. + cos ϕ ∆Z + (a∆f + f∆a ) ⋅ 2 sin ϕ cos ϕ
N cos ϕ ∆λ = − sin λ ∆X + cos λ ∆Y
( M + h)∆ϕ = − sin ϕ cos λ ∆X − sin ϕ sin λ ∆Y
e 2 sin ϕ cos ϕ ∆h = cos ϕ cos λ ∆X + cos ϕ sin λ ∆Y
+ cos ϕ ∆Z + ∆a
(1 − e 2 sin 2 ϕ )1 / 2 + sin ϕ ∆Z + (a∆f + f∆a ) sin 2 ϕ −∆a
a b
+ sin ϕ cos ϕ ( M + N ) ∆f
b a
( N + h ) cos ϕ ∆λ = − sin λ ∆X + cos λ ∆Y
∆h = cos ϕ cos λ ∆X + cos ϕ sin λ ∆Y
+ sin ϕ ∆Z − (1 − e sin ϕ ) ∆a
2 2 1/ 2
a(1 − f )
+ sin ϕ ∆f
2
(1 − e 2 sin 2 ϕ )1 / 2
h ellipsoid height
f latitude
l longitude
e eccentricity of the spheroid
M and N are the meridian and prime vertical radii of
curvatures. The equations for M and N are
a (1 − e )
2
M =
(1 − e 2 sin 2 ϕ )3 / 2
a
N =
(1 − e sin ϕ )
2 2 1/ 2
30 • Understanding Map Projections
30. G RID - BASED METHODS
NADCON and HARN methods New surveying and satellite measuring techniques
The United States uses a grid-based method to have allowed NGS and the states to calculate very
convert between geographic coordinate systems. accurate control grid networks. These grids are
Grid-based methods allow you to model the called HARN files. About two-thirds of the states
differences between the systems and are potentially have HARN grids. HARN transformations have an
the most accurate method. The area of interest is accuracy around 0.05 meters (NADCON, 1999).
divided into cells. The National Geodetic Survey The difference values in decimal seconds are stored
publishes grids to convert between NAD 1927 and in two files: one for longitude and the other for
other older geographic coordinate systems and NAD latitude. A bilinear interpolation is used to exactly
1983. We group these transformations into the calculate the difference between the two geographic
NADCON method. The main NADCON grid converts coordinate systems at a point. The grids are binary
the contiguous 48 states, Alaska, Puerto Rico, and files, but a program, nadgrd, from the NGS allows
the Virgin Islands between NAD 1927 and NAD you to convert the grids to an ASCII format. Shown
1983. The other NADCON grids convert older at the bottom of the page is the header and first
geographic coordinate systems for the ‘row’ of the CSHPGN.LOA file. This is the longitude
• Hawaiian Islands grid for Southern California. The format of the first
row of numbers is, in order, the number of columns,
• Puerto Rico and the Virgin Islands number of rows, unknown, minimum longitude, cell
size, minimum latitude, cell size, and unknown.
• St. George Island, Alaska
The next 37 values (in this case) are the longitude
• St. Lawrence Island, Alaska shifts from -122° to -113° at 32° N.
• St. Paul Island, Alaska
to NAD 1983. The accuracy is around 0.15 meters for
the contiguous states, 0.50 for Alaska, 0.20 for
Hawaii, and 0.05 for Puerto Rico and the Virgin
Islands. Accuracies can vary depending on how
good the geodetic data in the area was when the
grids were computed (NADCON, 1999).
NADCON EXTRACTED REGION NADGRD
37 21 1 -122.00000 .25000 32.00000 .25000 .00000
.007383 .004806 .002222 -.000347 -.002868 -.005296
-.007570 -.009609 -.011305 -.012517 -.013093 -.012901
-.011867 -.009986 -.007359 -.004301 -.001389 .001164
.003282 .004814 .005503 .005361 .004420 .002580
.000053 -.002869 -.006091 -.009842 -.014240 -.019217
-.025104 -.035027 -.050254 -.072636 -.087238 -.099279
-.110968
A portion of a grid file used for a HARN transformation.
Geographic transformations • 31
31. National Transformation, version 2
Like the United States, Canada uses a grid-based
method to convert between NAD 1927 and NAD
1983. The National Transformation version 2 (NTv2)
method is quite similar to NADCON. A set of binary
files contains the differences between the two
geographic coordinate systems. A bilinear
interpolation is used to calculate the exact values for
a point.
Unlike NADCON, which can only use one grid at a
time, NTv2 is designed to check multiple grids for
the most accurate shift information. A set of low-
density base grids exists for Canada. Certain areas
such as a city have high-density local subgrids that
overlay portions of the base or parent grids. If a
point is within one of the high-density grids, NTv2
will use it. Otherwise the point ‘falls through’ to the
low-density grid.
A higher density subgrid with four cells overlaying a lower
density base grid, also with four cells.
If a point falls in the lower-left part of the above
picture between the stars, the shifts are calculated
with the higher density subgrid. A point whose
coordinates are anywhere else will have its shifts
calculated with the lower density base grid. The
software automatically calculates which base or
subgrid to use.
32 • Understanding Map Projections
32. 4 Supported
map
projections
A map projection converts data from the
round earth onto a flat plane. Each map
projection is designed for a specific purpose
and distorts the data differently.This chapter
will describe each projection including:
• Method
• Linear graticules
• Limitations
• Uses and applications
• Parameters
31
33. A ITOFF
Used for the Winkel Tripel projection.
PROJECTION PARAMETERS
ArcInfo™: ARC, ARCPLOT™, ARCEDIT™,
ArcToolbox™
Supported on a sphere only.
:PROJECTION AITOFF
:PARAMETERS
Radius of the sphere of reference:
The central meridian is 0°. Longitude of central meridian:
False easting (meters):
DESCRIPTION False northing (meters):
A compromise projection used for world maps and
developed in 1889.
PROJECTION METHOD
Modified azimuthal. Meridians are equally spaced
and concave toward the central meridian. The
central meridian is a straight line and half the length
of the equator. Parallels are equally spaced curves,
concave toward the poles.
LINEAR GRATICULES
The equator and the central meridian.
PROPERTIES
Shape
Shape distortion is moderate.
Area
Moderate distortion.
Direction
Generally distorted.
Distance
The equator and central meridian are at true scale.
LIMITATIONS
Neither conformal nor equal area. Useful only for
world maps.
USES AND APPLICATIONS
Developed for use in general world maps.
32 • Understanding Map Projections
34. A LASKA G RID
Distance
The minimum scale factor is 0.997 at approximately
62°30' N, 156° W. Scale increases outward from this
point. Most of Alaska and the Aleutian Islands, but
excluding the panhandle, are bounded by a line of
true scale. The scale factor ranges from 0.997 to
1.003 for Alaska, which is one-fourth the range for a
corresponding conic projection (Snyder, 1987).
LIMITATIONS
Distortion becomes severe away from Alaska.
USES AND APPLICATIONS
Parameters are set by the software. Conformal mapping of Alaska as a complete state on
the Clarke 1866 spheroid or NAD27. This projection
DESCRIPTION is not optimized for use with other datums and
spheroids.
This projection was developed to provide a
conformal map of Alaska with less scale distortion
than other conformal projections. A set of PROJECTION PARAMETERS
mathematical formulas allows the definition of a
ArcInfo: ARC, ARCPLOT,ARCEDIT, ArcToolbox;
conformal transformation between two surfaces
PC ARC/INFO®; ArcCAD®
(Snyder, 1987).
:PROJECTION ALASKA_GRID
:PARAMETERS
PROJECTION METHOD
Modified planar. This is a sixth-order equation Projection-specific parameters are set by the
modification of an oblique Stereographic conformal software.
projection on the Clarke 1866 spheroid. The origin is
at 64° N, 152° W.
POINT OF TANGENCY
Conceptual point of tangency at 64° N, 152° W.
LINEAR GRATICULES
None.
PROPERTIES
Shape
Perfectly conformal.
Area
Varies about 1.2 percent over Alaska.
Direction
Local angles are correct everywhere.
Supported map projections• 33
35. A LASKA S ERIES E
LIMITATIONS
This projection is appropriate for mapping Alaska,
the Aleutian Islands, and the Bering Sea region only.
USES AND APPLICATIONS
1972 USGS revision of a 1954 Alaska map that was
published at 1:2,500,000 scale.
1974 map of the Aleutian Islands and the Bering Sea.
PROJECTION PARAMETERS
ArcInfo: ARC, ARCPLOT,ARCEDIT, ArcToolbox;
Parameters are set by the software. PC ARC/INFO; ArcCAD
:PROJECTION ALASKA_E
DESCRIPTION :PARAMETERS
This projection was developed in 1972 by the USGS
to publish a map of Alaska at 1:2,500,000 scale. Projection-specific parameters are set by the
software.
PROJECTION METHOD
Approximates Equidistant Conic, although it is
commonly referred to as a ‘Modified Transverse
Mercator’.
LINES OF CONTACT
The standard parallels at 53°30' N and 66°05'24" N.
LINEAR GRATICULES
The meridians are straight lines radiating from a
center point. The parallels closely approximate
concentric circular arcs.
PROPERTIES
Shape
Neither conformal nor equal area.
Area
Neither conformal nor equal area.
Direction
Distortion increases with distance from the standard
parallels.
Distance
Accurate along the standard parallels.
34 • Understanding Map Projections
36. A LBERS E QUAL A REA C ONIC
parallels are preserved, but because the scale along
the lines of longitude does not match the scale along
the lines of latitude, the final projection is not
conformal.
Area
All areas are proportional to the same areas on the
earth.
Direction
Locally true along the standard parallels.
Distance
The central meridian is 96° W. The first and second standard
parallels are 20° N and 60° N while the latitude of origin is Distances are best in the middle latitudes. Along
40° N. parallels, scale is reduced between the standard
parallels and increased beyond them. Along
DESCRIPTION meridians, scale follows an opposite pattern.
This conic projection uses two standard parallels to
reduce some of the distortion of a projection with LIMITATIONS
one standard parallel. Although neither shape nor Best results for regions predominantly east–west in
linear scale is truly correct, the distortion of these extent and located in the middle latitudes. Total
properties is minimized in the region between the range in latitude from north to south should not
standard parallels. This projection is best suited for exceed 30–35 degrees. No limitations on east to west
land masses extending in an east-to-west orientation range.
rather than those lying north to south.
USES AND APPLICATIONS
PROJECTION METHOD
Used for small regions or countries but not for
Conic. The meridians are equally spaced straight continents.
lines converging to a common point. Poles are
represented as arcs rather than as single points. Conterminous United States, normally using 29°30'
Parallels are unequally spaced concentric circles and 45°30' as the two standard parallels. For this
whose spacing decreases toward the poles. projection, the maximum scale distortion for the
48 states is 1.25 percent.
LINES OF CONTACT
Recommended choice of standard parallels can be
Two lines, the standard parallels, defined by degrees calculated by determining the range in latitude in
latitude. degrees north to south and dividing this range by
six. The “One-Sixth Rule” places the first standard
LINEAR GRATICULES parallel at one-sixth the range above the southern
All meridians. boundary and the second standard parallel minus
one-sixth the range below the northern limit. There
PROPERTIES are other possible approaches.
Shape
Shape along the standard parallels is accurate and
minimally distorted in the region between the
standard parallels and those regions just beyond.
The 90 degree angles between meridians and
Supported map projections• 35
37. PROJECTION PARAMETERS
ArcInfo: ARC,ARCPLOT,ARCEDIT, ArcToolbox;
PC ARC/INFO; ArcCAD
:PROJECTION ALBERS
:PARAMETERS
1st standard parallel:
2nd standard parallel:
Central meridian:
Latitude of projections origin:
False easting (meters):
False northing (meters):
Projection Engine: ArcMap, ArcCatalog,ArcSDE,
MapObjects 2.x, ArcView Projection Utility
Central Meridian
Standard Parallel 1
Standard Parallel 2
Latitude of Origin
False Easting
False Northing
ArcView GIS
Central Meridian:
Reference Latitude:
Standard Parallel 1:
Standard Parallel 2:
False Easting:
False Northing:
36 •Understanding Map Projections
38. A ZIMUTHAL E QUIDISTANT
Area
Distortion increases outward from the center point.
Direction
True directions from the center outward.
Distance
Distances for all aspects are accurate from the center
point outward. For the polar aspect, the distances
along the meridians are accurate, but there is a
pattern of increasing distortion along the circles of
latitude, outward from the center.
The center of the projection is 0°, 0°.
LIMITATIONS
DESCRIPTION Usually limited to 90 degrees from the center,
The most significant characteristic is that both although it can project the entire globe. Polar-aspect
distance and direction are accurate from the central projections are best for regions within a 30 degree
point. This projection can accommodate all aspects: radius because there is only minimal distortion.
equatorial, polar, and oblique. Degrees from center:
15 30 45 60 90
PROJECTION METHOD
Planar. The world is projected onto a flat surface Scale distortion in percent along parallels:
from any point on the globe. Although all aspects 1.2 4.7 11.1 20.9 57
are possible, the one used most commonly is the
polar aspect, in which all meridians and parallels are USES AND APPLICATIONS
divided equally to maintain the equidistant property. Routes of air and sea navigation. These maps will
Oblique aspects centered on a city are also common. focus on an important location as their central point
and use an appropriate aspect.
POINT OF TANGENCY
Polar aspect—Polar regions and polar navigation.
A single point, usually the North or the South Pole,
defined by degrees of latitude and longitude. Equatorial aspect—Locations on or near the equator,
such as Singapore.
LINEAR GRATICULES
Oblique aspect—Locations between the poles and
Polar—Straight meridians are divided equally by
the equator such as large-scale mapping of
concentric circles of latitude.
Micronesia.
Equatorial—The Equator and the projection’s central
If this projection is used on the entire globe, the
meridian are linear and meet at a 90 degree angle.
immediate hemisphere can be recognized and
Oblique—The central meridian is straight, but there resembles the Lambert Azimuthal projection. The
are no 90 degree intersections except along the outer hemisphere greatly distorts shapes and areas.
central meridian. In the extreme, a polar-aspect projection centered on
the North Pole will represent the South Pole as its
PROPERTIES largest outermost circle. The function of this extreme
projection is that, regardless of the conformal and
Shape area distortion, an accurate presentation of distance
Except at the center, all shapes are distorted. and direction from the center point is maintained.
Distortion increases from the center.
Supported map projections• 37
39. PROJECTION PARAMETERS
ArcInfo: ARC,ARCPLOT,ARCEDIT, ArcToolbox;
PC ARC/INFO; ArcCAD
Supported on a sphere only.
:PROJECTION AZIMUTHAL
:PARAMETERS
Radius of the sphere of reference:
Longitude of center of projection:
Latitude of center of projection:
False easting (meters):
False northing (meters):
Projection Engine: ArcMap™,ArcCatalog™,ArcSDE™,
MapObjects® 2.x, ArcView GIS® Projection Utility
Central Meridian
Latitude of Origin
False Easting
False Northing
ArcView GIS
Central Meridian:
Reference Latitude:
38 •Understanding Map Projections
40. B EHRMANN E QUAL A REA C YLINDRICAL
USES AND APPLICATIONS
Only useful for world maps.
PROJECTION PARAMETERS
This projection is supported on a sphere only.
Projection Engine:ArcMap, ArcCatalog,ArcSDE,
MapObjects 2.x, ArcView Projection Utility
The central meridian is 0°. Central Meridian
False Easting
False Northing
DESCRIPTION
This projection is an equal area cylindrical projection ArcView GIS
suitable for world mapping. Parameters are set by the software.
Central Meridian: 0.0
PROJECTION METHOD
Standard Parallel: 30.0
Cylindrical. Standard parallels are at 30° N and S. A
case of Lambert Equal Area Cylindrical.
LINES OF CONTACT
The two parallels at 30° N and S.
LINEAR GRATICULES
Meridians and parallels are linear.
PROPERTIES
Shape
Shape distortion is minimized near the standard
parallels. Shapes are distorted north–south between
the standard parallels and distorted east–west above
30° N and below 30° S.
Area
Area is maintained.
Direction
Directions are generally distorted.
Distance
Directions are generally distorted except along the
equator.
LIMITATIONS
Useful for world maps only.
Supported map projections• 39
41. B IPOLAR O BLIQUE C ONFORMAL C ONIC
DESCRIPTION display North America and South America only. If
This projection was developed specifically for having problems, check all feature types (particularly
mapping North and South America and maintains annotation and tics) and remove any features that
conformality. It is based upon the Lambert are beyond the range of the projection.
Conformal Conic, using two oblique conic
projections side by side. USES AND APPLICATIONS
Developed in 1941 by the American Geographical
PROJECTION METHOD Society as a low-error single map of North and South
Two oblique conics are joined with the poles 104 America.
degrees apart. A great circle arc 104 degrees long
Conformal mapping of North and South America as a
begins at 20° S and 110° W, cuts through Central
contiguous unit.
America, and terminates at 45° N and approximately
19°59'36" W. The scale of the map is then increased Used by USGS for geologic mapping of North
by approximately 3.5 percent. The origin of the America until replaced in 1979 by the Transverse
coordinates is 17°15' N, 73°02' W (Snyder, 1987). Mercator.
LINES OF CONTACT
PROJECTION PARAMETERS
The two oblique cones are each conceptually secant.
These standard lines do not follow any single ArcInfo: ARC, ARCPLOT,ARCEDIT, ArcToolbox;
parallel or meridian. PC ARC/INFO; ArcCAD
Supported on a sphere only. Projection-specific
LINEAR GRATICULES
parameters are set by the software.
Only from each transformed pole to the nearest
actual pole. :PROJECTION BIPOLAR_OBLIQUE
:PARAMETERS
PROPERTIES
Shape
Conformality is maintained except for a slight
discrepancy at the juncture of the two conic
projections.
Area
Minimal distortion near the standard lines, increasing
with distance.
Direction
Local directions are accurate because of
conformality.
Distance
True along standard lines.
LIMITATIONS
Specialized for displaying North and South America
only together. The Bipolar Oblique projection will
40 • Understanding Map Projections
42. B ONNE
Direction
Locally true along central meridian and standard
parallel.
Distance
Scale is true along the central meridian and each
parallel.
LIMITATIONS
Usually limited to maps of continents or smaller
regions. Distortion pattern makes other equal area
projections preferable.
USES AND APPLICATIONS
During the 19th and early 20th century for atlas
maps of Asia, Australia, Europe, and North America.
Replaced by the Lambert Azimuthal Equal Area
projection for continental mapping by Rand McNally
The central meridian is 0°.
& Co. and Hammond, Inc.
DESCRIPTION Large-scale topographic mapping of France and
This equal area projection has true scale along the Ireland, along with Morocco and some other
central meridian and all parallels. Equatorial aspect is Mediterranean countries (Snyder, 1987).
a Sinusoidal. Polar aspect is a Werner.
PROJECTION PARAMETERS
PROJECTION METHOD
Pseudoconic. Parallels of latitude are equally spaced ArcInfo: ARC, ARCPLOT,ARCEDIT, ArcToolbox;
concentric circular arcs, marked true to scale for PC ARC/INFO; ArcCAD
meridians. :PROJECTION BONNE
:PARAMETERS
POINT OF TANGENCY Longitude of projection center:
Latitude of projection center:
A single standard parallel with no distortion. False easting (meters):
False northing (meters):
LINEAR GRATICULES
The central meridian. Projection Engine:ArcMap, ArcCatalog,ArcSDE,
MapObjects 2.x, ArcView Projection Utility
PROPERTIES Central Meridian
Standard Parallel 1
Shape False Easting
False Northing
No distortion along the central meridian and
standard parallel; error increases away from these
lines.
Area
Equal area.
Supported map projections• 41
43. C ASSINI –S OLDNER
Area
No distortion along the central meridian. Distortion
increases with distance from the central meridian.
Direction
Generally distorted.
Distance
Scale distortion increases with distance from the
central meridian; however, scale is accurate along
the central meridian and all lines perpendicular to
the central meridian.
LIMITATIONS
The center of the projection is 0°, 0°.
Used primarily for large-scale mapping of areas near
the central meridian. The extent on a spheroid is
DESCRIPTION
limited to five degrees to either side of the central
This transverse cylindrical projection maintains scale meridian. Beyond that range, data projected to
along the central meridian and all lines parallel to it Cassini may not project back to the same position.
and is neither equal area nor conformal. It is most Transverse Mercator often is preferred due to
suited for large-scale mapping of areas difficulty measuring scale and direction on Cassini.
predominantly north–south in extent.
USES AND APPLICATIONS
PROJECTION METHOD
Normally used for large-scale maps of areas
A transverse cylinder is conceptually projected onto predominantly north–south in extent.
the globe and is tangent along the central meridian.
Cassini is analogous to the Equirectangular Used for the Ordnance Survey of Great Britain and
projection in the same way Transverse Mercator is to some German states in the late 19th century. Also
the Mercator projection. The name Cassini–Soldner used in Cyprus, former Czechoslovakia, Denmark,
refers to the more accurate ellipsoidal version Malaysia, and the former Federal Republic of
developed in the 19th century, used in this software. Germany.
POINT OF TANGENCY
Conceptually a line, specified as the central meridian.
LINEAR GRATICULES
The equator, central meridian, and meridians
90 degrees from the central meridian.
PROPERTIES
Shape
No distortion along the central meridian. Distortion
increases with distance from the central meridian.
42 • Understanding Map Projections
44. PROJECTION PARAMETERS
ArcInfo: ARC,ARCPLOT,ARCEDIT, ArcToolbox;
PC ARC/INFO; ArcCAD
:PROJECTION CASSINI
:PARAMETERS
Longitude of projection center:
Latitude of projection center:
False easting (meters):
False northing (meters):
Projection Engine: ArcMap, ArcCatalog,ArcSDE,
MapObjects 2.x, ArcView Projection Utility
Central Meridian
Latitude of Origin
Scale Factor
False Easting
False Northing
ArcView GIS
Central Meridian:
Reference Latitude:
Supported map projections • 43
45. C HAMBERLIN T RIMETRIC
LIMITATIONS
The three selected input points should be widely
spaced near the edge of the map limits.
Chamberlin can only be used in ArcInfo as an
OUTPUT projection because the inverse equations
(Chamberlin to geographic) have not been
published.
You can’t project an ArcInfo grid or lattice to
Chamberlin because the inverse equations are
required.
USES AND APPLICATIONS
Used by the National Geographic Society as the
The three points that define the projection are 120° W 48° N, standard map projection for most continents.
98° W 27° N, and 70° W 45° N.
PROJECTION PARAMETERS
DESCRIPTION
ArcInfo: ARC, ARCPLOT,ARCEDIT, ArcToolbox;
This is the standard projection developed and used
PC ARC/INFO; ArcCAD
by the National Geographic Society for continental
mapping. The distance from three input points to Supported on a sphere only.
any other point is approximately correct. :PROJECTION CHAMBERLIN
:PARAMETERS
PROJECTION METHOD Longitude of point A:
Modified planar. Latitude of point A:
Longitude of point B:
Latitude of point B:
LINEAR GRATICULES Longitude of point C:
None. Latitude of point C:
PROPERTIES
Shape
Shape distortion is low throughout if the three points
are placed near the map limits.
Area
Areal distortion is low throughout if the three points
are placed near the map limits.
Direction
Low distortion throughout.
Distance
Nearly correct representation of distance from three
widely spaced points to any other point.
44 • Understanding Map Projections
46. C RASTER P ARABOLIC
Distance
Scale is true along latitudes 36°46' N and S. Scale is
also constant along any given latitude and is
symmetrical around the equator.
LIMITATIONS
Useful only as a world map.
USES AND APPLICATIONS
Thematic world maps.
The central meridian is 0°. PROJECTION PARAMETERS
DESCRIPTION ArcInfo: ARC, ARCPLOT,ARCEDIT, ArcToolbox;
PC ARC/INFO; ArcCAD
This pseudocylindrical equal area projection is
primarily used for thematic maps of the world. Also Supported on a sphere only.
known as Putnins P4. :PROJECTION CRASTER_PARABOLIC
:PARAMETERS
PROJECTION METHOD Longitude of central meridian:
Pseudocylindrical.
LINEAR GRATICULES
The central meridian is a straight line half as long as
the equator. Parallels are unequally spaced, straight
parallel lines perpendicular to the central meridian.
Their spacing decreases very gradually as they move
away from the equator.
PROPERTIES
Shape
Free of distortion at the central meridian at 36°46' N
and S. Distortion increases with distance from these
points and is most severe at the outer meridians and
high latitudes. Interrupting the projection greatly
reduces this distortion.
Area
Equal area.
Direction
Local angles are correct at the intersection of
36°46' N and S with the central meridian. Direction is
distorted elsewhere.
Supported map projections• 45
47. C YLINDRICAL E QUAL A REA
PROPERTIES
Shape
Shape is true along the standard parallels of the
normal aspect (Type 1) or the standard lines of the
transverse and oblique aspects (Types 2 and 3).
Distortion is severe near the poles of the normal
aspect or 90° from the central line in the transverse
and oblique aspects.
Area
There is no area distortion on any of the projections.
The central meridian is 0° and the standard parallel is 40° N. Direction
The opposite parallel, 40° S, is also a standard parallel. Local angles are correct along standard parallels or
standard lines. Direction is distorted elsewhere.
DESCRIPTION
Lambert first described this equal area projection in Distance
1772, and it has been used infrequently. Scale is true along the equator (Type 1) or the
standard lines of the transverse and oblique aspects
PROJECTION METHOD (Types 2 and 3). Scale distortion is severe near the
Cylindrical. Type 1 is a normal, perspective poles of the normal aspect or 90° from the central
projection onto a cylinder tangent at the equator. line in the transverse and oblique aspects.
Type 2 and Type 3 are oblique aspects from which
normal and transverse aspects are also possible. LIMITATIONS
Recommended for narrow areas extending along the
POINTS OF INTERSECTION central line. Severe distortion of shape and scale
Type 1 is tangent at the equator. Type 2 can be near poles of Type 1 and 90° from the central line of
tangent or secant. Type 3 is tangent. the transverse and oblique aspects.
LINEAR GRATICULES USES AND APPLICATIONS
Type 1 Type 1 is suitable for equatorial regions.
In the normal, or equatorial aspect, all meridians and Suitable for regions of north–south extent or those
parallels are perpendicular straight lines. Meridians following an oblique central line when using a
are equally spaced and 0.32 times the length of the transverse or oblique view, respectively.
equator. Parallels are unequally spaced and farthest
apart near the equator. Poles are lines of length
equal to the equator.
Types 2 and 3
In a transverse aspect, the equator along with the
central meridian and a meridian perpendicular to the
equator are straight lines. In an oblique aspect, only
two meridians are straight lines.
46 • Understanding Map Projections
48. PROJECTION PARAMETERS
ArcInfo: ARC,ARCPLOT,ARCEDIT, ArcToolbox;
PC ARC/INFO; ArcCAD
Supported on a sphere only.
:PROJECTION CYLINDRICAL
:PARAMETERS
Enter projection type (1, 2, or 3):
Type 1 parameters
Longitude of central meridian:
Latitude of standard parallel:
Type 2 parameters
Longitude of 1st point:
Latitude of 1st point:
Longitude of 2nd point:
Latitude of 2nd point:
Scale factor:
Type 3 parameters
Longitude of center of projection:
Latitude of center of projection:
Azimuth:
Scale factor:
Projection Engine: ArcMap, ArcCatalog,ArcSDE,
MapObjects 2.x, ArcView Projection Utility
Central Meridian
Standard Parallel 1
False Easting
False Northing
ArcView GIS
This projection is supported on a sphere only.
Central Meridian:
Reference Latitude:
Supported map projections • 47