Curriculum

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[[Projects:projects]]:[[voyc]]

======Map Projections======

see [[Gallery of Map Projections]]\\
see [[Thematic Maps]]\\

Projecting a 3D sphere onto a 2D map results in distortions.

Place a lamp in the center of a translucent sphere. Let it project a shadow onto a sheet, hanging flat or curled in a cylinder.

All 2D maps are distorted.  Distortion occurs in:
  * shapes
  * areas
  * distances
  * directions
  * angles

Types of distortion correction:
  * conformal - preserves angles
  * equal-area - preserves areas

Each type of map projection has a different approach to distortion correction.

Three projection types, with variations:
  * conic
    * Albers
    * Equidistant
    * Lambert Conformal
  * cylindrical
    * **Equirectangular**
    * **Mercator**
  * planar
    * azimuthal perspective
      * **orthographic**


===== Web Mercator =====

In **2005**, Google Maps introduced a modification to the Mercator to allow faster calculations.\\

Web Mercator uses a spheroid model instead of Mercator's ellipsoid model.\\  
This allows a faster calculation but sacrifices some accuracy at low scales.\\

Web Mercator also introduces "zoom level".  Explained here at 
[[https://developer.tomtom.com/map-display-api/documentation/tomtom-orbis-maps/zoom-levels-and-tile-grid|TomTom]].

Web Mercator is now used in most online street mapping systems.\\

===== Comparisions =====

==== Azimuthal Equidistant vs Azimuthal Equal-area ====
{{https://map-projections.net/img/jpg/azimutal-equidistant-gpolar.jpg?300}}
{{ https://map-projections.net/img/jpg/azimutal-equal-area-gpolar.jpg?300}}
~CLEAR~

====Wall Charts====

====Mercator vs Web Mercator====

====Cylindrical vs Conic====





==== Formula ====

=== Equirectangular ===

\begin{align}
x &= \lambda  && \text{longitude} \\
y &= \varphi && \text{latitude}  \\
\end{align}

This projection is mathematically simple and is used sometimes for raw data, like altitude data for instance.

=== Mercator ===

\begin{align}
x &= R\left (\lambda - \lambda _{0} \right ) && \text{longitude} \\
y &= R \text{ln} \left [ \text{tan} \left( \frac{\pi}{4} + \frac{\varphi}{2}\right )\right ] 
&& \text{latitude}  \\
\end{align}

This is the Web Mercator variation used by Google Maps and most other online street mapping programs because of the speed of calculation.

=====Voyc Petri Projection=====

==Purpose==
Demonstrate the expansion of life forms from Africa outwards to the rest of the world.\\
see [[Thematic Maps#Out of Africa|Out of Africa]]\\

==Requirements==
  * circular shape, 86 mm diameter, to fit in a petri dish
  * origin in Lake Victoria
  * maintain relationship between eastern Russia and Alaska
  * equal-area



=====References=====
[[https://www.geographyrealm.com/types-map-projections/|Types of Map Projections]] by Elizabeth Borneman

[[https://www.geographyrealm.com/map-projection/|A Guide to Understanding Map Projections]] by Caitlin Dempsey, plagiarized from the Borneman article

[[https://projectionwizard.org/|Projection Wizard]] by Bojan Šavrič