see Gallery of Map Projections

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

https://en.wikipedia.org/wiki/Web_Mercator_projection
https://gist.github.com/shiffman/a0d2fde31f571163c730ba0da4a01c82
https://developer.tomtom.com/blog/decoded/understanding-map-tile-grids-and-zoom-levels

mercator uses ellipsoid model, has time-consuming calculation
webmercator uses spheroid model, introduces “zoom level”, and simplifies the calculation
a sphere is a subset of an ellipsoid object

Similar to mercator, but with much faster calculation.

Introduces “zoom level” TomTom

Introduced by Google Maps in 2005.
Now used in most online street mapping systems.

centered on the North Pole, equatorial aspect
Map: Caitlin Dempsey.
https://www.geographyrealm.com/types-map-projections/
https://projectionwizard.org/

Azimuthal Equal-Area https://en.wikipedia.org/wiki/Lambert_azimuthal_equal-area_projection

https://projectionwizard.org/#

https://duckduckgo.com/?q=Azimuthal+equal+area&t=brave&iax=images&ia=images&iai=https%3A%2F%2Fwww.map-projections.net%2Fimg%2Ftissot-15-w%2Fazimutal-equal-area-equator.jpg%3Fft%3D616b107f

azimuthal equidistant vs azimuthal equal-area

wall charts

mercator vs web mercator

cylindrical vs conic

\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.

\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.

Geography Realm edited by Caitlin Dempsey]]

Projection Wizard by BOJAN ŠAVRIČ