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Does North point straight up when you are looking at the Mollweide projection?
The main reasons for this are: 1 – North is always straight up, and 2 – at any point, the scale is always the same in every direction, and this makes the shapes of small areas look correct. But the Mercator projection has terrible trouble with the scale getting larger as you move away from the equator.
What distortion do you see on a Mollweide?
Distortion. Mollweide is an equal-area (equivalent) projection. Shapes, directions, angles, and distances are generally distorted. Points 40°44′ north and south at the central meridian have zero distortion.
Why is the Mercator map distorted?
Although the linear scale is equal in all directions around any point, thus preserving the angles and the shapes of small objects, the Mercator projection distorts the size of objects as the latitude increases from the equator to the poles, where the scale becomes infinite.
What is the range of a Mollweide projection?
The x -coordinate has a range of [−2 R√ 2, 2 R√ 2 ], and the y -coordinate has a range of [− R√ 2, R√ 2 ]. Equation (1) may be solved with rapid convergence (but slow near the poles) using Newton–Raphson iteration:
How to plot the world using map projections?
Using map projections Exercise 1. Plot the world with a Robinson projection, using gray shading for land. World coastline with Robinson projection. Exercise 2. Plot an image of world topography with the Mollweide projection. Note that some adjustment of the margins is required to fit the colorbar. World topography with Mollweide projection.
When did Karl Brandan Mollweide create the projection?
The projection trades accuracy of angle and shape for accuracy of proportions in area, and as such is used where that property is needed, such as maps depicting global distributions. The projection was first published by mathematician and astronomer Karl (or Carl) Brandan Mollweide (1774–1825) of Leipzig in 1805.
When do you report the datum for lat / long coordinates?
When noting lat/long coordinates or giving lat/long coordinates to someone, you must always report the datum which is used by the coordinates. Without the datum information, the user will have to guess which datum your lat/long coordinates are in, and this often leads to misalignment of features.