June 21, 2022

A:

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Q:

Rendering Points From Lat/Long To Mercator

I am attempting to render the points on the ground, such as buildings, shops, etc. Since the resolution of the native Mercator grid is 10x less than the resolution of the Lat/Long grid, I need to “Merge” the two grids based on their shared lat/long points. I understand how to do this procedurally, so I don’t need a function that does this. I just need a function that:

Maps the lat/long points on a linear grid to the Mercator grid,
Mapping the Mercator grid to the lat/long plane
Then plotting the projected points on the lat/long plane.

I can do the first of these in an O(1) time complexity using an inverted index but I am stuck on the next two tasks.
What I have tried:

I can use a simple PerspectiveTransform to project the lat/long points, but I need to know the Mercator scale at each lat/long point and this seems like it would be an O(n) problem since I would need to re-compute the Mercator projection for every row.
I can break up my latitude in pieces and break up my longitude in pieces, then compute my Mercator Projection in a loop for each piece. I’m also stuck determining how to interpolate between the two Mercator scales

It seems like I should just be able to divide the Mercator grid up into lat/long bins, project my points to the lat/long plane, then render as a raster image.

A:

I’m not sure if I understand your question correctly – I do not see how it is related to Mercator projection specifically.
You can project 2D world coordinates (that have grid effect in longitude direction) with a view/zoom factor to a plane. Probably you are familiar with OpenLayers, then you can zoom in/out and you will see the effect of a smaller area of the grid.
A bit more hard C++ related – you may want to look at the this vector map of the world, and it features web browser type zoom in/out capabilities.
And as far

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