How to calculate a spherical surface?

[burli]

Hi folks,
I'm still around here and I need a little bit of help to write a simple mapgen.

I want to write a mapgen that creates a surface withe the same radius of the earth an a hight resolution of 1/16 block.

That means that I get 64*64km sphere section with the same radius as the earth.

I'm not sure how to calculate that, especially with the 1/16 blocks.

Can someone help me?

Thanks
burli

[DrFrankenstone]

A formula for a sphere is: x² + y² + z² = r²

so rearrange that for y gives y = sqrt(r² - x² - z²)

The radius of earth is 6,371 km, so y = sqrt(6371000² - x² - z²)

But that earth is centered on (0,0,0) and you probably want it centered 6371km lower so that ground level at x=0, z=0 will be at y=0, so

y = sqrt(6371000² - x² - z²) - 6371000

Since Minetest's Lua doesn't have bitwise operators, you could get the 1/16 fractional values out of y like:

Code: Select all

yTruncated = math.floor(y)
sixteenths = math.floor(y * 16) - (yTruncated * 16)

(None of this is tested, and I couldn't tell if I understood the question, any mistakes left as exercises for the reader :))

[burli]

Sounds good too me. Will try it. Thanks