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The 4.1 version of TCG is compatible with Windows 7/Vista.Q:

How to find the height/length of a 3d space within a sphere?

I’m trying to get the perimeter of a 3d space within a sphere as a function of height above it. We can assume that my sphere’s center is at the origin and is the same size as my 3d space (where this refers to Z = 1, I’m assuming the unit sphere, which I think is an easy assumption to make).
I tried using Raycasting to find the length of the surface of the sphere, but I’m not sure what the return type should be, and after a bit of research it looks like I need the volumetric scalar field to do the trick (in the form of rays from the origin, hitting the surface of my sphere along the z direction, and counting the amount of hits).
I don’t want to use path tracing because I want to do this for a 2d projection of the space as well, and then have the height of the space be the given input.
Any suggestions on how to do this? My current guess is that it will take a lot of data (as much as the volume of the sphere is high, as the surface of the sphere can be at any Z for each x,y coordinate in my space), but I would like some input on whether this is the case and a solution if it is the case.

A:

Don’t do that. It’s way overkill. 馃檪 You could use the acos function to figure out the z range of your function. There are no triangles in a sphere, so there is no sampling, it’s just a simple 2d function. Not that hard to do in python either, just a little tricky on very small spheres.
A better approach is to use path tracing if you want to sample all surfaces at once. In that case you need a sphere function, with some kind of ray tracing setup, that is taking in the size of the sphere you’re sampling and the point of interest.
Put in a few math notes if you really need help.

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https://colab.research.google.com/drive/1mNsAk2L1mExPXaGqKui2_3RsKTUL8uIt
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https://colab.research.google.com/drive/1c0tyjgcp965JymLRGKhhlS4M26LnxsaY

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