How can i find a mathematical equation for a 3d geometry

Rhino Rhino for Windows
1

Hi
Dear all

i built a 3D surface (like semi-sphere) in rhino.
is there any way to find a mathematical equation for my geometry?
i gonna get an equation that cover my geometry!

best

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and how might you expect us to know without seeing it?

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dear @Michael_Pryor
i mean, you give me general information .
any way i attached it.

dome1.3dm (62.5 KB)

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image
image811×445 104 KB

sorry couldn’t resist

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Dear @Gijs

Could you please tell me, how do you do? and give some information or reference.

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what would you need that formula for? nurbs surfaces are usually described as parametric functions which might be a bit unhandy to work with (maybe different/simpler for revolved objects but i am just guessing), usually if you are interested in the exact parametric formula you model from the other side using formulas to actually create surfaces, i am not sure if its possible to read out the entire parametric formula and display it as such.

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i gonna use model’s formula to matlab code.

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yes i see and probably underlines what i wrote, i believe matlab is rather used to display already developed geometry to help understand and visualize it. i am just wildly guessing now that matlab is not using NURBS to describe surfaces. NURBS like Rhino describes “most” of its geometry, are usually used to generate surfaces for design and production intent. can you elaborate a bit more what your exact intentions are?

here is a very brief intro to what NURBS are and how they are computationally described. i am not sure my input will lead you anywhere closer to your goal but it may be interesting.

and here something very essential either i think

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Introduction to the mathematics used by Rhino: https://developer.rhino3d.com/guides/general/essential-mathematics/

OpenNURBS has a set of software toolkits which can be used in developing software to extract the geometry information from Rhino .3dm files.

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There is no way how to obtain the equation directly from geometry (which kind of equation - standard, parametric, polar, cylindrical…), but you can write some equations by hand with knowledge of analytical geometry. In case the sphere, the equation in standard form is
(x−x0)^2+(y−y0)^2+(z−z0)^2=r^2
where x0, y0 and z0 are coordinates of the center
r means radius
So you can easily find all these coefficients with built-in analytical tools in Rhino and substitute them into equation.

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Hello,
There is a website called mathcurve, a very handy encyclopedia when it comes to define 2d curves, 3d curves and surfaces through mathematical definitions. Please enjoy, it is priceless ! It is developed by Robert Ferreol !
https://www.mathcurve.com/surfaces.gb/surfaces.shtml
https://www.mathcurve.com/courbes3d.gb/courbes3d.shtml

Have fun,

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