I always wondered if it's possible to turn a 3D graphics type file into a parametric equation. For example, we'll take the free program "Blender" which allows you to model anything you can think of.

Example Image: Example

Is it possible to turn a random 3D shape I just made in Blender to a surface parametric equation? If it is possible then how?

(If this question doesn't belong to math.stackexchange section, then tell me where is the right section). (I know this is tagged Blender, it relates to any file format of 3D Graphics).

Thank you in advance.

P.S I have been told to post this question here (It was posted on math.stackexchange section).

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    Graphic Design SE is for .. graphic design questions. Much as I hate to send you back, this really is not about graphic design. The fact that you produced your object with Blender is irrelevant; you can create an object with any interactive 3D modeller and ask the same. Even the 3D modeller part is irrelevant. To me this seems a math question, more than anything else. By the way, it's similar to creating an equation for any 2D image. I guess that could give you a starting point to Google for, – usr2564301 Mar 20 '16 at 21:05
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    The answer is yes and no. Yes such function possibly exists but there is no general way of deriving it. Its like asking the underlying formula for everything. – joojaa Mar 20 '16 at 21:32
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    I'm voting to close this question as off-topic because It has nothing to do with graphic design. – joojaa Mar 21 '16 at 5:42
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    at the math section they voted to close it and here you're going to vote to close it, where can I post this then? – RonFarkash Mar 21 '16 at 11:50
  • @RonFarkash I dont think you can post this anywhere, there really is no site for 3D modeling on stackexchange . This could be a fit in engineering SE but not in this form. Your question needs much much more meat and reason than just vague parametric surfacing. If you post it in this form nearly on any stackexchange site it will be closed ASAP. Same applies to CG.SE. The question is just INCREDIBLY broad. – joojaa Mar 21 '16 at 17:59

This probably is in the realm of the MathOvewrflow or Computer graphics section.

I will just speculate.

No. Not any.

If you start with a parametric primitive and you deform it, it is still parametric.

But if you start sculpting it with booleans, intersections or localized deformations, no.

What you now have is intersection of possibly parametric solids and segments of those solids, so you now do not have one or two parameters, but a bunch of them on possibly different coordinating systems.

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  • Well no the answer is yes, there is somewhere a parametric surface that can do the shape you wish in fact several. But this is useless since you can not find it. And i can assure you if this is posted on computergraphics it will promptly be closed. The question in its core is not too bad it is just that the purpose and scope of the question is not well defined. Essentially this is a dream for many 3d artists since it would eliminate need for uv mapping, it would be a dream for manufacturing economy and so on. If i know how to do it i would sell that info out. – joojaa Mar 22 '16 at 9:15

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