How Will I Compute The Normals at Vertices using 3D Object?

[lastchance]

My problem is how do I select the proper distance/offset.

Read the vertices and find the maximum and minimum coordinates in each of x, y, z directions and hence the range of coordinates in each direction.

Apply your initial offset as a fixed fraction (say a few percent) of, say, the mean of these coordinate ranges.

You will inevitably have to vary your offset depending on what the object looks like (as it it may have very different ranges in x, y, z directions).

Impossible to give any further guidance until you explain what you actually intend to use the displaced surface for - you STILL haven't told us. (It's not an appropriate way to scale a figure, for example).

[kindgnice]

I will try my very best to explain the reason Sir why I am trying to use a "displaced" or "offset" value not too far away from the boundary constraints. Honestly, there are lots of methods in order to interpolate an implicit curve or surface. However, for this specific research paper...

https://www.cc.gatech.edu/~turk/my_papers/vimp_tog.pdf

... the selection of the offset constraint (normal constraint as termed by the author) is the best option since it best interpolates the surface very well.

For example, if we are going to use several boundary constraints and only one positive constraint, we can observe that...

https://i.imgur.com/RUrMRHL.png

If we add more constraints, like 3 additional boundary constraints, then the interpolation will be modified at some point... (Note: Green surface is some function greater than 0 or f(x)>0 and Red surface is some function less than 0 or f(x)<0)

https://i.imgur.com/Al81yNU.png

Extending this knowledge to 3D, some OBJ files are interpolated well without problem like the previous OBJ examples...

For the original HEART.obj...
https://i.imgur.com/hp7eWAB.png

The output implicit surface HEART.obj is...
https://i.imgur.com/GAryLPE.png

Also with this HEART.obj, giving different offset values shows almost same interpolated implicit surface output which means no problem at all.

However, if I use other OBJ files, the outputs are undesirable, and most of the time I do trial and errors to guess the offset values. Honestly, until now, I am trying to interpolate a certain OBJ file right now, and I started (literally) from offset 0.01,....,0.5...., 1.0,2.0,3.0,......25.0 and I am now in 25.0 offset value and still no good results. I also tried to take the mean of the ranges for each x, y and z coordinates but I ended up guessing (trial and errors) the offset values.

https://drive.google.com/file/d/1yntJBYyj_9W8tU-Sg14w5nNhgIpqBBhs/view?usp=sharing

Hmm, I am starting to think probably this is one of the limitations of this research paper especially in very closed sheets like as mentioned from the other papers I have read (a screenshot from the paper shown below):

https://i.imgur.com/RksaKas.png

But this is something that I need to investigate more further Sir... (Note: The figure shown above was taken from the research paper: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5395267

[kindgnice]

Thank you very much to those who shared their insights and especially to Sir Keskiverto and Sir Lastchance, I hope I can share and ask questions again with you in my next succeeding adventures of implicit surfaces and 3D objects. God bless you all. :)