Is there any methods (like circularity) to decide if the 3D construction close to sphere?

Hi,

I have got many 3D particles from 2D images and want to get a value to decide if this 3D particles close to perfect sphere. For a 2D shape, I know there is a way to calculate circularity, but is there a similar way for 3D constructions?

Thanks!

[Jan]

Please explain in which format you "have many 3D particles".

You can fit a sphere in a least square sense and measure the maximum or mean deviation of the radius of the partical coordinates. But than 2 circles could be accepted as "perfect sphere", if they are located exactly on the surface. Would this match your needs or do you need a kind of equi-distribution on the surface?

[Dongyu Liang]

Hi,

Thank you for the help and it is a good idea.

But I just realized the particles are not solid inside. Therefore, the sphericity may not be good for this. So, I am wondering is there any concepts to describe how the shape of an object close to hollow sphere?

Thanks!

[Jan]

Again: How are your input data are represented? As an image, as coordinates of points or edges, as STL-File, as polytops, as point cloud?

So what exactly is "an object" in your case. How can a "hollow sphere" be distinguished from a "not hollow sphere"? Do you expect an equi-distribution of points on the surface, or inside a volume? Is it defined if the obejct is convex at all?

[Dongyu Liang]

They are some mineral particles scaned by micro CT, so the inputs are set of 2D images in TiF to generate 3D structure. There are only particles which have been burned before scanning. So there are voids inside the particle to become like hollow sphere. To classify the particles, I want to know if there is any concepts to describe how the shape of those particles close to hollow sphere.

Thank you.

Answer 1

[Shubham Rawat]

Hi,

When finding sphericity for a single particle or object, you can define sphericity as the ratio of surface area of a sphere that has the same volume as the particle or object to the surface area of the particle itself.

Put into mathematical terms, the sphericity given by ​Ψ ("psi") is:

for the volume of the particle or object ​​ and surface area of the particle or object ​​. You can see why this is the case through a few mathematical steps to derive this formula.

Hope this Helps!​

[Dongyu Liang]

Hi,

Thank you for the help.

I just realized the particles are not solid inside. Therefore, the sphericity may not be good for this. So, I am wondering is there any concepts to describe how the shape of an object close to hollow sphere?

Thanks!