### Author Topic: solid volume calculated by the Construct Surface Mesh  (Read 774 times)

#### andree

• Newbie
• • Posts: 1 ##### solid volume calculated by the Construct Surface Mesh
« on: November 30, 2017, 01:40:19 PM »
Hello,

First I thank Ovito contributors for this incredibly useful software!!!
I noticed that the solid volume calculated by the Construct Surface Mesh does not change when the number of smoothing  iteration increases. By eye I have the impression that it should decrease. In particular, I got situation when the sphericity (S/(pi(6V/pi)^(2/3))) is smaller than 1 which is not mathematically possible.
Did I miss something in the manual? Is there any explanation?

many thanks,
Andree

#### Alexander Stukowski

• Hero Member
•     • • Posts: 638 ##### Re: solid volume calculated by the Construct Surface Mesh
« Reply #1 on: November 30, 2017, 05:41:04 PM »
Dear Andree,

Thanks for appreciating the work I did with developing OVITO.

The explanation for your observation is this: The solid volume is calculated before the surface smoothing step. Thus, the value is unaffected by the smoothing.

The reason for this choice is that calculating the volume enclosed by an arbitrary triangle mesh is difficult. In contrast, calculating the original volume is easy, because it is simply the union of all Delaunay tetrahedral elements that were classified as 'solid' by the algorithm. In fact, first the volume is determined, and then the surface around it is constructed later.

Why is it justified to use the original volume before smoothing? Because the smoothing procedure is supposed to be volume conserving! In practice it turns out that this is not quite right, but the assumption is that the error is not significant. At least so far it didn't justify the effort it would mean to implement a general volume calculation routine for the smoothed triangle mesh (which can deal with periodic boundary conditions and other difficulties).

Let me know if you have further questions.

-Alex