How to calculate volume?

Question

JavaScript

There is a .stl file, it contains information about a three-dimensional model, how to calculate the volume? Is there any way to work with such files (preferably in js or C#). I don't understand 3d at all. I would be grateful for any information on the topic.

solid cube
   facet normal 0 0 0
     outer loop
       vertex 0 0 0
       vertex 0 1 0
       vertex 1 1 0
     endloop
   endfacet
   facet normal 0 0 0
     outer loop
       vertex 0 0 0
       vertex 1 1 0
       vertex 1 0 0
     endloop
   endfacet
   facet normal 0 0 0
     outer loop
       vertex 0 0 0
       vertex 0 0 1
       vertex 0 1 1
     endloop
   endfacet
   facet normal 0 0 0
     outer loop
       vertex 0 0 0
       vertex 0 1 1
       vertex 0 1 0
     endloop
   endfacet
   facet normal 0 0 0
     outer loop
       vertex 0 0 0
       vertex 1 0 0
       vertex 1 0 1
     endloop
   endfacet
   facet normal 0 0 0
     outer loop
       vertex 0 0 0
       vertex 1 0 1
       vertex 0 0 1
     endloop
   endfacet
   facet normal 0 0 0
     outer loop
       vertex 0 0 1
       vertex 1 0 1
       vertex 1 1 1
     endloop
   endfacet
   facet normal 0 0 0
     outer loop
       vertex 0 0 1
       vertex 1 1 1
       vertex 0 1 1
     endloop
   endfacet
   facet normal 0 0 0
     outer loop
       vertex 1 0 0
       vertex 1 1 0
       vertex 1 1 1
     endloop
   endfacet
   facet normal 0 0 0
     outer loop
       vertex 1 0 0
       vertex 1 1 1
       vertex 1 0 1
     endloop
   endfacet
   facet normal 0 0 0
     outer loop
       vertex 0 1 0
       vertex 0 1 1
       vertex 1 1 1
     endloop
   endfacet
   facet normal 0 0 0
     outer loop
       vertex 0 1 0
       vertex 1 1 1
       vertex 1 1 0
     endloop
   endfacet
 endsolid cube

Answer 1

It is enough for each face
vertex x1 y1 z1
vertex x2 y2 z2
vertex x3 y3 z3 to
calculate the value Vj=(x1*(y2*z3-y3*z2)+x2*(y3*z1-y1*z3)+x3*(y1* z2-y2*z1))/6, and find the sum of these values ​​(some of them will be negative, but that's okay). For a closed model, it will be the desired volume.
It is easier to work with binary STL - there is no need to spend effort on parsing.

Answer 2

If the vertices are known, then the volume of the convex hull can be calculated. This can be done manually, or Wolfram Mathematica can do it.