How to calculate volume of a 3D mesh from wavefront .obj file?

Question

I am trying to parse wavefront .obj file. From wikipedia I learned it's format specification. I am interested in volume analysis. Before that i worked in .stl files. I can compute volume of tetrahedron by using dot and cross product. In .stl files triangular faces' coordinates are given i.e.

• point1(x1, y1, z1),
• point2(x2, y2, z2),
• point3(x3, y3, z3).

But in wavefront .obj files : Each face can contain three or more vertices. f v1 v2 v3 v4 ..... like this. I do not know how to calculate the volume now. Because my understanding is, it will produce a polyhedron. Any idea will be extremely helpful. Thanks!

Answer 1

Each polygonal face can be subdivided in triangles and therefore used for tetrahedrons. If you are lucky enough, you can find polygons with 4 vertices only (easy to be decomposed in two triangles on the fly). For polygons with more than 4 vertices you need a triangulation algorithm to decompose the planar polygon in triangles. You can check Ear Clipping for example.