General formula to calculate the Volume of a 3D shape

[rvr]

Hello,

I'm new here and I'm stuck on an issue. I looked through other threads but couldn't find aything that suited my needs. The problem is thus:

A 3d shape is created by connecting all the points of 2 faces. Each face is a closed 2D polygon with between 4 and 20 vertices. The polygons may be rotated along the X Y or Z axes and may be larger or smaller than each other. The volume of the 3D shape created by joining these 2 polygons with straight lines, must be calculated. I've added an image for the rectangular shape, the same thing is applicable to the polygons.

How can I calculate this volume? I've left my math (and I think my brains ) behind in school so I really need some help!!

 

[stapel]

I think more information is necessary, such as the amount of "twisting" (and how this is defined). The volume will vary accordingly.

 

[daon2]

^ Not only that, but also you haven't described how points are connected. This problem is to far too vague to give an answer to.

In the simplest case, where the polygons are parallel and connected in the simplest manner, the amount of twisting does not matter. It is a result of a theorem taught in multivariable calculus involving areas of cross sections (forget the name). If the polygons are the same size it is just the area of the cross section times the "height" of the object. If they are different sizes (and still parallel) then a straight-forward integral will do it.

 

[stapel]

In the simplest case, where the polygons are parallel and connected in the simplest manner, the amount of twisting does not matter.

Unless (I think) the height is a result of the twisting. If the faces and the joining edges are fixed, and then the twisting is applied, the degenerate case (I think) would reduce the height essentially to zero.

As you say, the exercise, as posted, is much too imprecise.