[R] How to define and calculate volume of 3D polygon?

[Duncan Murdoch]

On 19/05/2014, 10:42 AM, Alexander Shenkin wrote:
> Hi Folks,
>
> I have a set of x,y,z points in 3D space that defines the outline of a
> tree crown (5 - 15 perimeter points + 1 top & bottom point). I would
> like to calculate the volume of the corresponding 3D polygon based on
> those points.  I have been able to use geometry::convhulln, but I think
> this isn't the right algorithm, since the polygon needs to pass through
> each point in order, and not just snap a rubber-band around the outer
> points.
>
> Any suggestions for alternative algorithms and packages would be most
> welcome!

If you aren't using the convex hull, you need to specify more 
information.  The vertices of a polyhedron don't have a natural order, 
so passing through them "in order" doesn't make sense.

One way to specify this information is to specify which triples of 
vertices form triangular faces, as convhulln does.

I don't know of a package containing code to compute the volume, but a 
description of the algorithm is on this page:

http://www.ecse.rpi.edu/~wrf/Research/Short_Notes/volume.html

Duncan Murdoch


>
> Thanks,
> Allie
>
>      seq          x          y    z
> 1    1 -1.7310065  2.4502278 11.1
> 2    2 -1.9048260 -0.6096212  9.0
> 3    3  2.8652209  0.8891057 11.0
> 4    4  2.3929514 -3.4516349 11.2
> 5    5 -2.6436343  5.2745803 11.7
> 6    6 -4.3521504  4.6924180 11.7
> 7    7  6.1441732 -4.8051156 11.6
> 8    8 -6.2157823 -3.2193244  8.0
> 9    9  1.0024961 -2.8275434  9.0
> 10  10 -3.9656821  3.0452201  8.0
> 11  11  4.2070518 -1.5970958 11.0
> 12  12 -0.9461915  1.2902409  9.8
> 13  13  2.2792265  0.7517491 11.4
>
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