| Re: mesh_volume and tetra_volume [message #40355] |
Mon, 09 August 2004 09:28  |
Karl Schultz
Messages: 341
Registered: October 1999
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Senior Member |
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"Robert Schaefer" <robertschaefer@gmx.de> wrote in message
news:bffaee64.0408090124.5906ed23@posting.google.com...
> Hello, I want to get the volume out of a 3d object.
> First i tried with mesh_volume, but the returned values weren't
> similar to my calculated. I checked with mesh_issolid: return value:1,
> so it ios solid and should return the volume.
> When i check with tetra_volume the volume is similar to my calculated
> volume.
>
> Now my question: what is the difference between mesh_volume and
> tetra_volume?
MESH_VOLUME works by summing:
( a dot ( b cross c ) ) / 6
for every triangle in the mesh where a, b, and c are the verts of each
triangle in the mesh. This effectively calculates the signed volume of a
tetrahedron formed by the origin and the 3 triangle verts for each triangle
and then adds them up.
TETRA_VOLUME just adds up the volume of all the tets in the mesh using the
same idea as above.
How big a difference are you seeing? Is there anything strange about your
mesh, like being self-intersecting? How did you generate both the polygonal
mesh and the tetrahedral mesh?
Karl
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| Re: mesh_volume and tetra_volume [message #40490 is a reply to message #40355] |
Tue, 10 August 2004 01:02  |
robertschaefer
Messages: 10
Registered: August 2004
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Junior Member |
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"Karl Schultz" <kschultz_no_spam@rsinc.com> wrote in message news:<10hf9gscqmtdj41@corp.supernews.com>...
> "Robert Schaefer" <robertschaefer@gmx.de> wrote in message
> news:bffaee64.0408090124.5906ed23@posting.google.com...
>> Hello, I want to get the volume out of a 3d object.
>> First i tried with mesh_volume, but the returned values weren't
>> similar to my calculated. I checked with mesh_issolid: return value:1,
>> so it ios solid and should return the volume.
>> When i check with tetra_volume the volume is similar to my calculated
>> volume.
>>
>> Now my question: what is the difference between mesh_volume and
>> tetra_volume?
>
> MESH_VOLUME works by summing:
>
> ( a dot ( b cross c ) ) / 6
> for every triangle in the mesh where a, b, and c are the verts of each
> triangle in the mesh. This effectively calculates the signed volume of a
> tetrahedron formed by the origin and the 3 triangle verts for each triangle
> and then adds them up.
>
> TETRA_VOLUME just adds up the volume of all the tets in the mesh using the
> same idea as above.
>
> How big a difference are you seeing? Is there anything strange about your
> mesh, like being self-intersecting? How did you generate both the polygonal
> mesh and the tetrahedral mesh?
>
> Karl
My testobjekt is generated by dilatation of one point. I can not see
any strange about the mesh.
With computemesh i generate the triangles, like D.fanning in his
example (http://www.dfanning.com/graphics_tips/mesh.html). I signed
the calculated values between tetra_volume and mesh_volume are very
differnt:
accord sphere formula : 4./3.*!pi*16.^3 = 17157.3
total (vol) : 17611.0
volume with tetra_volume: 16308.0
mesh_volume : 11988.0
Any idea?
Robert
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