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Cut a 3D surface by a horizontal plane?

agilicz
Posted 5 years ago

Dear Community,

I've reconstructed a pond from its contourline polygons, and plotted it. The depth of the pond ranges from 0 ft to -70 ft. Now I would like to see where the water would be in the pond at -45ft depth? Mathematically: how to cut this 3D surface with a horizontal plane at -45 vertical value and plot both surface and obtained polygon? Unfortunately I'm unexperienced in this field and would appreciate your kind help here. Files are attached.

Tx in advance. Best regards, Andras

Attachments:
Pond.nb
PondPoints3D.xlsx
POSTED BY: agilicz
8 Replies
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agilicz
agilicz
Posted 5 years ago

Dear Seth,

Tx very much, works perfectly well for my goals, and I learned a lot. Now ready to take a bath in the pond :-)

Best regards, Andras
POSTED BY: agilicz
POSTED BY: Seth Chandler
agilicz
agilicz
Posted 5 years ago

Dear Seth,

Wow, tx very much, very elegant! Would it be also somehow possible to clip the plane outside the pond?

Tx in advance, best regards Andras
POSTED BY: agilicz

A different approach, where the shape of the pond is extracted from the mesh line primitives:

pr = ListSurfacePlot3D[allpoints,
  PlotRange -> {All, All, {-130, -45}},
  MeshFunctions -> {#3 &}, Mesh -> {{-45}}]
lns = Cases[Normal[pr[[1]]], Line[{{_, _, -45.}, __}], All];
Show[ListSurfacePlot3D[allpoints, MeshFunctions -> {#3 &}], 
 Graphics3D[{Opacity[.5], Blue, Polygon @@ lns[[1]]}]]
POSTED BY: Gianluca Gorni

Clever. I thought there might be many ways to do this. Yours will do better with ponds that have caves or that are not functions in the z direction.
POSTED BY: Seth Chandler

A pond with an island may be a problem, too.
POSTED BY: Gianluca Gorni
agilicz
agilicz
Posted 5 years ago

Dear Gianluca,

Thank you very much, works very nice! It will take me some time to fully understand it, but I'll do my best.

Tx and best regards, Andras
POSTED BY: agilicz

Here's a sketch of how to combine graphics, where myListSurfacePlot3D corresponds to the "pond" you created in your notebook:

Show[myListSurfacePlot3D,Graphics3D[{Opacity[0.5],Blue,InfinitePlane[{{0,0,-45},{1,0,-45},{0,1,-45}}]}]]
POSTED BY: Seth Chandler
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