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Slice through Graphics3D


is there any possibility to slice through a Graphics3D object? At the end I would like to have a stack of images slicing , e.g. $n$ times in $z$-direction: $((x,y,z_{0}), (x,y,z_{1}),…,(x,y,z_{n}))$


Here is an example of random spheres, which I would like to slice.


z = 100;
p = RandomReal[100, {z, 3}];
r = RandomReal[10, {z}];
obj = GraphicsComplex[p, Sphere[Range[z], r]];

t0 = AbsoluteTime[];
gr = Graphics3D[obj, Axes -> True]

I would be pleased about any suggestions.



Answer



You can do this by specifying a dynamic PlotRange. Here is an example using Manipulate. You will need to adapt your range for each dimension:


z = 100;
p = RandomReal[100, {z, 3}];
r = RandomReal[10, {z}];
obj = GraphicsComplex[p, Sphere[Range[z], r]];

t0 = AbsoluteTime[];
gr = Graphics3D[obj, Axes -> True]

Manipulate[
 Show[gr, PlotRange -> {{x, Automatic}, {y, Automatic}, {z, 
     Automatic}}], {x, 0, 100, 1}, {y, 0, 100, 1}, {z, 0, 100, 1}]

enter image description here


In order to generate images you will have to replace the Manipulate by a Table command and generate the images. Have a closer look at ViewPoint to specify the view on your Graphics3D object. This will allow you to generate images looking from the different directions.


Here is an example:



Manipulate[
 Show[gr, ViewPoint -> {0, -Infinity, 0}, 
  PlotRange -> {{x, Automatic}, {y, Automatic}, {z, Automatic}}], {x, 
  0, 100, 1}, {y, 0, 100, 1}, {z, 0, 100, 1}]

enter image description here


edit


To get sections you could also use PlotRange. Here is an example giving you slices of thickness 1 in y-direction:


Manipulate[
 Show[gr, ViewPoint -> {0, -Infinity, 0}, 

  PlotRange -> {{x, Automatic}, {y, y + 1}, {z, Automatic}}], {x, 0, 
  100, 1}, {y, 0, 100, 1}, {z, 0, 100, 1}]

enter image description here


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