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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.

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  • $\begingroup$ You can use PlotRange to emulate that to a certain degree, try: Manipulate[ gr = Graphics3D[obj, Axes -> True, PlotRange -> {Automatic, Automatic, {0, z}}], {{z, 100}, 0, 100}]. For the image stack, this will be more complicated... $\endgroup$ Commented Sep 25, 2013 at 6:56
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    $\begingroup$ If you only want circle sections, this could be solved in an analytic fashion. Intersections on general graphics objects are not implemented yet (9.01). $\endgroup$ Commented Sep 25, 2013 at 7:31
  • $\begingroup$ It seems that @YvesKlett is right so maybe you can confirm that your objects are only Spheres or provide a minimal example of the data you are working with so we can help with your case. $\endgroup$ Commented Sep 25, 2013 at 8:37
  • $\begingroup$ Related: mathematica.stackexchange.com/questions/25511/… $\endgroup$ Commented Sep 25, 2013 at 14:36

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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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If you have the analytical expressions for your surfaces (as it's the case for the spheres) there are lot of ways to do that by using any *3D[] plotting function like this:

Image3D@Table[ImageTake[ Image@Plot3D[Sin[x y], {x, -3, 3}, {y, -3, 3}, PlotRange -> {-1, s}, ClippingStyle -> {Transparent, Green}, Boxed -> False, Axes -> False, PlotStyle -> Transparent, Mesh -> None, ViewPoint -> {0, 0, -Infinity}], 10 {1, -1}, 10 {1, -1}], {s, -.9, .7, .1}]

Mathematica graphics

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    $\begingroup$ yuck... why green? Image search returns this :-) $\endgroup$ Commented Sep 25, 2013 at 14:43
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    $\begingroup$ @YvesKlett Green, as most things in the history of mathematics is just because I like it en.wikipedia.org/wiki/History_of_mathematical_notation :) $\endgroup$ Commented Sep 25, 2013 at 15:05

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