graphics3d - OpenSCAD like functionality with Mathematica?

I keep seeing reference to use of Mathematica as a CAD tool (for instance, this). I'd like to use it as such if feasible, but I'm having trouble locating equivalents of the functionality I use in my current design tool, OpenSCAD.

I know how to create simple shapes (Graphics3D[], Cylinder[], etc.) and I'm aware that Mathematica can export to STL format. But does Mathematica have equivalents of the following OpenSCAD functions, or is it the wrong tool for the kind of thing I'm trying to do?

linear_extrude()

union()

intersection()

difference()

translate()

rotate()

Answer

UPDATE

With release of Mathematica 10 built-in functionality we have new things and continue to add - please see:

Geometric Computation examples

Geometric Computation guide

Especially: Derived Geometric Regions

OLDER

Quick answers to some points:

My guess is you are interested in the operations related to 3D printing. Mathematica provides computational approach - which is very general and allows to compute a lot of things. To see possibilities I would really recommend to watch Yu-Sung Chang recent talk "Scan, Convert, and Print: Playing with 3D Objects in Mathematica":

In the notebook on slide 12 you find how to define Union, Difference, Intersection. Quick sample from that slide for Difference between a cube and a sphere:

sphereQ[{x_, y_, z_}, r_, center_: {0, 0, 0}] := Norm[{x, y, z} - center] < r;

cubeQ[{x_, y_, z_}, r_] := (Abs[x] < r && Abs[y] < r && Abs[z] < r);


RegionPlot3D[
 cubeQ[{x, y, z}, 1] && \[Not] 
   sphereQ[{x, y, z}, 1, {1, 1, 1}], {x, -1, 2}, {y, -1, 2}, {z, -1, 
  2}, PlotRangePadding -> .5, Mesh -> None, PlotPoints -> 50]

enter image description here

You can do other neat things like computing and thickening thin surfaces - all this is in the video:

ParametricPlot3D[{1.16^v Cos[v] (1 + Cos[u]), -1.16^v Sin[
    v] (1 + Cos[u]), -2 1.16^v (1 + Sin[u])}, {u, 0, 2 Pi}, {v, -15, 
  6}, Mesh -> False, PlotRange -> All, PlotStyle -> Thickness[.5], 

 PlotPoints -> 35]

enter image description here

Comments

plotting - Filling between two spheres in SphericalPlot3D

Manipulate[ SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, Mesh -> None, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], {n, 0, 1}] I cant' seem to be able to make a filling between two spheres. I've already tried the obvious Filling -> {1 -> {2}} but Mathematica doesn't seem to like that option. Is there any easy way around this or ... Answer There is no built-in filling in SphericalPlot3D . One option is to use ParametricPlot3D to draw the surfaces between the two shells: Manipulate[ Show[SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], ParametricPlot3D[{ r {Sin[t] Cos[1.5 Pi], Sin[t] Sin[1.5 Pi], Cos[t]}, r {Sin[t] Cos[0 Pi], Sin[t] Sin[0 Pi], Cos[t]}}, {r, 1, 2 - n}, {t, 0, Pi}, PlotStyle -> Yellow, Mesh -> {2, 15}]], {n, 0, 1}]

plotting - Plot 4D data with color as 4th dimension

I have a list of 4D data (x position, y position, amplitude, wavelength). I want to plot x, y, and amplitude on a 3D plot and have the color of the points correspond to the wavelength. I have seen many examples using functions to define color but my wavelength cannot be expressed by an analytic function. Is there a simple way to do this? Answer Here a another possible way to visualize 4D data: data = Flatten[Table[{x, y, x^2 + y^2, Sin[x - y]}, {x, -Pi, Pi,Pi/10}, {y,-Pi,Pi, Pi/10}], 1]; You can use the function Point along with VertexColors . Now the points are places using the first three elements and the color is determined by the fourth. In this case I used Hue, but you can use whatever you prefer. Graphics3D[ Point[data[[All, 1 ;; 3]], VertexColors -> Hue /@ data[[All, 4]]], Axes -> True, BoxRatios -> {1, 1, 1/GoldenRatio}]

plotting - Mathematica: 3D plot based on combined 2D graphs

I have several sigmoidal fits to 3 different datasets, with mean fit predictions plus the 95% confidence limits (not symmetrical around the mean) and the actual data. I would now like to show these different 2D plots projected in 3D as in but then using proper perspective. In the link here they give some solutions to combine the plots using isometric perspective, but I would like to use proper 3 point perspective. Any thoughts? Also any way to show the mean points per time point for each series plus or minus the standard error on the mean would be cool too, either using points+vertical bars, or using spheres plus tubes. Below are some test data and the fit function I am using. Note that I am working on a logit(proportion) scale and that the final vertical scale is Log10(percentage). (* some test data *) data = Table[Null, {i, 4}]; data[[1]] = {{1, -5.8}, {2, -5.4}, {3, -0.8}, {4, -0.2}, {5, 4.6}, {1, -6.4}, {2, -5.6}, {3, -0.7}, {4, 0.04}, {5, 1.0}, {1, -6.8}, {2, -4.7}, {3, -1.

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