I do have a somewhat complex question (that might be easy to solve, please bear with me I picked up Mathematica in the last two hours). I want to draw 3D shapes using Mathematica. Specifically I want to draw a rectangle, a cylinder and remove a complex shaped that can be drawn by using Plot or PolarPlot in 2D.
A good starting point would be simply removing another cylinder from my bigger cylinder. A good example on how I could draw all the shapes is shown below.
r = 1.2;
rPerf = 0.5;
b = 2.4;
w = 5;
l = w;
oringP = {-l/2, -l/2, 0};
cube1 = Cuboid[oringP, {w/2, l/2, 1}];
cyl1 = Cylinder[{{0, 0, 1}, {0, 0, b + 1}}, r];
cyl2 = Cylinder[{{0, 0, 1.5}, {0, 0, b + 1}}, rPerf];
myExampleDrawing =
Graphics3D[{EdgeForm[{Thick, Black}], cube1, cyl1, cyl2,
AspectRatio -> Automatic,
ImageSize -> 200}, Boxed -> False]
I found out I can use RegionDifference but that doesn't allow me to keep using Graphics3D which seems much more computational friendly and keeps smooth lines. I can generate something closer to the previous one, with the subtraction, by using the following line
RegionPlot3D[RegionUnion[RegionDifference[cyl1, cyl2], cube1], PlotPoints -> 70]
However, it has some artefacts on the union between the cuboid and the cylinder. Finally, I would like to have a complex shape instead of cyl2, extrude it much like in this thread where a function to extrude the points is used. Then finally I'd like to subtract this extruded complex shape from the cylinder. However, I don't seem to be able to reproduce the example code (extracted from the linked answer). The code is the following:
R[\[Theta]_] := (1 + 0.5 Sin[2 \[Theta]]);
shape1 = PolarPlot[R[\[Theta]], {\[Theta], 0, 2 \[Pi]}, Axes -> False,
PlotStyle -> {Orange, Thickness[0.02]}];
points = (Flatten@shape1[[1]])[[2, 1]];
Options[Extrude] =
Join[Options[Graphics3D], {Closed -> True, Capped -> True}];
Extrude[curve_, {zmin_, zmax_}, opts : OptionsPattern[]] :=
Module[{info, points, color, tube, caps},
info = Flatten@{curve[[1]]};
points = Select[info, Head[#] === Line &][[1, 1]];
If[OptionValue[Closed], points = points~Join~{points[[1]]}];
color = Select[info, Head[#] === Directive &];
If[Length[color] == 0, color = Orange,
color = First@Select[color[[1]], ColorQ]];
tube =
Polygon[Partition[
Flatten[Transpose[
points /. {x_, y_} -> {x, y, #} & /@ {zmin, zmax}], 1], 3, 1]];
If[OptionValue[Closed] && OptionValue[Capped],
caps = Polygon[points /. {x_, y_} -> {x, y, #}] & /@ {zmin, zmax};
tube = Flatten@{tube, caps}, tube = {tube}];
Graphics3D[Flatten@{EdgeForm[None], color, #} & /@ tube,
FilterRules[{opts}, Options[Graphics3D]]]];
Extrude[shape1, {-2, 5}, Boxed -> False]
It returns several errors.
So basically I want to understand if it is possible to:
- Create 3D geometries using subtraction of primitives and plot it using
Graphics3D - Extrude 2D geometries easily
- Create 3D geometries using subs traction of primitives and the extruded geometry while still plotting it with
Graphics3D
