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10

Using Composition I can apply RotationTransform, TranslationTransform , ShearingTransform one after the other. Graphics3D[{ Opacity[1] , Red , Arrow[{{0, 0, 0}, {1, 0, 0}}] , Green , Arrow[{{0, 0, 0}, {0, 1, 0}}] , Blue , Arrow[{{0, 0, 0}, {0, 0, 1}}] , Opacity[0.2] , GeometricTransformation[Cuboid[-{1, 1, 1}/4, {1, 1, 1}/4], ...


4

Just use MeshFunction. Manipulate[ParametricPlot3D[{Sin[\[Theta]] Cos[\[Phi]], Sin[\[Theta]] Sin[\[Phi]], Cos[\[Theta]]}, {\[Theta], 0, \[Pi]}, {\[Phi], 0, 2 \[Pi]}, PlotStyle -> Opacity[0.5], Mesh -> {{0.}}, MeshStyle -> {Red, Thick}, MeshFunctions -> {Sin[a] Cos[b] #1 + Sin[a] Sin[b] #2 + Cos[a] #3 &}], {a, 0, \[Pi]}, {b, 0, 2 \[Pi]}] ...


4

Looks to me to be a bug in RegionPlot. I say fhis beccause DiscretizeRegion @ TransformedRegion[Rectangle[{0, 0}, {1, 1}], {#1^(1/3) + #2, 1 + #2} &] gives as expected.



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