Is there some elegant way I could go about creating the "twisted spiral" surfaced dome as you see in the iconic "St. Basil's Cathedral" in Red-Square in Moscow?
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As usual, it looks as if this is simple enough to model, but the devil is in the details. Look closely at the flat space between each section, and notice how the twist is not entirely uniform either.
And I feel a non-destructive approach would be best, so that other variants of onion domes can be constructed fast.
start with a curve. I used the "extra objects-->Curves Galore, and used the flower:
I made some adjustments to the overall curve, and added a second circle in the same object while in edit mode (later I adjusted to this final version - it is hard to predict the exact shape at this stage):
Then I added a straight bezier profile curve, and subdivided this curve (W menu) about 5~7 times to get the resolution required for the lattice deformer at a later stage.:
Next, simple deformers are added to create a base twist and tapering (which makes it much easier to control when applying the lattice later). A taper, and a twist:
Create a lattice object. I used W:8 divisions.
apply the lattice deformer to the curve object, and start tinkering around with the size. Key ingredient: rotate each lattice sub division to control the twisting precisely. This offers much more control than the simple twist deformer, allowing for a visually more correct twist like the one seen in the original onion domes. Mine is a bit messy, because I was a bit in a hurry:
Done! Completely non-destructive onion dome, with a lot of control over the final result.
It literally take 20 seconds to change the profile curve, and generate quite complex bizarre looking domes:
Download the example blend here:
Addendum: adding small circles in the base curve object creates very pronounced "ridges" as seen in the original:
Well, there are several ways to approach this, the simplest of which is I think is to just do it in one shot (no need for modifiers). Just add a circle, scale in some points and 'twist' it. This is more or less the same as dukejib's answer. If you do it this way however, you get a bit more control over the mesh at each stage.
Add a circle to the scene in top view, select and scale in every other vertex until you get a pointy edged circle. The default 32 vertices are ok in this case, if you want the 'pegs' of the dome closer to each other or more defined, use more (but keep them evenly numbered).
From a side view, give it the rough shape of the dome by extruding up and tapering at the top and then add a few loopcuts with Ctrl + R and scale these accordingly.
Add a Subsurf modifier (you can do this quickly by using Ctrl + Subdivision Level (1 - 6)) and press the last button of the modifier to have it applied to the mesh while in edit mode. You can then ring select the loopcuts and 'fatten' them by scaling. Tweak this to give the mesh an overall more smooth and well rounded shape.
Select each loopcut and rotate about
15° on the Z axis until you get a nice twisted looking shape.
Finished. You can still further tweak this by rotating the loopcuts further or making the 'pegs' more pronounced by selecting them and scaling them while being constrained on the Z axis.
Create a Sphere. Delete the lower portion, as shown in picture. Enable Proportional Editing Tool. Select the Top Vertex and Scale the Sphere in Z Direction to give it more Height. Disable Proportional Editing Tool. Smooth Shade your mesh. Add Subsurf Modifier. Select every second Edge Loop. Scale them on x & y axis. Enable Proportional Editing Tool. Select the top Vertex and Rotate in Z axis. Finished Mesh.