I'm trying to create an arena.
Is there a quick way to extrude and scale proportionally the grandstands and make it more and more like that?
I would like to keep the height and the depth of each row equal to the other.
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Yes, there is a way to do what you want by extruding downward and scaling, but because the arena is ellipsoid, I don't think that this technique is going to prove the most efficient way to achieve what you want. In my view, there are at least three two quicker ways to accomplish what you seek. The first is to crate a profile of the cross section of the arena, as shown in this illustration, and use the "spin" tool in the tools tab of the tool shelf (T key). You need to determine the proper number of segments for the spin, and adjust the various profile segments as needed, as the arena is ellipsoid and not circular. Alternatively, you can create the cross section of the profile, and extrude constraining the extrusion to the X and Y axes, holding the z constant, and place the individual section boundaries as needed. A third method is to start with a cone primitive of suitable size, subdivide the sides of the cone, remove the point, and place it in the orientation so the larger opening is at the top, and the smaller at the bottom. Then subdivide the sides of the cone to create the appropriate number of levels, and craft the profiles as needed.
Separate off the first tier of seating (seat and back) into their own object. Add a new empty at the origin.
Select the seating object and add an array modifier with a fixed count of say 15 and clear the relative offset checkbox. Use object offset with the object set to the Empty. Check the Merge checkbox.
In front orthographic view, move the Empty up on Z until the seating rows are correctly aligned. In top orthographic view, scale the Empty until the tiers are correctly aligned.
Apply the array modifier, join back to the original object and remove doubles. You should have a clean mesh.