I'm trying to taper the object (on the bottom of the picture) in blender from it's cylindrical shape to match the profile of the tapered one (top of the picture). 
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$\begingroup$ lattice modifier $\endgroup$– atekOct 11, 2017 at 10:06
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3$\begingroup$ Use Simple Deform modifier and set it to Taper option $\endgroup$– Mr ZakOct 11, 2017 at 12:32
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2 Answers
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Shift a Add lattice
Scale the lattice so the model covers completely
Select the lattice and in the properties panel add some division to it
Select the mesh or cylinder and add lattice modifier
In the object select lattice
Now click the Lattice and tab to edit mode select the vert and scale up and down to get the shape
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That should be easy. Add a lattice to your scene. A basic one with just 8 vertices is best. Scale it in world space to match your engraved form. Don't do it in edit mode! Now, when the lattice object enwraps your engraved form completely, add a lattice modifier to it. Now, if you move a vertex of your lattice in edit mode, the mesh deforms accordingly.
Select the top four vertices of the lattice, press Shift+S and click Cursor To Selected. Now, you can simply scale these vertices, until your engraved form match the form of your cylinder.
