Activate the X-Map option on your output and create 3 X-Maps, 1 per shape.
Place the Shapes Pattern 2 on the timeline and set the locator on it.
Setting the MAP of each X-Map
Select the first X-Map and in the Warp panel, in the top right switch to MAP mode.
Move the points to the edges of the shape as precisely as possible.
Repeat these steps for the two other shapes.
Notice that for the semicircle and the Pi Letter this method can only extract a quad surface encompassing the shape and the resulting X-Map does not follow the curved lines of these shapes.
Warp each X-Map
Toggle the MAP back to WARP and warp each X-Map on its corresponding shape.
Start by warping with Curve type set to Keystone and switch to Curve when required.
Remember you can activate the Solo mode 
on each X-Map to avoid the other X-Maps getting in the way.
Once all shapes are correctly mapped, disable all the Solo modes.
Because the output has no warp applied to it, the Softedge pattern set on it enables us to see the entire projection zone.
Remove the Softedge pattern from the Output and display the Shapes Pattern 1 (white shapes) to fine-tune the warp of the shapes.
Create a fourth X-Map placed underneath these 3 X-Maps and display a white test pattern on it.
Warp this fourth X-Map to fit the back of the mapping box.
Notice that because the X-Maps for the semicircle and the Pi letter extract a quad region of the render surface, it displays black around the shape that overlap above the background and the result is not satisfying.
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