[Greenbuilding] DIY sloped tiled shower floor, simple version?

[Reuben Deumling]

Is there any reason I can't cut a bunch of shallow wedges laid in a radial
pattern that feather toward the drain, nail cement board on top, tape the
seams and lay down the tile?

This seems a lot simpler than some of the instructions I find online. My
sketch above doesn't include any membrane or treatment of the seams where
this sloped floor meets walls. The shower in question is in the corner of a
small upstairs bathroom. The walls will be tiled and I would like/think I
can get away with avoiding a step/lip where the sloped floor meets the rest
of the bathroom floor

All thoughts and suggestions are welcome.

Thanks
Reuben
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