The points would only be cut off if you cut the block exactly on the diagonal. If you cut it 1/4" passed the diagonal, the points would be preserved. If you wanted to construct the block 'correctly' with no bias edges:
construct the lower right portion of the block using the normal construction method you used for the rest of the quilt. Then cut the 5 black setting triangles using the chart or calculation from Bonnie Hunter's site.
http://quiltville.blogspot.com/2005/...nt-quilts.html