I really relate to your question about getting sharp points. I have tried several different methods, the one I always get the best results with is freezer paper and a glued under seam allowance. The first time I was not pleased with the glue I used but have now found the best one for my method, it made all the difference for me. I cut my shapes from the freezer paper to the exact shape of the applique, ( I cut several layers at a time) iron to the wrong side of the fabric and use the glue stick to secure the seam allowance to the back side. This gives me the perfect points and smooth curves I want. You will need to cut away your background fabric to remove the freezer paper but it is worth it. I also use 100 weight silk thread to do the applique stiitch with and have found that if I use a very sharp thin needle I do not even catch the paper in my stitches, only the very edge of the folded fabric. The products used make all the difference. Here is what I use, frezer paper from the quilt shop not the grocery store ( it is much stiffer) YLI 100 weight silk thread, John James Golden Glide Milliners needles size 10 or 11, Avery glue pen from an office supply store. ( I will not every use the fabric glue sticks again ). On your points you can trim down your seam allowance to about 1/8in. and fold over very carefully to get nicw sharp points and the glue will keep them that way while you stitch. Hope this helps (sorry to be so long)