Some of the curves which are used in woodworking have a very large radius. The curves are worth doing and doing well as they make the difference!
I am currently making some table legs which are tapered on the inside edge of the leg. The taper is curved slightly. You clearly can't draw this with a pair of compasses and evn if you did, how would you then get the curve onto the piece of wood.
There are many different method which you will find on youtube for solving this problem, but this in my opinion is the easiest.
Establish from your designs what the length of the arc is and what the height of the arc is (the deviation from a straight line). In my case the length was 750mm and the deviation was 15mm.
Make a thin piece of wood (10mmx10mm) which is the length of the arc plus about 50mm. I have a long bit of wood in my workshop which I use for this purpose. This piece of wood has to be a consistent thickness all along and also straight. Job for my Axminster planer/thicknesser.
Cut a piece of MDF which is the length of the arc plus about 100mm. You will need enough room on this MDF sheet to clamp your final piece of wood to. So think about the width before cutting the MDF. My MDF was 1000mmx200mm.
Place the strip of wood on the edge of the MDF and put two nails in behind the back edge of the strip at either end of it. Establish where the middle of the strip is and push it inwards to form the curve that you want. Now put a nail in the middle of the strip to hold it in that position. Finally put nails through the strip at regular intervals to ensure that the strip cannot move.
Roughly cut the curve out of the MDF using the band saw. Now turn the MDF over and using a template cutter with a bottom bearing on your router precisely cut the curve onto the MDF edge. Now you can remove the bendy piece of wood from the MDF and use this MDF board as a jig to cut your curve in your piece of wood.