I will start with how to draw templates for curved seams and you will need a compass for this, the kind you can find in a child's geometry set.
1. I start each new hexagon template by marking on the corners of the hexagon on the incompetech paper and marking all points within the hexagon three triangles apart.
2. As a starter you can set your compass to three triangles' length, giving tighter curves, or six triangles' length, giving gentler curves. You can of course also set the compass to different lengths and see where that takes you but the 3 triangles and 6 triangles lengths make nice neat patterns within the hexagon.
3. Place the point of the compass on any of the dots you have drawn on the hexagon (all the dots three triangles apart) and try drawing arcs connecting other dots in the hexagon to see what patterns you come up with. Try this with the compass set to both 3 triangles and 6 triangles length.
4. Keep drawing and erasing parts of your drawing, mixing in some straight lines and see what you end up with.
5. For the purposes of this tutorial, I have drawn three 6 triangles length arcs from the centre to three of the outside corners of the hexagon to make a curved tumbling block.
6. When you cut the fabric out around the template shape, clip the curved edges which means you cut into the seams about three or four times with a cut that ends about 1/8" from the template edge. I have slotted pins through the clips here so you can see where I've clipped.
7. Baste as for a normal template but use much shorter basting stitches along the curved edges, constantly pulling the fabric with the needle to hub the template edge.
8. Lay out all the section face down and mark meeting points along the two seams (ignore the fact that there are other designs on the back of my templates!). I marked these points with a FRIXION Pilot pen - the marks disappear when ironed. Sorry about the bad pics today - I was lazy and took them all with my iphone and they don't do close up as well as a better camera.
9. Sew the curved seams in exactly the same way as you whipstitched straight EPP seams only line up the edges for the actual stitch you are doing. So sew a stitch, pull the thread tight then line up the edges for the next stitch. Sew the next stitch, pull the thread tight and then line up the edges for the next stitch. As you sew along the seam, watch that your marked points are meeting and adjust if they are not.
10. Voila, you have a curved seam EPP hexagon. I would love to see photos if any of you try this - and please do ask questions if you get stuck or if something in this post is not quite clear. These two blocks were also made using the same curved seam technique.