Here is a method for creating improve curves that seems like it shouldn't work, but it does! It uses strips with gentle curves, and lots of ironing, what I call "Iron the sh*t out of it."
I'll show you how to cut gentle curves and how to insert a piece to either create a pop of color or 'fix' a curve that isn't allowing for your next piece, in both a concave and convex situation.
I started with these strips and scraps of approx 2" strips:
Then I randomly cut each strip with a wavy curve: (notice this is NOT the method of stacking the strips right sides up and cutting the SAME curve. Each strip has its own curve:
Select 2 pieces that have roughly similar curves. Notice they don't match up. Its ok.
Flip one piece over the other, right sides together and line up the TOP of the strips. Start sewing VERY SLOWLY.
As you stitch DO NOT pull the fabric, but gently reposition so the edges line up.
Press by pushing the new strip flat. It will fight you a bit. Use steam or spray as needed.
You can get it to lay flat. Especially if it is narrow. This method is not good for wide strips.
Notice that the bottom of the purple strip is not connected to the pink all the way to the edge (I did that just to show this can be done) cut off the 'tail' of the purple, to create a single 'edge' for the next piece.
The next piece (green) encloses the thin point of purple (line drawn just to show the seam, since these are both dark fabrics)
In selecting the next piece, note that these two have exactly opposite curves (bellies poking out at each other) these will NOT go together well. Select another piece!
This one is better.
Flip the light green stripe over the dark green and slowly sew that seam.
In selecting the next piece (the purple) notice the hole I am pointing to (opposite problem of bellies sticking out) But rather than select another piece, I'm going to solve this by inserting a small section in the space in green stripe.
I
sewed this pink strip into the concave bowl of the green stripe.
Then after pressing it, I trimmed it into a bump to fit the shape needed for the purple strip next. Honestly, this bump is too big, but it causes another problem I solved next.
This is a nice technique for adding a small pop of color in a wavy set of strips.
This purple strip was NOT going to lay flat. It might have worked if it was narrower, but I had to cut these 'easing' notches to get it to lie flat when pressing. (If you sew clothing, this is often done on curved seams.)
Then I cut the purple narrower to remove the notches:
I added a final strip of green and consider this done.
The final step is to square this piece up, to be used in a project.
Here are two links to the other way of creating improv curved piecing. They both use the method of stacking fabric, right sides up and cutting the curve at the same time. This 'guarantees' the strips will fit into each other. Notice that none of these methods include seam allowance so you will always have size shrinkage. Work with strips or blocks significantly larger than your finished block.