Making a Sail-Shade-- Plane with curves

Question

So here's the thing. I'm trying to make a sailshade. I'm going to be making many of these over time, so I want to find a fast and accurate way of doing this. Basically, a sailshade is normally 3 or so fixed points with a curve between the fixed points.

That's how most of them look, although some are more complex.

What i'm trying to do is make a plane that i can shape and stretch to how it needs to be, that way i don't have to constantly modify all the vertices. Sadly, i'm not an expert at Blender yet, and was wondering if there was some way to 'control' the curves that i put on the plane? For example, i could have a square plane with 8 'control points'. 1 on each point (4) and 1 between each point (4) to control the curves.

I'm pretty sure his is possible... but I haven't quite figured it out yet... Anyone able to help?

Please and thank you!

That isn't exactly the solution i was looking for, using a cloth modifier doesn't really work for what i'm doing.

Answer 1

In addition to Duarte's answer, I'll add another method. It will use the subdivision surface modifier as well, but another method to create the sharp corners

1. Add a plane. Subdivide it once. Add a solidify, bevel and subdivision surface modifier.
   
2. Since the sail would have a thickness anyway, the bevel modifier comes in handy. Otherwise just scale the value down untill it is no longer noticeable (but no 0). Use a high number of segments and a high angle. The angle has to separate the corners from the sides. The corner angles are going to be > 90 in your example, so I entered 80°.
   
3. You can now easily edit the shapes. Other shapes (not just quads) are equally possible as long as there is a distinction between side angle and corner angle.
   

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You could also use NURBS surfaces. Add a surface, delete the standard additional points and close the endpoints, by checking Endpoint U and V.