Simple script?

I want to model sails, both for boats and for shading purposes. They should have the forms of triangle, square, pentagon and hexagon and can be flat (like a plane). Each edge tends to move to the direction of the center when it is under suspension. If the edge-length is 10 meters for example, the middle of the edge goes approximatly 30 cm to the center. Look here:
Until here it is quite easy. I’ve done it using PET.

But I want to resize the sails in a fast and intuitive way, and the relations between edge-length and suspension distance should stay the same. For example: I would like (to show to customers) to put one corner of the triangle (square, …) to the corner of a house, but I don’t want to model the exact form every time newly.

I think the best way to do this, is a Python script. But I am not good in mathematics and a Python beginner, so I have to ask for some hints here. I thougt, a Python script should allow me to set vertices (for example a, b and c in the case of a triangle) and the script should complete the form with vertices in between and at last fill it with edges and faces. If I could enter a percentage for the distance in the middle (shown with the blue line), it would be perfect.

Anybody out there with an idea to do this script? Having a formula?

Thanks in advance!


Thanks for everybody’s help!!