In the image above, I created the orange mesh (2D) by scaling a circle in an axis. So I got an ellipsis.
I created the black one point by point by moving each point of a circle with the mouse. The black curve is not an ellipsis, this is what I want.
How can I obtain the same result by applying a transformation which will move all points from the ellipsis between surrounded points, but surrounded points should not move and moved points should stay inside the rectangle defined by surrounded points.
In other words, I'd like to control the shape linking two perpendicular lines.