I have a set of several closed curves in 3d (like image below is showing my set of curves from 3 views).
To clarify my idea, i ask my questions in two different ways showed by diction 1 and diction 2 in next. Both questions are same, and I'm bringing them just for explaining what I need.
diction 1- Each closed curve is consist of many points and all points in each curve have same height. Calculating any of these curves is a time consuming task, so i would like to know is there a method to interpolate between two successive curve and make a new curve instead of calculating it from the time consuming task?
diction 2- You can see in image every closed curve have same height in every point of it. (because of perspective view, the side view seems is not so, but in real it is). Is there a method to approximate a curve between two successive curves with only data of those two curves? For example think we remove 7'th curve (counting from down to up) and we want to approximate it with data of 6'th curve and 8'th curve. Is there a method to do so?
- Update - in many CAD/CAM applications there is a command named Loft which will create a surface from several curves like this image (from this page)
What is the math behind the Loft operation?