Creating an Equation from Coordinates to "Save" a Curve

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Creating an equation from a set of coordinates, particularly for complex shapes like an hourglass, can be challenging due to the potential for multiple equations fitting the same points. B-splines and Bezier curves are suggested as effective mathematical methods for modeling such curves. Users are encouraged to explore B-spline surfaces for flexibility and precision. Bezier curves are also highlighted as a viable option for achieving the desired representation of the shape. Overall, these techniques can help "save" the curve in a mathematical form.
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I was wondering if anyone had a good method for creating an equation from a set of coordinates. Let's say I have a vase (hourglass shaped). I have x,y coordinates that map the outline of the shape to about a 0.05" tolerance. Is there some mathmatical process that I can use to, in effect "save" this curve in an equation. I tried regression, but the shape isn't exact and I am aware that there could be many equations that could potentialy follow those points.

There must be some way to do it.

Thanks
 
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Have you looked at B-splines? Look up "B spline surfaces" with Google or any search engine.
 
Thanks for the suggestion. I just discovered Bezier curves this weekend. I think they'll work for my purpose, although I'll keep the B splines in mind.

Thanks
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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