Creating an Equation from Coordinates to "Save" a Curve

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SUMMARY

The discussion centers on methods for creating mathematical equations from a set of coordinates that outline a shape, specifically an hourglass-shaped vase. The user initially attempted regression but found it inadequate due to the non-exact nature of the shape. Recommendations included exploring B-splines and Bezier curves as viable solutions for accurately representing the curve with a tolerance of 0.05 inches. Both B-splines and Bezier curves are established techniques for curve fitting and surface modeling in computational geometry.

PREREQUISITES
  • Understanding of B-splines and their applications in curve fitting.
  • Familiarity with Bezier curves and their mathematical properties.
  • Basic knowledge of regression analysis techniques.
  • Proficiency in handling coordinate systems and geometric shapes.
NEXT STEPS
  • Research "B-spline surfaces" for advanced curve modeling techniques.
  • Learn about "Bezier curve algorithms" for practical applications in design.
  • Explore "curve fitting methods" to understand various approaches beyond regression.
  • Investigate "computational geometry" for broader context and applications.
USEFUL FOR

Mathematicians, computer graphics designers, and engineers involved in shape modeling and curve fitting will benefit from this discussion.

jjj888
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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
 

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