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Mathematica

How to find an intersection of bezier curve and any function

Mitja Jan?i?, University
Posted 10 years ago

I have a table:

{{0., 0., 0.}, {0.002, 0.08942, -0.08942}, {0.008, 
  0.233889, -0.178706}, {0.018, 0.366918, -0.267724}, {0.031, 
  0.496136, -0.350769}, {0.049, 0.639568, -0.439999}, {0.07, 
  0.779356, -0.5245}, {0.095, 0.922931, -0.609077}, {0.124, 
  1.06945, -0.693271}, {0.156, 1.21404, -0.77438}, {0.191, 
  1.35745, -0.852947}, {0.229, 1.50013, -0.929279}, {0.271, 
  1.64566, -1.00987}}

Using this table I draw a BezierCurve, with first column as the x axis, second column as the top displacement and third column as the bottom displacement. Now I want to find an intersection with the Bezier Curve above and with a vertical line at x=0.08. Obviously I should get two points and the value I would be interested in (at given x) is the difference y between the two points. Now how do I do that? :/ I am confused since Bezier Curve isn't a f(x) function... Please help! :D
POSTED BY: Mitja Jan?i?
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BTW: I tried this Graphics[BezierCurve[Transpose[{data[[All, 1]], data[[All, 2]]}]]]* KroneckerDelta[0.08] but it doesn't really work theway I imagined. :/
POSTED BY: Mitja Jan?i?

My freely available package CurvesGraphics6 (http://www.dimi.uniud.it/gorni/Mma) defines BezierCurveFunction that you may find useful:

Solve[(BezierCurveFunction[{{0., 0., 0.}, {0.002, 
        0.08942, -0.08942}, {0.008, 0.233889, -0.178706}, {0.018, 
        0.366918, -0.267724}, {0.031, 0.496136, -0.350769}, {0.049, 
        0.639568, -0.439999}, {0.07, 0.779356, -0.5245}, {0.095, 
        0.922931, -0.609077}, {0.124, 1.06945, -0.693271}, {0.156, 
        1.21404, -0.77438}, {0.191, 1.35745, -0.852947}, {0.229, 
        1.50013, -0.929279}, {0.271, 1.64566, -1.00987}}][
     t] /. {x_, _, _} :> x) == .08]
POSTED BY: Gianluca Gorni
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