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Optimize intersection feature for Quadratic Bezier curves#217

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rBazan98 wants to merge 3 commits intomathandy:masterfrom
rBazan98:optimization/quadratic-bezier-intersections
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Optimize intersection feature for Quadratic Bezier curves#217
rBazan98 wants to merge 3 commits intomathandy:masterfrom
rBazan98:optimization/quadratic-bezier-intersections

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@rBazan98 rBazan98 commented Nov 19, 2023

This approach determines intersections of two Quadratic Bezier curves by directly solving the parametric equations for Cartesian coordinates associated with each Bezier curve instead of finding intersections by interpolation.

Notation used is as follows:

  • 'xn' and 'yn' represents coordinates of each control points 0, 1, and 2.
  • Parametric forms of coordinates used: X = At^2 + Bt + x0 and Y = Ct^2 + Dt + y0.
  • Equation at^4 + bt^3 + ct^2 + d = 0 identifies intersections as roots.

Optimization made by solving the parametric ecuation of both quadratic bezier curves
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