I want to write an algorithm that morphs or transforms an arc of a circle to a straight line joining both ends of the arc. I would like to understand the maths behind this such a transformation. How can this be done?

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conveneau71 · Accepted Answer

If   x  (  t  ) is a parametrization of your circle arc (see the other answers for how to find one), and   y  (  t  ) a parametrization of the straight line segment joining the endpoints of the arc, then      F    λ    (  t  )  =  (  1  −  λ  )  x  (  t  )  +  λ  y  (  t  )is the parametrizations for the circle arc when   λ  =  0, the parametrization of the line segment when   λ  =  1, and some intermediate form when   λ  ∈  (  0  ,  1  ) is something in between. This technique is called linear interpolation and is one way (out of infinitely many) to achieve such a blend.So draw       F    λ    (  t  ) for   λ  =  0 and then slowly increase the value of   λ and repeatedly daw the resulting curve.

I want to write an algorithm that morphs or transforms

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