Parabola 2

Parabola

    Parabola is obviously given by two of its dots and by contact dotsdots in them. Ratio

    For a line AC, where dot B ∈AC is defined ratio (ABC) = (B-A)/(C-B).


Construction of a parabola

    Let's assume that we have got given dots A, D and C and t ∈<0,1>. For dots E, B and F then it is valid : ratio (AED) = ratio (EBF) = ratio (DFC). Construction of a parabola lies in drawing a dot of parabola B with parameter r = t /(1-t).

Then 

1. computes the point E, F : 

     E : ratio(AED) = r ( <=> E = (1-t)*A + t*D )
     F : ratio(DFC) = r ( <=> F = (1-t)*D + t*C )

2. compute the point B :

     B : ratio(EBF) = r ( <=> B = (1-t)*E + t*F )

3. The point B is the parabola with the corresponding parameter t

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Parabola

Source code
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