I have following points (-|b-a|,a), (0,b), (|c-b|,c) with a, b and c as two-dimensional vectors. These should be interpolated component-by-component with a second-degree polynomial p.
My problem now is, that I don't know how the polynomial should look like: $p(-|b-a|)= \alpha(-|b-a|)^2 + \beta(-|b-a|)+\gamma = a$
$p(-|b_x - a_x|) = \alpha(-|b_x-a_x|)^2 + \beta(-|b_x-a_x|)+\gamma = a_x$ $p(-|b_y - a_y|) = \alpha(-|b_y-a_y|)^2 + \beta(-|b_y-a_y|)+\gamma = a_y$
Is my conversion correct?