My Math Forum Condition for straight line preservation

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 March 12th, 2018, 04:03 AM #1 Newbie   Joined: Oct 2013 Posts: 20 Thanks: 0 Condition for straight line preservation We have not affine transform but rational transform: $\displaystyle x' = (a \cdot x + b \cdot y +c)/(1+d \cdot x + e \cdot y)$ $\displaystyle y' = (f \cdot x + g \cdot y +h)/(1+i \cdot x + j \cdot y)$ To find coefficients, it need 5 points and 10 nonlinear equations. But better would be only 4 (or even 3) points with additional condition: transform must preserve straight line between $\displaystyle (x_1,y_1)$ and $\displaystyle (x_2,y_2)$ Last edited by Borneq; March 12th, 2018 at 04:10 AM.

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