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March 12th, 2018, 03:03 AM   #1
Joined: Oct 2013

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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 03:10 AM.
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