How to properly do function rotation?

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For any arbitrary function (for example $y=x^2$), how to (translate) and then (rotate and translate) it?



I have used the Homogeneous coordinates to do the required operation and here is the result (for example let rotation angle $theta = 90$):enter image description here



  1. In the first image there is no problem.

  2. In the first image it was moved to the second quadrant, what if i want it to be like the following:enter image description here

i.e. to do the transformation about point P.



Last thing to ask about, is there any difference between doing (rotation then translation) and doing (translation then rotation )?



Thanks in advance.




matrices transformation rotations




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  • What about translate and rotate the coordinate system itself. If you parameterize your function in terms of a pair of unit vectors $u$ and $v$ so instead of $x$ and $y$ you have $x u$ and $y v$ then rotating the vectors $u$ and $v$ will be enough to rotate all functions on that coordinate system.
    – Mauricio Cele Lopez Belon
    Aug 27 at 23:41














up vote
1
down vote

favorite












For any arbitrary function (for example $y=x^2$), how to (translate) and then (rotate and translate) it?



I have used the Homogeneous coordinates to do the required operation and here is the result (for example let rotation angle $theta = 90$):enter image description here



  1. In the first image there is no problem.

  2. In the first image it was moved to the second quadrant, what if i want it to be like the following:enter image description here

i.e. to do the transformation about point P.



Last thing to ask about, is there any difference between doing (rotation then translation) and doing (translation then rotation )?



Thanks in advance.




matrices transformation rotations




share|cite|improve this question






















  • What about translate and rotate the coordinate system itself. If you parameterize your function in terms of a pair of unit vectors $u$ and $v$ so instead of $x$ and $y$ you have $x u$ and $y v$ then rotating the vectors $u$ and $v$ will be enough to rotate all functions on that coordinate system.
    – Mauricio Cele Lopez Belon
    Aug 27 at 23:41












up vote
1
down vote

favorite









up vote
1
down vote

favorite











For any arbitrary function (for example $y=x^2$), how to (translate) and then (rotate and translate) it?



I have used the Homogeneous coordinates to do the required operation and here is the result (for example let rotation angle $theta = 90$):enter image description here



  1. In the first image there is no problem.

  2. In the first image it was moved to the second quadrant, what if i want it to be like the following:enter image description here

i.e. to do the transformation about point P.



Last thing to ask about, is there any difference between doing (rotation then translation) and doing (translation then rotation )?



Thanks in advance.




matrices transformation rotations




share|cite|improve this question














For any arbitrary function (for example $y=x^2$), how to (translate) and then (rotate and translate) it?



I have used the Homogeneous coordinates to do the required operation and here is the result (for example let rotation angle $theta = 90$):enter image description here



  1. In the first image there is no problem.

  2. In the first image it was moved to the second quadrant, what if i want it to be like the following:enter image description here

i.e. to do the transformation about point P.



Last thing to ask about, is there any difference between doing (rotation then translation) and doing (translation then rotation )?



Thanks in advance.





matrices transformation rotations





share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Aug 27 at 1:50

























asked Aug 26 at 23:11









Ahmed

1669




1669











  • What about translate and rotate the coordinate system itself. If you parameterize your function in terms of a pair of unit vectors $u$ and $v$ so instead of $x$ and $y$ you have $x u$ and $y v$ then rotating the vectors $u$ and $v$ will be enough to rotate all functions on that coordinate system.
    – Mauricio Cele Lopez Belon
    Aug 27 at 23:41
















  • What about translate and rotate the coordinate system itself. If you parameterize your function in terms of a pair of unit vectors $u$ and $v$ so instead of $x$ and $y$ you have $x u$ and $y v$ then rotating the vectors $u$ and $v$ will be enough to rotate all functions on that coordinate system.
    – Mauricio Cele Lopez Belon
    Aug 27 at 23:41















What about translate and rotate the coordinate system itself. If you parameterize your function in terms of a pair of unit vectors $u$ and $v$ so instead of $x$ and $y$ you have $x u$ and $y v$ then rotating the vectors $u$ and $v$ will be enough to rotate all functions on that coordinate system.
– Mauricio Cele Lopez Belon
Aug 27 at 23:41




What about translate and rotate the coordinate system itself. If you parameterize your function in terms of a pair of unit vectors $u$ and $v$ so instead of $x$ and $y$ you have $x u$ and $y v$ then rotating the vectors $u$ and $v$ will be enough to rotate all functions on that coordinate system.
– Mauricio Cele Lopez Belon
Aug 27 at 23:41















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