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Rotation matrix not about origin/reflection not through origin

HI

So we're doing matrix transformation in FP1 recently, and we learned the rotational matrix about origin and reflection matrix in a line through origin

And a question popped up in my mind, "well, what if a rotation/reflection NOT about origin?"

I THINK I figured rotation one out... translation first and move it to origin, then rotate it, translate it back (is this right?)

But what about reflection? Do I just do a reflection in a line through origin with the same gradient as the other line, then somehow translate it accordingly? In that case what would the translation value be...does it have to do with the y intercept maybe?

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Original post by C0balt
HI

So we're doing matrix transformation in FP1 recently, and we learned the rotational matrix about origin and reflection matrix in a line through origin

And a question popped up in my mind, "well, what if a rotation/reflection NOT about origin?"

I THINK I figured rotation one out... translation first and move it to origin, then rotate it, translate it back (is this right?)


Yep, that's the method.


But what about reflection? Do I just do a reflection in a line through origin with the same gradient as the other line


Basically.


then somehow translate it accordingly? In that case what would the translation value be...does it have to do with the y intercept maybe?

Posted from TSR Mobile


Translate before and translate back after, as before.

A translation moves the line to the origin, perform the reflection, and translate back. Except in this case there are many possibilities for moving the line to the origin.
You could go with the y-intercept - translate down by that amount, reflect, then back up.
Or the x-intercept - traslate left by that, reflect, then back right.

Those are the two straight forward translations (there are others, not as nice).
Reply 2
Avatar for james22
james22
16
To add to the above, you cannot represtent reflections/rotations by a matrix unless they are reflections/rotations through the origin.
Original post by james22
To add to the above, you cannot represtent reflections/rotations by a matrix unless they are reflections/rotations through the origin.


Certainly, for the standard coordinate system.

Homogeneous coordinates however....
@OP: If you fancy, a research project there.
(edited 9 years ago)
Reply 4
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C0balt
OP
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Wtf it says thread is closed When I try to quote people on mobile...

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Reply 5
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C0balt
OP
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Original post by ghostwalker
Yep, that's the method.

Basically.

Translate before and translate back after, as before.

A translation moves the line to the origin, perform the reflection, and translate back. Except in this case there are many possibilities for moving the line to the origin.
You could go with the y-intercept - translate down by that amount, reflect, then back up.
Or the x-intercept - traslate left by that, reflect, then back right.

Those are the two straight forward translations (there are others, not as nice).

Cool. Thanks
I guess I've seen the "others" on wikipedia which scared the hell out of me XD

You guys seem to be better than my maths teacher lol I asked him but he didn't know x.x
Reply 6
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C0balt
OP
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Original post by james22
To add to the above, you cannot represtent reflections/rotations by a matrix unless they are reflections/rotations through the origin.

Oh really :eek:
Reply 7
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C0balt
OP
16
Original post by ghostwalker
Certainly, for the standard coordinate system.

Homogeneous coordinates however....
@OP: If you fancy, a research project there.

lol cool, will have a look at it. Can't imagine coordinates that's homogeneous in my head XD
Reply 8
Avatar for james22
james22
16
Original post by C0balt
Oh really :eek:


Any transformation represented by a matrix must send the origin to the origin, since if M is a matrix then M*0=0.

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