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Let's say I have a cloud of points, and I know the equation of the symmetry plane. I'd like to mirror every single point with respect to this plane. It might be much simpler than I think, but I have some difficulties on finding a way to do that in Java.

I have the $x,y,z$ position of each point, its distance from the symmetry plane, the equation of the plane. How can I find the $x,y,z$ of the mirrored point ? I was trying to find the point of intersection between the symmetry plane and the line that passes through the point I have to mirror and with its normal being the symmetry plane.

I think it's more an Algebra problem than a Java one. But I still don't know how to do it without Java. I was trying to calculate a linear system :

Line: $ax+by+cz+d=0$

Plane $a'x+b'y+c'z+d' =0$

But it looks like some informations are missing and I can't solve it (only two equations). I hope I explained myself properly.

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    "But I still don't know how to do it without Java" - Sorry, but this really is a math problem. Also, you should put a 'homework' label on this if that's what it is. If you can figure out how to do it mathematically, I'm sure everyone would be happy to help you get it working in java2011-12-06
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    It's not homework and yes while I was writing I figured that it was more a Math problem than a Java one..2011-12-06
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    Should I delete this one and ask it on math.se ?2011-12-06
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    See this: http://www.9math.com/book/projection-point-plane2011-12-06
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    Thanks leonbloy I think your suggestion should work =D2011-12-06
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    Yes it should, requires matrix algebra, and it will be a breeze to write the code after that.2011-12-06
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    Well..thank you all guys..it seems to work properly..I just needed the formula..no problems in Java =D2011-12-06
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    $ax+by+cz+d=0$ does not define a line in 3-space; it defines a plane.2011-12-06
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    Yeah...I finally solved the problem, I needed another equation to define the line in a 3d space, but now that I have the intersection point I don't need it anymore...thanks though..2011-12-07

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