Camera space to world space?

[paulscode]

What is the correct method for converting from camera space into world space?  I thought it was this:

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vector.matMul( camera.getBack().invert3x3() );
vector.add( camera.getPosition() );

I am getting an unexpected result with this.  In the case where I set the camera position and orientation as:

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        camera.setPosition( 0, 50, 0 );
        camera.setOrientation( new SimpleVector( 0, -1, 0 ), new SimpleVector( 0, 0, -1 ) );


Then try to convert the following vector:

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SimpleVector vector = new SimpleVector( 50, 0, 0 );
vector.matMul( camera.getBack().invert3x3() );
vector.add( camera.getPosition() );

I get a resulting vector of (-50.0, 50.0, 0.0).  But shouldn't it be (50.0, 50.0, 0.0)?  Am I incorrect about what the result should be, or am I doing the conversion incorrectly?

To visualize the problem, this is the result I am expecting to see:

[EgonOlsen]

Seems to be flaw in setOrientation() to me. Right now, i'm highly confused about all the coordinate system and space conversions taking place, but...actually i would expect this to be a null operation:
   
   

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    camera.setOrientation( new SimpleVector( 0, 0, 1 ), new SimpleVector( 0, -1, 0 ));
   
   
...but the actual null operation is
   
   

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    camera.setOrientation( new SimpleVector( 0, 0, 1 ), new SimpleVector( 0, 1, 0 ).normalize() );
   
   
which is correct when viewed from the rotation matrix' point of view but it's not what you would expect given jPCT's coordinate system.
   
Also, getUpVector() should return the same value that you've given the setOrientation()-method, but actually it doesn't. I'll fix this. For now, simply doing a skalarMul with -1 with the up vector should do the trick.