math - WPF 3D - rotate a model around it's own axes -

suppose have simple wpf 3d scene set single rectangle rotated -45 degrees around x axis so:

<viewport3d>     <viewport3d.camera>         <perspectivecamera position="0,0,4"/>     </viewport3d.camera>     <modelvisual3d>         <modelvisual3d.content>             <directionallight color="white" direction="-1,-1,-3" />         </modelvisual3d.content>     </modelvisual3d>     <modelvisual3d>         <modelvisual3d.content>             <geometrymodel3d>                 <geometrymodel3d.geometry>                     <meshgeometry3d positions="-1,-1,0  1,-1,0  -1,1,0  1,1,0"                                     triangleindices="0,1,2 1,3,2"/>                 </geometrymodel3d.geometry>                 <geometrymodel3d.material>                     <diffusematerial brush="red"/>                 </geometrymodel3d.material>             </geometrymodel3d>         </modelvisual3d.content>         <modelvisual3d.transform>             <transform3dgroup>                 <rotatetransform3d>                     <rotatetransform3d.rotation>                         <axisanglerotation3d axis="1,0,0" angle="-45"/>                     </rotatetransform3d.rotation>                 </rotatetransform3d>             </transform3dgroup>         </modelvisual3d.transform>     </modelvisual3d> </viewport3d> 

this gives me following:

alt text http://www.freeimagehosting.net/uploads/4aa48434a9.png

now want rotate image 45 degrees around model's z axis. if put second rotatetransform3d in so:

                <rotatetransform3d>                     <rotatetransform3d.rotation>                         <axisanglerotation3d axis="0,0,1" angle="45"/>                     </rotatetransform3d.rotation>                 </rotatetransform3d> 

it rotates around scene's z axis. particular x rotation i've worked out need is:

                <rotatetransform3d>                     <rotatetransform3d.rotation>                         <axisanglerotation3d axis="0,1,1" angle="45"/>                     </rotatetransform3d.rotation>                 </rotatetransform3d> 

but here maths fails me. tell me how work out arbitrary x (and y if to) rotation?

ok, spoke mathematician friend , gave me answer:

so think need if you're rotating around vector (1,0,0) angle of 'a' (i.e rotating around x-axis transforming object in y-z plane).

further rotations around

x' - (1,0,0) stays same!

y' - (0,cosa,sina)

z' - (0,-sina,cosa)

a similar principle hold rotations in x-z plane (0,1,0)

x' - (-sina,0, cosa)

y' - (0,1,0) - same

z' - (sina,o,cosa)

and in x-y plane around (0,0,1)

x' - (-sina,cosa,0)

y' - (cosa,sina,0)

z' - (0,0,1) stays same

tada!

update: created function calculate matrix rotate object in 3 axes. can used matrixtransform3d.

    matrix3d calculaterotationmatrix(double x, double y, double z)     {         matrix3d matrix = new matrix3d();          matrix.rotate(new quaternion(new vector3d(1, 0, 0), x));         matrix.rotate(new quaternion(new vector3d(0, 1, 0) * matrix, y));         matrix.rotate(new quaternion(new vector3d(0, 0, 1) * matrix, z));          return matrix;     }