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<StructureSection load='' size='340' side='right' caption='' scene='43/433638/Fullview_cartoon/20'>
<StructureSection load='' size='340' side='right' caption='' scene='43/433638/Fullview_cartoon/21'>


==Examples of how quaterions are used==
==Examples of how quaterions are used==
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Jmol shows structures (e.g. atomic positions) on a display and allows the view to be rotated and individual atomic positions to be manipulated. The display has Cartesion coordinates (the x-axis goes right, the y-axis goes up, and the z-axis points at the viewer). The atoms have Cartesian coordinates x, y, z. The meaning of the axes is sometimes arbitrary (NMR structures) or along certain crystallographic directions (X-ray structures). When you rotate the model, the coordinate system of the model is rotated (same coordinates x, y, z, but axes of coordinate system point in different directions) with respect to the display coordinate system.
Jmol shows structures (e.g. atomic positions) on a display and allows the view to be rotated and individual atomic positions to be manipulated. The display has Cartesion coordinates (the x-axis goes right, the y-axis goes up, and the z-axis points at the viewer). The atoms have Cartesian coordinates x, y, z. The meaning of the axes is sometimes arbitrary (NMR structures) or along certain crystallographic directions (X-ray structures). When you rotate the model, the coordinate system of the model is rotated (same coordinates x, y, z, but axes of coordinate system point in different directions) with respect to the display coordinate system.


<jmol><jmolButton><script>axes on</script><text>show axes</text></jmolButton></jmol>
<jmol><jmolButton><script>axes MOLECULAR; axes on</script><text>show axes</text></jmolButton></jmol>


When a new structure is loaded, the model axes point left, up, and out of the screen. The Jmol command "reset" puts that coordinate system back into that initial orientation.
When a new structure is loaded, the model axes point left, up, and out of the screen. The Jmol command "reset" puts that coordinate system back into that initial orientation.


<jmol><jmolButton><script>reset</script><text>reset to initial orientation</text></jmolButton></jmol>
<jmol><jmolButton><script>reset; axes MOLECULAR; axes on</script><text>reset to initial orientation</text></jmolButton></jmol>


==Changing orientations using quaternions==
==Changing orientations using quaternions==
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The Jmol command "q = quaternion()" assigns the current orientation to q.  
The Jmol command "q = quaternion()" assigns the current orientation to q.  


<jmol><jmolButton><script>q = quaternion()</script><text>save orientation</text></jmolButton></jmol>
<jmol><jmolButton><script>q = quaternion()</script><text>store orientation</text></jmolButton></jmol>


So, again, how is an orientation different from a rotation? An orientation is the rotation necessary to get the coordinate system from the "reset" orientation to the current orientation. The quaternion ''q0'' for the initial orientation corresponds to no rotation, i.e. {0 0 1 0}. To get back to an orientation ''q'' after rotating, use "moveto 0 quaternion q". After you saved an orientation, click the reset button above and then go back to the saved orientation with the button below.
So, again, how is an orientation different from a rotation? An orientation is the rotation necessary to get the coordinate system from the "reset" orientation to the current orientation. The quaternion ''q0'' for the initial orientation corresponds to no rotation, i.e. {0 0 1 0}. To get back to an orientation ''q'' after rotating, use "moveto 0 quaternion q". After you saved an orientation, click the reset button above and then go back to the saved orientation with the button below.


<jmol><jmolButton><script>moveto 0 quaternion @q</script><text>go to saved orientation</text></jmolButton></jmol>
<jmol><jmolButton><script>moveto 0 quaternion @q</script><text>go to stored orientation instantly</text></jmolButton></jmol>
 
<jmol><jmolButton><script>moveto 2 quaternion @q</script><text>go to stored orientation gradually</text></jmolButton></jmol>


Relevant Jmol command examples:
Relevant Jmol command examples:
  q = quaternion() # store current orientation
  q = quaternion() # store current orientation
  moveto 0 quaternion @q # go back to stored orientation instantly
  moveto 0 quaternion @q # go back to stored orientation instantly
  moveto 1 quaternion @q # go back to stored orientation gradually
  moveto 2 quaternion @q # go back to stored orientation gradually (2 sec)
   
   
==Combining two rotations==
==Combining two rotations==
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Choosing x = 1, y = 0.5, z = 0 and tilt = 10, the buttons illustrate the commands.
Choosing x = 1, y = 0.5, z = 0 and tilt = 10, the buttons illustrate the commands.
<jmol><jmolButton><script>s = quaternion(); r = quaternion({1 0.5 0},10); tilted = r * s; moveto 1 quaternion @tilted </script><text>tilt 10 degrees away from view</text></jmolButton></jmol>
<jmol><jmolButton><script>s = quaternion(); r = quaternion({1 0.5 0},10); tilted = r * s; moveto 1 quaternion @tilted </script><text>tilt 10 degrees away from view</text></jmolButton></jmol>


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Here is an example:  
Here is an example:  
<jmol><jmolButton><script>q0 = quaternion(); qr = quaternion({1 1 0}, 90); rotate @qr</script><text>rotate all the way</text></jmolButton></jmol>
<jmol><jmolButton><script>q0 = quaternion(); qr = quaternion({1 1 0}, 180); rotate @qr</script><text>rotate all the way</text></jmolButton></jmol>


<jmol><jmolButton><script>moveto 0 quaternion @q0</script><text>back to last orientation</text></jmolButton></jmol>
<jmol><jmolButton><script>moveto 0 quaternion @q0</script><text>back to last orientation</text></jmolButton></jmol>


<jmol><jmolButton><script>q10 = @qr / 10; rotate @q10</script><text>rotate one tenth</text></jmolButton></jmol>
<jmol><jmolButton><script>q10 = @qr / 10; rotate @q10</script><text>rotate one tenth</text></jmolButton></jmol>
<jmol><jmolButton><script>q10 = @qr / 10;
moveto 0 quaternion @q0;delay 0.5;
qn = q10 * q0; moveto 0.5 quaternion @qn;
qn = (q10 * 3) * q0; moveto 0.3 quaternion @qn;
qn = (q10 * 7) * q0; moveto 0.2 quaternion @qn;
qn = (q10 * 9) * q0; moveto 0.3 quaternion @qn;
qn = (q10 * 10.1) * q0; moveto 0.5 quaternion @qn;
qn = (q10 * 10) * q0; moveto 0.5 quaternion @qn;
</script><text>rotate all the way with variable speed</text></jmolButton></jmol>


Relevant Jmol command examples:
Relevant Jmol command examples:
  qr = quaternion({1 1 0}, 90) #define the overall rotation
  qr = quaternion({1 1 0}, 180) #define the overall rotation
  q10 = @qr / 10 #q10 is rotating only one tenth of the way
  q10 = @qr / 10 #q10 is rotating only one tenth of the way
  rotate @q10 # rotate the view by the given amount
  rotate @q10 # rotate the view by the given amount
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  moveto @duration quaternion @q1 # reorient the view back to q1 in duration seconds
  moveto @duration quaternion @q1 # reorient the view back to q1 in duration seconds
   
   
==Moveto vs Rotate command==
The rotate command only rotates (no zoom or translation), and always at the same speed. If you want to have control over the rotation speed, you have to use moveto instead. Moveto takes the final orientation as a parameter, and moves to it from whatever the current orientation is. On the other hand, the rotate command is relative to the starting orientation. If you want to turn a rotate command into a moveto command, you have to calculate the final orientation in the following way:
start = quaternion();
final = rotation * start; #equation 1
Then, you can use the moveto command.
On the flip side, if you have the final and start orientations, and need the rotation, you use quaternion division:
rotation = final / start; #equation 2
Equation 2 is derived by right-dividing equation 1 by start to isolate rotation on the right hand side


==Moving atoms==
some other time...
</StructureSection>
</StructureSection>
==Resources==
==Resources==
http://sacredsoftware.net/tutorials/quaternion.html
http://sacredsoftware.net/tutorials/quaternion.html

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Karsten Theis
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