Bill DeWitt (bdewitt@gateway.net) asked for more information about vrotate and other vector expressions.

The advantages of using vrotate? By keeping the vector in a variable, you can get the actual value of the vector. I find this so useful that I made a simple macro and loaded it in my standard include files:

#macro ReportV(size)
  #render concat("\nReported Vector is <" + str(size.x,3,3) + "," +
          str(size.y,3,3) + "," + str(size.z,3,3) + ">" )
#end

For a more specific application: elliptical planetary orbit. Lets make a model planet rotate along it's axis.

**** COMING SOON ****

	Step 1 Creating the scene
	Here is the scene we are going to work with. The red sphere sits on the floor. Here is the code to set this scene up: light_source { <0,0,-1000> color rgb 1 rotate <45,30,0> } plane { y,-0.25 pigment { checker color rgb 0.9 color rgb 0.5 } } #declare rv = <115,165,-65>; #declare p1 = <1,0,-1>; sphere { p1,0.25 pigment { red 1 } finish { phong 1 } } rv is our rotation vector, and p1 is the position of the sphere.
	Step 2 Rotate around the x axis
	Vrotate works exactly the same as the rotate command, it only applies to vectors where rotate applies to objects. Like any rotation this is done by rotating around the x axis first. Note that the two code blocks below place the sphere in the same place... the texture would be applied differently: // BLOCK ONE #declare p2 = vrotate(p1,<rv.x,0,0>); sphere { p2, 0.25 pigment { red 1 } finish { phong 1 } } // BLOCK TWO sphere { p1, 0.25 pigment { red 1 } finish { phong 1 } rotate <rv.x,0,0> } Below is an example of this in a bit more detail. The red curve shows the full range of rotation for the sphere.
	Step 3 Rotate around the y axis
	Next, we rotate around tht y axis... #declare p3 = vrotate(p1,<rv.x,rv.y,0>); sphere { p3, 0.25 pigment { red 1 } finish { phong 1 } } and this time the green curve indicates this rotation.
	Step 4 Rotate around the z axis
	And finally we rotate around the z axis. Normally you probably wont need to (or want to) rotate around all three axes. Two will suffice. #declare p4 = vrotate(p1,<rv.x,rv.y,rv.z>); sphere { p4, 0.25 pigment { red 1 } finish { phong 1 } } And (need we say it?) the blue curve shows the rotation around the z axis.

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