"If" syntax question

*To*: mathgroup at smc.vnet.net*Subject*: [mg105145] "If" syntax question*From*: Michael Greene <mgreene at csumb.edu>*Date*: Sun, 22 Nov 2009 06:10:24 -0500 (EST)

I downloaded the cylinder net demonstration code to show my middle school class. I thought it was pretty good but needed a few enhancements before I used it in class. One thing I wanted the animation to show was the circle radius rotating when the circles were left in their flat orientation. So I modified the demonstration and came up with: Manipulate[With[{da = 2 Pi/30}, With[ { r1 = RotationTransform[s1*Pi/2, {1, 0, 0}, {0, h/2, 0}], r2 = RotationTransform[-s1*Pi/2, {1, 0, 0}, {0, -h/2, 0}], r3 = RotationTransform[-s2*Pi, {0, 0, 01}, {00, -r - h/2, 0}] }, With[{ d1 = Table[(r1[{r Cos[a], r Sin[a] + h/2 + r, 0}]), {a, 0, 2 Pi, da}], d2 = Table[r2[{r Cos[a], r Sin[a] - h/2 - r, 0}], {a, 0, 2 Pi, da}], l1 = {r3[{0, -h/2, 0}], {0, -r - h/2, 0}}}, Graphics3D[{Opacity[.5], EdgeForm[], {EdgeForm[{Blue}], Polygon[d1]}, {EdgeForm[{Blue}], Polygon[d2]}, Line[r3[l1]], Table[ Polygon[{ {-a, +h/2, 0}, {-a + r da, h/2, 0}, {-a + r da, -h/2, 0}, {-a, -h/2, 0}}], {a, 0, +(1 - s2) (r 2 Pi) - r da, r da}], Take[Table[Polygon[{ {r Cos[a], +h/2, r + r Sin[a]}, {r Cos[a + da], h/2, r + r Sin[a + da]}, {r Cos[a + da], -h/2, r + r Sin[a + da]}, {r Cos[a], -h/2, r + r Sin[a]}}], {a, -Pi/2, -Pi/2 + (2 Pi - 2 Pi/60), 2 Pi/60}], Round[s2 60]]}, ImageSize -> {500, 400}, Boxed -> False, SphericalRegion -> True, PlotRange -> {Automatic, {-3, 3}, {0, 2}}]]]], {{r, 1/2, "radius"}, .1, 1}, {{h, 1, "Height"}, .1, 1}, {{s1, 0, "rotate caps"}, 0, 1, ControlType -> Trigger, DefaultDuration -> 1}, {{s2, 0, "wrap"}, 0, 1, ControlType -> Trigger, DefaultDuration -> 2}] which does what I wanted when you click just the "Wrap" button. The circle clearly makes a single rotation as the rectangle rolls "up" into a cylinder. I have a separate modification that shows the radius sticking to the end caps as they get rotated into position when you click the "rotate caps" button. Both modifications to the original involve the third rotation operator (function?), r3. They differ only in the parameters being passed to the third RotationTransform call. My first attempt at melding the two disparate calls was to modify the r3 definition with the following does nothing code: r3=If[{s3=0},RotationTransform[-s2*Pi, {0, 0, 01}, {00, -r - h/2, 0}],RotationTransform[-s2*Pi, {0, 0, 01}, {00, -r - h/2, 0}]] I say "does nothing" because the true and false outputs are identical. I was just testing Mathematica to see if that usage was OK. The parser didn't like that modification and the code quite working. My question is, why didn't the r3=If... syntax work? What kind of thing is r3 that it can't be one function under one condition and a separate function under another? Perhaps there is some syntactical clue I have to give the parser that indicates my intention here?