Re: "If" syntax question

*To*: mathgroup at smc.vnet.net*Subject*: [mg105178] Re: "If" syntax question*From*: David Bailey <dave at removedbailey.co.uk>*Date*: Mon, 23 Nov 2009 06:53:34 -0500 (EST)*References*: <6029eb910911210735s5be59d99wf16925fd4cdc7302@mail.gmail.com> <heb69s$abq$1@smc.vnet.net>

Michael Greene wrote: > Oops. I corrected the expression to use == instead of = in the conditional. > Still don't get what I'm trying for which is a single 3d point coordinate. > > 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}]] > > > On Sat, Nov 21, 2009 at 7:35 AM, Michael Greene <mgreene at csumb.edu> wrote: > >> 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? >> >> >> > > s3 doesn't have a value, so the 3-argument form of If doesn't evaluate. The problem has nothing to do with r3. David Bailey http://www.dbaileyconsultancy.co.uk