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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


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