Moving an AutoCad DXF solid along a 3D path in Mathematica

Question

I came across this post and found belisarius' answer interesting. Wondering whether he someone can post ~~his~~ complete mma code and give some explanation. In general, my question is about how to achieve this kind of annimation/plotting behavior in mma. It looks amazing to me!

Many thanks.

@belisarius: Opened it to the world, then promptly smacked your solution down! :) — Simon, Apr 09 '11 at 05:45
@Simon Yeah. I was working on it since Qiang left me a comment on the other question. We have all the rep business setup in order :) — Dr. belisarius, Apr 09 '11 at 05:46
@belisarius: A perfect plan! BTW, talking about the "rep business" I chucked 100rep down on the [default ColorData in Plot](http://stackoverflow.com/questions/5399216/how-to-change-the-default-colordata-used-in-mathematicas-plot) question... since the problem's probably impossible (unless you work at WRI) I doubt that it will help things. — Simon, Apr 09 '11 at 05:47

Dr. belisarius · Accepted Answer · 2011-04-11T14:11:34.443

3

Please tell me if further explanation is needed.

x[t_] := {Cos@t, Sin@t, .1  t} /; t <= 3 Pi;
x[t_] := {Cos@t, Sin@t, .3 Pi  (4 - t/Pi)} /; t > 3 Pi;
plotRange = {{-110, 110}, {-110, 110}, {-10, 110}};
z1 = ParametricPlot3D[100 x[t], {t, 0, 4 Pi}, PlotRange -> plotRange];
hel = Import["ExampleData/helicopter.dxf.gz", 
   ViewPoint -> {10, 10, 10}, AlignmentPoint -> {80, 80, 80}];

zz = Table[
   Show[z1, 
    Graphics3D[
     Translate[Rotate[First[hel], t + Pi/2, {0, 0, 1}], 100 x[t]]], 
    PlotRange -> plotRange], {t, 0, 4 Pi, 4 Pi/15}];
Export["c:\\test.gif", zz, "DisplayDurations" -> .5]

(* Or
 Animate[Show[z1, 
   Graphics3D[
    Translate[Rotate[First[hel], t + Pi/2, {0, 0, 1}], 100 x[t]]], 
   PlotRange -> plotRange], {t, 0, 4 Pi}]

enter image description here

One could calculate the heli rotation using the curve derivatives. Too lazy to do it right now.

Edit

To comply with Sjoerd's home decoration rules:

enter image description here

edited Apr 11 '11 at 14:11

answered Apr 09 '11 at 05:29

Dr. belisarius

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You forgot to add this: `Sound[Play[ Sin[50 t] (Sin[100 t] + Sin[140 t] + Sin[180 t]), {t, 0, 20}]]` – Sjoerd C. de Vries Apr 10 '11 at 22:22
@Sjoerd This one is for your UFO movie in skeptics: `Sound[Play[ Sin[5000 t] (Sin[100 t] + Sin[140 t] + Sin[180 t]), {t, 0, 5}]]` – Dr. belisarius Apr 10 '11 at 22:32
@belisarius ;-) The stabilized movie was made using Mathematica's new image processing tools, BTW. It was a great learning project. – Sjoerd C. de Vries Apr 10 '11 at 22:58
@Sjoerd I have been playing around with those tools too. You can do amazing things in a few steps. The performance is not very good, but they are a great sandbox for testing algorithms. – Dr. belisarius Apr 10 '11 at 23:32
@belisarius I changed your animation. If you do not approve, please roll back the edit. – Mr.Wizard Apr 11 '11 at 02:58
@Mr.Wizard You'd better use t+Pi instead. – Sjoerd C. de Vries Apr 11 '11 at 11:46
@Sjoerd, what did I screw up this time? :) – Mr.Wizard Apr 11 '11 at 11:48
1

@Mr.Wizard Could we have a blue helicopter instead of a pink one? It doesn't match my carpet. – Sjoerd C. de Vries Apr 11 '11 at 11:52
1

@Sjoerd @belisarius You guys are crazy! – Mr.Wizard Apr 11 '11 at 12:28
1

Also, the blue one is slightly out of sync with mine. Please fix it. – Mr.Wizard Apr 11 '11 at 12:29
1

@Mr.Wizard @belisarius ;-) It's all in the eye of the beholder. – Sjoerd C. de Vries Apr 11 '11 at 12:37
1

@Mr. I synchronized mine with Saturn's rings fourth harmonic, which is of utmost importance to preserve the Ying balance in Sjoerd's home decoration initiative, as clearly indicated by his interventions in the skeptics discussion board. – Dr. belisarius Apr 11 '11 at 12:42
@Sjoerd oh come on, what's the _worst_ that could happen? ... ... ... ;-) – Mr.Wizard Apr 11 '11 at 13:24
1

@Mr.Wizard A millstone bound to your leg, thrown in the lake? Or perhaps getting a job as PR guy for Stephen Wolfram. – Sjoerd C. de Vries Apr 11 '11 at 13:28
@Sjoerd Hmmm ... How big is that millstone? – Dr. belisarius Apr 11 '11 at 13:43
1

belisarius, anyone watching your edits without reading these comments is going to be really confused. lol – Mr.Wizard Apr 11 '11 at 14:25
1

Look mama, the helicopter got a friend! – Sjoerd C. de Vries Apr 11 '11 at 14:53

Moving an AutoCad DXF solid along a 3D path in Mathematica

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