How to Dynamically Locate (get coordinates) of a point, inside a Manipulate?

Question

I've been searching all around the "Documentation Center" and other forums and just can't get to solve this issue. I'd like to dynamically locate a point (get it's coordinates) inside a Manipulate. This point is in fact a function of another parameter (hence the Manipulate).

Here's the setup. First I create the functions that will provide with the points coordinates :

T01[q1_] = {{Cos[q1 Degree], 0, Sin[q1 Degree], 0}, {0, 1, 0, 
0}, {-Sin[q1 Degree], 0, Cos[q1 Degree], 0}, {0, 0, 0, 
1}}; (*Matrice de passage de R0 à R1*) 

T12[q2_, l1_] = {{Cos[q2 Degree], 0, Sin[q2 Degree], 0}, {0, 1, 0, 
    0}, {-Sin[q2 Degree], 0, Cos[q2 Degree], -l1}, {0, 0, 0, 
    1}}; (*Matrice de passage de R1 à R2*)

T02[q1_, q2_, l1_] = 
  T01[q1].T12[q2, l1]; (*Matrice de passage de R0 à R2*)

E2[l2_] = {0, 0, -l2, 1}; (*position de l'effecteur dans le repère R2*)

E0[q1_, q2_, l1_, l2_] = 
  T02[q1, q2, l1].E2[l2]; (*position de l'effecteur dans R0*)

O22 = {0, 0, 0, 1};(*position du centre articulaire O2 dans R2*)

O20[q1_, q2_, l1_] = T02[q1, q2, l1].O22;(*position de 02 dans R0*)

O11 = {0, 0, 0, 1};(*position de O1 dans R1*)

O10[q1_, q2_] = T01[q1].O11;(*position de O1 dans R0*)

I'm in fact interested in showing the $E_0$ coordinates dynamically if possible inside the manipulate window...

So then I create the Manipulate environment which shows a double pendulum parameterized by the $q_1$ and $q_2$ variables :

Manipulate[
 ListLinePlot[
  {
   {O10[q1, q2][[1]], O10[q1, q2][[3]]}, {O20[q1, q2, 400][[1]], 
    O20[q1, q2, 400][[3]]}, {E0[q1, q2, 400, 300][[1]], 
    E0[q1, q2, 400, 300][[3]]}
   }, PlotRange -> {{-710, 710}, {-710, 710}}, 
  AspectRatio -> Automatic, PlotMarkers -> Automatic, Ticks -> None
  ], {{q1, 5, "\!\(\*SubscriptBox[\(q\), \(1\)]\)"}, -170, 
  170}, {{q2, 5, "\!\(\*SubscriptBox[\(q\), \(2\)]\)"}, -170, 170}
 ]

I tried the Locator function without success, also I tried the Dynamic function but I just couldn't get to make it work for the $E_0$ variable...

Does anybody has any idea that might help?

Thanks in advance.

Answer 1

  Manipulate[ListLinePlot[
  Tooltip@ {{O10[q1, q2][[1]], 
  O10[q1, q2][[3]]}, {O20[q1, q2, 400][[1]], 
  O20[q1, q2, 400][[3]]}, {E0[q1, q2, 400, 300][[1]], 
  E0[q1, q2, 400, 300][[3]]}}, 
  PlotRange -> {{-710, 710}, {-710, 710}}, AspectRatio -> Automatic, 
  PlotMarkers -> Automatic,  Ticks -> None], 
  {{q1, 5, Subscript["q", 1]}, -170,  170}, 
  {{q2, 5, Subscript["q", 2]}, -170, 170}]

Update: Displaying the current value of E0

To display E0 outside Manipulate one can use the Manipulate option LocalizeVariables->False and put the label insideDynamic -- as the OP did in his answer. Displaying inside Manipulate can be done in several ways:

Using PlotLegends: Add the following option to ListLinePlot

 PlotLegends -> Placed[Row[{"E0  = ", 
  MatrixForm[ N@{E0[q1, q2, 400, 300][[1]], E0[q1, q2, 400, 300][[3]]}]}],  Above]
 (* or, if you like, Below, Left, Right ... instead of Above *)

Using PlotLabel: Use the option setting

 PlotLabel -> Row[{"E0  = ", 
  MatrixForm[ N@{E0[q1, q2, 400, 300][[1]], E0[q1, q2, 400, 300][[3]]}]}]

Using Column: Change the first argument of Manipulate to

 Column[{Row[{"E0  = ", 
  MatrixForm[ N@{E0[q1, q2, 400, 300][[1]], E0[q1, q2, 400, 300][[3]]}]}], 
 ListLinePlot[ Tooltip@{{O10[q1, q2][[1]],  O10[q1, q2][[3]]}, {O20[q1, q2, 400][[1]], 
  O20[q1, q2, 400][[3]]}, {E0[q1, q2, 400, 300][[1]],  E0[q1, q2, 400, 300][[3]]}}, 
 PlotRange -> {{-710, 710}, {-710, 710}}, AspectRatio -> Automatic, 
 PlotMarkers -> Automatic, Ticks -> None]}, Center]

Answer 2

In addition to the code supplied by kguler I would like to answer your slightly hidden question at the end of your own answer. Manipulate is a very powerful concept in Mathematica. You can put nearly everything inside a Manipulate. For your problem, I created a Column consisting of the ListLinePlot and a Row containing the current E0 vector.

Manipulate[
 Column[{ListLinePlot[Tooltip@{{O10[q1, q2][[1]], 
       O10[q1, q2][[3]]}, {O20[q1, q2, 400][[1]], 
       O20[q1, q2, 400][[3]]}, {E0[q1, q2, 400, 300][[1]], 
       E0[q1, q2, 400, 300][[3]]}}, 
       PlotRange -> {{-710, 710}, {-710, 710}}, AspectRatio -> Automatic,
       PlotMarkers -> Automatic, Ticks -> None],
   Spacer[4],
   Row[{"\!\(\*SubscriptBox[\(E\), \(0\)]\)=", {E0[q1, q2, 400, 300][[1]], 
   E0[q1, q2, 400, 300][[3]]} // MatrixForm}]}, 
 Alignment -> Center], 
{{q1, 5, Subscript["q", 1]}, -170, 170}, 
{{q2, 5, Subscript["q", 2]}, -170, 170}, 
LocalizeVariables -> False]

This gives you:

As a tip: putting your stuff into Manipulate is an easy and fast way to create interactive code you can play with. Hope it helps!

Answer 3

@kguler : Ok, thanks a lot for your answer kguler!

Also, I may look like an idiot answering my own question but here it is...

So, I continued my little research on how to properly localize the variables I needed to localize and here's what I found :

{
 Manipulate[
  ListLinePlot[
   Tooltip@{{O10[q1, q2][[1]], 
      O10[q1, q2][[3]]}, {O20[q1, q2, 400][[1]], 
      O20[q1, q2, 400][[3]]}, {E0[q1, q2, 400, 300][[1]], 
      E0[q1, q2, 400, 300][[3]]}}, 
   PlotRange -> {{-710, 710}, {-710, 710}}, AspectRatio -> Automatic, 
   PlotMarkers -> Automatic, 
   Ticks -> None], {{q1, 5, Subscript["q", 1]}, -170, 
   170}, {{q2, 5, Subscript["q", 2]}, -170, 170}, 
  LocalizeVariables -> False], "\!\(\*SubscriptBox[\(E\), \(0\)]\)="
  Dynamic[{E0[q1, q2, 400, 300][[1]], E0[q1, q2, 400, 300][[3]]} // 
    MatrixForm]}

This provides me with a neat dynamical display of the variable I wanted to watch over for : $E_0$.

Here's what I obtained :

Now, what would be really great would be to somehow integrate this display inside the manipulate zone...

I hope this can be useful to others!