Framework behind Graph plots. DynamicNamespace and friends

Question

As shown in DynamicLocation usage, we can use it to quickly create very nice functionality, that it to refer to graphics' primitives relative coordinates without calculations of boundary etc.

As shown in the answer for that topic, except of DynamicLocation many related things appear:

DynamicNamespace, "DynamicName", TagBox cell expressions.

What is a big picture and how to use it properly?

Answer 1

# post under construction but feel free to add anything

# undocumented feature

# based on observation so it may be wrong

TODO:

This post does not cover few things yet, among others:

• how to convert DynamicLocation to absolute numeric coordinates. You can use menu item Evalaution / Convert Dynamic To Literal on a generated GraphicsBox and it will do that, but this packet works only with seleciton, not with expressions/cell expressions. Would be really useful to know this. And it shpuld be possible because Graphs plots usually don't contain DynamicLocation but explicit coordinates.

• does DynamicLocation work with Offset somehow?

TL;DR;

• The big picture seems to be a framework for marking boxes with IDs which later can be used to find/replace/modify them (boxes).

  See: How to set focus of a dialog window? for an example with FrontEnd`BoxReferenceFind

• In Graph/Graphics world additional tools are available so that marked graphics primitives (Disk etc) location can be expressed symbolically, without knowing its numeric values.

  See example from the OP gif:

  LocatorPane[ Dynamic @ x, Graphics[{
    EdgeForm@Thick, FaceForm@None, DynamicName[Rectangle[], "box"]
  , Arrow[{Dynamic[x], DynamicLocation["box", Automatic]}
  ]}]]
  

Symbols guide

• DynamicName

  DynamicName[obj_, id_String, type___] typesets to

  TagBox[objBoxes, type <> "DynamicName",  BoxID->id]
  

  type can be "Private", "Public" or can be skipped but this additional argument is not supported inside Graphics.

  DynamicName is a handy way to create "marked boxes" to which we can refer later. This way we can write top level code instead of working with cell expressions.

  Additionaly, usage of TagBox makes it fully capable of a round trip to and from boxes:

  ToBoxes @ DynamicName["A", "test"]
  InputForm @ MakeExpression @ %
  

  TagBox["\"A\"", "DynamicName", BoxID -> "test"]
  HoldComplete[DynamicName["A", "test"]]
  

  DynamicName is preferred over explicit e.g. Rectangle[BoxID -> "id"] because of that roundtrip ability and because some primitives will not accept options. E.g. CircleBox will complain as there are no CircleBoxOptions in general, as opposed to RectangleBoxOptions RoundingRadius etc.

• DynamicNamespace

  DynamicNamespace[name_String, expr_, options___] typesets to NamespaceBox[name, exprBoxes, opts]

  Name is optional. Don't know if that argument allows anything fancy yet.

  DynamicNamespace helps with modular coding and resolving conflicts for the same DynamicNames. E.g. Withouth the NamespaceBox only the first appearance of a specific BoxID will be known. See example 1.

• DynamicLocation

  DynamicLocation[name_String, spec1_, spec2_] can be used in graphics primitives as a replacement for point coordinates but pointing to a primitive marked by BoxID -> name.

  • spec1 can be None or Automatic. None will point to the center of the marked primitive.

    Its behavior depends in what primitives we use it, e.g. Automatic for spec1 for line-like (Line,Arrow, etc) will point to the closest point on the edge of marked primitive with respect to parent location. See example 2.

  • spec2 is ignored when spec1 is None but otherwise can take alignment like specification, {Left, Top} etc or Scaled[t].

    Scaled[t] can parametrize position on a marked primitive's edge. Can be used for polygon/line-like primitives. See example 3.

Examples

1. DynamicNamespace usage:

   Compare

   disk[pos_] := {
       DynamicName[Disk[pos], "name"]
     , Arrow[{pos + {2, 2}, DynamicLocation["name", Automatic]}]
   }
       (*compare this *)
   
   Graphics[ { disk[{0, 0}], disk[{0, -2}], disk[{3, 0}] }, PlotRange -> 5 ]
   
       (* with this *)
   
   Graphics[ 
      DynamicNamespace /@ { disk[{0, 0}], disk[{0, -2}], disk[{3, 0}] }
    , PlotRange -> 5 
   ]
   

   

   In the first example all DynamicLocation["name", Automatic] point to the same, first found, BoxID -> "name". If we combine graphics from different source we can't predict names and DynamicNamespace localizes them for us preventing conflics.

2. Context sensitive DynamicLocation:

   LocatorPane[Dynamic@x, 
    Graphics[{EdgeForm@Thick, FaceForm@None, 
      DynamicName[Rectangle[], "box"], 
      Arrow[{Dynamic[x], DynamicLocation["box", Automatic]}]
      ,
      Circle[DynamicLocation["box", Automatic]]
      }, PlotRange -> 2]]
   

   As we can see DynamicLocation["box", Automatic] means something different for Circle and for Arrow.

3. Edge parametrization with the third argument of DynamicLocation:

   DynamicModule[{t = 0}, Column[{
     Slider@Dynamic@t, 
     Graphics[{
       EdgeForm@Thick, FaceForm@None, DynamicName[Arrow@CirclePoints[7], "box"]
     , Thick, Arrow[{{0, 0}, DynamicLocation["box", Automatic, Scaled@Dynamic@t] }]
     }, PlotRange -> 2]
   }]]
   

   

4. Usability in Graphics3D

   It looks like it is purely 2D feature but it works in Graphics3D Epilog, which is 2D, together with 3D primitives!

   Graphics3D[
       { DynamicName[Cuboid[{-2, -2, 0}], "box"]
       , DynamicName[Cuboid[{1, 1, -2}], "box2"]
       }
     , Epilog -> Dynamic @ {
           Arrow[{Scaled[{0, 0}], DynamicLocation["box", Automatic]}]
         , Arrow[{DynamicLocation["box", Automatic],           DynamicLocation["box2", Automatic] }]
       }
     , PlotRange -> 2
   ]
   

   

Answer 2

I think this is a very useful share for how to use this new feature,such make a smart arrow connect the explanation text with the object,for example

Graphics[{DynamicName[Disk[], "disk"], 
  DynamicName[Style[Text["This is a black disk", {3, 2}], 18, Red],"Explanation"], 
  DynamicName[Style[Text["This is a black disk", {0, 2}], 18, Blue],"AnotherExplanation"], 
  Arrow[{DynamicLocation["Explanation", Automatic],DynamicLocation["disk", Automatic]}], 
Arrow[{DynamicLocation["AnotherExplanation",Automatic],DynamicLocation["disk", Automatic]}]}]

You don't need to specify the specific coordinate for your Arrow.I think it is useful..