How To interactively create a Polygon in a Graphic?

Question

Background: suppose I start with the following (working) snippet.

 Manipulate[Graphics[Line[{{0, 0}, p}], PlotRange -> 2], {{p, {1, 1}}, Locator}]

Ideally, I would like to be able to add points with their own locator to the graphic and via selecting or otherwise add Polygons, Circles, BezierCurves, etc.

Question: How can I interactively add a point to a Graphic that can be moved via its own locator? How can I select three or more points on such a Graphic and create a Polygon from them? ( I need the coordinates from the points, and which geometries have been created for later usage. )

* UPDATE* Thanks to FJRA's answer ( LocatorAutoCreate ) I can now rephrase the question as follows. From the following snippet

 Manipulate[
  Graphics[Map[Point[#] &, pts], 
   PlotRange -> 1], {{pts, {{0, 0}, {.5, 0}, {0, .5}}}, Locator, 
   LocatorAutoCreate -> True}]

Question: How can I select multiple points and create a polygon from them. Ideally, I would like to select a geometry: i.e. Circle, Polygon, BezierCurve.

Answer 1

This isn't exactly what you asked for, but it might do the trick. This solution allows you to create a number of different shapes (circle, polygon, line, Bezier curve, etc.). To add a shape, press the "New object" button. You can add points to an existing shape by clicking anywhere in the plane.

Note that I'm using LocatorAutoCreate -> All instead of True which means that you don't need a modifier key to add points. Deleting locators is the same as with LocatorAutoCreate -> True.

You can edit an existing object by pressing the "Edit object" button and choosing the right object. The "Print shapes" button prints a list of the shapes where each shape is represented by a list of coordinates and a string indicating the type.

DynamicModule[{types, fun},
 types = {"Circle", "Disk", "Polygon", "Line", "Bezier", "Spline"};
 fun[{}, ___] := {};
 fun[{a_}, ___] := {};
 fun[pts_, type_] := Switch[type,
   "Circle", Circle[pts[[1]], Norm[pts[[2]] - pts[[1]]]],
   "Disk", Disk[pts[[1]], Norm[pts[[2]] - pts[[1]]]],
   "Polygon", {EdgeForm[Black], FaceForm[Opacity[.5]], Polygon[pts]},
   "Line", Line[pts],
   "Bezier", BezierCurve[pts],
   "Spline", BSplineCurve[pts]];

 Manipulate[
  ptlst[[object]] = pts;
  typelst[[object]] = type;
  grlst = MapThread[fun, {ptlst, typelst}];
  Graphics[grlst, PlotRange -> {{-3, 3}, {-3, 3}}],

  {{pts, {}}, Locator, LocatorAutoCreate -> All},
  {{ptlst, {{}}}, None},
  {{typelst, {"Line"}}, None},
  {{object, 1}, None},
  {grlst, None},
  {{type, "Line", "Object type"}, types},
  Row[{Button["New object",
     If[Length[ptlst[[-1]]] > 0,
      AppendTo[ptlst, {}]; AppendTo[typelst, type];
      object = Length[typelst];
      pts = {}]],
    Dynamic@PopupView[Graphics[#, ImageSize -> 50] & /@ grlst,
      Dynamic[object, (object = #; pts = ptlst[[#]]; type = typelst[[#]]) &],
       Button["Edit object"]],
    Button["Print shapes", Print[Transpose[{ptlst, typelst}]]]}]
  ]]

Answer 2

Maybe option LocatorAutoCreate -> True is what you need, it is documented in the help. This is the example shown in the Manipulate tutorial:

Manipulate[Graphics[Polygon[pts], PlotRange -> 1],
 {{pts, {{0, 0}, {.5, 0}, {0, .5}}}, Locator, 
  LocatorAutoCreate -> True}]

what they don't say in the docs is that for adding a point in linux you need to press Ctrl + Alt + click.

UPDATE:

Maybe you can add an extra control to select the graphics object you want to see:

    Manipulate[
     Graphics[g[pts], PlotRange -> 1],
     {g, {Point, Line, Polygon, BSplineCurve, BezierCurve}, ControlType -> PopupMenu},
     {{pts, {{0, 0}, {.5, 0}, {0, .5}}}, Locator, LocatorAutoCreate -> True}]