在绘图过程中使用定位器坐标为矩阵建立索引

Question

I would like to "draw" into a matrix in Mathematica. That is, I would like to use the mouse to (say, using EventHandler) change the value at a matrix index to 1 from, say, 0. The simplest approach would seem to be to use Locator coordinates, p, take the Rounded value of those coordinates, and assign the matrix location at that value with 1. This does not appear to work because the form "Sequence @@ Round[p]" in M[[Sequence @@ Round[p]]]=1 does not result in a proper index because p is itself a Dynamic quantity (as can be seen using FullForm).

It would appear to be extremely useful to do something like this, but I can find no references to this, or any other method that takes a Locator coordinate output and uses it as an index to an array.

Any ideas greatly appreciated.

Answer 1

My experience is that locators are great for what they are, but attempts to generalize them don't work out very well. Fortunately, what you want to do is still pretty straightforward.

clickFunction[point,moreargs]:=Module[{}, see below ];

DynamicModule[{},

  ClickPane[
    Dynamic[Show[ what you want to click on ]],
    clickFunction[#,moreargs]
  ]
]

When the user clicks in the pane, clickFunction is called with the coordinates of the mouse pointer and possibly other arguments. You can place Dynamic[] around individual arguments in the click function call (with addition of the symbols inside the first argument of DynamicModule, to make them Dynamic). The clickFunction can also return values, using the form

 ({v1,v2,v3,..}=clickFunction[#,moreargs])&

The symbols in the list of return values can be dynamic, but should not have the Dynamic wrapper.

clickFunction needs to figure out what was clicked on. For each area on your click pane (assuming it is rectangular),use its lower left and upper right corners to create x and y inequalities which return true or false when the point argument is in or out of the rectangle. You can keep these in a list that you traverse with an appropriate function to detect what is clicked.

Don't shy away from Dynamic[]. I tried to do things with Manipulate[] (and Locators) for far too long, thinking Dynamic[] was a big learning curve. It's not.