a busy cat

I want to add dots to the maze so far I know only how to get one dot on the maze. I don't know if there is way without using coordinates.

So it would look like this with the dots added

a busy cat
(source: trelford.com)


closed as unclear what you're asking by Mr.Wizard Mar 8 '17 at 13:21

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    $\begingroup$ This question seems to be too broad or unclear in isolation. Please include the context necessary to make sense of the question. $\endgroup$ – Mr.Wizard Dec 6 '16 at 1:58

I feel this answer is as sensible as the question.

First, binarise the image:

m = Import["maz1.jpg"]
bin = Opening[ColorNegate@Binarize[m], 6]


Find the biggest white space, and thin it into a skeleton

thin = Thinning[SelectComponents[bin, "Count", -1], Method -> "MedialAxis"]


I used "MedialAxis" here to make it squarer, at the cost of extra bits hanging off. But we'll trim those later.

Turn it into a graph:

g = MorphologicalGraph[thin, VertexSize -> 4, VertexStyle -> Yellow]


Extract the coordinates of the vertices:

vertices = VertexCoordinates /. AbsoluteOptions[g, VertexCoordinates];
vrules = Sort[Rule @@@ Transpose[{VertexList[g], vertices}]];

Pick out the edges that don't have a vertex of degree 1:

bad = Pick[VertexList[g], VertexDegree[g], 1];
good = Select[EdgeList[g], ! MemberQ[bad, First@#] && ! MemberQ[bad, Last@#] &];

Calculate dots along each good edge at a vaguely even spacing:

dots = Union@Flatten[Module[{a = #1 /. vrules, b = #2 /. vrules, d},
      d = 1 + 1/10 Round[EuclideanDistance[a, b], 10];
      a + #/d (b - a) & /@ Range[0, d]] & @@@ good, 1];

Show[m, Graphics[{Yellow, Point /@ dots}]]



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