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Visualizing a geometric problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg113183] Visualizing a geometric problem
  • From: Velina Veleva <vvveleva at gmail.com>
  • Date: Sun, 17 Oct 2010 06:05:40 -0400 (EDT)

I am trying to figure out a way to move two points, X and Y,
independently of one another along the edges of an equilateral
triangle with vertices A, B, and C.  There are also some collision
rules that need to be taken into account:

(1)  If X is at a vertex, say vertex A, then Y cannot be on A or on
the edges adjacent to it.  i.e., Y can only be on vertices B or C or
the edge BC.
(2)  If X is on an edge, say AB, then Y cannot be on A, nor B, nor any
of the edges adjacent to A and B.  i.e., Y must be on vertex C

I have figured out how to move the two points along the triangle using
a pair of sliders, but I can't figure out how to implement the
collision rules. I tried using the Exclusions option for Slider but
the results are not what I expect.  I would prefer to drag the points
along the triangle rather than using sliders, so if someone knows how
to do that instead it would be helpful. Ideally, I would be able to
move the two points from a vertex to either one of the edges instead
of coming to a stop at one of them. Here is my code so far.

MyTriangle[t_] :=
 Piecewise[{{{-1, 0} + (t/100) {1, Sqrt[3]},
    100 > t >= 0}, {{0, Sqrt[3]} + (t/100 - 1) {1, -Sqrt[3]},
    200 > t >= 100},
   {{1, 0} + (t/100 - 2) {-2, 0}, 300 >= t >= 0}}]
excluded[x_] := \[Piecewise] {
   {Range[0, 99]~Join~Range[201, 299], x == 0},
   {Range[0, 199], x == 100},
   {Range[101, 299], x == 200},
   {Range[0, 199]~Join~Range[201, 299], 0 < x < 100},
   {Range[1, 299], 100 < x < 200},
   {Range[0, 99]~Join~Range[101, 299], 200 < x < 300}
  }
{Dynamic[t], Dynamic[x]}
{Slider[Dynamic[t], {0, 299, 1}, Exclusions -> Dynamic[excluded[x]]],
 Dynamic[t]}
{Slider[Dynamic[x], {0, 299, 1}, Exclusions -> Dynamic[excluded[t]]],
 Dynamic[x]}
Dynamic[Graphics[{PointSize[Large], Point[MyTriangle[t]],
   Point[MyTriangle[x]],
   Line[{{-1, 0}, {1, 0}, {0, Sqrt[3]}, {-1, 0}}]},
  PlotRange -> {{-1.2, 4.2}, {-.2, 2}}]]


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