Re: Visualizing a geometric problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg113221] Re: Visualizing a geometric problem*From*: Maxim <m.r at inbox.ru>*Date*: Tue, 19 Oct 2010 05:56:08 -0400 (EDT)*References*: <i9ehon$6rh$1@smc.vnet.net>

On Oct 17, 5:05 am, Velina Veleva <vvvel... at gmail.com> wrote: > 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}}]] Here's how you can implement the collision rules using a custom tracking function for the control variables: DynamicModule[ {verts = {{-1., 0.}, {1., 0.}, {0., Sqrt[3.]}}, sides = {{2., 0.}, {-1., Sqrt[3.]}, {-1., -Sqrt[3.]}}, xy = {{0., 0.}, {0., Sqrt[3.]}}, lambdas, dists, sidei, verti, i, j}, LocatorPane[Dynamic[xy, Function[newxy, If[newxy == xy, Return[]]; {i, j} = If[newxy[[1]] == xy[[1]], {2, 1}, {1, 2}]; lambdas = MapThread[(newxy[[i]] - #).#2/#2.#2 &, {verts, sides}]; lambdas = Clip[lambdas, {.025, .975}, {0., 1.}]; dists = MapThread[ Norm[newxy[[i]] - #3*#2 - #] &, {verts, sides, lambdas}]; sidei = First@Ordering@dists; If[! lambdas[[sidei]] != 0. != 1., verti = Mod[sidei + Boole[lambdas[[sidei]] == 1.], 3, 1]; xy[[i]] = verts[[verti]]; If[xy[[j]] != Sequence @@ verts[[Delete[{1, 2, 3}, verti]]], xy[[j]] = Mean@verts[[Delete[{1, 2, 3}, verti]]]], xy[[i]] = lambdas[[#]]*sides[[#]] + verts[[#]] &@sidei; xy[[j]] = verts[[Mod[sidei + 2, 3, 1]]]; ]]], Graphics[Line@verts[[{1, 2, 3, 1}]]], LocatorAutoCreate -> False]] Maxim Rytin m.r at inbox.ru