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A gap appears at the locations of Exclusions at t=1,t=1+t0 when the top slider for t0 is set to Play. How can these gaps be avoided or filled in?

 Manipulate[ y[t_, t0_] := 1/(1 - (t - t0)); y0[x_] := y[x, 0]; yT[x_] := y[x, t0]; Plot[{y0[t], yT[t]}, {t, -3, 7}, Exclusions -> {t == 1, t == 1 + t0}, PlotStyle -> {{Thick, Black}}, PlotRange -> {0, 3}, Frame -> True, Axes -> False, ImageSize -> 1.2 {500, 330}, BaseStyle -> {FontSize -> 16}, FrameLabel -> {t, x}, RotateLabel -> False, PlotRangePadding -> {{2, 0}, {.1, .1}}, Epilog -> {PointSize[0.015], Red, Dashed, Line[{{-4, y0[s]}, {s, y0[s]}}], Point[{{-4, y0[s]}, {s, y0[s]}, {s + t0, yT[s + t0]}}], Black, Dashing[{}], Line[{{-4, 0}, {-4, 3}}], Red, Point[{-4, y1[s]}], Black, Arrowheads[.03], Arrow[{{-4, 3}, {-4, 3.1}}], Red, Dashing[{}], Line[{{s, y0[s]}, {s + t0, yT[s + t0]}}]}], {{t0, 2}, -2, 5, 0.01}, {{s, 0}, -2, 0.67, 0.01} ]
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    $\begingroup$ You're plotting two different functions and each has a reasonable choice of Exclusions independent of the other. Why don't you use to Plot command and combine the results with Show? You might also try the TrackedSymbols -> {t0,s} in your Manipulate command. Finally, with 9 questions now asked, I think it would be reasonable for you to properly format your code - it's just a matter of indenting your code block four spaces. $\endgroup$ Commented Aug 10, 2014 at 12:59
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    $\begingroup$ Your epilog contains Point[{-4, y1[s]}], but y1 is not defined. $\endgroup$ Commented Aug 10, 2014 at 13:53
  • $\begingroup$ I used Mark's suggestion and made the changes suggested by m_goldberg. All worked well. BTW, the "y1" was a typo; it should have been "y0" $\endgroup$ Commented Aug 11, 2014 at 19:51

2 Answers 2

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I followed Mark McClure's suggestion concerning making two plots and combining them with Show, and it indeed fixes your gap problem.

Manipulate[ Show[ Plot[y0[t], {t, -3, 6.5}, PlotRange -> {0, 3}, PlotStyle -> {{Thick, Black}}, Exclusions -> {t == 1}], Plot[yT[t], {t, -3, 6.5}, PlotRange -> {0, 3}, PlotStyle -> {{Thick, Black}}, Exclusions -> {t == 1 + t0}], Frame -> True, Axes -> False, ImageSize -> 1.2 {500, 330}, BaseStyle -> {FontSize -> 16}, FrameLabel -> {"t", "x"}, RotateLabel -> False, PlotRangePadding -> {{2, 0}, {.1, .1}}, Epilog -> { {Arrowheads[.03], Arrow[{{-4, 0}, {-4, 3}}]}, {Red, PointSize[0.015], Point[{{-4, y0[s]}, {s, y0[s]}, {s + t0, yT[s + t0]}, {-4, y1[s]}}]}, {Red, Line[{{s, y0[s]}, {s + t0, yT[s + t0]}}], Dashed, Line[{{-4, y0[s]}, {s, y0[s]}}]} }], {{t0, 2.}, -2., 5., 0.01, ImageSize -> Large}, {{s, 0.}, -2., 0.67, 0.01, ImageSize -> Large}, Initialization :> ( y[t_, t0_] := 1/(1 - (t - t0)); y0[x_] := y[x, 0]; y1[x_] := y[x, 1]; yT[x_] := y[x, t0] )]

maninpulate

While I was at it, I rewrote your epilog to make it more logical and concise, and I introduced an initialization option so that your local functions are only defined once (in your code they are redefined every time the content pane is refreshed). I also made a guess about y1.

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  • $\begingroup$ I feel strangely compelled to upvote this! $\endgroup$ Commented Aug 11, 2014 at 0:45
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Combinining consecutive Lines into a single Line and moving the function definitions to Initialization (as suggested by @m_goldberg)

Manipulate[MapAt[# /. {x__, lines : Line[_] ..} :> {x,Line[Join @@ ({lines}[[All, 1]])]} &, Plot[{y0[t], yT[t]}, {t, -3, 7}, Exclusions -> {t == 1, t == 0.5, t == 0.5 + t0, t == 1 + t0}, (* with few more exclusions *) PlotStyle -> {{Thick, Black}}, PlotRange -> {0, 3}, Frame -> True, Axes -> False, ImageSize -> 1.2 {500, 330}, BaseStyle -> {FontSize -> 16}, FrameLabel -> {t, x}, RotateLabel -> False, PlotRangePadding -> {{2, 0}, {.1, .1}}, Epilog -> {PointSize[0.015], Red, Dashed, Line[{{-4, y0[s]}, {s, y0[s]}}], Point[{{-4, y0[s]}, {s, y0[s]}, {s + t0, yT[s + t0]}}], Black, Dashing[{}], Line[{{-4, 0}, {-4, 3}}], Red, Point[{-4, yT[s]}], Black, Arrowheads[.03], Arrow[{{-4, 3}, {-4, 3.1}}], Red, Dashing[{}], Line[{{s, y0[s]}, {s + t0, yT[s + t0]}}]}], {1}] , {{t0, 2}, -2, 5, 0.01}, {{s, 0}, -2, 0.67, 0.01}, Initialization :> (y[t_, t0_] := 1/(1 - (t - t0)); y0[x_] := y[x, 0]; yT[x_] := y[x, t0])]

Before (with Plot[...] instead of MapAt[..., Plot[...], ...]):

enter image description here

After:

enter image description here

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  • $\begingroup$ I do not understand the use of MapAt ... and the code that follows on the first line of your suggestion. $\endgroup$ Commented Aug 11, 2014 at 19:56

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