Skip to main content

plotting - Is there an easy way to put time ticks on a parametric plot?


I have a parametric plot showing a path of an object in x and y (position), where each is a function of t (time), on which I would like to put a time tick, every second let's say. This would be to indicate where the object is moving fast (widely spaced ticks) or slow (closely spaced ticks). Each tick would just be short line that crosses the plot at that point in time, where that short line is normal to the plotted curve at that location.


I'm sure I can figure out a way to do it using lots of calculations and graphics primitives, but I'm wondering if there is something built-in that I have missed in the documentation that would make this easier.


(Note: this is about ticks on the plotted curve itself -- this doesn't have anything to do with the ticks on the axes or frame.)



Answer



To create the ticks perpendicular to the curve, I calculate the direction of the normal to the curve where the ticks are to be placed and then orient a line segment along that direction. The following code does that.



ClearAll[ParametricTimePlot]
SetAttributes[ParametricTimePlot, HoldAll]
ParametricTimePlot[fun_, {var_, min_, max_, steps_}, len_, 
    opts : OptionsPattern[]] := 
    Show[
        ParametricPlot[fun, {var, min, max}, opts],
        Graphics[
            Rotate[Translate[Line[{{-len/2, 0}, {len/2, 0}}], #1], ArcTan @@ #2]
        ] & @@@ (N@Table[{fun, RotationMatrix[Ï€/2].D[fun, var]} /. var -> i, 
            {i, min + steps, max, steps}])

    ]

Use the above function as:


ParametricTimePlot[{ Sqrt[t] Cos[t], Sqrt[t] Sin[t]}, {t, 0, 2 π, 
    π/10}, 0.1, PlotStyle -> Blue]

enter image description here



If you want to keep it simple and just show the dots, then this is very straightforward:


ClearAll[ParametricTimePlot]

SetAttributes[ParametricTimePlot, HoldAll]
ParametricTimePlot[fun_, {var_, min_, max_, steps_}, opts : OptionsPattern[]] :=     
    ParametricPlot[fun, {var, min, max}, opts] 
    ~Show~
    ListPlot[Table[fun /. var -> i, {i, min, max, steps}], 
        PlotStyle -> Red, PlotMarkers -> {Automatic, 8}]

ParametricTimePlot[{ Sqrt[t] Cos[t], Sqrt[t] Sin[t]}, {t, 0, 2 Pi, Pi/10}, 
    PlotStyle -> Blue]


enter image description here


Comments

Post a Comment

Popular posts from this blog

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...
Post a Comment
Read more

How to thread a list

I have data in format data = {{a1, a2}, {b1, b2}, {c1, c2}, {d1, d2}} Tableform: I want to thread it to : tdata = {{{a1, b1}, {a2, b2}}, {{a1, c1}, {a2, c2}}, {{a1, d1}, {a2, d2}}} Tableform: And I would like to do better then pseudofunction[n_] := Transpose[{data2[[1]], data2[[n]]}]; SetAttributes[pseudofunction, Listable]; Range[2, 4] // pseudofunction Here is my benchmark data, where data3 is normal sample of real data. data3 = Drop[ExcelWorkBook[[Column1 ;; Column4]], None, 1]; data2 = {a #, b #, c #, d #} & /@ Range[1, 10^5]; data = RandomReal[{0, 1}, {10^6, 4}]; Here is my benchmark code kptnw[list_] := Transpose[{Table[First@#, {Length@# - 1}], Rest@#}, {3, 1, 2}] &@list kptnw2[list_] := Transpose[{ConstantArray[First@#, Length@# - 1], Rest@#}, {3, 1, 2}] &@list OleksandrR[list_] := Flatten[Outer[List, List@First[list], Rest[list], 1], {{2}, {1, 4}}] paradox2[list_] := Partition[Riffle[list[[1]], #], 2] & /@ Drop[list, 1] RM[list_] := FoldList[Transpose[{First@li...
Post a Comment
Read more

front end - keyboard shortcut to invoke Insert new matrix

I frequently need to type in some matrices, and the menu command Insert > Table/Matrix > New... allows matrices with lines drawn between columns and rows, which is very helpful. I would like to make a keyboard shortcut for it, but cannot find the relevant frontend token command (4209405) for it. Since the FullForm[] and InputForm[] of matrices with lines drawn between rows and columns is the same as those without lines, it's hard to do this via 3rd party system-wide text expanders (e.g. autohotkey or atext on mac). How does one assign a keyboard shortcut for the menu item Insert > Table/Matrix > New... , preferably using only mathematica? Thanks! Answer In the MenuSetup.tr (for linux located in the $InstallationDirectory/SystemFiles/FrontEnd/TextResources/X/ directory), I changed the line MenuItem["&New...", "CreateGridBoxDialog"] to read MenuItem["&New...", "CreateGridBoxDialog", MenuKey["m", Modifiers-...
Post a Comment
Read more