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RE: Uneven FrameTicks with ExtendGraphics

• To: mathgroup at smc.vnet.net
• Subject: [mg36586] RE: [mg36560] Uneven FrameTicks with ExtendGraphics
• From: "Wolf, Hartmut" <Hartmut.Wolf at t-systems.com>
• Date: Fri, 13 Sep 2002 01:13:55 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

>-----Original Message-----
>From: Tom Aldenberg [mailto:Tom.Aldenberg at rivm.nl]
To: mathgroup at smc.vnet.net
>Sent: Wednesday, September 11, 2002 7:28 PM
>Subject: [mg36586] [mg36560] Uneven FrameTicks with ExtendGraphics
>
>
>Dear MathGroup,
>
>To plot FrameTicks outward with the same style as the Frame, I use
>ExtendGraphics in the following way.
>
>Needs["ExtendGraphics`Ticks`"];
>
>tf[min_,max_] := TickFunction[min, max, MajorStyle -> 
>{Thickness[0.003]},
>    MajorLength - > {0, 0.01}, MinorStyle -> {Thickness[0.003]},
>MinorLength -> {0, 0.005}]
>
>Plot [-2.4 (x+6) (x-8), {x, -6.2, 9.2}, FrameTicks -> {tf, tf, 
>None, None},
>AspectRatio -> 18/25, Frame -> True, DefaultFont -> 
>{"Helvetica-Bold", 12},
>Axes -> None,
>FrameStyle -> Thickness[0.003], FrameLabel -> {"x", "y", None, None},
>PlotStyle -> Thickness[0.006],
>ImageSize -> 504];
>
>(instead of the same Plot statement with FrameTicks -> {Automatic,
>Automatic, None, None})
>
>This arrangement of major and minor ticks is clearly unacceptable. The
>minor ticks do not divide
> intervals of adjacent labelled major ticks into equal parts.
>
>Are there other solutions? I have noticed that some major statistical
>(plotting) programs don't do minor ticks at all.
>
>Tom Aldenberg
>RIVM
>Bilthoven
>Netherlands
>
>

Several alternatives (if the default ticks of Plot, Show that is, wouldn't
do):

(1) generate the ticks explicitly (to get control over supplied min, max
values for TickFunction):

yticks = tf[-40., 120.]
xticks = tf[-6.2, 9.2]

Plot[-2.4 (x + 6) (x - 8), {x, -6.2, 9.2}, 
  FrameTicks -> {xticks, yticks, None, None}, ...]


(2) try the Option TickNumbers, e.g.

tf[min_, max_] := 
  TickFunction[min, max, MajorStyle -> {Thickness[0.005]}, 
    MajorLength -> {0, 0.01}, MinorStyle -> {Thickness[0.003]}, 
    MinorLength -> {0, 0.005}, TickNumbers -> {5, 25}]

gives an acceptable result, or TickNumbers -> {6, 18};
with TickNumbers -> {8, 8} you'll have no minor ticks.


(3) redefine the tick function's helper

Begin["ExtendGraphics`Ticks`Private`"]

?? TickPosition

"TickPosition[ min, max, num] returns a list of at most num nicely rounded
positions between min and max.  These can be used for tick mark positions."

TickPosition[x0_Real, x1_Real, (num_Integer)?Positive] := 
  Block[{dist, scale, min, max, i, delta, space}, 
   space = {1., 2., 2.5, 5., 10.}; dist = (x1 - x0)/num; 
    scale = 10.^Floor[Log[10, dist]]; dist = dist/scale; 
    If[dist < 1., dist *= 10.; scale /= 10.]; 
    If[dist >= 10., dist /= 10.; scale *= 10.]; 
    delta = First[Select[space, #1 >= dist & ]]*scale; 
    min = Ceiling[x0/delta]*delta; Table[Floor[x/delta + 0.5]*delta, 
     {x, min, x1, delta}]]

End[]

There are some things to play with: space, scale, the definition for delta,
to get at more nicely rounded positions; or rewrite completely.

(4) for best control, define the ticks all by yourself, e.g. 

yticks1 = Table[{t, t, {0, 0.01`}, {Thickness[0.003`]}} , {t, -25, 100, 25}]
yticks2 = 
  DeleteCases[
    Table[{t, "", {0, 0.005`}, {Thickness[0.003`]}} , {t, -25, 100, 
        12.5}], {t_, __} /; Mod[t, 25] == 0]
xticks = Join[xticks1, xticks2]

xticks1 = Table[{t, t, {0, 0.01`}, {Thickness[0.003`]}} , {t, -5, 7.5, 2.5}]
xticks2 = 
  DeleteCases[
    Table[{t, "", {0, 0.005`}, {Thickness[0.003`]}} , {t, -7.5, 8.5, 
        1.25}], {t_, __} /; Mod[t, 2.5] == 0]
yticks = Join[yticks1, yticks2]


--
Hartmut Wolf