Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
1997
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 1997

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Double axes and gridlines in 2D-plots

  • To: mathgroup at smc.vnet.net
  • Subject: [mg7656] Re: [mg7577] Double axes and gridlines in 2D-plots
  • From: "caffa" <caffa at iabg.de>
  • Date: Thu, 26 Jun 1997 01:36:43 -0400 (EDT)
  • Organization: IABG
  • Sender: owner-wri-mathgroup at wolfram.com

Andreas Siemer wrote:

> 1.) I want to plot two quantities in one x-y-plot with two y-axes
>     (left and right). How can I do that?
> 2.) Is there an easy way to invoke a nice arrangement of major and
>     minor grid lines in a 2-D-plot?

Part 1

Let us call z-axis the right y-axis. First of all we define the
transformation y ---> z and viceversa. E.g.:

In[1]:=
       ztoy[z_]:=2/5 z+20
In[2]:=
       ytoz[y_]:=5/2y-50

This gives:

In[3]:=
       Table[{ztoy[z],z},{z,-100,0,50}]//TableForm
Out[3]//TableForm=
        -20   -100
         0     -50
         20     0
In[4]:=
       Table[{y,ytoz[y]},{y,-20,20,20}]//TableForm
Out[4]//TableForm=
        -20   -100
         0     -50
         20     0

We are going to use Plot with the option FrameTicks. We need either a
list with elements in the form {position, label} or a function which
generates such a list. We choose the second possibility. A nice tick
position list can be generated with a library function:

In[5]:=
       Needs["Graphics`Graphics`"]
In[6]:=
       ?LinearScale
       "LinearScale[xmin, xmax] gives a list of \"nice\" values
       between xmin and xmax suitable for use as tick mark positions. 
       LinearScale[xmin, xmax, n] attempts to find n such values."
In[7]:=
       LinearScale[100,200]
Out[7]=
       {{100.,100},{120.,120},{140.,140},{160.,160},{180.,180},{200.,2
       00}}

The position should be transformed in y-coordinates, and we like to
have the label colored:

In[8]:=
       zcolor=RGBColor[1,0,0];
In[9]:=
       tickspec[{position_,label_}]:=
          {ztoy[position],StyleForm[label,FontColor->zcolor]}
In[10]:=
       zmarks[ymin_,ymax_]:=
           Map[tickspec,LinearScale[ytoz[ymin],ytoz[ymax]]]

Example

In[11]:=
       zmarks[-20,20]
Out[11]=
       {{-20.,-100},{-12.,-80},{-4.,-60},{4.,-40},{12.,-20},{20.,0}}

Let us now define to functions to be plotted  respectively according
to the y- and the z-scale:

In[12]:=
       yfunc[x_]:=2x-20
In[13]:=
       zfunc[x_]:=-20-3 x

Here is the result

In[14]:=
       Plot[{yfunc[x],ztoy[zfunc[x]]},{x,0,20},
        Axes->None,Frame->True,
        FrameTicks->{Automatic,Automatic,None,zmarks},
        PlotStyle->{{},zcolor}]
Out[14]:=
        - Graphics -

Part 2

We need a function which generates a list of element in the form
{coordinate, style}:

In[15]:=
       gridfunc[step_,nsub_,style1_,style2_][min_,max_]:=
            Flatten[
               Table[  {t+i step/nsub,If[i==0,{style1},{style2}]},
               {t,min-Mod[min,step],max,step},{i,0,nsub-1}],1]

Example

In[16]:=
       gridfunc[1,4,dum1,dum2][0.,2.]
Out[16]=
       {{0.,{dum1}},{0.25,{dum2}},{0.5,{dum2}},{0.75,{dum2}},
        {1.,{dum1}},{1.25,{dum2}},{1.5,{dum2}},{1.75,{dum2}},
        {2.,{dum1}},{2.25,{dum2}},{2.5,{dum2}},{2.75,{dum2}}}

Here is the result we seek

In[17]:=
       Plot[Sin[x],{x,0,2},
        Frame->True,
        GridLines->
           {gridfunc[0.4,4,Thickness[0.01],Thickness[0.005]],
            gridfunc[0.3,3,Thickness[0.01],Thickness[0.005]]}]
Out[17]=
       - Graphics -


I hope it helps.
















-----------------------------------------------------------
Dr. Vittorio G. Caffa            Tel.:   (089) 6088-2054
IABG, Abt. CC22                  Fax:    (089) 6088-2121
Einsteinstr. 20                  E-Mail:   caffa at iabg.de
D-85521 Ottobrunn


  • Prev by Date: Re Need a new type of Hold
  • Next by Date: ThinkQuest Calculus Application on the web
  • Previous by thread: Double axes and gridlines in 2D-plots
  • Next by thread: Help: Simulink Look-Up Table