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AxiomGraphics
last edited 4 months ago by Bill Page

Edit detail for AxiomGraphics revision 2 of 2
1 2
Editor: Bill Page
Time: 2008/06/26 19:21:25 GMT-7
Note: gnuDraw 
removed:
-The 'draw' command works only under an X-Windows environment (unix/linux).
-Work is underway to create a new user interface (AxiomUI) that among other
-things will allow graphics to be viewed under other operating systems.  If
-you're interested in graphics, please pitch in!
-

changed:
-The graphics commands are described in Chapter 7 of the AxiomBook.
  The graphics commands are described in Chapter 7 of the AxiomBook.

added:
<em>
The 'draw' command works only under an X-Windows environment
(unix/linux). Work is underway to create a new user interface
(AxiomUI) that among other things will allow graphics to be
viewed under other operating systems.  If you're interested in
graphics, please pitch in!
</em>


changed:
-environment on the Web server) we are not yet able to display the
-graph here . But we can still extract the graph data from the view
-port. Then for example we can display the list of data points that
-would be plotted in the graph.
environment on the Web server) we are not yet able to display
the graph here. However we description below a similar command
named 'gnuDraw' that can be used to generate similar graphics on
this web site.

gnuDraw

  It is possible to produce graphics similar to Axioms using
gnuplot on this web site. To do this you need to include the
GnuDraw (GDRAW) library

\begin{axiom}
)lib GDRAW
\end{axiom}

The following examples are taken from Chapter 7 Graphics of
the AxiomBook.

Section: 7.1 Two-Dimensional Graphics

The general format for drawing a function defined by a formula
f(x) is::

  gnudraw(f(x), x = a..b, "filename.dat", options)

where a..b defines the range of x, 'options' are additional
draw options and "filename.dat" will contain the gnuplot
script necessary to create the graph.

\begin{axiom}
gnuDraw(sin(x), x=%pi/10..%pi,"AxiomGraphics1.dat")
\end{axiom}

This file may be displayed on the web page using::

  !/begin{gnuplot}
  load "filename.dat"
  /end{gnuplot}

\begin{gnuplot}
load "AxiomGraphics1.dat"
\end{gnuplot}

Technical Details

  We can extract the graph data from the view port. For example
we can display the list of data points that would be plotted in
the graph.

removed:
-
-
-Obsolete Instructions
-
-  You need the latest version of Axiom from the Savannah CVS::
- 
-    cd /tmp                     <-- or someplace where you want axiom
-    export CVS_RSH=ssh
-    cvs -z3 -d:ext:anoncvs@savannah.gnu.org/cvsroot/axiom co axiom
-    cd axiom
-    export AXIOM=/tmp/axiom/mnt/linux
-    export PATH=$AXIOM/bin:$PATH
-    make
-    .... (get coffee)
-    sman  (lots of warnings but the axiom interpreter should start)
-    draw(sin(x), x=-10..10)
-    draw(sin(x*y), x=-10..10, y=-10..10)
- 
-The sman process will eventually be merged into the axiom command
-as soon as I finish up the graphics integration. The sman (superman)
-process is used to communicate between the axiom interpreter and the
-graphics process. If you just start axiom directly with the axiom
-command rather than the sman command the draw function won't 
-do anything.
-
-  -- or --
-
-You need the latest version of Axiom from the arch website::
- 
-  cd /tmp                     <-- or someplace where you want axiom
-  tla get axiom--main--1 axiom
-  cd axiom
-  export AXIOM=/tmp/axiom/mnt/linux
-  export PATH=$AXIOM/bin:$PATH
-  make
-  .... (get coffee)
-  sman  (lots of warnings but the axiom interpreter should start)
-  draw(sin(x), x=-10..10)
-  draw(sin(x*y), x=-10..10, y=-10..10)
- 
-The sman process will eventually be merged into the axiom command
-as soon as I finish up the graphics integration. The sman (superman)
-process is used to communicate between the axiom interpreter and the
-graphics process. If you just start axiom directly with the axiom
-command rather than the sman command the draw function won't 
-do anything.
-

Graphics in Axiom

The graphics commands are described in Chapter 7 of the AxiomBook. The syntax is: 

    draw(f(x), x=a..b, options)
    draw(f(x,y), x=a..b, y=c..d, options)

axiom
vp1:=draw(sin(x), x=%pi/10..%pi)
axiom
Compiling function %B with type DoubleFloat -> DoubleFloat 
   Graph data being transmitted to the viewport manager...
   FriCAS2D data being transmitted to the viewport manager...
LatexWiki Image(1)
Type: TwoDimensionalViewport?

This command creates a "view port" and would normally (on linux for example) also display the graph.

The draw command works only under an X-Windows environment (unix/linux). Work is underway to create a new user interface (AxiomUI) that among other things will allow graphics to be viewed under other operating systems. If you're interested in graphics, please pitch in!

Although due to technical limitations of this system (no Xwindows environment on the Web server) we are not yet able to display the graph here. However we description below a similar command named gnuDraw that can be used to generate similar graphics on this web site.

gnuDraw

It is possible to produce graphics similar to Axioms using gnuplot on this web site. To do this you need to include the GnuDraw (GDRAW) library

axiom
)lib GDRAW

   GnuDraw is now explicitly exposed in frame initial
   GnuDraw will be automatically loaded when needed from
      /var/zope2/var/LatexWiki/GDRAW.NRLIB/code

The following examples are taken from Chapter 7 Graphics of the AxiomBook.

Section: 7.1 Two-Dimensional Graphics

The general format for drawing a function defined by a formula f(x) is: 

  gnudraw(f(x), x = a..b, "filename.dat", options)

where a..b defines the range of x, options are additional draw options and "filename.dat" will contain the gnuplot script necessary to create the graph.

axiom
gnuDraw(sin(x), x=%pi/10..%pi,"AxiomGraphics1.dat")
axiom
Compiling function %F with type DoubleFloat -> DoubleFloat 
   Graph data being transmitted to the viewport manager...
   FriCAS2D data being transmitted to the viewport manager...
Type: Void

This file may be displayed on the web page using: 

  !/begin{gnuplot}
  load "filename.dat"
  /end{gnuplot}

LatexWiki Image

Technical Details

We can extract the graph data from the view port. For example we can display the list of data points that would be plotted in the graph.

(Note: we disable LaTeX output typesetting in order to save space.)

axiom
)set output tex off
axiom
)set output algebra on

g1:=getGraph(vp1,1)

   (3)  Graph with 1 point list
Type: GraphImage?
axiom
pointLists(g1)

   (4)
   [
     [[0.31415926535897931,0.3090169943749474,1.0,3.0],
      [0.37306412761378793,0.36447049987914965,1.0,3.0],
      [0.43196898986859655,0.41865973753742808,1.0,3.0],
      [0.49087385212340517,0.47139673682599764,1.0,3.0],
      [0.5497787143782138,0.5224985647159488,1.0,3.0],
      [0.60868357663302242,0.57178796022761225,1.0,3.0],
      [0.66758843888783104,0.61909394930983397,1.0,3.0],
      [0.72649330114263966,0.66425243791128175,1.0,3.0],
      [0.78539816339744828,0.70710678118654746,1.0,3.0],
      [0.8443030256522569,0.74750832686259672,1.0,3.0],
      [0.90320788790706552,0.78531693088074495,1.0,3.0],
      [0.96211275016187414,0.82040144352551359,1.0,3.0],
      [1.0210176124166828,0.85264016435409218,1.0,3.0],
      [1.0799224746714913,0.88192126434835494,1.0,3.0],
      [1.1388273369262998,0.90814317382508114,1.0,3.0],
      [1.1977321991811083,0.93121493475880346,1.0,3.0],
      [1.2566370614359168,0.95105651629515342,1.0,3.0],
      [1.3155419236907253,0.96759909236025965,1.0,3.0],
      [1.3744467859455338,0.98078528040323032,1.0,3.0],
      [1.4333516482003423,0.99056934044357714,1.0,3.0],
      [1.4922565104551508,0.99691733373312785,1.0,3.0],
      [1.5511613727099594,0.99980724048206482,1.0,3.0],
      [1.6100662349647679,0.99922903624072301,1.0,3.0],
      [1.6689710972195764,0.99518472667219704,1.0,3.0],
      [1.7278759594743849,0.98768834059513799,1.0,3.0],
      [1.7867808217291934,0.97676588132087272,1.0,3.0],
      [1.8456856839840019,0.96245523645364772,1.0,3.0],
      [1.9045905462388104,0.9448060464668786,1.0,3.0],
      [1.9634954084936189,0.92387953251128752,1.0,3.0],
      [2.0224002707484274,0.89974828405222229,1.0,3.0],
      [2.0813051330032359,0.87249600707279817,1.0,3.0],
      [2.1402099952580445,0.84221723371628776,1.0,3.0],
      [2.199114857512853,0.80901699437494878,1.0,3.0],
      [2.2580197197676615,0.77301045336273855,1.0,3.0],
      [2.31692458202247,0.73432250943568722,1.0,3.0],
      [2.3758294442772785,0.69308736254563774,1.0,3.0],
      [2.434734306532087,0.64944804833018577,1.0,3.0],
      [2.4936391687868955,0.60355594195357376,1.0,3.0],
      [2.552544031041704,0.55557023301960473,1.0,3.0],
      [2.6114488932965125,0.50565737337798722,1.0,3.0],
      [2.670353755551321,0.45399049973954964,1.0,3.0],
      [2.7292586178061295,0.40074883310314402,1.0,3.0],
      [2.7881634800609381,0.34611705707749618,1.0,3.0],
      [2.8470683423157466,0.29028467725446577,1.0,3.0],
      [2.9059732045705551,0.23344536385590897,1.0,3.0],
      [2.9648780668253636,0.17579627993435823,1.0,3.0],
      [3.0237829290801721,0.11753739745784152,1.0,3.0],
      [3.0826877913349806,0.058870803651193036,1.0,3.0],
      [3.1415926535897931,1.2246467991473532E-16,1.0,3.0]]
     ]
Type: List List Point DoubleFloat?
axiom
)set output algebra off
axiom
)set output tex on

Using lower level functions the points in such a graph can also be constructed as follows:

First we need this domain

axiom
)expose GraphImage

   GraphImage is now explicitly exposed in frame initial

axiom
lineSegments := [[point [sin(x*%pi/10)$DoubleFloat, _
                  x*%pi/10], point [sin((x+1)*%pi/10)$DoubleFloat, _
                 (x+1)*%pi/10]] for x in 1..10]
LatexWiki Image(2)
Type: List List Point DoubleFloat?

axiom
lineColors := [light blue() for i in 1..10]
LatexWiki Image(3)
Type: List Palette

axiom
pointColors  := [dark blue() for i in 1..10]
LatexWiki Image(4)
Type: List Palette

axiom
lineSize := [6 for i in 1..10]
LatexWiki Image(5)
Type: List PositiveInteger

axiom
g2:=makeGraphImage(lineSegments, lineColors, pointColors, lineSize)

   Graph data being transmitted to the viewport manager...
LatexWiki Image(6)
Type: GraphImage?
axiom
)set output tex off
axiom
)set output algebra on

pointLists(g2)

   (10)
   [
     [[0.3090169943749474,0.31415926535897931,22.0,5.0],
      [0.58778525229247314,0.62831853071795862,22.0,5.0]]
     ,

     [[0.58778525229247314,0.62831853071795862,22.0,5.0],
      [0.80901699437494745,0.94247779607693793,22.0,5.0]]
     ,

     [[0.80901699437494745,0.94247779607693793,22.0,5.0],
      [0.95105651629515353,1.2566370614359172,22.0,5.0]]
     ,

     [[0.95105651629515353,1.2566370614359172,22.0,5.0],
      [1.0,1.5707963267948966,22.0,5.0]]
     ,

     [[1.0,1.5707963267948966,22.0,5.0],
      [0.95105651629515364,1.8849555921538759,22.0,5.0]]
     ,

     [[0.95105651629515364,1.8849555921538759,22.0,5.0],
      [0.80901699437494745,2.1991148575128552,22.0,5.0]]
     ,

     [[0.80901699437494745,2.1991148575128552,22.0,5.0],
      [0.58778525229247325,2.5132741228718345,22.0,5.0]]
     ,

     [[0.58778525229247325,2.5132741228718345,22.0,5.0],
      [0.30901699437494751,2.8274333882308138,22.0,5.0]]
     ,

     [[0.30901699437494751,2.8274333882308138,22.0,5.0],
      [1.2246467991473532E-16,3.1415926535897931,22.0,5.0]]
     ,

     [[1.2246467991473532E-16,3.1415926535897931,22.0,5.0],
      [- 0.3090169943749469,3.455751918948772,22.0,5.0]]
     ]
Type: List List Point DoubleFloat?
axiom
)set output algebra off
axiom
)set output tex on