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FriCASGraphics

Edit detail for FriCASGraphics revision 1 of 1

	1
Editor: test1 Time: 2015/06/01 20:17:37 GMT+0
Note:

changed:
-
Graphics in FriCAS

  The graphics commands are described in Chapter 7 of the FriCASBook.
The syntax is::
    
    draw(f(x), x=a..b, options)
    draw(f(x,y), x=a..b, y=c..d, options)

\begin{axiom}
vp1:=draw(sin(x), x=%pi/10..%pi)
\end{axiom}

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

<em>
The 'draw' command works only under an X-Windows environment
(unix/linux).  There were attemps to create a new user interface
(AxiomUI. fricasserver) that among other things will allow graphics to be
viewed under other operating systems.  But currently they stalled...
If you're interested in graphics, please pitch in!
</em>

Although due to technical limitations of this system (no Xwindows
environment on the Web server) we are not yet able to use 'draw'
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 FriCAS using
gnuplot on this web site. This uses GnuDraw (GDRAW) library
which is included in FriCAS (starting from version 1.2.4).

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

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,"FriCASGraphics1.dat")
\end{axiom}

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

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

See below.

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.)

\begin{axiom}
)set output tex off
)set output algebra on
g1:=getGraph(vp1,1)
pointLists(g1)
)set output algebra off
)set output tex on
\end{axiom}

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

First we need this domain
\begin{axiom}
)expose GraphImage
\end{axiom}

\begin{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]
\end{axiom}
\begin{axiom}
lineColors := [light blue() for i in 1..10]
\end{axiom}
\begin{axiom}
pointColors  := [dark blue() for i in 1..10]
\end{axiom}
\begin{axiom}
lineSize := [6 for i in 1..10]
\end{axiom}
\begin{axiom}
g2:=makeGraphImage(lineSegments, lineColors, pointColors, lineSize)
)set output tex off
)set output algebra on
pointLists(g2)
)set output algebra off
)set output tex on
\end{axiom}

\begin{gnuplot}
load "FriCASGraphics1.dat"
\end{gnuplot}

Graphics in FriCAS

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

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

fricas

vp1:=draw(sin(x), x=%pi/10..%pi)

fricas

Compiling function %B with type DoubleFloat -> DoubleFloat 
   Graph data being transmitted to the viewport manager...
   FriCAS2D data being transmitted to the viewport manager...

$\label{eq1}\mbox{\rm \hbox{\axiomType{TwoDimensionalViewport}\ } :}\verb#"sin(x)"#$

(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). There were attemps to create a new user interface (AxiomUI. fricasserver) that among other things will allow graphics to be viewed under other operating systems. But currently they stalled... 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 use draw 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 FriCAS using gnuplot on this web site. This uses GnuDraw? (GDRAW) library which is included in FriCAS (starting from version 1.2.4).

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

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.

fricas

gnuDraw(sin(x), x=%pi/10..%pi,"FriCASGraphics1.dat")

fricas

Compiling function %E with type DoubleFloat -> DoubleFloat

Type: Void

This file may be displayed on the web page using:

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

See below.

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.)

fricas

)set output tex off

fricas

)set output algebra on

g1:=getGraph(vp1,1)

   (3)  Graph with 1 point list

Type: GraphImage?

fricas

pointLists(g1)

   (4)
   [
     [[0.3141592653589793, 0.3090169943749474, 1.0, 3.0],
      [0.37306412761378793, 0.36447049987914965, 1.0, 3.0],
      [0.43196898986859655, 0.4186597375374281, 1.0, 3.0],
      [0.4908738521234052, 0.47139673682599764, 1.0, 3.0],
      [0.5497787143782138, 0.5224985647159488, 1.0, 3.0],
      [0.6086835766330224, 0.5717879602276122, 1.0, 3.0],
      [0.667588438887831, 0.619093949309834, 1.0, 3.0],
      [0.7264933011426397, 0.6642524379112817, 1.0, 3.0],
      [0.7853981633974483, 0.7071067811865475, 1.0, 3.0],
      [0.8443030256522569, 0.7475083268625967, 1.0, 3.0],
      [0.9032078879070655, 0.785316930880745, 1.0, 3.0],
      [0.9621127501618741, 0.8204014435255136, 1.0, 3.0],
      [1.0210176124166828, 0.8526401643540922, 1.0, 3.0],
      [1.0799224746714913, 0.8819212643483549, 1.0, 3.0],
      [1.1388273369262998, 0.9081431738250811, 1.0, 3.0],
      [1.1977321991811083, 0.9312149347588035, 1.0, 3.0],
      [1.2566370614359168, 0.9510565162951534, 1.0, 3.0],
      [1.3155419236907253, 0.9675990923602596, 1.0, 3.0],
      [1.3744467859455338, 0.9807852804032303, 1.0, 3.0],
      [1.4333516482003423, 0.9905693404435771, 1.0, 3.0],
      [1.4922565104551508, 0.9969173337331279, 1.0, 3.0],
      [1.5511613727099594, 0.9998072404820648, 1.0, 3.0],
      [1.6100662349647679, 0.999229036240723, 1.0, 3.0],
      [1.6689710972195764, 0.995184726672197, 1.0, 3.0],
      [1.7278759594743849, 0.987688340595138, 1.0, 3.0],
      [1.7867808217291934, 0.9767658813208727, 1.0, 3.0],
      [1.845685683984002, 0.9624552364536477, 1.0, 3.0],
      [1.9045905462388104, 0.9448060464668786, 1.0, 3.0],
      [1.963495408493619, 0.9238795325112875, 1.0, 3.0],
      [2.0224002707484274, 0.8997482840522223, 1.0, 3.0],
      [2.081305133003236, 0.8724960070727982, 1.0, 3.0],
      [2.1402099952580445, 0.8422172337162878, 1.0, 3.0],
      [2.199114857512853, 0.8090169943749488, 1.0, 3.0],
      [2.2580197197676615, 0.7730104533627385, 1.0, 3.0],
      [2.31692458202247, 0.7343225094356872, 1.0, 3.0],
      [2.3758294442772785, 0.6930873625456377, 1.0, 3.0],
      [2.434734306532087, 0.6494480483301858, 1.0, 3.0],
      [2.4936391687868955, 0.6035559419535738, 1.0, 3.0],
      [2.552544031041704, 0.5555702330196047, 1.0, 3.0],
      [2.6114488932965125, 0.5056573733779872, 1.0, 3.0],
      [2.670353755551321, 0.45399049973954964, 1.0, 3.0],
      [2.7292586178061295, 0.400748833103144, 1.0, 3.0],
      [2.788163480060938, 0.3461170570774962, 1.0, 3.0],
      [2.8470683423157466, 0.2902846772544658, 1.0, 3.0],
      [2.905973204570555, 0.23344536385590897, 1.0, 3.0],
      [2.9648780668253636, 0.17579627993435823, 1.0, 3.0],
      [3.023782929080172, 0.11753739745784152, 1.0, 3.0],
      [3.0826877913349806, 0.058870803651193036, 1.0, 3.0],
      [3.141592653589793, 1.2246467991473532e-16, 1.0, 3.0]]
     ]

Type: List(List(Point(DoubleFloat?)))

fricas

)set output algebra off

fricas

)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

fricas

)expose GraphImage

   GraphImage is now explicitly exposed in frame initial

fricas

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]

$\label{eq2}\begin{array}{@{}l} \displaystyle \left[{ \begin{array}{@{}l} \displaystyle \left[{\left[{0.3090169943749474}, \:{0.3141592653589793}\right]}, \: \right. \ \ \displaystyle \left.{\left[{0.5877852522924731}, \:{0.6283185307179586}\right]}\right]$

(2)

Type: List(List(Point(DoubleFloat?)))

fricas

lineColors := [light blue() for i in 1..10]

$\label{eq3}\begin{array}{@{}l} \displaystyle \left[{[{\mbox{\rm \hbox{\axiomType{Hue}\ } :}{22}\mbox{\rm \hbox{\axiomType{Weight}\ } :}{1.0}}\mbox{\rm ] from the}\hbox{\axiomType{Light}\ } \mbox{\rm palette}}, \: \right. \ \ \displaystyle \left.{[{\mbox{\rm \hbox{\axiomType{Hue}\ } :}{22}\mbox{\rm \hbox{\axiomType{Weight}\ } :}{1.0}}\mbox{\rm ] from the}\hbox{\axiomType{Light}\ } \mbox{\rm palette}}, \: \right. \ \ \displaystyle \left.{[{\mbox{\rm \hbox{\axiomType{Hue}\ } :}{22}\mbox{\rm \hbox{\axiomType{Weight}\ } :}{1.0}}\mbox{\rm ] from the}\hbox{\axiomType{Light}\ } \mbox{\rm palette}}, \: \right. \ \ \displaystyle \left.{[{\mbox{\rm \hbox{\axiomType{Hue}\ } :}{22}\mbox{\rm \hbox{\axiomType{Weight}\ } :}{1.0}}\mbox{\rm ] from the}\hbox{\axiomType{Light}\ } \mbox{\rm palette}}, \: \right. \ \ \displaystyle \left.{[{\mbox{\rm \hbox{\axiomType{Hue}\ } :}{22}\mbox{\rm \hbox{\axiomType{Weight}\ } :}{1.0}}\mbox{\rm ] from the}\hbox{\axiomType{Light}\ } \mbox{\rm palette}}, \: \right. \ \ \displaystyle \left.{[{\mbox{\rm \hbox{\axiomType{Hue}\ } :}{22}\mbox{\rm \hbox{\axiomType{Weight}\ } :}{1.0}}\mbox{\rm ] from the}\hbox{\axiomType{Light}\ } \mbox{\rm palette}}, \: \right. \ \ \displaystyle \left.{[{\mbox{\rm \hbox{\axiomType{Hue}\ } :}{22}\mbox{\rm \hbox{\axiomType{Weight}\ } :}{1.0}}\mbox{\rm ] from the}\hbox{\axiomType{Light}\ } \mbox{\rm palette}}, \: \right. \ \ \displaystyle \left.{[{\mbox{\rm \hbox{\axiomType{Hue}\ } :}{22}\mbox{\rm \hbox{\axiomType{Weight}\ } :}{1.0}}\mbox{\rm ] from the}\hbox{\axiomType{Light}\ } \mbox{\rm palette}}, \: \right. \ \ \displaystyle \left.{[{\mbox{\rm \hbox{\axiomType{Hue}\ } :}{22}\mbox{\rm \hbox{\axiomType{Weight}\ } :}{1.0}}\mbox{\rm ] from the}\hbox{\axiomType{Light}\ } \mbox{\rm palette}}, \: \right. \ \ \displaystyle \left.{[{\mbox{\rm \hbox{\axiomType{Hue}\ } :}{22}\mbox{\rm \hbox{\axiomType{Weight}\ } :}{1.0}}\mbox{\rm ] from the}\hbox{\axiomType{Light}\ } \mbox{\rm palette}}\right]$

(3)

Type: List(Palette)

fricas

pointColors  := [dark blue() for i in 1..10]

$\label{eq4}\begin{array}{@{}l} \displaystyle \left[{[{\mbox{\rm \hbox{\axiomType{Hue}\ } :}{22}\mbox{\rm \hbox{\axiomType{Weight}\ } :}{1.0}}\mbox{\rm ] from the}\hbox{\axiomType{Dark}\ } \mbox{\rm palette}}, \: \right. \ \ \displaystyle \left.{[{\mbox{\rm \hbox{\axiomType{Hue}\ } :}{22}\mbox{\rm \hbox{\axiomType{Weight}\ } :}{1.0}}\mbox{\rm ] from the}\hbox{\axiomType{Dark}\ } \mbox{\rm palette}}, \: \right. \ \ \displaystyle \left.{[{\mbox{\rm \hbox{\axiomType{Hue}\ } :}{22}\mbox{\rm \hbox{\axiomType{Weight}\ } :}{1.0}}\mbox{\rm ] from the}\hbox{\axiomType{Dark}\ } \mbox{\rm palette}}, \: \right. \ \ \displaystyle \left.{[{\mbox{\rm \hbox{\axiomType{Hue}\ } :}{22}\mbox{\rm \hbox{\axiomType{Weight}\ } :}{1.0}}\mbox{\rm ] from the}\hbox{\axiomType{Dark}\ } \mbox{\rm palette}}, \: \right. \ \ \displaystyle \left.{[{\mbox{\rm \hbox{\axiomType{Hue}\ } :}{22}\mbox{\rm \hbox{\axiomType{Weight}\ } :}{1.0}}\mbox{\rm ] from the}\hbox{\axiomType{Dark}\ } \mbox{\rm palette}}, \: \right. \ \ \displaystyle \left.{[{\mbox{\rm \hbox{\axiomType{Hue}\ } :}{22}\mbox{\rm \hbox{\axiomType{Weight}\ } :}{1.0}}\mbox{\rm ] from the}\hbox{\axiomType{Dark}\ } \mbox{\rm palette}}, \: \right. \ \ \displaystyle \left.{[{\mbox{\rm \hbox{\axiomType{Hue}\ } :}{22}\mbox{\rm \hbox{\axiomType{Weight}\ } :}{1.0}}\mbox{\rm ] from the}\hbox{\axiomType{Dark}\ } \mbox{\rm palette}}, \: \right. \ \ \displaystyle \left.{[{\mbox{\rm \hbox{\axiomType{Hue}\ } :}{22}\mbox{\rm \hbox{\axiomType{Weight}\ } :}{1.0}}\mbox{\rm ] from the}\hbox{\axiomType{Dark}\ } \mbox{\rm palette}}, \: \right. \ \ \displaystyle \left.{[{\mbox{\rm \hbox{\axiomType{Hue}\ } :}{22}\mbox{\rm \hbox{\axiomType{Weight}\ } :}{1.0}}\mbox{\rm ] from the}\hbox{\axiomType{Dark}\ } \mbox{\rm palette}}, \: \right. \ \ \displaystyle \left.{[{\mbox{\rm \hbox{\axiomType{Hue}\ } :}{22}\mbox{\rm \hbox{\axiomType{Weight}\ } :}{1.0}}\mbox{\rm ] from the}\hbox{\axiomType{Dark}\ } \mbox{\rm palette}}\right]$

(4)

Type: List(Palette)

fricas

lineSize := [6 for i in 1..10]

$\label{eq5}\left[ 6, \: 6, \: 6, \: 6, \: 6, \: 6, \: 6, \: 6, \: 6, \: 6 \right]$

(5)

Type: List(PositiveInteger?)

fricas

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

$\label{eq6}\mbox{\rm \hbox{\axiomType{Graph}\ } with}{10}\mbox{\rm point lists}$

(6)

Type: GraphImage?

fricas

)set output tex off

fricas

)set output algebra on

pointLists(g2)

   (10)
   [
     [[0.3090169943749474, 0.3141592653589793],
      [0.5877852522924731, 0.6283185307179586]]
     ,

     [[0.5877852522924731, 0.6283185307179586],
      [0.8090169943749475, 0.9424777960769379]]
     ,

     [[0.8090169943749475, 0.9424777960769379],
      [0.9510565162951535, 1.2566370614359172]]
     ,
    [[0.9510565162951535, 1.2566370614359172], [1.0, 1.5707963267948966]],
    [[1.0, 1.5707963267948966], [0.9510565162951536, 1.8849555921538759]],

     [[0.9510565162951536, 1.8849555921538759],
      [0.8090169943749475, 2.199114857512855]]
     ,

     [[0.8090169943749475, 2.199114857512855],
      [0.5877852522924732, 2.5132741228718345]]
     ,

     [[0.5877852522924732, 2.5132741228718345],
      [0.3090169943749475, 2.827433388230814]]
     ,

     [[0.3090169943749475, 2.827433388230814],
      [1.2246467991473532e-16, 3.141592653589793]]
     ,

     [[1.2246467991473532e-16, 3.141592653589793],
      [- 0.3090169943749469, 3.455751918948772]]
     ]

Type: List(List(Point(DoubleFloat?)))

fricas

)set output algebra off

fricas

)set output tex on

load "FriCASGraphics1.dat"