Maxima, a Computer Algebra System Maxima, a Computer Algebra System
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| 48.1 Introduction to draw | ||
| 48.2 Functions and Variables for draw | ||
| 48.3 Functions and Variables for pictures | ||
| 48.4 Functions and Variables for worldmap |
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draw is a Maxima-Gnuplot interface.
There are three main functions to be used at Maxima level: draw2d, draw3d and draw.
Follow this link for more elaborated examples of this package:
http://www.telefonica.net/web2/biomates/maxima/gpdraw
You need Gnuplot 4.2 to run this program.
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Default value: auto
If xrange is auto, the range for the x coordinate is computed automatically.
If the user wants a specific interval for x, it must be given as a Maxima list, as in xrange=[-2, 3].
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) draw2d(xrange = [-3,5],
explicit(x^2,x,-1,1))$
See also yrange and zrange.
Default value: auto
If yrange is auto, the range for the y coordinate is computed automatically.
If the user wants a specific interval for y, it must be given as a Maxima list, as in yrange=[-2, 3].
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) draw2d(yrange = [-2,3],
explicit(x^2,x,-1,1),
xrange = [-3,3])$
See also xrange and zrange.
Default value: auto
If zrange is auto, the range for the z coordinate is computed automatically.
If the user wants a specific interval for z, it must be given as a Maxima list, as in zrange=[-2, 3].
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) draw3d(yrange = [-3,3],
zrange = [-2,5],
explicit(x^2+y^2,x,-1,1,y,-1,1),
xrange = [-3,3])$
See also xrange and yrange.
Default value: false
If logx is true, the x axis will be drawn in the logarithmic scale.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) draw2d(explicit(log(x),x,0.01,5),
logx = true)$
See also logy and logz.
Default value: false
If logy is true, the y axis will be drawn in the logarithmic scale.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) draw2d(logy = true,
explicit(exp(x),x,0,5))$
See also logx and logz.
Default value: false
If logz is true, the z axis will be drawn in the logarithmic scale.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) draw3d(logz = true,
explicit(exp(u^2+v^2),u,-2,2,v,-2,2))$
See also logx and logy.
Default value: screen
Selects the terminal to be used by Gnuplot; possible values are: screen (default), png, jpg, eps, eps_color, gif, animated_gif, wxt and aquaterm.
Since this is a global graphics option, its position in the scene description does not matter. It can be also used as an argument of function draw.
Examples:
(%i1) load(draw)$
(%i2) /* screen terminal (default) */
draw2d(explicit(x^2,x,-1,1))$
(%i3) /* png file */
draw2d(terminal = 'png,
pic_width = 300,
explicit(x^2,x,-1,1))$
(%i4) /* jpg file */
draw2d(terminal = 'jpg,
pic_width = 300,
pic_height = 300,
explicit(x^2,x,-1,1))$
(%i5) /* eps file */
draw2d(file_name = "myfile",
explicit(x^2,x,-1,1),
terminal = 'eps)$
(%i6) /* wxwidgets window */
draw2d(explicit(x^2,x,-1,1),
terminal = 'wxt)$
An animated gif file,
(%i1) load(draw)$
(%i2) draw(
delay = 100,
file_name = "zzz",
terminal = 'animated_gif,
gr2d(explicit(x^2,x,-1,1)),
gr2d(explicit(x^3,x,-1,1)),
gr2d(explicit(x^4,x,-1,1)));
End of animation sequence
(%o2) [gr2d(explicit), gr2d(explicit), gr2d(explicit)]
Option delay is only active in animated gif's; it is ignored in any other case.
See also file_name, pic_width, pic_height and delay.
Default value: "" (empty string)
This option can be used to set the font face to be used by the terminal. Only one font face and size can be used throughout the plot.
Since this is a global graphics option, its position in the scene description does not matter.
See also font_size.
Gnuplot doesn't handle fonts by itself, it leaves this task to the support libraries of the different terminals, each one with its own philosophy about it. A brief summary follows:
Example:
(%i1) load(draw)$
(%i2) draw2d(font = "Arial",
font_size = 20,
label(["Arial font, size 20",1,1]))$
GDFONTPATH; in this case, it is only necessary to set option font to the font's name. It is also possible to give the complete path to the font file.
Examples:
Option font can be given the complete path to the font file:
(%i1) load(draw)$
(%i2) path: "/usr/share/fonts/truetype/freefont/" $
(%i3) file: "FreeSerifBoldItalic.ttf" $
(%i4) draw2d(
font = concat(path, file),
font_size = 20,
color = red,
label(["FreeSerifBoldItalic font, size 20",1,1]),
terminal = png)$
If environment variable GDFONTPATH is set to the path where font files are allocated, it is possible to set graphic option font to the name of the font.
(%i1) load(draw)$
(%i2) draw2d(
font = "FreeSerifBoldItalic",
font_size = 20,
color = red,
label(["FreeSerifBoldItalic font, size 20",1,1]),
terminal = png)$
"Times-Roman", "Times-Italic", "Times-Bold", "Times-BoldItalic", "Helvetica", "Helvetica-Oblique", "Helvetica-Bold", "Helvetic-BoldOblique", "Courier", "Courier-Oblique", "Courier-Bold", and "Courier-BoldOblique".
Example:
(%i1) load(draw)$
(%i2) draw2d(
font = "Courier-Oblique",
font_size = 15,
label(["Courier-Oblique font, size 15",1,1]),
terminal = eps)$
fontconfig utility."Times-Roman".The gnuplot documentation is an important source of information about terminals and fonts.
Default value: 12
This option can be used to set the font size to be used by the terminal. Only one font face and size can be used throughout the plot. font_size is active only when option font is not equal to the empty string.
Since this is a global graphics option, its position in the scene description does not matter.
See also font.
Default value: false
If grid is true, a grid will be drawn on the xy plane.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) draw2d(grid = true,
explicit(exp(u),u,-2,2))$
Default value: "" (empty string)
Option title, a string, is the main title for the scene. By default, no title is written.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) draw2d(explicit(exp(u),u,-2,2),
title = "Exponential function")$
Default value: "" (empty string)
Option xlabel, a string, is the label for the x axis. By default, no label is written.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) draw2d(xlabel = "Time",
explicit(exp(u),u,-2,2),
ylabel = "Population")$
See also ylabel, and zlabel.
Default value: "" (empty string)
Option ylabel, a string, is the label for the y axis. By default, no label is written.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) draw2d(xlabel = "Time",
ylabel = "Population",
explicit(exp(u),u,-2,2) )$
See also xlabel, and zlabel.
Default value: "" (empty string)
Option zlabel, a string, is the label for the z axis. By default, no label is written.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) draw3d(zlabel = "Z variable",
ylabel = "Y variable",
explicit(sin(x^2+y^2),x,-2,2,y,-2,2),
xlabel = "X variable" )$
See also xlabel, and ylabel.
Default value: auto
This graphic option controls the way tic marks are drawn on the x axis.
xtics is bounded to symbol auto, tic marks are drawn automatically.xtics is bounded to symbol none, tic marks are not drawn.xtics is bounded to a positive number, this is the distance between two consecutive tic marks.xtics is bounded to a list of length three of the form [start,incr,end], tic marks are plotted from start to end at intervals of length incr.xtics is bounded to a set of numbers of the form {n1, n2, ...}, tic marks are plotted at values n1, n2, ...xtics is bounded to a set of pairs of the form {["label1", n1], ["label2", n2], ...}, tic marks corresponding to values n1, n2, ... are labeled with "label1", "label2", ..., respectively.Since this is a global graphics option, its position in the scene description does not matter.
Examples:
Disable tics.
(%i1) load(draw)$
(%i2) draw2d(xtics = 'none,
explicit(x^3,x,-1,1) )$
Tics every 1/4 units.
(%i1) load(draw)$
(%i2) draw2d(xtics = 1/4,
explicit(x^3,x,-1,1) )$
Tics from -3/4 to 3/4 in steps of 1/8.
(%i1) load(draw)$
(%i2) draw2d(xtics = [-3/4,1/8,3/4],
explicit(x^3,x,-1,1) )$
Tics at points -1/2, -1/4 and 3/4.
(%i1) load(draw)$
(%i2) draw2d(xtics = {-1/2,-1/4,3/4},
explicit(x^3,x,-1,1) )$
Labeled tics.
(%i1) load(draw)$
(%i2) draw2d(xtics = {["High",0.75],["Medium",0],["Low",-0.75]},
explicit(x^3,x,-1,1) )$
See also ytics, and ztics.
Default value: auto
This graphic option controls the way tic marks are drawn on the y axis.
See xtics for a complete description.
Default value: auto
This graphic option controls the way tic marks are drawn on the z axis.
See xtics for a complete description.
Default value: false
If xtics_rotate is true, tic marks on the x axis are rotated 90 degrees.
Since this is a global graphics option, its position in the scene description does not matter.
Default value: false
If ytics_rotate is true, tic marks on the y axis are rotated 90 degrees.
Since this is a global graphics option, its position in the scene description does not matter.
Default value: false
If ztics_rotate is true, tic marks on the z axis are rotated 90 degrees.
Since this is a global graphics option, its position in the scene description does not matter.
Default value: false
If xtics_axis is true, tic marks and their labels are plotted just along the x axis, if it is false tics are plotted on the border.
Since this is a global graphics option, its position in the scene description does not matter.
Default value: false
If ytics_axis is true, tic marks and their labels are plotted just along the y axis, if it is false tics are plotted on the border.
Since this is a global graphics option, its position in the scene description does not matter.
Default value: false
If ztics_axis is true, tic marks and their labels are plotted just along the z axis, if it is false tics are plotted on the border.
Since this is a global graphics option, its position in the scene description does not matter.
Default value: false
If xaxis is true, the x axis is drawn.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) draw2d(explicit(x^3,x,-1,1),
xaxis = true,
xaxis_color = blue)$
See also xaxis_width, xaxis_type and xaxis_color.
Default value: 1
xaxis_width is the width of the x axis. Its value must be a positive number.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) draw2d(explicit(x^3,x,-1,1),
xaxis = true,
xaxis_width = 3)$
See also xaxis, xaxis_type and xaxis_color.
Default value: dots
xaxis_type indicates how the x axis is displayed; possible values are solid and dots.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) draw2d(explicit(x^3,x,-1,1),
xaxis = true,
xaxis_type = solid)$
See also xaxis, xaxis_width and xaxis_color.
Default value: "black"
xaxis_color specifies the color for the x axis. See color to know how colors are defined.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) draw2d(explicit(x^3,x,-1,1),
xaxis = true,
xaxis_color = red)$
See also xaxis, xaxis_width and xaxis_type.
Default value: false
If yaxis is true, the y axis is drawn.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) draw2d(explicit(x^3,x,-1,1),
yaxis = true,
yaxis_color = blue)$
See also yaxis_width, yaxis_type and yaxis_color.
Default value: 1
yaxis_width is the width of the y axis. Its value must be a positive number.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) draw2d(explicit(x^3,x,-1,1),
yaxis = true,
yaxis_width = 3)$
See also yaxis, yaxis_type and yaxis_color.
Default value: dots
yaxis_type indicates how the y axis is displayed; possible values are solid and dots.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) draw2d(explicit(x^3,x,-1,1),
yaxis = true,
yaxis_type = solid)$
See also yaxis, yaxis_width and yaxis_color.
Default value: "black"
yaxis_color specifies the color for the y axis. See color to know how colors are defined.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) draw2d(explicit(x^3,x,-1,1),
yaxis = true,
yaxis_color = red)$
See also yaxis, yaxis_width and yaxis_type.
Default value: false
If zaxis is true, the z axis is drawn in 3D plots. This option has no effect in 2D scenes.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) draw3d(explicit(x^2+y^2,x,-1,1,y,-1,1),
zaxis = true,
zaxis_type = solid,
zaxis_color = blue)$
See also zaxis_width, zaxis_type and zaxis_color.
Default value: 1
zaxis_width is the width of the z axis. Its value must be a positive number. This option has no effect in 2D scenes.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) draw3d(explicit(x^2+y^2,x,-1,1,y,-1,1),
zaxis = true,
zaxis_type = solid,
zaxis_width = 3)$
See also zaxis, zaxis_type and zaxis_color.
Default value: dots
zaxis_type indicates how the z axis is displayed; possible values are solid and dots. This option has no effect in 2D scenes.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) draw3d(explicit(x^2+y^2,x,-1,1,y,-1,1),
zaxis = true,
zaxis_type = solid)$
See also zaxis, zaxis_width and zaxis_color.
Default value: "black"
zaxis_color specifies the color for the z axis. See color to know how colors are defined. This option has no effect in 2D scenes.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) draw3d(explicit(x^2+y^2,x,-1,1,y,-1,1),
zaxis = true,
zaxis_type = solid,
zaxis_color = red)$
See also zaxis, zaxis_width and zaxis_type.
Default value: false
Allocates the xy-plane in 3D scenes. When xyplane is false, the xy-plane is placed automatically; when it is a real number, the xy-plane intersects the z-axis at this level. This option has no effect in 2D scenes.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) draw3d(xyplane = %e-2,
explicit(x^2+y^2,x,-1,1,y,-1,1))$
Default value: 60
rot_vertical is the angle (in degrees) of vertical rotation (around the x axis) to set the view point in 3d scenes.
The angle is bounded to the [0, 180] interval.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) draw3d(rot_vertical = 170,
explicit(sin(x^2+y^2),x,-2,2,y,-2,2) )$
See also rot_horizontal.
Default value: 30
rot_horizontal is the angle (in degrees) of horizontal rotation (around the z axis) to set the view point in 3d scenes.
The angle is bounded to the [0, 360] interval.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) draw3d(rot_vertical = 170,
rot_horizontal = 360,
explicit(sin(x^2+y^2),x,-2,2,y,-2,2) )$
See also rot_vertical.
Default value: "" (empty string)
xy_file is the name of the file where the coordinates will be saved after clicking with the mouse button and hitting the 'x' key. By default, no coordinates are saved.
Since this is a global graphics option, its position in the scene description does not matter.
Default value: "" (empty string)
Expert Gnuplot users can make use of this option to fine tune Gnuplot's behaviour by writing settings to be sent before the plot or splot command.
The value of this option must be a string or a list of strings (one per line).
Since this is a global graphics option, its position in the scene description does not matter.
Example:
The dumb terminal is not supported by package draw, but it is possible to set it by making use of option user_preamble,
(%i1) load(draw)$
(%i2) draw2d(explicit(exp(x)-1,x,-1,1),
parametric(cos(u),sin(u),u,0,2*%pi),
user_preamble="set terminal dumb")$
Default value: "maxima_out"
This is the name of the file where terminals png, jpg, eps and eps_color will save the graphic.
Since this is a global graphics option, its position in the scene description does not matter. It can be also used as an argument of function draw.
Example:
(%i1) load(draw)$
(%i2) draw2d(file_name = "myfile",
explicit(x^2,x,-1,1),
terminal = 'png)$
See also terminal, pic_width, and pic_height.
Default value: 5
This is the delay in 1/100 seconds of frames in animated gif files.
Since this is a global graphics option, its position in the scene description does not matter. It can be also used as an argument of function draw.
Example:
(%i1) load(draw)$
(%i2) draw(
delay = 100,
file_name = "zzz",
terminal = 'animated_gif,
gr2d(explicit(x^2,x,-1,1)),
gr2d(explicit(x^3,x,-1,1)),
gr2d(explicit(x^4,x,-1,1)));
End of animation sequence
(%o2) [gr2d(explicit), gr2d(explicit), gr2d(explicit)]
Option delay is only active in animated gif's; it is ignored in any other case.
See also terminal, pic_width, and pic_height.
Default value: 640
This is the width of the bitmap file generated by terminals png and jpg.
Since this is a global graphics option, its position in the scene description does not matter. It can be also used as an argument of function draw.
Example:
(%i1) load(draw)$
(%i2) draw2d(terminal = 'png,
pic_width = 300,
pic_height = 300,
explicit(x^2,x,-1,1))$
See also terminal, file_name, and pic_height.
Default value: 640
This is the height of the bitmap file generated by terminals png and jpg.
Since this is a global graphics option, its position in the scene description does not matter. It can be also used as an argument of function draw.
Example:
(%i1) load(draw)$
(%i2) draw2d(terminal = 'png,
pic_width = 300,
pic_height = 300,
explicit(x^2,x,-1,1))$
See also terminal, file_name, and pic_width.
Default value: 12
This is the width (measured in cm) of the Postscipt file generated by terminals eps and eps_color.
Since this is a global graphics option, its position in the scene description does not matter. It can be also used as an argument of function draw.
Example:
(%i1) load(draw)$
(%i2) draw2d(terminal = 'eps,
eps_width = 3,
eps_height = 3,
explicit(x^2,x,-1,1))$
See also terminal, file_name, and eps_height.
Default value: 8
This is the height (measured in cm) of the Postscipt file generated by terminals eps and eps_color.
Since this is a global graphics option, its position in the scene description does not matter. It can be also used as an argument of function draw.
Example:
(%i1) load(draw)$
(%i2) draw2d(terminal = 'eps,
eps_width = 3,
eps_height = 3,
explicit(x^2,x,-1,1))$
See also terminal, file_name, and eps_width.
Default value: true
If axis_bottom is true, the bottom axis is shown in 2d scenes.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) draw2d(axis_bottom = false,
explicit(x^3,x,-1,1))$
See also axis_left, axis_top, axis_right, and axis_3d.
Default value: true
If axis_left is true, the left axis is shown in 2d scenes.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) draw2d(axis_left = false,
explicit(x^3,x,-1,1))$
See also axis_bottom, axis_top, axis_right, and axis_3d.
Default value: true
If axis_top is true, the top axis is shown in 2d scenes.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) draw2d(axis_top = false,
explicit(x^3,x,-1,1))$
See also axis_bottom, axis_left, axis_right, and axis_3d.
Default value: true
If axis_right is true, the right axis is shown in 2d scenes.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) draw2d(axis_right = false,
explicit(x^3,x,-1,1))$
See also axis_bottom, axis_left, axis_top, and axis_3d.
Default value: true
If axis_3d is true, the x, y and z axis are shown in 3d scenes.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) draw3d(axis_3d = false,
explicit(sin(x^2+y^2),x,-2,2,y,-2,2) )$
See also axis_bottom, axis_left, axis_top, and axis_right for axis in 2d.
Default value: color
palette indicates how to map the real values of a matrix passed to object image onto color components.
palette is a vector of length three with components ranging from -36 to +36; each value is an index for a formula mapping the levels onto red, green and blue colors, respectively:
0: 0 1: 0.5 2: 1 3: x 4: x^2 5: x^3 6: x^4 7: sqrt(x) 8: sqrt(sqrt(x)) 9: sin(90x) 10: cos(90x) 11: |x-0.5| 12: (2x-1)^2 13: sin(180x) 14: |cos(180x)| 15: sin(360x) 16: cos(360x) 17: |sin(360x)| 18: |cos(360x)| 19: |sin(720x)| 20: |cos(720x)| 21: 3x 22: 3x-1 23: 3x-2 24: |3x-1| 25: |3x-2| 26: (3x-1)/2 27: (3x-2)/2 28: |(3x-1)/2| 29: |(3x-2)/2| 30: x/0.32-0.78125 31: 2*x-0.84 32: 4x;1;-2x+1.84;x/0.08-11.5 33: |2*x - 0.5| 34: 2*x 35: 2*x - 0.5 36: 2*x - 1
negative numbers mean negative colour component.
palette = gray and palette = color are short cuts for palette = [3,3,3] and palette = [7,5,15], respectively.
Since this is a global graphics option, its position in the scene description does not matter.
Examples:
(%i1) load(draw)$
(%i2) im: apply(
'matrix,
makelist(makelist(random(200),i,1,30),i,1,30))$
(%i3) /* palette = color, default */
draw2d(image(im,0,0,30,30))$
(%i4) draw2d(palette = gray, image(im,0,0,30,30))$
(%i5) draw2d(palette = [15,20,-4],
colorbox=false,
image(im,0,0,30,30))$
See also colorbox.
Default value: true
If colorbox is true, a color scale is drawn together with image objects.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) im: apply('matrix,
makelist(makelist(random(200),i,1,30),i,1,30))$
(%i3) draw2d(image(im,0,0,30,30))$
(%i4) draw2d(colorbox=false, image(im,0,0,30,30))$
See also palette.
Default value: false
If enhanced3d is true, surfaces are colored in 3d plots; in other words, it sets Gnuplot's pm3d mode.
See option palette to learn how palettes are specified.
Example:
(%i1) load(draw)$
(%i2) draw3d(surface_hide = true,
enhanced3d = true,
palette = gray,
explicit(20*exp(-x^2-y^2)-10,x,-3,3,y,-3,3))$
Default value: 1
point_size sets the size for plotted points. It must be a non negative number.
This option has no effect when graphic option point_type is set to dot.
This option affects the following graphic objects:
gr2d: points.gr3d: points.Example:
(%i1) load(draw)$
(%i2) draw2d(points(makelist([random(20),random(50)],k,1,10)),
point_size = 5,
points(makelist(k,k,1,20),makelist(random(30),k,1,20)))$
Default value: 1
point_type indicates how isolated points are displayed; the value of this option can be any integer index greater or equal than -1, or the name of a point style: $none (-1), dot (0), plus (1), multiply (2), asterisk (3), square (4), filled_square (5), circle (6), filled_circle (7), up_triangle (8), filled_up_triangle (9), down_triangle (10), filled_down_triangle (11), diamant (12) and filled_diamant (13).
This option affects the following graphic objects:
gr2d: points.gr3d: points.Example:
(%i1) load(draw)$
(%i2) draw2d(xrange = [0,10],
yrange = [0,10],
point_size = 3,
point_type = diamant,
points([[1,1],[5,1],[9,1]]),
point_type = filled_down_triangle,
points([[1,2],[5,2],[9,2]]),
point_type = asterisk,
points([[1,3],[5,3],[9,3]]),
point_type = filled_diamant,
points([[1,4],[5,4],[9,4]]),
point_type = 5,
points([[1,5],[5,5],[9,5]]),
point_type = 6,
points([[1,6],[5,6],[9,6]]),
point_type = filled_circle,
points([[1,7],[5,7],[9,7]]),
point_type = 8,
points([[1,8],[5,8],[9,8]]),
point_type = filled_diamant,
points([[1,9],[5,9],[9,9]]) )$
Default value: false
When points_joined is true, points are joined by lines; when false, isolated points are drawn. A third possible value for this graphic option is impulses; in such case, vertical segments are drawn from points to the x-axis (2D) or to the xy-plane (3D).
This option affects the following graphic objects:
gr2d: points.gr3d: points.Example:
(%i1) load(draw)$
(%i2) draw2d(xrange = [0,10],
yrange = [0,4],
point_size = 3,
point_type = up_triangle,
color = blue,
points([[1,1],[5,1],[9,1]]),
points_joined = true,
point_type = square,
line_type = dots,
points([[1,2],[5,2],[9,2]]),
point_type = circle,
color = red,
line_width = 7,
points([[1,3],[5,3],[9,3]]) )$
Default value: false
Option filled_func controls how regions limited by functions should be filled. When filled_func is true, the region bounded by the function defined with object explicit and the bottom of the graphic window is filled with fill_color. When filled_func contains a function expression, then the region bounded by this function and the function defined with object explicit will be filled. By default, explicit functions are not filled.
This option affects only the 2d graphic object explicit.
Example:
Region bounded by an explicit object and the bottom of the graphic window.
(%i1) load(draw)$
(%i2) draw2d(fill_color = red,
filled_func = true,
explicit(sin(x),x,0,10) )$
Region bounded by an explicit object and the function defined by option filled_func. Note that the variable in filled_func must be the same as that used in explicit.
(%i1) load(draw)$
(%i2) draw2d(fill_color = grey,
filled_func = sin(x),
explicit(-sin(x),x,0,%pi));
See also fill_color and explicit.
Default value: false
If transparent is true, interior regions of polygons are filled according to fill_color.
This option affects the following graphic objects:
gr2d: polygon, rectangle, and ellipse.Example:
(%i1) load(draw)$
(%i2) draw2d(polygon([[3,2],[7,2],[5,5]]),
transparent = true,
color = blue,
polygon([[5,2],[9,2],[7,5]]) )$
Default value: true
If border is true, borders of polygons are painted according to line_type and line_width.
This option affects the following graphic objects:
gr2d: polygon, rectangle, and ellipse.Example:
(%i1) load(draw)$
(%i2) draw2d(color = brown,
line_width = 8,
polygon([[3,2],[7,2],[5,5]]),
border = false,
fill_color = blue,
polygon([[5,2],[9,2],[7,5]]) )$
Default value: false
If head_both is true, vectors are plotted with two arrow heads. If false, only one arrow is plotted.
This option is relevant only for vector objects.
Example:
(%i1) load(draw)$
(%i2) draw2d(xrange = [0,8],
yrange = [0,8],
head_length = 0.7,
vector([1,1],[6,0]),
head_both = true,
vector([1,7],[6,0]) )$
See also head_length, head_angle, and head_type.
Default value: 2
head_length indicates, in x-axis units, the length of arrow heads.
This option is relevant only for vector objects.
Example:
(%i1) load(draw)$
(%i2) draw2d(xrange = [0,12],
yrange = [0,8],
vector([0,1],[5,5]),
head_length = 1,
vector([2,1],[5,5]),
head_length = 0.5,
vector([4,1],[5,5]),
head_length = 0.25,
vector([6,1],[5,5]))$
See also head_both, head_angle, and head_type.
Default value: 45
head_angle indicates the angle, in degrees, between the arrow heads and the segment.
This option is relevant only for vector objects.
Example:
(%i1) load(draw)$
(%i2) draw2d(xrange = [0,10],
yrange = [0,9],
head_length = 0.7,
head_angle = 10,
vector([1,1],[0,6]),
head_angle = 20,
vector([2,1],[0,6]),
head_angle = 30,
vector([3,1],[0,6]),
head_angle = 40,
vector([4,1],[0,6]),
head_angle = 60,
vector([5,1],[0,6]),
head_angle = 90,
vector([6,1],[0,6]),
head_angle = 120,
vector([7,1],[0,6]),
head_angle = 160,
vector([8,1],[0,6]),
head_angle = 180,
vector([9,1],[0,6]) )$
See also head_both, head_length, and head_type.
Default value: filled
head_type is used to specify how arrow heads are plotted. Possible values are: filled (closed and filled arrow heads), empty (closed but not filled arrow heads), and nofilled (open arrow heads).
This option is relevant only for vector objects.
Example:
(%i1) load(draw)$
(%i2) draw2d(xrange = [0,12],
yrange = [0,10],
head_length = 1,
vector([0,1],[5,5]), /* default type */
head_type = 'empty,
vector([3,1],[5,5]),
head_type = 'nofilled,
vector([6,1],[5,5]))$
See also head_both, head_angle, and head_length.
Default value: false
If unit_vectors is true, vectors are plotted with module 1. This is useful for plotting vector fields. If unit_vectors is false, vectors are plotted with its original length.
This option is relevant only for vector objects.
Example:
(%i1) load(draw)$
(%i2) draw2d(xrange = [-1,6],
yrange = [-1,6],
head_length = 0.1,
vector([0,0],[5,2]),
unit_vectors = true,
color = red,
vector([0,3],[5,2]))$
Default value: center
label_alignment is used to specify where to write labels with respect to the given coordinates. Possible values are: center, left, and right.
This option is relevant only for label objects.
Example:
(%i1) load(draw)$
(%i2) draw2d(xrange = [0,10],
yrange = [0,10],
points_joined = true,
points([[5,0],[5,10]]),
color = blue,
label(["Centered alignment (default)",5,2]),
label_alignment = 'left,
label(["Left alignment",5,5]),
label_alignment = 'right,
label(["Right alignment",5,8]))$
See also label_orientation, and color.
Default value: horizontal
label_orientation is used to specify orientation of labels. Possible values are: horizontal, and vertical.
This option is relevant only for label objects.
Example:
In this example, a dummy point is added to get an image. Package draw needs always data to draw an scene.
(%i1) load(draw)$
(%i2) draw2d(xrange = [0,10],
yrange = [0,10],
point_size = 0,
points([[5,5]]),
color = navy,
label(["Horizontal orientation (default)",5,2]),
label_orientation = 'vertical,
color = "#654321",
label(["Vertical orientation",1,5]))$
See also label_alignment and color.
Default value: "black"
color specifies the color for plotting lines, points, borders of polygons and labels.
Colors can be given as names or in hexadecimal rgb code.
Available color names are: "white", "black", "gray0", "grey0", "gray10", "grey10", "gray20", "grey20", "gray30", "grey30", "gray40", "grey40", "gray50", "grey50", "gray60", "grey60", "gray70", "grey70", "gray80", "grey80", "gray90", "grey90", "gray100", "grey100", "gray", "grey", "light-gray", "light-grey", "dark-gray", "dark-grey", "red", "light-red", "dark-red", "yellow", "light-yellow", "dark-yellow", "green", "light-green", "dark-green", "spring-green", "forest-green", "sea-green", "blue", "light-blue", "dark-blue", "midnight-blue", "navy", "medium-blue", "royalblue", "skyblue", "cyan", "light-cyan", "dark-cyan", "magenta", "light-magenta", "dark-magenta", "turquoise", "light-turquoise", "dark-turquoise", "pink", "light-pink", "dark-pink", "coral", "light-coral", "orange-red", "salmon", "light-salmon", "dark-salmon", "aquamarine", "khaki", "dark-khaki", "goldenrod", "light-goldenrod", "dark-goldenrod", "gold", "beige", "brown", "orange", "dark-orange", "violet", "dark-violet", "plum" and "purple".
Cromatic componentes in hexadecimal code are introduced in the form "#rrggbb".
Example:
(%i1) load(draw)$
(%i2) draw2d(explicit(x^2,x,-1,1), /* default is black */
color = "red",
explicit(0.5 + x^2,x,-1,1),
color = blue,
explicit(1 + x^2,x,-1,1),
color = "light-blue", /* double quotes if - is used */
explicit(1.5 + x^2,x,-1,1),
color = "#23ab0f",
label(["This is a label",0,1.2]) )$
See also fill_color.
Default value: "red"
fill_color specifies the color for filling polygons and 2d explicit functions.
See color to learn how colors are specified.
Default value: 0
fill_density is a number between 0 and 1 that specifies the intensity of the fill_color in bars objects.
See bars for examples.
Default value: 1
line_width is the width of plotted lines. Its value must be a positive number.
This option affects the following graphic objects:
gr2d: points, polygon, rectangle, ellipse, vector, explicit, implicit, parametric and polar.gr3d: points and parametric.Example:
(%i1) load(draw)$
(%i2) draw2d(explicit(x^2,x,-1,1), /* default width */
line_width = 5.5,
explicit(1 + x^2,x,-1,1),
line_width = 10,
explicit(2 + x^2,x,-1,1))$
See also line_type.
Default value: solid
line_type indicates how lines are displayed; possible values are solid and dots.
This option affects the following graphic objects:
gr2d: points, polygon, rectangle, ellipse, vector, explicit, implicit, parametric and polar.gr3d: points, explicit, parametric and parametric_surface.Example:
(%i1) load(draw)$
(%i2) draw2d(line_type = dots,
explicit(1 + x^2,x,-1,1),
line_type = solid, /* default */
explicit(2 + x^2,x,-1,1))$
See also line_width.
Default value: 30
In 2d, nticks gives the initial number of points used by the adaptive plotting routine for explicit objects. It is also the number of points that will be shown in parametric and polar curves.
This option affects the following graphic objects:
gr2d: ellipse, explicit, parametric and polar.gr3d: parametric.Example:
(%i1) load(draw)$
(%i2) draw2d(transparent = true,
ellipse(0,0,4,2,0,180),
nticks = 5,
ellipse(0,0,4,2,180,180) )$
Default value: 10
adapt_depth is the maximum number of splittings used by the adaptive plotting routine.
This option is relevant only for 2d explicit functions.
Default value: "" (empty string)
key is the name of a function in the legend. If key is an empty string, no key is assigned to the function.
This option affects the following graphic objects:
gr2d: points, polygon, rectangle, ellipse, vector, explicit, implicit, parametric, and polar.gr3d: points, explicit, parametric, and parametric_surface.Example:
(%i1) load(draw)$
(%i2) draw2d(key = "Sinus",
explicit(sin(x),x,0,10),
key = "Cosinus",
color = red,
explicit(cos(x),x,0,10) )$
Default value: 30
xu_grid is the number of coordinates of the first variable (x in explicit and u in parametric 3d surfaces) to build the grid of sample points.
This option affects the following graphic objects:
gr3d: explicit and parametric_surface.Example:
(%i1) load(draw)$
(%i2) draw3d(xu_grid = 10,
yv_grid = 50,
explicit(x^2+y^2,x,-3,3,y,-3,3) )$
See also yv_grid.
Default value: 30
yv_grid is the number of coordinates of the second variable (y in explicit and v in parametric 3d surfaces) to build the grid of sample points.
This option affects the following graphic objects:
gr3d: explicit and parametric_surface.Example:
(%i1) load(draw)$
(%i2) draw3d(xu_grid = 10,
yv_grid = 50,
explicit(x^2+y^2,x,-3,3,y,-3,3) )$
See also xu_grid.
Default value: false
If surface_hide is true, hidden parts are not plotted in 3d surfaces.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) draw(columns=2,
gr3d(explicit(exp(sin(x)+cos(x^2)),x,-3,3,y,-3,3)),
gr3d(surface_hide = true,
explicit(exp(sin(x)+cos(x^2)),x,-3,3,y,-3,3)) )$
Default value: none
Option contour enables the user to select where to plot contour lines. Possible values are:
none: no contour lines are plotted.base: contour lines are projected on the xy plane.surface: contour lines are plotted on the surface.both: two contour lines are plotted: on the xy plane and on the surface.map: contour lines are projected on the xy plane, and the view point is set just in the vertical.Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$
(%i2) draw3d(explicit(20*exp(-x^2-y^2)-10,x,0,2,y,-3,3),
contour_levels = 15,
contour = both,
surface_hide = true) $
Default value: 5
This graphic option controls the way contours are drawn. contour_levels can be set to a positive integer number, a list of three numbers or an arbitrary set of numbers:
contour_levels is bounded to positive integer n, n contour lines will be drawn at equal intervals. By default, five equally spaced contours are plotted.contour_levels is bounded to a list of length three of the form [lowest,s,highest], contour lines are plotted from lowest to highest in steps of s.contour_levels is bounded to a set of numbers of the form {n1, n2, ...}, contour lines are plotted at values n1, n2, ...Since this is a global graphics option, its position in the scene description does not matter.
Examples:
Ten equally spaced contour lines. The actual number of levels can be adjusted to give simple labels.
(%i1) load(draw)$
(%i2) draw3d(color = green,
explicit(20*exp(-x^2-y^2)-10,x,0,2,y,-3,3),
contour_levels = 10,
contour = both,
surface_hide = true) $
From -8 to 8 in steps of 4.
(%i1) load(draw)$
(%i2) draw3d(color = green,
explicit(20*exp(-x^2-y^2)-10,x,0,2,y,-3,3),
contour_levels = [-8,4,8],
contour = both,
surface_hide = true) $
Isolines at levels -7, -6, 0.8 and 5.
(%i1) load(draw)$
(%i2) draw3d(color = green,
explicit(20*exp(-x^2-y^2)-10,x,0,2,y,-3,3),
contour_levels = {-7, -6, 0.8, 5},
contour = both,
surface_hide = true) $
See also contour.
Default value: 1
columns is the number of columns in multiple plots.
Since this is a global graphics option, its position in the scene description does not matter. It can be also used as an argument of function draw.
Example:
(%i1) load(draw)$
(%i2) scene1: gr2d(title="Ellipse",
nticks=30,
parametric(2*cos(t),5*sin(t),t,0,2*%pi))$
(%i3) scene2: gr2d(title="Triangle",
polygon([4,5,7],[6,4,2]))$
(%i4) draw(scene1, scene2, columns = 2)$
Default value: [50, 50]
ip_grid sets the grid for the first sampling in implicit plots.
This option is relevant only for implicit objects.
Default value: [5, 5]
ip_grid_in sets the grid for the second sampling in implicit plots.
This option is relevant only for implicit objects.
Default value: 10
x_voxel is the number of voxels in the x direction to be used by the marching cubes algorithm implemented by the 3d implicit object.
Default value: 10
y_voxel is the number of voxels in the y direction to be used by the marching cubes algorithm implemented by the 3d implicit object.
Default value: 10
z_voxel is the number of voxels in the z direction to be used by the marching cubes algorithm implemented by the 3d implicit object.
Function gr2d builds an object describing a 2D scene. Arguments are graphic options and graphic objects. This scene is interpreted sequentially: graphic options affect those graphic objects placed on its right. Some graphic options affect the global appearence of the scene.
This is the list of graphic objects available for scenes in two dimensions: points, polygon, rectangle, bars, ellipse, label, vector, explicit, implicit, polar, parametric, image and geomap.
See also the following global graphic options: xrange, yrange, logx, logy, terminal, grid, title, xlabel, ylabel, xtics, ytics, xtics_rotate, ytics_rotate, xtics_axis, ytics_axis, xaxis, yaxis, xaxis_width, yaxis_width, xaxis_type, yaxis_type, xaxis_color, yaxis_color, xy_file, file_name, pic_width, pic_height, eps_width, eps_height, user_preamble, axis_bottom, axis_left, axis_top and axis_right.
To make use of this function, write first load(draw).
Function gr3d builds an object describing a 3d scene. Arguments are graphic options and graphic objects. This scene is interpreted sequentially: graphic options affect those graphic objects placed on its right. Some graphic options affect the global appearence of the scene.
This is the list of graphic objects available for scenes in three dimensions: points, label, vector, explicit, implicit, parametric, parametric_surface and geomap.
See also the following global graphic options: xrange, yrange, zrange, logx, logy, logz, terminal, grid, title, xlabel, ylabel, zlabel, xtics, ytics, ztics, xtics_rotate, ytics_rotate, ztics_rotate, xtics_axis, ytics_axis, ztics_axis, xaxis, yaxis, zaxis, xaxis_width, yaxis_width, zaxis_width, xaxis_type, yaxis_type, zaxis_type, xaxis_color, yaxis_color, zaxis_color, xy_file, user_preamble, axis_bottom, axis_left, axis_top, file_name, pic_width, pic_height, eps_width, eps_height, axis_right, rot_vertical, rot_horizontal, axis_3d, xu_grid, yv_grid, surface_hide, contour, contour_levels, palette, colorbox and enhanced3d.
To make use of this function, write first load(draw).
Draws points in 2D and 3D.
This object is affected by the following graphic options: point_size, point_type, points_joined, line_width, key, line_type and color.
2D
points ([[x1,y1], [x2,y2],...]) or points ([x1,x2,...], [y1,y2,...]) plots points [x1,y1], [x2,y2], etc. If abscissas are not given, they are set to consecutive positive integers, so that points ([y1,y2,...]) draws points [1,y1], [2,y2], etc. If matrix is a two-column or two-row matrix, points (matrix) draws the associated points. If matrix is a one-column or one-row matrix, abscissas are assigned automatically.
Example:
(%i1) load(draw)$
(%i2) draw2d(
key = "Small points",
points(makelist([random(20),random(50)],k,1,10)),
point_type = circle,
point_size = 3,
points_joined = true,
key = "Great points",
points(makelist(k,k,1,20),makelist(random(30),k,1,20)),
point_type = filled_down_triangle,
key = "Automatic abscissas",
color = red,
points([2,12,8]))$
(%i1) load(draw)$
(%i2) draw2d(
points_joined = impulses,
line_width = 2,
color = red,
points(makelist([random(20),random(50)],k,1,10)))$
3D
points ([[x1,y1,z1], [x2,y2,z2],...]) or points ([x1,x2,...], [y1,y2,...], [z1,z2,...]) plots points [x1,y1,z1], [x2,y2,z2], etc. If matrix is a three-column or three-row matrix, points (matrix) draws the associated points.
Examples:
One tridimensional sample,
(%i1) load(draw)$
(%i2) load (numericalio)$
(%i3) s2 : read_matrix (file_search ("wind.data"))$
(%i4) draw3d(title = "Daily average wind speeds",
point_size = 2,
points(args(submatrix (s2, 4, 5))) )$
Two tridimensional samples,
(%i1) load(draw)$
(%i2) load (numericalio)$
(%i3) s2 : read_matrix (file_search ("wind.data"))$
(%i4) draw3d(
title = "Daily average wind speeds. Two data sets",
point_size = 2,
key = "Sample from stations 1, 2 and 3",
points(args(submatrix (s2, 4, 5))),
point_type = 4,
key = "Sample from stations 1, 4 and 5",
points(args(submatrix (s2, 2, 3))) )$
Draws polygons in 2D.
2D
polygon ([[x1,y1], [x2,y2],...]) or polygon ([x1,x2,...], [y1,y2,...]): plots on the plane a polygon with vertices [x1,y1], [x2,y2], etc..
This object is affected by the following graphic options: transparent, fill_color, border, line_width, key, line_type and color.
Example:
(%i1) load(draw)$
(%i2) draw2d(color = "#e245f0",
line_width = 8,
polygon([[3,2],[7,2],[5,5]]),
border = false,
fill_color = yellow,
polygon([[5,2],[9,2],[7,5]]) )$
Draws rectangles in 2D.
2D
rectangle ([x1,y1], [x2,y2]) draws a rectangle with opposite vertices [x1,y1] and [x2,y2].
This object is affected by the following graphic options: transparent, fill_color, border, line_width, key, line_type and color.
Example:
(%i1) load(draw)$
(%i2) draw2d(fill_color = red,
line_width = 6,
line_type = dots,
transparent = false,
fill_color = blue,
rectangle([-2,-2],[8,-1]), /* opposite vertices */
transparent = true,
line_type = solid,
line_width = 1,
rectangle([9,4],[2,-1.5]),
xrange = [-3,10],
yrange = [-3,4.5] )$
Draws vertical bars in 2D.
2D
bars ([x1,h1,w1], [x2,h2,w2, ...]) draws bars centered at values x1, x2, ... with heights h1, h2, ... and widths w1, w2, ...
This object is affected by the following graphic options: key, fill_color, fill_density and line_width.
Example:
(%i1) load(draw)$
(%i2) draw2d(
key = "Group A",
fill_color = blue,
fill_density = 0.2,
bars([0.8,5,0.4],[1.8,7,0.4],[2.8,-4,0.4]),
key = "Group B",
fill_color = red,
fill_density = 0.6,
line_width = 4,
bars([1.2,4,0.4],[2.2,-2,0.4],[3.2,5,0.4]),
xaxis = true);
Draws ellipses and circles in 2D.
2D
ellipse (xc, yc, a, b, ang1, ang2) plots an ellipse centered at [xc, yc] with horizontal and vertical semi axis a and b, respectively, from angle ang1 to angle ang2.
This object is affected by the following graphic options: nticks, transparent, fill_color, border, line_width, line_type, key and color.
Example:
(%i1) load(draw)$
(%i2) draw2d(transparent = false,
fill_color = red,
color = gray30,
transparent = false,
line_width = 5,
ellipse(0,6,3,2,270,-270),
/* center (x,y), a, b, start & end in degrees */
transparent = true,
color = blue,
line_width = 3,
ellipse(2.5,6,2,3,30,-90),
xrange = [-3,6],
yrange = [2,9] )$
Writes labels in 2D and 3D.
This object is affected by the following graphic options: label_alignment, label_orientation and color.
2D
label([string,x,y]) writes the string at point [x,y].
Example:
(%i1) load(draw)$
(%i2) draw2d(yrange = [0.1,1.4],
color = "red",
label(["Label in red",0,0.3]),
color = "#0000ff",
label(["Label in blue",0,0.6]),
color = "light-blue",
label(["Label in light-blue",0,0.9],
["Another light-blue",0,1.2]) )$
3D
label([string,x,y,z]) writes the string at point [x,y,z].
Example:
(%i1) load(draw)$
(%i2) draw3d(explicit(exp(sin(x)+cos(x^2)),x,-3,3,y,-3,3),
color = red,
label(["UP 1",-2,0,3], ["UP 2",1.5,0,4]),
color = blue,
label(["DOWN 1",2,0,-3]) )$
Draws vectors in 2D and 3D.
This object is affected by the following graphic options: head_both, head_length, head_angle, head_type, line_width, line_type, key and color.
2D
vector([x,y], [dx,dy]) plots vector [dx,dy] with origin in [x,y].
Example:
(%i1) load(draw)$
(%i2) draw2d(xrange = [0,12],
yrange = [0,10],
head_length = 1,
vector([0,1],[5,5]), /* default type */
head_type = 'empty,
vector([3,1],[5,5]),
head_both = true,
head_type = 'nofilled,
line_type = dots,
vector([6,1],[5,5]))$
3D
vector([x,y,z], [dx,dy,dz]) plots vector [dx,dy,dz] with origin in [x,y,z].
Example:
(%i1) load(draw)$
(%i2) draw3d(color = cyan,
vector([0,0,0],[1,1,1]/sqrt(3)),
vector([0,0,0],[1,-1,0]/sqrt(2)),
vector([0,0,0],[1,1,-2]/sqrt(6)) )$
Draws explicit functions in 2D and 3D.
2D
explicit(fcn,var,minval,maxval) plots explicit function fcn, with variable var taking values from minval to maxval.
This object is affected by the following graphic options: nticks, adapt_depth, line_width, line_type, key, filled_func, fill_color and color.
Example:
(%i1) load(draw)$
(%i2) draw2d(line_width = 3,
color = blue,
explicit(x^2,x,-3,3) )$
(%i3) draw2d(fill_color = brown,
filled_func = true,
explicit(x^2,x,-3,3) )$
3D
explicit(fcn,var1,minval1,maxval1,var2,minval2,maxval2) plots explicit function fcn, with variable var1 taking values from minval1 to maxval1 and variable var2 taking values from minval2 to maxval2.
This object is affected by the following graphic options: xu_grid, yv_grid, line_type, key and color.
Example:
(%i1) load(draw)$
(%i2) draw3d(key = "Gauss",
color = "#a02c00",
explicit(20*exp(-x^2-y^2)-10,x,-3,3,y,-3,3),
yv_grid = 10,
color = blue,
key = "Plane",
explicit(x+y,x,-5,5,y,-5,5),
surface_hide = true)$
See also filled_func for filled functions.
Draws implicit functions in 2D and 3D.
2D
implicit(fcn,x,xmin,xmax,y,ymin,ymax) plots the implicit function defined by fcn, with variable x taking values from xmin to xmax, and variable y taking values from ymin to ymax.
This object is affected by the following graphic options: ip_grid, ip_grid_in, line_width, line_type, key and color.
Example:
(%i1) load(draw)$
(%i2) draw2d(terminal = eps,
grid = true,
line_type = solid,
key = "y^2=x^3-2*x+1",
implicit(y^2=x^3-2*x+1, x, -4,4, y, -4,4),
line_type = dots,
key = "x^3+y^3 = 3*x*y^2-x-1",
implicit(x^3+y^3 = 3*x*y^2-x-1, x,-4,4, y,-4,4),
title = "Two implicit functions" )$
3D
implicit (fcn,x,xmin,xmax, y,ymin,ymax, z,zmin,zmax) plots the implicit surface defined by fcn, with variable x taking values from xmin to xmax, variable y taking values from ymin to ymax and variable z taking values from zmin to zmax. This object implements the marching cubes algorithm.
This object is affected by the following graphic options: x_voxel, y_voxel, z_voxel, line_width, line_type, key and color.
Example:
(%i1) load(draw)$
(%i2) draw3d(
color=blue,
implicit((x^2+y^2+z^2-1)*(x^2+(y-1.5)^2+z^2-0.5)=0.015,
x,-1,1,y,-1.2,2.3,z,-1,1),
surface_hide=true);
Draws 2D functions defined in polar coordinates.
2D
polar (radius,ang,minang,maxang) plots function radius(ang) defined in polar coordinates, with variable ang taking values from minang to maxang.
This object is affected by the following graphic options: nticks, line_width, line_type, key and color.
Example:
(%i1) load(draw)$
(%i2) draw2d(user_preamble = "set grid polar",
nticks = 200,
xrange = [-5,5],
yrange = [-5,5],
color = blue,
line_width = 3,
title = "Hyperbolic Spiral",
polar(10/theta,theta,1,10*%pi) )$
Draws 3D functions defined in spherical coordinates.
3D
spherical (radius,azi,minazi,maxazi,zen,minzen,maxzen) plots function radius(azi,zen) defined in spherical coordinates, with azimuth azi taking values from minazi to maxazi and zenith zen taking values from minzen to maxzen.
This object is affected by the following graphic options: xu_grid, yv_grid, line_type, key and color.
Example:
(%i1) load(draw)$ (%i2) draw3d(spherical(1,a,0,2*%pi,z,0,%pi))$
Draws 3D functions defined in cylindrical coordinates.
3D
cylindrical (radius,z,minz,maxz,azi,minazi,maxazi) plots function radius(z,azi) defined in cylindrical coordinates, with variable z taking values from minz to maxz and azimuth azi taking values from minazi to maxazi.
This object is affected by the following graphic options: xu_grid, yv_grid, line_type, key and color.
Example:
(%i1) load(draw)$ (%i2) draw3d(cylindrical(1,z,-2,2,az,0,2*%pi))$
Draws parametric functions in 2D and 3D.
This object is affected by the following graphic options: nticks, line_width, line_type, key and color.
2D
parametric (xfun,yfun,par,parmin,parmax) plots parametric function [xfun,yfun], with parameter par taking values from parmin to parmax.
Example:
(%i1) load(draw)$
(%i2) draw2d(explicit(exp(x),x,-1,3),
color = red,
key = "This is the parametric one!!",
parametric(2*cos(rrr),rrr^2,rrr,0,2*%pi))$
3D
parametric (xfun,yfun,zfun,par,parmin,parmax) plots parametric curve [xfun,yfun,zfun], with parameter par taking values from parmin to parmax.
Example:
(%i1) load(draw)$
(%i2) draw3d(explicit(exp(sin(x)+cos(x^2)),x,-3,3,y,-3,3),
color = royalblue,
parametric(cos(5*u)^2,sin(7*u),u-2,u,0,2),
color = turquoise,
line_width = 2,
parametric(t^2,sin(t),2+t,t,0,2),
surface_hide = true,
title = "Surface & curves" )$
Renders images in 2D.
2D
image (im,x0,y0,width,height) plots image im in the rectangular region from vertex (x0,y0) to (x0+width,y0+height) on the real plane. Argument im must be a matrix of real numbers, a matrix of vectors of length three or a picture object.
If im is a matrix of real numbers or a levels picture object, pixel values are interpreted according to graphic option palette, which is a vector of length three with components ranging from -36 to +36; each value is an index for a formula mapping the levels onto red, green and blue colors, respectively:
0: 0 1: 0.5 2: 1 3: x 4: x^2 5: x^3 6: x^4 7: sqrt(x) 8: sqrt(sqrt(x)) 9: sin(90x) 10: cos(90x) 11: |x-0.5| 12: (2x-1)^2 13: sin(180x) 14: |cos(180x)| 15: sin(360x) 16: cos(360x) 17: |sin(360x)| 18: |cos(360x)| 19: |sin(720x)| 20: |cos(720x)| 21: 3x 22: 3x-1 23: 3x-2 24: |3x-1| 25: |3x-2| 26: (3x-1)/2 27: (3x-2)/2 28: |(3x-1)/2| 29: |(3x-2)/2| 30: x/0.32-0.78125 31: 2*x-0.84 32: 4x;1;-2x+1.84;x/0.08-11.5 33: |2*x - 0.5| 34: 2*x 35: 2*x - 0.5 36: 2*x - 1
negative numbers mean negative colour component.
palette = gray and palette = color are short cuts for palette = [3,3,3] and palette = [7,5,15], respectively.
If im is a matrix of vectors of length three or an rgb picture object, they are interpreted as red, green and blue color components.
Examples:
If im is a matrix of real numbers, pixel values are interpreted according to graphic option palette.
(%i1) load(draw)$
(%i2) im: apply(
'matrix,
makelist(makelist(random(200),i,1,30),i,1,30))$
(%i3) /* palette = color, default */
draw2d(image(im,0,0,30,30))$
(%i4) draw2d(palette = gray, image(im,0,0,30,30))$
(%i5) draw2d(palette = [15,20,-4],
colorbox=false,
image(im,0,0,30,30))$
See also colorbox.
If im is a matrix of vectors of length three, they are interpreted as red, green and blue color components.
(%i1) load(draw)$
(%i2) im: apply(
'matrix,
makelist(
makelist([random(300),
random(300),
random(300)],i,1,30),i,1,30))$
(%i3) draw2d(image(im,0,0,30,30))$
Package draw automatically loads package picture. In this example, a level picture object is built by hand and then rendered.
(%i1) load(draw)$
(%i2) im: make_level_picture([45,87,2,134,204,16],3,2);
(%o2) picture(level, 3, 2, {Array: #(45 87 2 134 204 16)})
(%i3) /* default color palette */
draw2d(image(im,0,0,30,30))$
(%i4) /* gray palette */
draw2d(palette = gray,
image(im,0,0,30,30))$
An xpm file is read and then rendered.
(%i1) load(draw)$
(%i2) im: read_xpm("myfile.xpm")$
(%i3) draw2d(image(im,0,0,10,7))$
See also make_level_picture, make_rgb_picture and read_xpm.
URL http://www.telefonica.net/web2/biomates/maxima/gpdraw/image contains more elaborated examples.
Default value: false
boundaries_array is where the graphic object geomap looks for boundaries coordinates.
Each component of boundaries_array is an array of floating point quantities, the coordinates of a polygonal segment or map boundary.
See also geomap.
Draws cartographic maps in 2D and 3D.
2D
This function works together with global variable boundaries_array.
Argument numlist is a list containing numbers or lists of numbers. All these numbers must be integers greater or equal than zero, representing the components of global array boundaries_array.
Each component of boundaries_array is an array of floating point quantities, the coordinates of a polygonal segment or map boundary.
geomap (numlist) flattens its arguments and draws the associated boundaries in boundaries_array.
This object is affected by the following graphic options: line_width, line_type and color.
Examples:
A simple map defined by hand:
(%i1) load(draw)$
(%i2) /* Vertices of boundary #0: {(1,1),(2,5),(4,3)} */
( bnd0: make_array(flonum,6),
bnd0[0]:1.0, bnd0[1]:1.0, bnd0[2]:2.0,
bnd0[3]:5.0, bnd0[4]:4.0, bnd0[5]:3.0 )$
(%i3) /* Vertices of boundary #1: {(4,3),(5,4),(6,4),(5,1)} */
( bnd1: make_array(flonum,8),
bnd1[0]:4.0, bnd1[1]:3.0, bnd1[2]:5.0, bnd1[3]:4.0,
bnd1[4]:6.0, bnd1[5]:4.0, bnd1[6]:5.0, bnd1[7]:1.0)$
(%i4) /* Vertices of boundary #2: {(5,1), (3,0), (1,1)} */
( bnd2: make_array(flonum,6),
bnd2[0]:5.0, bnd2[1]:1.0, bnd2[2]:3.0,
bnd2[3]:0.0, bnd2[4]:1.0, bnd2[5]:1.0 )$
(%i5) /* Vertices of boundary #3: {(1,1), (4,3)} */
( bnd3: make_array(flonum,4),
bnd3[0]:1.0, bnd3[1]:1.0, bnd3[2]:4.0, bnd3[3]:3.0)$
(%i6) /* Vertices of boundary #4: {(4,3), (5,1)} */
( bnd4: make_array(flonum,4),
bnd4[0]:4.0, bnd4[1]:3.0, bnd4[2]:5.0, bnd4[3]:1.0)$
(%i7) /* Pack all together in boundaries_array */
( boundaries_array: make_array(any,5),
boundaries_array[0]: bnd0, boundaries_array[1]: bnd1,
boundaries_array[2]: bnd2, boundaries_array[3]: bnd3,
boundaries_array[4]: bnd4 )$
(%i8) draw2d(geomap([0,1,2,3,4]))$
Auxiliary package worldmap sets global variable boundaries_array to real world boundaries in (longitude, latitude) coordinates. These data are in the public domain and come from http://www-cger.nies.go.jp/grid-e/gridtxt/grid19.html. Package worldmap defines also boundaries for countries, continents and coastlines as lists with the necessary components of boundaries_array (see file share/draw/worldmap.mac for more information). Package draw does not automatically load worldmap.
(%i1) load(draw)$
(%i2) load(worldmap)$
(%i3) c1: gr2d(geomap(Canada,United_States,
Mexico,Cuba))$
(%i4) c2: gr2d(geomap(Africa))$
(%i5) c3: gr2d(geomap(Oceania,China,Japan))$
(%i6) c4: gr2d(geomap(France,Portugal,Spain,
Morocco,Western_Sahara))$
(%i7) draw(columns = 2,
c1,c2,c3,c4)$
Package worldmap is also useful for plotting countries as polygons. In this case, graphic object geomap is no longer necessary and the polygon object is used instead. Since lists are now used and not arrays, maps rendering will be slower. See also make_poly_country and make_poly_continent to understand the following code.
(%i1) load(draw)$ (%i2) load(worldmap)$ (%i3) mymap: append( [color = white], /* borders are white */ [fill_color = red], make_poly_country(Bolivia), [fill_color = cyan], make_poly_country(Paraguay), [fill_color = green], make_poly_country(Colombia), [fill_color = blue], make_poly_country(Chile), [fill_color = "#23ab0f"], make_poly_country(Brazil), [fill_color = goldenrod], make_poly_country(Argentina), [fill_color = "midnight-blue"], make_poly_country(Uruguay))$ (%i4) apply(draw2d, mymap)$
3D
geomap (numlist) projects map boundaries on the sphere of radius 1 centered at (0,0,0). It is possible to change the sphere or the projection type by using geomap (numlist,3Dprojection).
Available 3D projections:
[spherical_projection,x,y,z,r]: projects map boundaries on the sphere of radius r centered at (x,y,z).
(%i1) load(draw)$
(%i2) load(worldmap)$
(%i3) draw3d(geomap(Australia), /* default projection */
geomap(Australia,
[spherical_projection,2,2,2,3]))$
[cylindrical_projection,x,y,z,r,rc]: re-projects spherical map boundaries on the cylinder of radius rc and axis passing through the poles of the globe of radius r centered at (x,y,z).
(%i1) load(draw)$
(%i2) load(worldmap)$
(%i3) draw3d(geomap([America_coastlines,Eurasia_coastlines],
[cylindrical_projection,2,2,2,3,4]))$
[conic_projection,x,y,z,r,alpha]: re-projects spherical map boundaries on the cones of angle alpha, with axis passing through the poles of the globe of radius r centered at (x,y,z). Both the northern and southern cones are tangent to sphere.
(%i1) load(draw)$
(%i2) load(worldmap)$
(%i3) draw3d(geomap(World_coastlines,
[conic_projection,0,0,0,1,90]))$
See also http://www.telefonica.net/web2/biomates/maxima/gpdraw/geomap for more elaborated examples.
Draws parametric surfaces in 3D.
3D
parametric_surface (xfun,yfun,zfun,par1,par1min,par1max,par2,par2min,par2max) plots parametric surface [xfun,yfun,zfun], with parameter par1 taking values from par1min to par1max and parameter par2 taking values from par2min to par2max.
This object is affected by the following graphic options: xu_grid, yv_grid, line_type, key and color.
Example:
(%i1) load(draw)$
(%i2) draw3d(title = "Sea shell",
xu_grid = 100,
yv_grid = 25,
rot_vertical = 100,
rot_horizontal = 20,
surface_hide = true,
parametric_surface(0.5*u*cos(u)*(cos(v)+1),
0.5*u*sin(u)*(cos(v)+1),
u*sin(v) - ((u+3)/8*%pi)^2 - 20,
u, 0, 13*%pi, v, -%pi, %pi) )$