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42.1 Introduction to draw | ||
42.2 Functions and Variables for draw | ||
42.3 Functions and Variables for pictures | ||
42.4 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://riotorto.users.sourceforge.net/gnuplot
You need Gnuplot 4.2 or newer to run this program.
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Function gr2d
builds an object describing a 2D scene. Arguments are
graphic options, graphic objects, or lists containing both graphic
options and 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:
bars
,
ellipse
,
explicit
,
image
,
implicit
,
label
,
parametric
,
points
,
polar
,
polygon
,
quadrilateral
,
rectangle
,
triangle
,
vector
, and
geomap
(this one defined in package worldmap
).
See also draw
and draw2d
.
To make use of this object, write first load(draw)
.
Function gr3d
builds an object describing a 3d scene. Arguments are
graphic options, graphic objects, or lists containing both graphic
options and 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:
cylindrical
,
elevation_grid
,
explicit
,
implicit
,
label
,
mesh
,
parametric
,
parametric_surface
,
points
,
quadrilateral
,
spherical
,
triangle
,
tube
,
vector
, and
geomap
(this one defined in package worldmap
).
See also draw
and draw3d
.
To make use of this object, write first load(draw)
.
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Plots a series of scenes; its arguments are gr2d
and/or gr3d
objects, together with some options, or lists of scenes and options.
By default, the scenes are put together in one column.
Function draw
accepts the following global options: terminal
,
columns
, dimensions
, file_name
and delay
.
Functions draw2d
and draw3d
are short cuts to be used
when only one scene is required, in two or three dimensions, respectively.
See also gr2d
and gr3d
.
To make use of this function, write first load(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)$
The two draw sentences are equivalent:
(%i1) load(draw)$ (%i2) draw(gr3d(explicit(x^2+y^2,x,-1,1,y,-1,1))); (%o2) [gr3d(explicit)] (%i3) draw3d(explicit(x^2+y^2,x,-1,1,y,-1,1)); (%o3) [gr3d(explicit)]
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)]
See also gr2d
, gr3d
, draw2d
and draw3d
.
This function is a short cut for
draw(gr2d(options, ..., graphic_object, ...))
.
It can be used to plot a unique scene in 2d.
To make use of this function, write first load(draw)
.
See also draw
and gr2d
.
This function is a short cut for
draw(gr3d(options, ..., graphic_object, ...))
.
It can be used to plot a unique scene in 3d.
To make use of this function, write first load(draw)
.
See also draw
and gr3d
.
Saves the current plot into a file. Accepted graphics options are:
terminal
, dimensions
, file_name
and
background_color
.
Example:
(%i1) load(draw)$ (%i2) /* screen plot */ draw(gr3d(explicit(x^2+y^2,x,-1,1,y,-1,1)))$ (%i3) /* same plot in eps format */ draw_file(terminal = eps, dimensions = [5,5]) $
This function enables Maxima to work in one-window multiplot mode with terminal
term; accepted arguments for this function are screen
,
wxt
, aquaterm
and none
.
When multiplot mode is enabled, each call to draw
sends a new plot to the
same window, without erasing the previous ones. To disable the multiplot mode,
write multiplot_mode(none)
.
When multiplot mode is enabled, global option terminal
is blocked and you
have to disable this working mode before changing to another terminal.
This feature does not work in Windows platforms.
Example:
(%i1) load(draw)$ (%i2) set_draw_defaults( xrange = [-1,1], yrange = [-1,1], grid = true, title = "Step by step plot" )$ (%i3) multiplot_mode(screen)$ (%i4) draw2d(color=blue, explicit(x^2,x,-1,1))$ (%i5) draw2d(color=red, explicit(x^3,x,-1,1))$ (%i6) draw2d(color=brown, explicit(x^4,x,-1,1))$ (%i7) multiplot_mode(none)$
Sets user graphics options. This function is useful for plotting a sequence of graphics with common graphics options. Calling this function without arguments removes user defaults.
Example:
(%i1) load(draw)$ (%i2) set_draw_defaults( xrange = [-10,10], yrange = [-2, 2], color = blue, grid = true)$ (%i3) /* plot with user defaults */ draw2d(explicit(((1+x)**2/(1+x*x))-1,x,-10,10))$ (%i4) set_draw_defaults()$ (%i5) /* plot with standard defaults */ draw2d(explicit(((1+x)**2/(1+x*x))-1,x,-10,10))$
To make use of this function, write first load(draw)
.
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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: 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: 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_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_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: white
Sets the background color for terminals gif
, png
, jpg
,
and gif
. Default background color is white.
This option das not work with terminals epslatex
and epslatex_standalone
.
See also color
.
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: auto
If cbrange
is auto
, the range for the values which are
colored when enhanced3d
is not false
is computed
automatically. Values outside of the color range use color of the
nearest extreme.
When enhanced3d
or colorbox
is false
, option
cbrange
has no effect.
If the user wants a specific interval for the colored values, it must
be given as a Maxima list, as in cbrange=[-2, 3]
.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$ (%i2) draw3d ( enhanced3d = true, color = green, cbrange = [-3,10], explicit(x^2+y^2, x,-2,2,y,-2,2)) $
See also enhanced3d
, colorbox
and cbtics
.
Default value: auto
This graphic option controls the way tic marks are drawn on the colorbox
when option enhanced3d
is not false
.
When enhanced3d
or colorbox
is false
, option cbtics
has no effect.
See xtics
for a complete description.
Example :
(%i1) load(draw)$ (%i2) draw3d ( enhanced3d = true, color = green, cbtics = {["High",10],["Medium",05],["Low",0]}, cbrange = [0, 10], explicit(x^2+y^2, x,-2,2,y,-2,2)) $
See also enhanced3d
, colorbox
and cbrange
.
Default value: blue
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 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, explicit(1.5 + x^2,x,-1,1), color = "#23ab0f", label(["This is a label",0,1.2]) )$
See also fill_color
.
Default value: true
If colorbox
is true
, a color scale without label is drawn
together with image
2D objects, or coloured 3d objects. If
colorbox
is false
, no color scale is shown. If colorbox
is a string, a color scale with label is drawn.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
Color scale and images.
(%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))$
Color scale and 3D coloured object.
(%i1) load(draw)$ (%i2) draw3d( colorbox = "Magnitude", enhanced3d = true, explicit(x^2+y^2,x,-1,1,y,-1,1))$
See also palette
.
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: 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: "data.gnuplot"
This is the name of the file with the numeric data needed by Gnuplot to build the requested plot.
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
.
See example in gnuplot_file_name
.
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
, dimensions
.
Default value: [600,500]
Dimensions of the output terminal. Its value is a list formed by the width and the height. The meaning of the two numbers depends on the terminal you are working with.
With terminals gif
, animated_gif
, png
, jpg
,
svg
, screen
, wxt
, and aquaterm
,
the integers represent the number of points in each direction. If they
are not intergers, they are rounded.
With terminals eps
, eps_color
, pdf
, and
pdfcairo
, both numbers represent hundredths of cm, which
means that, by default, pictures in these formats are 6 cm in
width and 5 cm in height.
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:
Option dimensions
applied to file output and to wxt canvas.
(%i1) load(draw)$ (%i2) draw2d( dimensions = [300,300], terminal = 'png, explicit(x^4,x,-1,1)) $ (%i3) draw2d( dimensions = [300,300], terminal = 'wxt, explicit(x^4,x,-1,1)) $
Option dimensions
applied to eps output.
We want an eps file with A4 portrait dimensions.
(%i1) load(draw)$ (%i2) A4portrait: 100*[21, 29.7]$ (%i3) draw3d( dimensions = A4portrait, terminal = 'eps, explicit(x^2-y^2,x,-2,2,y,-2,2)) $
Default value: true
When true
, functions to be drawn are considered as complex functions
whose real part value should be plotted; when false
, nothing will be
plotted when the function does not give a real value.
This option affects objects explicit
and parametric
in 2D and 3D,
and parametric_surface
.
Example:
Option draw_realpart
affects objects explicit
and
parametric
.
(%i1) load(draw)$ (%i2) draw2d( draw_realpart = false, explicit(sqrt(x^2 - 4*x) - x, x, -1, 5), color = red, draw_realpart = true, parametric(x,sqrt(x^2 - 4*x) - x + 1, x, -1, 5) );
Default value: none
If enhanced3d
is none
, surfaces are not colored in 3D plots. In
order to get a colored surface, a list must be assigned to option
enhanced3d
, where the first element is an expression and the rest are
the names of the variables or parameters used in that expression. A list such
[f(x,y,z), x, y, z]
means that point [x,y,z]
of the surface is
assigned number f(x,y,z)
, which will be colored according to the actual
palette
. For those 3D graphic objects defined in terms of parameters, it
is possible to define the color number in terms of the parameters, as in
[f(u), u]
, as in objects parametric
and tube
, or
[f(u,v), u, v]
, as in object parametric_surface
. While all 3D
objects admit the model based on absolute coordinates,
[f(x,y,z), x, y, z]
, only two of them, namely explicit
and
elevation_grid
, accept also models defined on the [x,y]
coordinates, [f(x,y), x, y]
. 3D graphic object implicit
accepts
only the [f(x,y,z), x, y, z]
model. Object points
accepts also
the [f(x,y,z), x, y, z]
model, but when points have a chronological
nature, model [f(k), k]
is also valid, being k
an ordering
parameter.
When enhanced3d
is assigned something different to none
, options
color
and surface_hide
are ignored.
The names of the variables defined in the lists may be different to those used in the definitions of the graphic objects.
In order to maintain back compatibility, enhanced3d = false
is
equivalent to enhanced3d = none
, and enhanced3d = true
is
equivalent to enhanced3d = [z, x, y, z]
. If an expression is given to
enhanced3d
, its variables must be the same used in the surface
definition. This is not necessary when using lists.
See option palette
to learn how palettes are specified.
Examples:
explicit
object with coloring defined by the [f(x,y,z), x, y, z]
model.
(%i1) load(draw)$ (%i2) draw3d( enhanced3d = [x-z/10,x,y,z], palette = gray, explicit(20*exp(-x^2-y^2)-10,x,-3,3,y,-3,3))$
explicit
object with coloring defined by the [f(x,y), x, y]
model.
The names of the variables defined in the lists may be different to those used
in the definitions of the graphic objects; in this case, r
corresponds
to x
, and s
to y
.
(%i1) load(draw)$ (%i2) draw3d( enhanced3d = [sin(r*s),r,s], explicit(20*exp(-x^2-y^2)-10,x,-3,3,y,-3,3))$
parametric
object with coloring defined by the [f(x,y,z), x, y, z]
model.
(%i1) load(draw)$ (%i2) draw3d( nticks = 100, line_width = 2, enhanced3d = [if y>= 0 then 1 else 0, x, y, z], parametric(sin(u)^2,cos(u),u,u,0,4*%pi)) $
parametric
object with coloring defined by the [f(u), u]
model.
In this case, (u-1)^2
is a shortcut for [(u-1)^2,u]
.
(%i1) load(draw)$ (%i2) draw3d( nticks = 60, line_width = 3, enhanced3d = (u-1)^2, parametric(cos(5*u)^2,sin(7*u),u-2,u,0,2))$
elevation_grid
object with coloring defined by the [f(x,y), x, y]
model.
(%i1) load(draw)$ (%i2) m: apply( matrix, makelist(makelist(cos(i^2/80-k/30),k,1,30),i,1,20)) $ (%i3) draw3d( enhanced3d = [cos(x*y*10),x,y], elevation_grid(m,-1,-1,2,2), xlabel = "x", ylabel = "y");
tube
object with coloring defined by the [f(x,y,z), x, y, z]
model.
(%i1) load(draw)$ (%i2) draw3d( enhanced3d = [cos(x-y),x,y,z], palette = gray, xu_grid = 50, tube(cos(a), a, 0, 1, a, 0, 4*%pi) )$
tube
object with coloring defined by the [f(u), u]
model.
Here, enhanced3d = -a
would be the shortcut for
enhanced3d = [-foo,foo]
.
(%i1) load(draw)$ (%i2) draw3d( tube_extremes = [open, closed], palette = [26,15,-2], enhanced3d = [-foo, foo], tube(a, a, a^2, 1, a, -2, 2) )$
implicit
and points
objects with coloring defined by the
[f(x,y,z), x, y, z]
model.
(%i1) load(draw)$ (%i2) draw3d( enhanced3d = [x-y,x,y,z], 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)) $ (%i3) m: makelist([random(1.0),random(1.0),random(1.0)],k,1,2000)$ (%i4) draw3d( point_type = filled_circle, point_size = 2, enhanced3d = [u+v-w,u,v,w], points(m) ) $
When points have a chronological nature, model [f(k), k]
is also valid,
being k
an ordering parameter.
(%i1) load(draw)$ (%i2) m:makelist([random(1.0), random(1.0), random(1.0)],k,1,5)$ (%i3) draw3d( enhanced3d = [sin(j), j], point_size = 3, point_type = filled_circle, points_joined = true, points(m)) $
Default value: y
Depending on its value, which can be x
, y
, or xy
,
graphic object errors
will draw points with horizontal, vertical,
or both, error bars. When error_type=boxes
, boxes will be drawn
instead of crosses.
See also errors
.
Default value: "maxima_out"
This is the name of the file where terminals png
, jpg
, gif
,
eps
, eps_color
, pdf
, pdfcairo
and svg
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
, dimensions
.
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: 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: ""
(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: 10
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: "maxout.gnuplot"
This is the name of the file with the necessary commands to be processed by Gnuplot.
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 = "my_file", gnuplot_file_name = "my_commands_for_gnuplot", data_file_name = "my_data_for_gnuplot", terminal = png, explicit(x^2,x,-1,1)) $
See also data_file_name
.
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: 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: 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: 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: [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: ""
(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: 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: 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: 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: false
If logcb
is true
, the tics in the colorbox will be drawn in the
logarithmic scale.
When enhanced3d
or colorbox
is false
, option logcb
has no effect.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$ (%i2) draw3d ( enhanced3d = true, color = green, logcb = true, logz = true, palette = [-15,24,-9], explicit(exp(x^2-y^2), x,-2,2,y,-2,2)) $
See also enhanced3d
, colorbox
and cbrange
.
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: 29
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: color
palette
indicates how to map gray levels onto color components. It works
together with option enhanced3d
in 3D graphics, who associates every
point of a surfaces to a real number or gray level. It also works with gray
images. With palette
, levels are transformed into colors.
There are two ways for defining these transformations.
First, palette
can be 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.
Second, palette
can be a user defined lookup table. In this case,
the format for building a lookup table of length n
is
palette = [color_1, color_2, ..., color_n]
, where color_i
is
a well formed color (see option color
), such that
color_1
is assigned to the lowest gray level and color_n
to the
highest. The rest of colors are interpolated.
Since this is a global graphics option, its position in the scene description does not matter.
Examples:
It works together with option enhanced3d
in 3D graphics.
(%i1) load(draw)$ (%i2) draw3d( enhanced3d = [z-x+2*y,x,y,z], palette = [32, -8, 17], explicit(20*exp(-x^2-y^2)-10,x,-3,3,y,-3,3))$
It also works with gray images.
(%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))$
palette
can be a user defined lookup table.
In this example, low values of x
are colored
in red, and higher values in yellow.
(%i1) load(draw)$ (%i2) draw3d( palette = [red, blue, yellow], enhanced3d = x, explicit(x^2+y^2,x,-1,1,y,-1,1)) $
See also colorbox
and enhanced3d
.
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: none
When proportional_axes
is equal to xy
or xyz
,
a 2D or 3D scene will be drawn with axes proportional to their relative
lengths.
Since this is a global graphics option, its position in the scene description does not matter.
This option works with Gnuplot version 4.2.6 or greater.
Examples:
Single 2D plot.
(%i1) load(draw)$ (%i2) draw2d( ellipse(0,0,1,1,0,360), transparent=true, color = blue, line_width = 4, ellipse(0,0,2,1/2,0,360), proportional_axes = xy) $
Multiplot.
(%i1) load(draw)$ (%i2) draw( terminal = wxt, gr2d(proportional_axes = xy, explicit(x^2,x,0,1)), gr2d(explicit(x^2,x,0,1), xrange = [0,1], yrange = [0,2], proportional_axes=xy), gr2d(explicit(x^2,x,0,1)))$
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: screen
Selects the terminal to be used by Gnuplot; possible values are:
screen
(default), png
, pngcairo
, jpg
, eps
,
eps_color
, pdf
, pdfcairo
, gif
, animated_gif
,
wxt
, svg
, and aquaterm
.
Terminals screen
, wxt
and aquaterm
can be also defined as
a list with two elements: the name of the terminal itself and a non negative
integer number. In this form, multiple windows can be opened at the same time,
each with its corresponding number. This feature does not work in Windows
platforms.
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
.
N.B. pdfcairo requires Gnuplot 4.3 or newer.
pdf
requires Gnuplot to be compiled with the option --enable-pdf
and libpdf must be installed. The pdf library is available from:
http://www.pdflib.com/en/download/pdflib-family/pdflib-lite/
Examples:
(%i1) load(draw)$ (%i2) /* screen terminal (default) */ draw2d(explicit(x^2,x,-1,1))$ (%i3) /* png file */ draw2d(terminal = 'png, explicit(x^2,x,-1,1))$ (%i4) /* jpg file */ draw2d(terminal = 'jpg, dimensions = [300,300], explicit(x^2,x,-1,1))$ (%i5) /* eps file */ draw2d(file_name = "myfile", explicit(x^2,x,-1,1), terminal = 'eps)$ (%i6) /* pdf file */ draw2d(file_name = "mypdf", dimensions = 100*[12.0,8.0], explicit(x^2,x,-1,1), terminal = 'pdf)$ (%i7) /* wxwidgets window */ draw2d(explicit(x^2,x,-1,1), terminal = 'wxt)$
Multiple windows.
(%i1) load(draw)$ (%i2) draw2d(explicit(x^5,x,-2,2), terminal=[screen, 3])$ (%i3) draw2d(explicit(x^2,x,-2,2), terminal=[screen, 0])$
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
, dimensions
and delay
.
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: none
If transform
is none
, the space is not transformed and
graphic objects are drawn as defined. When a space transformation is
desired, a list must be assigned to option transform
. In case of
a 2D scene, the list takes the form [f1(x,y), f2(x,y), x, y]
.
In case of a 3D scene, the list is of the form
[f1(x,y,z), f2(x,y,z), f3(x,y,z), x, y, z]
.
The names of the variables defined in the lists may be different to those used in the definitions of the graphic objects.
Examples:
Rotation in 2D.
(%i1) load(draw)$ (%i2) th : %pi / 4$ (%i3) draw2d( color = "#e245f0", proportional_axes = 'xy, line_width = 8, triangle([3,2],[7,2],[5,5]), border = false, fill_color = yellow, transform = [cos(th)*x - sin(th)*y, sin(th)*x + cos(th)*y, x, y], triangle([3,2],[7,2],[5,5]) )$
Translation in 3D.
(%i1) load(draw)$ (%i2) draw3d( color = "#a02c00", explicit(20*exp(-x^2-y^2)-10,x,-3,3,y,-3,3), transform = [x+10,y+10,z+10,x,y,z], color = blue, explicit(20*exp(-x^2-y^2)-10,x,-3,3,y,-3,3) )$
Default value: false
If transparent
is false
, 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: [open, open]
A list with two possible elements, open
and closed
,
indicating whether the extremes of a graphic object tube
remain open
or must be closed. By default, both extremes are left open.
Example:
(%i1) load(draw)$ (%i2) draw3d( tube_extremes = [open, closed], tube(0, 0, a, 1, a, 0, 8) )$
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: ""
(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: [60,30]
A pair of angles, measured in degrees, indicating the view direction in a 3D scene. The first angle is the vertical rotation around the x axis, in the range [0, 180]. The second one is the horizontal rotation around the z axis, in the range [0, 360].
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$ (%i2) draw3d(view = [170, 360], explicit(sin(x^2+y^2),x,-2,2,y,-2,2) )$
Default value: false
Indicates whether 3D surfaces in enhanced3d
mode show the grid joinning
the points or not.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$ (%i2) draw3d( enhanced3d = [sin(x),x,y], wired_surface = true, explicit(x^2+y^2,x,-1,1,y,-1,1)) $
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. It is also used by graphic
object region
.
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: "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 xaxis_secondary
is true
, function values can be plotted with
respect to the second x axis, which will be drawn on top of the scene.
Note that this is a local graphics option which only affects to 2d plots.
Example:
(%i1) load(draw)$ (%i2) draw2d( key = "Bottom x-axis", explicit(x+1,x,1,2), color = red, key = "Above x-axis", xtics_secondary = true, xaxis_secondary = true, explicit(x^2,x,-1,1)) $
See also xrange_secondary
, xtics_secondary
,
xtics_rotate_secondary
, xtics_axis_secondary
and
xaxis_secondary
.
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: 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: ""
(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: 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 xrange_secondary
is auto
, the range for the second x
axis is computed automatically.
If the user wants a specific interval for the second x axis, it must be
given as a Maxima list, as in xrange_secondary=[-2, 3]
.
Since this is a global graphics option, its position in the scene description does not matter.
See also xrange
, yrange
, zrange
and
yrange_secondary
.
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: 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 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 xtics_rotate_secondary
is true
, tic marks on the secondary
x axis are rotated 90 degrees.
Since this is a global graphics option, its position in the scene description does not matter.
Default value: auto
This graphic option controls the way tic marks are drawn on the second x axis.
See xtics
for a complete description.
Default value: false
If xtics_secondary_axis
is true
, tic marks and their labels are
plotted just along the secondary 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: 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: ""
(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: 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: 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. It is also used by graphic
object region
.
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: "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 yaxis_secondary
is true
, function values can be plotted with
respect to the second y axis, which will be drawn on the right side of
the scene.
Note that this is a local graphics option which only affects to 2d plots.
Example:
(%i1) load(draw)$ (%i2) draw2d( explicit(sin(x),x,0,10), yaxis_secondary = true, ytics_secondary = true, color = blue, explicit(100*sin(x+0.1)+2,x,0,10));
See also yrange_secondary
, ytics_secondary
,
ytics_rotate_secondary
and ytics_axis_secondary
.
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: 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: ""
(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: 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
, yrange_secondary
and zrange
.
Default value: auto
If yrange_secondary
is auto
, the range for the second y
axis is computed automatically.
If the user wants a specific interval for the second y axis, it must be
given as a Maxima list, as in yrange_secondary=[-2, 3]
.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$ (%i2) draw2d( explicit(sin(x),x,0,10), yaxis_secondary = true, ytics_secondary = true, yrange = [-3, 3], yrange_secondary = [-20, 20], color = blue, explicit(100*sin(x+0.1)+2,x,0,10)) $
See also xrange
, yrange
and zrange
.
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: 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 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 ytics_rotate_secondary
is true
, tic marks on the secondary
y axis are rotated 90 degrees.
Since this is a global graphics option, its position in the scene description does not matter.
Default value: auto
This graphic option controls the way tic marks are drawn on the second y axis.
See xtics
for a complete description.
Default value: false
If ytics_secondary_axis
is true
, tic marks and their labels are
plotted just along the secondary 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: 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: 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.
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: "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: 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: 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: ""
(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
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: 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 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 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.
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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 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
, wired_surface
,
enhanced3d
and color
.
Example:
(%i1) load(draw)$ (%i2) draw3d(cylindrical(1,z,-2,2,az,0,2*%pi))$
Draws matrix mat in 3D space. z values are taken from mat, the abscissas range from x0 to x0 + width and ordinates from y0 to y0 + height. Element a(1,1) is projected on point (x0,y0+height), a(1,n) on (x0+width,y0+height), a(m,1) on (x0,y0), and a(m,n) on (x0+width,y0).
This object is affected by the following graphic options: line_type
,
line_width
, key
, wired_surface
, enhanced3d
,
and color
.
In older versions of Maxima, elevation_grid
was called mesh
.
See also mesh
.
Example:
(%i1) load(draw)$ (%i2) m: apply( matrix, makelist(makelist(random(10.0),k,1,30),i,1,20)) $ (%i3) draw3d( color = blue, elevation_grid(m,0,0,3,2), xlabel = "x", ylabel = "y", surface_hide = 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, starting at angle
ang1 with an amplitude equal 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] )$
Draws points with error bars, horizontally, vertically or both, depending on the
value of option error_type
.
2D
If error_type = x
, arguments to errors
must be of the form
[x, y, xdelta]
or [x, y, xlow, xhigh]
. If error_type = y
,
arguments must be of the form [x, y, ydelta]
or [x, y, ylow, yhigh]
.
If error_type = xy
or error_type = boxes
, arguments to errors
must be of the form [x, y, xdelta, ydelta]
or
[x, y, xlow, xhigh, ylow, yhigh]
.
See also error_type
.
This object is affected by the following graphic options: error_type
,
points_joined
, line_width
, key
, line_type
,
color
, fill_density
, xaxis_secondary
, and
yaxis_secondary
.
Option fill_density
is only relevant when error_type=boxes
.
Examples:
Horizontal error bars.
(%i1) load(draw)$ (%i2) draw2d( error_type = y, errors([[1,2,1], [3,5,3], [10,3,1], [17,6,2]]))$
Vertical and horizontal error bars.
(%i1) load(draw)$ (%i2) draw2d( error_type = xy, points_joined = true, color = blue, errors([[1,2,1,2], [3,5,2,1], [10,3,1,1], [17,6,1/2,2]]));
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
, draw_realpart
, 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 the explicit function fcn, with
the variable var1 taking values from minval1 to maxval1 and
the variable var2 taking values from minval2 to maxval2.
This object is affected by the following graphic options:
draw_realpart
, xu_grid
, yv_grid
, line_type
,
line_width
, key
, wired_surface
, enhanced3d
, 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.
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
.
http://www.telefonica.net/web2/biomates/maxima/gpdraw/image contains more elaborated examples.
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
,
wired_surface
, enhanced3d
, 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);
Writes labels in 2D and 3D.
Colored labels work only with Gnuplot 4.3. This is a known bug in package
draw
.
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 a quadrangular mesh in 3D.
3D
Argument row_i is a list of n 3D points of the form
[[x_i1,y_i1,z_i1], ...,[x_in,y_in,z_in]]
, and all rows are
of equal length. All these points define an arbitrary surface in 3D and
in some sense it's a generalization of the elevation_grid
object.
This object is affected by the following graphic options: line_type
,
line_width
, color
, key
, wired_surface
,
enhanced3d
, and transform
.
Examples:
A simple example.
(%i1) load(draw)$ (%i2) draw3d( mesh([[1,1,3], [7,3,1],[12,-2,4],[15,0,5]], [[2,7,8], [4,3,1],[10,5,8], [12,7,1]], [[-2,11,10],[6,9,5],[6,15,1], [20,15,2]])) $
Plotting a triangle in 3D.
(%i1) load(draw)$ (%i2) draw3d( line_width = 2, mesh([[1,0,0],[0,1,0]], [[0,0,1],[0,0,1]])) $
Two quadrilaterals.
(%i1) load(draw)$ (%i2) draw3d( surface_hide = true, line_width = 3, color = red, mesh([[0,0,0], [0,1,0]], [[2,0,2], [2,2,2]]), color = blue, mesh([[0,0,2], [0,1,2]], [[2,0,4], [2,2,4]])) $
Draws parametric functions in 2D and 3D.
This object is affected by the following graphic options: nticks
,
line_width
, line_type
, key
, color
and
enhanced3d
.
2D
parametric(xfun, yfun, par, parmin, parmax)
plots the parametric function [xfun, yfun]
, with the
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
The command parametric(xfun, yfun, zfun, par,
parmin, parmax)
plots the parametric curve [xfun,
yfun, zfun]
, with the 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" )$
Draws parametric surfaces in 3D.
3D
parametric_surface(xfun, yfun, zfun, par1,
par1min, par1max, par2,
plots the parametric surface
par2min, par2max)[xfun, yfun, zfun]
, with
the parameter par1 taking values from par1min to par1max and
the parameter par2 taking values from par2min to par2max.
This object is affected by the following graphic options:
draw_realpart
, xu_grid
, yv_grid
, line_type
,
line_width
, key
, wired_surface
, enhanced3d
, and
color
.
Example:
(%i1) load(draw)$ (%i2) draw3d(title = "Sea shell", xu_grid = 100, yv_grid = 25, view = [100,20], 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) )$
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
. In 3D mode, it is also affected by
enhanced3d
.
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.
If 1d_y_array is a 1D lisp array of numbers,
points(1d_y_array)
plots them setting abscissas to consecutive
positive integers. points(1d_x_array, 1d_y_array)
plots points with their coordinates taken from the two arrays passed as
arguments. If 2d_xy_array is a 2D array with two columns, or with two
rows, points(2d_xy_array)
plots the corresponding points on the
plane.
Examples:
Two types of arguments for points
, a list of pairs and two lists
of separate coordinates.
(%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]))$
Drawing impulses.
(%i1) load(draw)$ (%i2) draw2d( points_joined = impulses, line_width = 2, color = red, points(makelist([random(20),random(50)],k,1,10)))$
Array with ordinates.
(%i1) load(draw)$ (%i2) a: make_array (flonum, 100) $ (%i3) for i:0 thru 99 do a[i]: random(1.0) $ (%i4) draw2d(points(a)) $
Two arrays with separate coordinates.
(%i1) load(draw)$ (%i2) x: make_array (flonum, 100) $ (%i3) y: make_array (fixnum, 100) $ (%i4) for i:0 thru 99 do ( x[i]: float(i/100), y[i]: random(10) ) $ (%i5) draw2d(points(x, y)) $
A two-column 2D array.
(%i1) load(draw)$ (%i2) xy: make_array(flonum, 100, 2) $ (%i3) for i:0 thru 99 do ( xy[i, 0]: float(i/100), xy[i, 1]: random(10) ) $ (%i4) draw2d(points(xy)) $
Drawing an array filled with function read_array
.
(%i1) load(draw)$ (%i2) a: make_array(flonum,100) $ (%i3) read_array (file_search ("pidigits.data"), a) $ (%i4) draw2d(points(a)) $
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.
When arguments are lisp arrays, points(1d_x_array, 1d_y_array,
1d_z_array)
takes coordinates from the three 1D arrays. If
2d_xyz_array is a 2D array with three columns, or with three rows,
points(2d_xyz_array)
plots the corresponding 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))) )$
Unidimensional arrays,
(%i1) load(draw)$ (%i2) x: make_array (fixnum, 10) $ (%i3) y: make_array (fixnum, 10) $ (%i4) z: make_array (fixnum, 10) $ (%i5) for i:0 thru 9 do ( x[i]: random(10), y[i]: random(10), z[i]: random(10) ) $ (%i6) draw3d(points(x,y,z)) $
Bidimensional colored array,
(%i1) load(draw)$ (%i2) xyz: make_array(fixnum, 10, 3) $ (%i3) for i:0 thru 9 do ( xyz[i, 0]: random(10), xyz[i, 1]: random(10), xyz[i, 2]: random(10) ) $ (%i4) draw3d( enhanced3d = true, points_joined = true, points(xyz)) $
Color numbers explicitly specified by the user.
(%i1) load(draw)$ (%i2) pts: makelist([t,t^2,cos(t)], t, 0, 15)$ (%i3) col_num: makelist(k, k, 1, length(pts))$ (%i4) draw3d( enhanced3d = ['part(col_num,k),k], point_size = 3, point_type = filled_circle, points(pts))$
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 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 a quadrilateral.
2D
quadrilateral([x1, y1], [x2, y2], [x3,
y3], [x4, y4])
draws a quadrilateral with vertices
[x1, y1]
, [x2, y2]
, [x3,
y3]
, and [x4, y4]
.
This object is affected by the following graphic options:
transparent
, fill_color
, border
, line_width
,
key
, xaxis_secondary
, yaxis_secondary
, line_type
,
transform
and color
.
Example:
(%i1) load(draw)$ (%i2) draw2d( quadrilateral([1,1],[2,2],[3,-1],[2,-2]))$
3D
quadrilateral ([x1, y1, z1], [x2, y2,
z2], [x3, y3, z3], [x4, y4, z4])
draws a quadrilateral with vertices [x1, y1, z1]
,
[x2, y2, z2]
, [x3, y3, z3]
,
and [x4, y4, z4]
.
This object is affected by the following graphic options: line_type
,
line_width
, color
, key
, enhanced3d
, and
transform
.
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] )$
Plots a region on the plane defined by inequalities.
2D
expr is an expression formed by inequalities and boolean operators
and
, or
, and not
. The region is bounded by the rectangle
defined by [minval1, maxval1] and [minval2,
maxval2].
This object is affected by the following graphic options: fill_color
,
key
, x_voxel
, and y_voxel
.
Example:
(%i1) load(draw)$ (%i2) draw2d( x_voxel = 30, y_voxel = 30, region(x^2+y^2<1 and x^2+y^2 > 1/2, x, -1.5, 1.5, y, -1.5, 1.5));
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
, wired_surface
,
enhanced3d
, and color
.
Example:
(%i1) load(draw)$ (%i2) draw3d(spherical(1,a,0,2*%pi,z,0,%pi))$
Draws a triangle.
2D
triangle([x1, y1], [x2, y2], [x3,
y3])
draws a triangle with vertices [x1, y1]
,
[x2, y2]
, and [x3,y3]
.
This object is affected by the following graphic options:
transparent
, fill_color
, border
, line_width
,
key
, xaxis_secondary
, yaxis_secondary
, line_type
,
transform
, and color
.
Example:
(%i1) load(draw)$ (%i2) draw2d( triangle([1,1],[2,2],[3,-1]))$
3D
triangle([x1, y1, z1], [x2, y2, z2],
[x3, y3, z3])
draws a triangle with vertices [x1,
y1, z1]
, [x2, y2, z2]
, and
[x3, y3, z3]
.
This object is affected by the following graphic options: line_type
,
line_width
, color
, key
, enhanced3d
, and
transform
.
Draws a tube in 3D with varying diameter.
3D
[xfun,yfun,zfun]
is the parametric curve with parameter
p taking values from pmin to pmax. Circles of radius
rfun are placed with their centers on the parametric curve and
perpendicular to it.
This object is affected by the following graphic options: xu_grid
,
yv_grid
, line_type
, line_width
, key
,
wired_surface
, enhanced3d
, color
, and tube_extremes
.
Example:
(%i1) load(draw)$ (%i2) draw3d( enhanced3d = true, xu_grid = 50, tube(cos(a), a, 0, cos(a/10)^2, a, 0, 4*%pi) )$
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)) )$
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Returns pixel from picture. Coordinates x and y range from 0 to
width-1
and height-1
, respectively.
Returns a levels picture object. make_level_picture(data)
builds the picture object from matrix data.
make_level_picture(data, width, height)
builds the
object from a list of numbers; in this case, both the width and the
height must be given.
The returned picture object contains the following four parts:
level
Example:
Level picture from matrix.
(%i1) load(draw)$ (%i2) make_level_picture(matrix([3,2,5],[7,-9,3000])); (%o2) picture(level, 3, 2, {Array: #(3 2 5 7 0 255)})
Level picture from numeric list.
(%i1) load(draw)$ (%i2) make_level_picture([-2,0,54,%pi],2,2); (%o2) picture(level, 2, 2, {Array: #(0 0 54 3)})
Returns an rgb-coloured picture object. All three arguments must be levels picture; with red, green and blue levels.
The returned picture object contains the following four parts:
rgb
Example:
(%i1) load(draw)$ (%i2) red: make_level_picture(matrix([3,2],[7,260])); (%o2) picture(level, 2, 2, {Array: #(3 2 7 255)}) (%i3) green: make_level_picture(matrix([54,23],[73,-9])); (%o3) picture(level, 2, 2, {Array: #(54 23 73 0)}) (%i4) blue: make_level_picture(matrix([123,82],[45,32.5698])); (%o4) picture(level, 2, 2, {Array: #(123 82 45 33)}) (%i5) make_rgb_picture(red,green,blue); (%o5) picture(rgb, 2, 2, {Array: #(3 54 123 2 23 82 7 73 45 255 0 33)})
Returns the negative of a (level or rgb) picture.
Returns true
in case of equal pictures, and false
otherwise.
Returns true
if the argument is a well formed image,
and false
otherwise.
Reads a file in xpm and returns a picture object.
Transforms an rgb picture into a level one by averaging the red, green and blue channels.
If argument color is red
, green
or blue
,
function take_channel
returns the corresponding color channel of
picture im.
Example:
(%i1) load(draw)$ (%i2) red: make_level_picture(matrix([3,2],[7,260])); (%o2) picture(level, 2, 2, {Array: #(3 2 7 255)}) (%i3) green: make_level_picture(matrix([54,23],[73,-9])); (%o3) picture(level, 2, 2, {Array: #(54 23 73 0)}) (%i4) blue: make_level_picture(matrix([123,82],[45,32.5698])); (%o4) picture(level, 2, 2, {Array: #(123 82 45 33)}) (%i5) make_rgb_picture(red,green,blue); (%o5) picture(rgb, 2, 2, {Array: #(3 54 123 2 23 82 7 73 45 255 0 33)}) (%i6) take_channel(%,'green); /* simple quote!!! */ (%o6) picture(level, 2, 2, {Array: #(54 23 73 0)})
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This package automatically loads package draw
.
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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 a list of polygonal segments (boundaries), labeled by
its numbers (boundaries_array
coordinates). This is of great
help when building new geographical entities.
Example:
Map of Europe labeling borders with their component number in
boundaries_array
.
(%i1) load(worldmap)$ (%i2) european_borders: region_boundaries(-31.81,74.92,49.84,32.06)$ (%i3) numbered_boundaries(european_borders)$
Makes the necessary polygons to draw a colored continent or a list of countries.
Example:
(%i1) load(worldmap)$ (%i2) /* A continent */ make_poly_continent(Africa)$ (%i3) apply(draw2d, %)$ (%i4) /* A list of countries */ make_poly_continent([Germany,Denmark,Poland])$ (%i5) apply(draw2d, %)$
Makes the necessary polygons to draw a colored country. If islands exist, one country can be defined with more than just one polygon.
Example:
(%i1) load(worldmap)$ (%i2) make_poly_country(India)$ (%i3) apply(draw2d, %)$
Returns a polygon
object from boundary indices. Argument
nlist is a list of components of boundaries_array
.
Example:
Bhutan is defined by boundary numbers 171, 173
and 1143, so that make_polygon([171,173,1143])
appends arrays of coordinates boundaries_array[171]
,
boundaries_array[173]
and boundaries_array[1143]
and
returns a polygon
object suited to be plotted by
draw
. To avoid an error message, arrays must be
compatible in the sense that any two consecutive
arrays have two coordinates in the extremes in common. In this
example, the two first components of boundaries_array[171]
are
equal to the last two coordinates of boundaries_array[173]
, and
the two first of boundaries_array[173]
are equal to the two first
of boundaries_array[1143]
; in conclussion, boundary numbers
171, 173 and 1143 (in this order) are compatible and the colored
polygon can be drawn.
(%i1) load(worldmap)$ (%i2) Bhutan; (%o2) [[171, 173, 1143]] (%i3) boundaries_array[171]; (%o3) {Array: #(88.750549 27.14727 88.806351 27.25305 88.901367 27.282221 88.917877 27.321039)} (%i4) boundaries_array[173]; (%o4) {Array: #(91.659554 27.76511 91.6008 27.66666 91.598022 27.62499 91.631348 27.536381 91.765533 27.45694 91.775253 27.4161 92.007751 27.471939 92.11441 27.28583 92.015259 27.168051 92.015533 27.08083 92.083313 27.02277 92.112183 26.920271 92.069977 26.86194 91.997192 26.85194 91.915253 26.893881 91.916924 26.85416 91.8358 26.863331 91.712479 26.799999 91.542191 26.80444 91.492188 26.87472 91.418854 26.873329 91.371353 26.800831 91.307457 26.778049 90.682457 26.77417 90.392197 26.903601 90.344131 26.894159 90.143044 26.75333 89.98996 26.73583 89.841919 26.70138 89.618301 26.72694 89.636093 26.771111 89.360786 26.859989 89.22081 26.81472 89.110237 26.829161 88.921631 26.98777 88.873016 26.95499 88.867737 27.080549 88.843307 27.108601 88.750549 27.14727)} (%i5) boundaries_array[1143]; (%o5) {Array: #(91.659554 27.76511 91.666924 27.88888 91.65831 27.94805 91.338028 28.05249 91.314972 28.096661 91.108856 27.971109 91.015808 27.97777 90.896927 28.05055 90.382462 28.07972 90.396088 28.23555 90.366074 28.257771 89.996353 28.32333 89.83165 28.24888 89.58609 28.139999 89.35997 27.87166 89.225517 27.795 89.125793 27.56749 88.971077 27.47361 88.917877 27.321039)} (%i6) Bhutan_polygon: make_polygon([171,173,1143])$ (%i7) draw2d(Bhutan_polygon)$
Detects polygonal segments of global variable boundaries_array
fully contained in the rectangle with vertices (x1, y1) -upper left-
and (x2, y2) -bottom right-.
Example:
Returns segment numbers for plotting southern Italy.
(%i1) load(worldmap)$ (%i2) region_boundaries(10.4,41.5,20.7,35.4); (%o2) [1846, 1863, 1864, 1881, 1888, 1894] (%i3) draw2d(geomap(%))$
Detects polygonal segments of global variable boundaries_array
containing at least one vertex in the rectangle defined by vertices (x1,
y1) -upper left- and (x2, y2) -bottom right-.
Example:
(%i1) load(worldmap)$ (%i2) region_boundaries_plus(10.4,41.5,20.7,35.4); (%o2) [1060, 1062, 1076, 1835, 1839, 1844, 1846, 1858, 1861, 1863, 1864, 1871, 1881, 1888, 1894, 1897] (%i3) draw2d(geomap(%))$
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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(worldmap)$ (%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]))$
The auxiliary package worldmap
sets the global variable
boundaries_array
to the real world boundaries in coordinates. The data
is in the public domain and come from
http://www-cger.nies.go.jp/grid-e/gridtxt/grid19.html.
The 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). The package worldmap
automatically loads
package worldmap
.
(%i1) load(worldmap)$ (%i2) c1: gr2d(geomap(Canada,United_States, Mexico,Cuba))$ (%i3) c2: gr2d(geomap(Africa))$ (%i4) c3: gr2d(geomap(Oceania,China,Japan))$ (%i5) c4: gr2d(geomap(France,Portugal,Spain, Morocco,Western_Sahara))$ (%i6) 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(worldmap)$ (%i2) 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))$ (%i3) 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(worldmap)$ (%i2) 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(worldmap)$ (%i2) 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(worldmap)$ (%i2) 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.
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