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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: false
If xrange
is false
, 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: false
If yrange
is false
, 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: false
If zrange
is false
, 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 yrange
and zrange
.
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
, 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
.
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)$
See also file_name
, pic_width
, and pic_height
.
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
stores a Maxima string with 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
stores a Maxima string with 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
stores a Maxima string with 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
stores a Maxima string with 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: true
If xtics
is true
, tics will be written in the x axis.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$ (%i2) /* No tics in the x-axis */ draw2d(xtics = false, explicit(exp(u),u,-2,2))$
See also ytics
, and ztics
.
Default value: true
If ytics
is true
, tics will be written in the y axis.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$ (%i2) draw2d(ytics = false, explicit(exp(u),u,-2,2), xtics = false)$
See also xtics
, and ztics
.
Default value: true
If ztics
is true
, tics will be written in the z axis.
Since this is a global graphics option, its position in the scene description does not matter.
Example:
(%i1) load(draw)$ (%i2) /* No tics in the z-axis */ draw3d(ztics = false, explicit(sin(x^2+y^2),x,-2,2,y,-2,2) )$
See also xtics
, and ytics
.
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: 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 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
If points_joined
is true
, points are joined by lines.
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
filled_func
indicates whether a function is filled (true
)
or not (false
).
This option affects only the 2d graphic object explicit
.
Example:
(%i1) load(draw)$ (%i2) draw2d(fill_color = red, filled_func = true, explicit(sin(x),x,0,10) )$
See also fill_color
.
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: 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: 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
nticks
is the number of sample points used by the plotting routine.
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
contour_levels
is the number of levels in contour plots.
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: 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.
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
, 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
, 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
, parametric
and
parametric_surface
.
See also the following graphic options: xrange
, yrange
,
zrange
, logx
, logy
, logz
, terminal
,
grid
, title
, xlabel
, ylabel
, zlabel
,
xtics
, ytics
, ztics
, 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.
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]))$
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.
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 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 ligght-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)$
Draws implicit functions in 2D.
2D
implicit(fcn,xvar,xminval,xmaxval,yvar,yminval,ymaxval)
plots the implicit function defined by fcn, with variable xvar taking values
from xminval to xmaxval, and variable yvar taking values
from yminval to ymaxval.
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" )$
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 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.
2D
This function works together with global variable boundaries_array
.
Arguments are numbers or lists 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 (n1,n2,...)
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
and continents 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)$
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) )$
Plots a series of scenes; its arguments are gr2d
and/or gr3d
objects, together with some options. By default, the scenes are put together
in one column.
Function draw
accepts two possible options: terminal
and columns
.
Functions draw2d
and draw3d
are short cuts to be used
when only one scene is required, in two or three dimensions, respectively.
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)$
This function is a short cut for
draw2d(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)
.
This function is a short cut for
draw3d(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)
.
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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 true
if the argument is a well formed image,
and false
otherwise.
Returns true
in case of equal pictures, and false
otherwise.
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
3*width*height
with pixel data ranging
from 0 to 255. Each pixel is represented by three consecutive numbers
(red, green, blue).
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)})
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)})
Returns the negative of a (level
or rgb
) picture.
Transforms an rgb
picture into a level
one by
averaging the red, green and blue channels.
Returns pixel from picture. Coordinates x and y range from 0 to
width-1
and height-1
, respectively.
Reads a file in xpm and returns a picture object.
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Detects polygonal segments of global variable boundaries_array
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(draw)$ (%i2) load(worldmap)$ (%i3) region_boundaries(10.4,41.5,20.7,35.4); (%o3) [1846, 1863, 1864, 1881, 1888, 1894] (%i4) draw2d(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(draw)$ (%i2) load(worldmap)$ (%i3) european_borders: region_boundaries(-31.81,74.92,49.84,32.06)$ (%i4) numbered_boundaries(european_borders)$
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(draw)$ (%i2) load(worldmap)$ (%i3) Bhutan; (%o3) [[171, 173, 1143]] (%i4) boundaries_array[171]; (%o4) {Array: #(88.750549 27.14727 88.806351 27.25305 88.901367 27.282221 88.917877 27.321039)} (%i5) boundaries_array[173]; (%o5) {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)} (%i6) boundaries_array[1143]; (%o6) {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)} (%i7) Bhutan_polygon: make_polygon([171,173,1143])$ (%i8) draw2d(Bhutan_polygon)$
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(draw)$ (%i2) load(worldmap)$ (%i3) make_poly_country(India)$ (%i4) apply(draw2d, %)$
Makes the necessary polygons to draw a colored continent or a list of countries.
Example:
(%i1) load(draw)$ (%i2) load(worldmap)$ (%i3) /* A continent */ make_poly_continent(Africa)$ (%i4) apply(draw2d, %)$ (%i5) /* A list of countries */ make_poly_continent([Germany,Denmark,Poland])$ (%i6) apply(draw2d, %)$
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