(maxima.info)Visualization with VTK
55.3 Visualization with VTK
===========================
Function scene creates 3D images and animations using the _Visualization
ToolKit_ (VTK) software. In order to use that function, Xmaxima and VTK
should be installed in your system (including the TCL bindings of VTK,
which in some system might come in a separate package).
-- Function: scene (<objects>, ..., <options>, ...);
Accepts an empty list or a list of several 'objects' and 'options'.
The program launches Xmaxima, which opens an external window
representing the given objects in a 3-dimensional space and
applying the options given. Each object must belong to one of the
following 4 classes: sphere, cube, cylinder or cone (see 'Scene
objects'). Objects are identified by giving their name or by a
list in which the first element is the class name and the following
elements are options for that object.
*Example*. A hexagonal pyramid with a blue background:
(%i1) scene(cone, [background,"#9980e5"])$
By holding down the left button of the mouse while it is moved on
the graphics window, the camera can be rotated showing different
views of the pyramid. The two plot options 'elevation' and
'azimuth' can also be used to change the initial orientation of the
viewing camera. The camera can be moved by holding the middle
mouse button while moving it and holding the right-side mouse
button while moving it up or down will zoom in or out.
Each object option should be a list starting with the option name,
followed by its value. The list of allowed options can be found in
the 'Scene object's options' section.
*Example*. This will show a sphere falling to the ground and
bouncing off without losing any energy. To start or pause the
animation, press the play/pause button.
(%i1) p: makelist ([0,0,2.1- 9.8*t^2/2], t, 0, 0.64, 0.01)$
(%i2) p: append (p, reverse(p))$
(%i3) ball: [sphere, [radius,0.1], [thetaresolution,20],
[phiresolution,20], [position,0,0,2.1], [color,red],
[animate,position,p]]$
(%i4) ground: [cube, [xlength,2], [ylength,2], [zlength,0.2],
[position,0,0,-0.1],[color,violet]]$
(%i5) scene (ball, ground, restart)$
The <restart> option was used to make the animation restart
automatically every time the last point in the position list is
reached. The accepted values for the colors are the same as for
the 'color' option of plot2d.
55.3.1 Scene options
--------------------
-- Scene option: azimuth [azimuth, <angle>]
Default value: '135'
The rotation of the camera on the horizontal (x, y) plane. <angle>
must be a real number; an angle of 0 means that the camera points
in the direction of the y axis and the x axis will appear on the
right.
-- Scene option: background [background, <color>]
Default value: 'black'
The color of the graphics window's background. It accepts color
names or hexadecimal red-green-blue strings (see the 'color' option
of plot2d).
-- Scene option: elevation [elevation, <angle>]
Default value: '30'
The vertical rotation of the camera. The <angle> must be a real
number; an angle of 0 means that the camera points on the
horizontal, and the default angle of 30 means that the camera is
pointing 30 degrees down from the horizontal.
-- Scene option: height [height, <pixels>]
Default value: '500'
The height, in pixels, of the graphics window. <pixels> must be a
positive integer number.
-- Scene option: restart [restart, <value>]
Default value: 'false'
A true value means that animations will restart automatically when
the end of the list is reached. Writing just "restart" is
equivalent to [restart, <true>].
-- Scene option: tstep [tstep, <time>]
Default value: '10'
The amount of time, in mili-seconds, between iterations among
consecutive animation frames. <time> must be a real number.
-- Scene option: width [width, <pixels>]
Default value: '500'
The width, in pixels, of the graphics window. <pixels> must be a
positive integer number.
-- Scene option: windowname [windowtitle, <name>]
Default value: '.scene'
<name> must be a string that can be used as the name of the Tk
window created by Xmaxima for the 'scene' graphics. The default
value '.scene' implies that a new top level window will be created.
-- Scene option: windowtitle [windowtitle, <name>]
Default value: 'Xmaxima: scene'
<name> must be a string that will be written in the title of the
window created by 'scene'.
55.3.2 Scene objects
--------------------
-- Scene object: cone [cone, <options>]
Creates a regular pyramid with height equal to 1 and a hexagonal
base with vertices 0.5 units away from the axis. Options 'height'
and 'radius' can be used to change those defaults and option
'resolution' can be used to change the number of edges of the base;
higher values will make it look like a cone. By default, the axis
will be along the x axis, the middle point of the axis will be at
the origin and the vertex on the positive side of the x axis; use
options 'orientation' and 'center' to change those defaults.
*Example*. This shows a pyramid that starts rotating around the z
axis when the play button is pressed.
(%i1) scene([cone, [orientation,0,30,0], [tstep,100],
[animate,orientation,makelist([0,30,i],i,5,360,5)]], restart)$
-- Scene object: cube [cube, <options>]
A cube with edges of 1 unit and faces parallel to the xy, xz and yz
planes. The lengths of the three edges can be changed with options
'xlength', 'ylength' and 'zlength', turning it into a rectangular
box and the faces can be rotated with option 'orientation'.
-- Scene object: cylinder [cylinder, <options>]
Creates a regular prism with height equal to 1 and a hexagonal base
with vertices 0.5 units away from the axis. Options 'height' and
'radius' can be used to change those defaults and option
'resolution' can be used to change the number of edges of the base;
higher values will make it look like a cylinder. The default
height can be changed with the option 'height'. By default, the
axis will be along the x axis and the middle point of the axis will
be at the origin; use options 'orientation' and 'center' to change
those defaults.
-- Scene object: sphere [sphere, <options>]
A sphere with default radius of 0.5 units and center at the origin.
55.3.3 Scene object's options
-----------------------------
-- Object option: animation [animation, <property>, <positions>]
<property> should be one of the following 4 object's properties:
'origin', 'scale', 'position' or 'orientation' and <positions>
should be a list of points. When the play button is pressed, the
object property will be changed sequentially through all the values
in the list, at intervals of time given by the option 'tstep'. The
rewind button can be used to point at the start of the sequence
making the animation restart after the play button is pressed
again.
See also 'track'.
-- Object option: capping [capping, <number>]
Default value: '1'
In a cone or a cylinder, it defines whether the base (or bases)
will be shown. A value of 1 for <number> makes the base visible
and a value of 0 makes it invisible.
-- Object option: center [center, <point>]
Default value: '[0, 0, 0]'
The coordinates of the object's geometric center, with respect to
its 'position'. <point> can be a list with 3 real numbers, or 3
real numbers separated by commas. In a cylinder, cone or cube it
will be at half its height and in a sphere at its center.
-- Object option: color [color, <colorname>]
Default value: 'white'
The color of the object. It accepts color names or hexadecimal
red-green-blue strings (see the 'color' option of plot2d).
-- Object option: endphi [endphi, <angle>]
Default value: '180'
In a sphere phi is the angle on the vertical plane that passes
through the z axis, measured from the positive part of the z axis.
<angle> must be a number between 0 and 180 that sets the final
value of phi at which the surface will end. A value smaller than
180 will eliminate a part of the sphere's surface.
See also 'startphi' and 'phiresolution'.
-- Object option: endtheta [endtheta, <angle>]
Default value: '360'
In a sphere theta is the angle on the horizontal plane (longitude),
measured from the positive part of the x axis. <angle> must be a
number between 0 and 360 that sets the final value of theta at
which the surface will end. A value smaller than 360 will
eliminate a part of the sphere's surface.
See also 'starttheta' and 'thetaresolution'.
-- Object option: height [height, <value>]
Default value: '1'
<value> must be a positive number which sets the height of a cone
or a cylinder.
-- Object option: linewidth [linewidth, <value>]
Default value: '1'
The width of the lines, when option 'wireframe' is used. <value>
must be a positive number.
-- Object option: opacity [opacity, <value>]
Default value: '1'
<value> must be a number between 0 and 1. The lower the number,
the more transparent the object will become. The default value of
1 means a completely opaque object.
-- Object option: orientation [orientation, <angles>]
Default value: '[0, 0, 0]'
Three angles by which the object will be rotated with respect to
the three axis. <angles> can be a list with 3 real numbers, or 3
real numbers separated by commas. *Example*: '[0, 0, 90]' rotates
the x axis of the object to the y axis of the reference frame.
-- Object option: origin [origin, <point>]
Default value: '[0, 0, 0]'
The coordinates of the object's origin, with respect to which its
other dimensions are defined. <point> can be a list with 3 real
numbers, or 3 real numbers separated by commas.
-- Object option: phiresolution [phiresolution, <num>]
Default value: ''
The number of sub-intervals into which the phi angle interval from
'startphi' to 'endphi' will be divided. <num> must be a positive
integer.
See also 'startphi' and 'endphi'.
-- Object option: points [points]
Only the vertices of the triangulation used to render the surface
will be shown. *Example*: '[sphere, [points]]'
See also 'surface' and 'wireframe'.
-- Object option: pointsize [pointsize, <value>]
Default value: '1'
The size of the points, when option 'points' is used. <value> must
be a positive number.
-- Object option: position [position, <point>]
Default value: '[0, 0, 0]'
The coordinates of the object's position. <point> can be a list
with 3 real numbers, or 3 real numbers separated by commas.
-- Object option: radius [radius, <value>]
Default value: '0.5'
The radius or a sphere or the distance from the axis to the base's
vertices in a cylinder or a cone. <value> must be a positive
number.
-- Object option: resolution [resolution, <number>]
Default value: '6'
<number> must be a integer greater than 2 that sets the number of
edges in the base of a cone or a cylinder.
-- Object option: scale [scale, <factors>]
Default value: '[1, 1, 1]'
Three numbers by which the object will be scaled with respect to
the three axis. <factors> can be a list with 3 real numbers, or 3
real numbers separated by commas. *Example*: '[2, 0.5, 1]'
enlarges the object to twice its size in the x direction, reduces
the dimensions in the y direction to half and leaves the z
dimensions unchanged.
-- Object option: startphi [startphi, <angle>]
Default value: '0'
In a sphere phi is the angle on the vertical plane that passes
through the z axis, measured from the positive part of the z axis.
<angle> must be a number between 0 and 180 that sets the initial
value of phi at which the surface will start. A value bigger than
0 will eliminate a part of the sphere's surface.
See also 'endphi' and 'phiresolution'.
-- Object option: starttheta [starttheta, <angle>]
Default value: '0'
In a sphere theta is the angle on the horizontal plane (longitude),
measured from the positive part of the x axis. <angle> must be a
number between 0 and 360 that sets the initial value of theta at
which the surface will start. A value bigger than 0 will eliminate
a part of the sphere's surface.
See also 'endtheta' and 'thetaresolution'.
-- Object option: surface [surface]
The surfaces of the object will be rendered and the lines and
points of the triangulation used to build the surface will not be
shown. This is the default behavior, which can be changed using
either the option 'points' or 'wireframe'.
-- Object option: thetaresolution [thetaresolution, <num>]
Default value: ''
The number of sub-intervals into which the theta angle interval
from 'starttheta' to 'endtheta' will be divided. <num> must be a
positive integer.
See also 'starttheta' and 'endtheta'.
-- Object option: track [track, <positions>]
<positions> should be a list of points. When the play button is
pressed, the object position will be changed sequentially through
all the points in the list, at intervals of time given by the
option 'tstep', leaving behind a track of the object's trajectory.
The rewind button can be used to point at the start of the sequence
making the animation restart after the play button is pressed
again.
*Example*. This will show the trajectory of a ball thrown with
speed of 5 m/s, at an angle of 45 degrees, when the air resistance
can be neglected:
(%i1) p: makelist ([0,4*t,4*t- 9.8*t^2/2], t, 0, 0.82, 0.01)$
(%i2) ball: [sphere, [radius,0.1], [color,red], [track,p]]$
(%i3) ground: [cube, [xlength,2], [ylength,4], [zlength,0.2],
[position,0,1.5,-0.2],[color,green]]$
(%i4) scene (ball, ground)$
See also 'animation'.
-- Object option: xlength [xlength, <length>]
Default value: '1'
The height of a cube in the x direction. <length> must be a
positive number. See also 'ylength' and 'zlength'.
-- Object option: ylength [ylength, <length>]
Default value: '1'
The height of a cube in the y direction. <length> must be a
positive number. See also 'xlength' and 'zlength'.
-- Object option: zlength [zlength, <length>]
Default value: '1'
The height of a cube in z the direction. <length> must be a
positive number. See also 'xlength' and 'ylength'.
-- Object option: wireframe [wireframe]
Only the edges of the triangulation used to render the surface will
be shown. *Example*: '[cube, [wireframe]]'
See also 'surface' and 'points'.
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