plot::PointList3d

Finite lists of 3D points

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Syntax

plot::PointList3d(pts, <a = amin .. amax>, options)
plot::PointList3d(M3d, <a = amin .. amax>, options)

Description

plot::PointList3d holds lists of points in 3D.

This is a container for a large finite number of points. It lets you avoid constructing large numbers of objects of type plot::Point3d, for two reasons. First, the point types have non-negligible overhead and constructing and plotting a large number of them (say, five thousand) takes more time than plotting the same number of points in a single container object. Second, having five thousand points in the object browser takes a significant amount of memory and is not as lucid as having a single point list.

The attribute Points3d is displayed in the inspector in the user interface only for short lists.

plot::PointList3d internally uses lists for storing the points. It is therefore not recommended to add a large number of points one-by-one.

If you specify the color of one point, you must specify the colors of all other points in the list. See Example 2.

Attributes

Attribute	Purpose	Default Value
AffectViewingBox	influence of objects on the ViewingBox of a scene	TRUE
Color	the main color	RGB::MidnightBlue
Frames	the number of frames in an animation	50
Legend	makes a legend entry
LegendText	short explanatory text for legend
LegendEntry	add this object to the legend?	FALSE
Name	the name of a plot object (for browser and legend)
ParameterEnd	end value of the animation parameter
ParameterName	name of the animation parameter
ParameterBegin	initial value of the animation parameter
ParameterRange	range of the animation parameter
Points3d	list of 3D points
PointSize	the size of points	1.5
PointColor	the color of points	RGB::MidnightBlue
PointStyle	the presentation style of points	FilledCircles
TimeEnd	end time of the animation	10.0
TimeBegin	start time of the animation	0.0
TimeRange	the real time span of an animation	0.0 .. 10.0
Title	object title
TitleFont	font of object titles	[" sans-serif ", 11]
TitlePosition	position of object titles
TitleAlignment	horizontal alignment of titles w.r.t. their coordinates	Center
TitlePositionX	position of object titles, x component
TitlePositionY	position of object titles, y component
TitlePositionZ	position of object titles, z component
Visible	visibility	TRUE
VisibleAfter	object visible after this time value
VisibleBefore	object visible until this time value
VisibleFromTo	object visible during this time range
VisibleAfterEnd	object visible after its animation time ended?	TRUE
VisibleBeforeBegin	object visible before its animation time starts?	TRUE

Examples

Example 1

plot::PointList3d provides a basic form of scatter plot:

plot(plot::PointList3d([[1,1,1], [1,2,2], [1,3,2], [1,3,4],
                        [2,1,1], [2,2,3], [2,3.5, 4]],
                       PointSize=5))

We can use this, for example, to get a visual test of random number generators:

r := frandom(0):
plot(plot::PointList3d([[r(), r(), r()] $ i=1..10000])):

r := random(10^10)*1e-10:
plot(plot::PointList3d([[r(), r(), r()] $ i=1..10000])):

frandom and random fill the cube nicely, without noticeable patterns. The following generator, however, should probably not be used:

randseed := 12345:
r := proc()
     begin
       randseed := (randseed * 17 + 8) mod 10^10:
       1e-10 * randseed;
     end:
plot(plot::PointList3d([[r(), r(), r()] $ i=1..10000])):

Example 2

plot::PointList3d lets you specify the colors of the points. For example, the following list contains three points. When you plot this list, the first point appears in red, and the second point appears in green, and the third point appears in blue:

plot(plot::PointList3d([[1,1,1,RGB::Red],
                        [2,2,2,RGB::Green],
                        [1,3,3,RGB::Blue]],
                        PointSize=5))

If you specify the color of one point, you must also specify the colors of all other points in the list:

plot(plot::PointList3d([[1,1,1,RGB::Red],
                        [2,2,2],
                        [1,3,3]],
                        PointSize=5))

Error: Attribute 'Points3d' in the 'PointList3d' object must be a list of lists of three expressions and an optional color value. [plot]

Parameters

pts	A list of points. A point must not be of type plot::Point3d. Each point must be a list of three expressions (the coordinates) and an optional RGB or RGBa color. The lists specifying the points and the colors must all have the same length. pts is equivalent to the attributes Points3d.
M3d	An array or a matrix with three columns. Each row provides the coordinates of one point. M3d is equivalent to the attribute Points3d.
a	Animation parameter, specified as a = amin..amax, where amin is the initial parameter value, and amax is the final parameter value.