Finite lists of 3D points

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.


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


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.


AttributePurposeDefault Value
AffectViewingBoxinfluence of objects on the ViewingBox of a sceneTRUE
Colorthe main colorRGB::MidnightBlue
Framesthe number of frames in an animation50
Legendmakes a legend entry 
LegendTextshort explanatory text for legend 
LegendEntryadd this object to the legend?FALSE
Namethe name of a plot object (for browser and legend) 
ParameterEndend value of the animation parameter 
ParameterNamename of the animation parameter 
ParameterBegininitial value of the animation parameter 
ParameterRangerange of the animation parameter 
Points3dlist of 3D points 
PointSizethe size of points1.5
PointColorthe color of pointsRGB::MidnightBlue
PointStylethe presentation style of pointsFilledCircles
TimeEndend time of the animation10.0
TimeBeginstart time of the animation0.0
TimeRangethe real time span of an animation0.0 .. 10.0
Titleobject title 
TitleFontfont of object titles[" sans-serif ", 11]
TitlePositionposition of object titles 
TitleAlignmenthorizontal alignment of titles w.r.t. their coordinatesCenter
TitlePositionXposition of object titles, x component 
TitlePositionYposition of object titles, y component 
TitlePositionZposition of object titles, z component 
VisibleAfterobject visible after this time value 
VisibleBeforeobject visible until this time value 
VisibleFromToobject visible during this time range 
VisibleAfterEndobject visible after its animation time ended?TRUE
VisibleBeforeBeginobject visible before its animation time starts?TRUE


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]],

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()
       randseed := (randseed * 17 + 8) mod 10^10:
       1e-10 * randseed;
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:


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

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



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.


An array or a matrix with three columns. Each row provides the coordinates of one point.

M3d is equivalent to the attribute Points3d.


Animation parameter, specified as a = amin..amax, where amin is the initial parameter value, and amax is the final parameter value.

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