Scatter plots can be made using the Maxima plugin. I didn't respond initially, because the interface has never been tested with 1M points. Yet the backend gnuplot should be able to do that. I just don't know whether there are some limitations in the conversion functions.

The example uses a Maxima Draw3D plot region. You can interactively rotate and resize the plot with the mouse.

Scatter plot_Kr.sm (148 KiB) downloaded 131 time(s).

WOW! Thank you very much mkraska. Amazing.

You are welcome.
If the plot is sufficiently stable, you can remove the restart command.
You also can remove the first occurances of points_joined and points(). I just used them to demonstrate a selection of options.

I think that a limit for stability is 40k points. Very difficult to rotate the graphic, but..it is a limit. A normal behavior I will consider until 5k points (to plot in ~5 s and easily rotate).

Again, thank you, because this will help me achieve my program (interaction volume for concrete design). And rarely I will need more than 5k points (I think 1M points was clearly an unthought exaggeration).

Here, the images:

SMath (40k points):




Mathcad(40k points): (plotting limit of Mathcad)



File:

Scatter plot_Kr-1.sm (152 KiB) downloaded 96 time(s).

Wrote

Very difficult to rotate the graphic

No problem to rotate the graphic ... didn't try 5 k.
All native random in CAS are "uniform"
unless specified [Weibull, Normal, Logistic].
We have those in Smath as utilities.
All modules NUMERIC.
Cheers ... Jean

Wrote

I think that a limit for stability is 40k points. Very difficult to rotate the graphic, but..it is a limit. A normal behavior I will consider until 5k points (to plot in ~5 s and easily rotate).

Again, thank you, because this will help me achieve my program (interaction volume for concrete design). And rarely I will need more than 5k points (I think 1M points was clearly an unthought exaggeration).

Thank you for sharing test results.

There is another option for Maxima based plots in SMath.
You can use the same list of commands as argument list to the function Draw3D(). You can directly put this command into the placeholder of an Image region. This region displays images given by file name. And not really just by chance, the Draw3D() command returns the file name of the generated image. The drawback is that the image is just be scaled upon resizing the region and can't be rotated interactively.

This is sometimes more stable than using the interactive regions.

For further polishing the plot you can basically rely on the official maxima documentation of the draw package. However, not all options are supported by SMath. The german handbook (section 8.1) gives a good overview of what can be done with Maxima and SMath.

Note that pointsize (and possibly other options) don't account for high DPI settings. 0.01 is rarely visible on 4K.

Wrote

No problem to rotate the 5k graphic

24 Quaternions possible rotations ...
export the preferred angular system.
Would nice to add the cube outline.
Martin: what can you do with that in native SS 6179 ?
Cheers ... Jean.

Rotate 3D TREASURY_4 Quaternions MODULO Matrix.sm (45 KiB) downloaded 82 time(s).

On my steam engine: compute/rotate 5k in 19 seconds.

Rotate 3D TREASURY_4 Quaternions MODULO Matrix.sm (50 KiB) downloaded 97 time(s).

Thank you mkraska for the information. I am already learning and having fun with german from your excellent handbook and surely will do my effort to optimize my plot in Maxima.
And Jean thank you for your codes, even if I don't understand that field of quaternions, that seems complex and I realize there are important features like the non-linear solver.

Wrote

I don't understand that field of quaternions

Quaternions rotation is even more important than Euler.
The other one is the 4 parameters rotation.
As given, each Modulo give 24 rotations each.
Add other combinations from alpha/beta !!!!!

Vibrations of a rectangular membrane (animation in3D Plot)


Vibration Restangular3dplot.sm (9 KiB) downloaded 141 time(s).