I don't get a few of your words exactly. But, I understood as follows: (If wrong, let me know)

1. You have a position (x,y,z) and a corresponding data (say temperature) for each (x,y,z).

2. You want to plot this in a graph

Soln:

There are plenty of visualization software available both open source and commercial. You might have seen weather or rain fall radar maps in TVs or website, where they plot exactly the same way you want.

I personally would suggest paraview to plot your data. https://www.paraview.org/

But, there are many more, gnuplot, you can see a list over here

https://en.wikipedia.org/wiki/List_of_information_graphics_software

Dear Panchatcharam Mariappan,

Thank you VERY much for trying to help. In fact (not to put you off in any way or to end this conversation), I have been pointed to Octave (MATLAB emulator) as a platform used by a mathematician who already has put in a few days of work on my behalf ... but who is away for a week or two, as I try to proceed. If you were to open the file I pointed to, you would see that it has Temperature as the "Z" axis already.

To make our lives easier, I am posting file 20180430 0635 N Vectors in x,y,z = Refractivity,Wavelength,Temperature space MEDres .jpg to the discussion, hoping that it will display completely, without requiring you to download it.

I am too far away from the math I comprehended in 1965 to make it easy for me to communicate in these regards, but the idea is to be able to graph vectors normal to the plane of the triangles formed at chosen intersections of X,Y,Z axes (the variable microscope-stage conditions during my counts). The four columns in my case are (units and scalings aside):

Immersion-Liquid Refractivity, Wavelength, Temperature, and dependent vector % (various estimates based upon my counts).

So far, my other helper has put the fourth dimension (%) on the Z axis, which is not helpful. Instead, the % vector casts the problem into what I now call W,X,Y,Z space.

My primary reference for this (also referenced in the image shared here) is pp. 459-462 of

Fisher, R. C., and A. D. Ziebur, 1964. Calculus and Analytic Geometry. Prentice-Hall, Inc., Englewood Cliffs, N. J., 766 pp.

Although I never used it, I had been thinking that "A Programming Language" (APL) might be the perfect software for this exercise. Maybe the open-source Octave is better. Maybe one of the programs you have pointed me to would be better. I'm not well-enough informed to judge the best platform, and it may be that my math friend will toss off the solution as soon as he recognizes the gist of the problem.

Anyway, I hope that this helps you to assess the situation more completely. I am gratified to have captured your interest and to have you engaged in helping me. Thank you!

All best wishes! :-) -Steve-

Grr! ;-) I don't know how to remove previous efforts to put make whole image show up without actually having to download it. All I can do is to try again: Trying file

20180430 0635 N Vectors in x,y,z = Refractivity,Wavelength,Temperature space xLOres .jpg

Does that work? :-)

Sorry to have to share these difficulties, Friends. -s-

I give up on that image-sharing problem. I'll try getting some help from site administrators. -s-

Presumably there is one independent variable and 3 dependent ones. So you will need to prepare a series of graphs where two variables are plotted against the independent one. That is to say, to prepare a series of 3-dimensional pictures that contain the independent variable as the base-line and the two dependent ones as a carpet floating in the field.

Dear Stephen A. Langford

Mathematics can explore and investigate the n-dimensional manifolds. You can study the inspiring examples about the Klein bottle and the tesseract in dimension four, and this may help you to show how images in dimension four work. On the other hand, level surfaces (we consider one of the parameter as constant) are the best solution to reflect the hidden graph of some 4- dimensional manifold into the 3- dimensional images where our brain can imagine the figure completely. See for example

https://youtu.be/j-ixGKZlLVc

Regards

Thanks Issam Kaddoura. I am currently playing with Golden Software Voxler®4 (Golden Software, Golden, Colorado). You might enjoy becoming acquainted with its free Demo version:

https://www.goldensoftware.com/products/voxler/trial

You might also enjoy browsing some of my postings to Research Gate:

https://tinyurl.com/to8tsbt

With all best wishes, -Steve- [email protected]

Thanks

Nice job

I should add that the world of Voxler® is very new and strange to me. I wonder whether there are any who use it and might be interested in doing some hand holding. I find the learning curve to be quite steep. But I am persistent. :-)

-Steve- [email protected] … https://tinyurl.com/to8tsbt

Стивен Артур возможно Вам поможет моё понимание построения 3Д сферы Пуанкаре - Перельмана, как оболочки 4Д шара Программа построения этих тел в кватернионных и октавных представлениях изложены и проиллюстрированы в монографии и целом ряде статей.

Dear Gennady Semenovich Melnikov! :-)

Thank God for

https://translate.google.com/#view=home&op=translate&sl=auto&tl=en

which provides me with the following comprehension of your Russian (which our daughter would be able to read, I am proud to add):

"Stephen Arthur maybe my understanding of the construction of the 3D Poincaré - Perelman sphere, as the shells of the 4D sphere, will help you. The program for constructing these bodies in quaternionic and octave representations is presented and illustrated in a monograph and a number of articles."

My plea for help on implementation of the experimental design presented in that graphic has been sporadically ongoing since the Summer of 1965. But it is obviated by my recent purchase of Voxler®4. I spent most of yesterday exploring how to graph it in the full version of Golden Software's Voxler®4, with which you might like to play. The free demo is at: https://www.goldensoftware.com/products/voxler/trial

Yesterday I discovered that using T°C as Z in the XYZC data set yielded a single vector parallel to the X (RI) axis. In other words, Temperature turned out to be a not useful Z axis. Today I have swapped C=% into the Z spot and moved T°C into the C spot, whereupon I am nicely able to map what I interpret to be heat flow in the sample. Please see the two (2) attached files.

That said, I must also say that Voxler®4 has what is for me a rather steep learning curve. I stumble along only somewhat successfully as I learn to move around it, not yet finding some expected features and not yet having truly gained a firm comprehension, all the time, of what I am doing or of how best to interpret results. Much as I would like to have time to delve into your own work, the simple truth is that I don't.

On the other hand, if you would like to see at least my two latest posts,

19. Work Logs, 19 July through 31 July 2020 Present Cross-Hatch Kriging & Other Innovative Modeling Approaches Successfully to Image Even Underlying EM Structure, it Seems. https://tinyurl.com/y3ocmxd6 or https://tinyurl.com/y5gporno

20. Work Logs, 4 August 2020 through 8 August 2020: Explorations via Voxler®4 of EM Structures and Temperature Vectors, as expressed by Gabbro Sample Refractive Index (RI) Displays.

https://tinyurl.com/yydhf2yv or https://tinyurl.com/y6o8rnyn

and maybe would like to browse what is also available at

https://tinyurl.com/to8tsbt

perhaps you could tell me how my work relates to yours, if it does.

I also hope that some people who have gained true competency in the use of Voxler®4 will read this and will be willing privately [[email protected]] to offer me some screen-sharing time to tutor me, while we explore my data in ways I have yet to envision or test.

Thank you again for your kind offer, Gennady Semenovich Melnikov! I sometimes wish that I would not need to sleep, because there is so much that I don't know, that I should know, and that I do not have time or energy enough to learn while also trying to do what needs doing with my own data (publicly available at https://tinyurl.com/v9u4hkf , by the way).

With all best wishes for your continuing successes!

Sincerely, -Steve- [email protected]

я бегло посмотрел на Ваши упражнения с Voxler®4, Вы на правильном пути и не заморачивайте себе голову новыми знаниями.

С уважением Геннадий Семенович.

Thank you for sharing your kind view,

"I have a quick look at your exercises with Voxler®4, you are on the right track and do not bother yourself with new knowledge.

"Best regards, Gennady Semenovich", Gennady Semenovich Melnikov!

Much appreciated.

All best wishes, -Steve- [email protected] ... https://tinyurl.com/to8tsbt

Уважаемый Steve- просмотрите лишь короткую статью

Article © 2015г., Г.С. Мельников, ОАО « ГОИ ИМ. С.И. Вавилова», г. С...

из неё Вы поймёте как в мультимерности строить зависимость от времени.

С уважением Геннадий Семёнович.

Thank you for sharing your kind view.

Gennady Semenovich Melnikov ...

Уважаемый Геннадий: Дано »В статье исследуются принципы построения геометрических моделей пространства-времени: • 4D-модели пространства-времени де Ситтера, Минковского • 3D + 3T модели пространства-времени Роберто Ороса ди Бартини и математически обосновывается справедливость постулат семимерной модели • 3D + 3T + 0 D пространство-время ... Показано, что циклические времена для смежных подпространств, вращающихся объектов Мира и Анти-Мира, являются зеркально-синфазными, т.е. смещены на 180 ° и идут в разные стороны », я должен сказать:

Я не использую XYZC для измерения времени в позиции C. Ненавижу это говорить, но ваше любезное предложение не имеет ничего общего с моей научной работой. Я работаю с длиной волны, понимая, что она похожа на частоту, поэтому они оба связаны со временем. И я понимаю, что RI = c / v; и это время там задействовано, но эти единицы сокращаются. Но это все, что мне нужно знать о времени, по крайней мере, для настоящих целей.

Но спасибо, что указали мне на свою статью. Хотел бы я тоже выучить русский язык! :-)

С уважением, -Steve-

Thanks for wanting to help, Afraa Ibrahim

All best wishes, -Steve-

I also have a similar problem and it seems I have to develop my own software.

I need to draw a normal 3D space with each x,y,z points containing a Quran word with zoom/pan/tilt (which is available) but then I need to join furthest same-value words together (preferably with links of widths proportional to word length (number of letters).

Details at https://archive.codeplex.com/?p=3dquran

Please email me if you find a solution to your problem [email protected]