Make a three.js backend for 3d plotting

[jason]

Usage: show( plot3d, viewer='threejs' ) or plot3d( ..., viewer='threejs')

---

SEE ​https://github.com/mrdoob/three.js/

See the big discussion at ​http://groups.google.com/group/sage-devel/browse_thread/thread/d3e4a24aebc906a2

Some resources:

​http://learningthreejs.com/

​http://aerotwist.com/lab/getting-started-with-three-js/

​http://dev.opera.com/articles/view/porting-3d-graphics-to-the-web-webgl-intro-part-2/

​https://github.com/mrdoob/three.js

​http://sagenb.org/home/pub/4176/ (experiment in sage)

[kcrisman]

Jason, William, can you put whatever code exists on here since public worksheets are disabled? We don't want this just in the cloud.sagemath :-)

[was]

​https://github.com/williamstein/sd48/blob/master/threejs/grout-demo.sagews

[kcrisman]

Just as an update, this is now apparently working in cloud.sagemath.

[was]

Replying to kcrisman:

Just as an update, this is now apparently working in cloud.sagemath.

It sort of works, but it isn't included by default. It will be soon though, so that anybody can at least test out some minimal functionality. I'll post when that happens.

[jason]

Just FYI, there are now three different threejs backends: SMC, the threejs command in the sage cell, and the pythreejs-based backend that works in the sage cell too.

[novoselt]

Jason - what is the status of the last one? Will it be pushed to get "standard" or there is still work to be done there and with your switch nobody is available to steer it?

The first two were definitely lacking features, in particular "things that don't scale with zoom" plus some transparency issues.

[jason]

The transparency issues are not fixed---those are inherent in how three.js draws things, and stem from limitations of webgl (there are experiements overcoming them in webgl, which might be interesting to look at, though; the author of mathbox is looking at them, for example).

I think that anything "pushed to standard" should be supported by SMC and the sage cell. Right now, the pythreejs solution requires an communication framework that is/emulates the ipython comm/widget framework. Something like that would need to be implemented for SMC to get it to work there. I think that would be a great project in itself, though---there is starting to be some good development of interactive things for the IPython notebook, and it would be great to use those things from SMC too.

[kcrisman]

I think that anything "pushed to standard" should be supported by SMC and the sage cell. Right now, the pythreejs solution requires an communication framework that is/emulates the ipython comm/widget framework. Something like that would need to be implemented for SMC to get it to work there. I think that would be a great project in itself, though---there is starting to be some good development of interactive things for the IPython notebook, and it would be great to use those things from SMC too.

But I thought SMC only uses the js plotting - does it also do Jmols too? (You'll notice I still haven't had time to properly try out SMC, and won't for some time).

---

See also #16004 as a related ticket I also haven't had enough time to review properly.

[mbejger]

Replying to jason:

Just FYI, there are now three different threejs backends: SMC, the threejs command in the sage cell, and the pythreejs-based backend that works in the sage cell too.

Thanks :-) I am interested in enhancing the capabilities of SageManifolds? (#14865), which is still under development, so I guess the most natural thing would be to somehow use threejs locally. Probably this question was asked already many times, but what is the current status of threejs in sage notebook (local ipython notebook)?

[kcrisman]

Thanks :-) I am interested in enhancing the capabilities of SageManifolds? (#14865), which is still under development, so I guess the most natural thing would be to somehow use threejs locally. Probably this question was asked already many times, but what is the current status of threejs in sage notebook (local ipython notebook)?

The Sagenb is not really at all an Ipython notebook, though it may have inspired earlier versions thereof. Anyway, the current status is that you can get it to work - see the examples above - but no one has put time into this. Partly because the sagenb is in maintenance mode currently (though it would be nice to have it more actively developed) but also because of the slight backwards functionality loss involved as you see in previous comments.

[paulmasson]

Here's some basic Three.js support for Graphics3d objects. It is modeled on the corresponding function in SageMathCell: simply use threejs() to wrap any combination of points, lines and surfaces. This will save an HTML file with the JavaScript needed to render the scene and open it in a browser.

There are a great many features that can be added in the future, but I first would like to see how much interest there is in this. There have been problems surfacing with Jmol (#20978 for example) and I certainly think it would be preferable to have a native viewer that can be updated more quickly. The HTML format is also more portable than Jmol files, since it only requires a modern browser to run.

This version relies on an external CDN to retrieve the Three.js library, since it does not currently download to the hard drive during the build process. I'll need help on figuring out how to change that at some point, since I'm sure people will want to be able to view saved files offline.

---

Last 10 new commits:

​3d1cd2a	Handle nested lists
​efb3d0a	Handle nested lists
​f70ac3d	Add line plots
​55f12e6	Add point plots
​b4c8414	Adjust centering and camera
​374809a	Rebase to move point bounds off points
​9a42352	Add auto z-aspect
​d560683	Minor rebase
​aa322ad	Add axis labels
​7cedf75	Check for equal bounds

[egourgoulhon]

Wow! I've just tried it and it's very nice! Thank you very much for this enhancement!

A question: is it possible to customize the axes labels (e.g. via the keyword argument axes_labels, as in 2D plots)?

[kcrisman]

A question: is it possible to customize the axes labels (e.g. via the keyword argument axes_labels, as in 2D plots)?

See e.g. ​here - this would be a very good enhancement, though I guess it would have to then depend on the backend.

Can you think of anything it does not do? I seem to recall that there were things jsmol did with shading etc. that three.js couldn't, when this was discussed ~ 5 years ago.

[egourgoulhon]

Replying to kcrisman:

A question: is it possible to customize the axes labels (e.g. via the keyword argument axes_labels, as in 2D plots)?

See e.g. ​here

Yes, set_axes_labels is the (not very satisfactory) workaround I wrote to deal with this when using Jmol ;-)

• this would be a very good enhancement, though I guess it would have to then depend on the backend.

Maybe not: looking at the source code, in line 155 of src/sage/plot/plot3d/threejs.py, there is

addLabel( 'x=' + ( xMid ).toFixed(d).toString(), xMid, b[1].y+offset, a[2]*b[0].z );

It seems easy to replace 'x=' by another string.

Can you think of anything it does not do?

Not at the moment. I'll play with it further.

[egourgoulhon]

PS: Another relevant project is K3D, which was presented at Sage Days 74:

​https://wiki.sagemath.org/K3D-tools

[paulmasson]

Replying to egourgoulhon:

PS: Another relevant project is K3D, which was presented at Sage Days 74:

​https://wiki.sagemath.org/K3D-tools

It's good to know about this project, but I'm aiming for something more general and not focused just on notebooks. Matplotlib lets you create and save image files for 2d plots. I'd like something equivalent for 3d plots, which for Three.js is a self-contained HTML file.

[paulmasson]

Replying to egourgoulhon:

Replying to kcrisman:

• this would be a very good enhancement, though I guess it would have to then depend on the backend.

Maybe not: looking at the source code, in line 155 of src/sage/plot/plot3d/threejs.py, there is

addLabel( 'x=' + ( xMid ).toFixed(d).toString(), xMid, b[1].y+offset, a[2]*b[0].z );

It seems easy to replace 'x=' by another string.

Since this is done in a browswer, and they all understand Unicode now, there won't be issues with missing fonts like in matplotlib. This is an easy customization.

[paulmasson]

Replying to kcrisman:

Can you think of anything it does not do? I seem to recall that there were things jsmol did with shading etc. that three.js couldn't, when this was discussed ~ 5 years ago.

I would find it difficult to believe that current Three.js can't match anything in Jmol. The transparency issue mentioned above can likely be handled with the alphaMap property that appeared in Three.js about the same time as the comment, and if not that way then by a custom shader which isn't difficult to implement.

[paulmasson]

Replying to egourgoulhon:

Wow! I've just tried it and it's very nice! Thank you very much for this enhancement!

A question: is it possible to customize the axes labels (e.g. via the keyword argument axes_labels, as in 2D plots)?

Thanks for trying it out! I'm trying to decide between reading the show() options of the plots fed into threejs() or just have a separate dictionary, but should probably do the latter. That would include options for setting axes labels, setting digits after the decimal in labels, turning off axes labels altogether, turning off the bounding box and setting an explicit aspect ratio in all directions. Let me know what other options would be interesting.

There is already automatic scaling in the z-direction to avoid the tall thin box that appears in the current version on the cell server (and SMC), but that can easily be overridden. I can also easily add face colors to support surfaces with color maps. Lights for the scene are meant to be customizable as well and can stand some additional improvement.

The initial camera position is not yet completely adaptive to the possible variety of input plots, so ideas on that would be welcome.

[novoselt]

We most definitely want this in, so please keep working!!!

Note that we have optional threejs package (SageMathCell is using it) - if we have a functioning viewer we can easily make is standard as it is small and very fast to install.

Interface-wise let's stick to show for the actual showing of stuff and plot/plot3d for producing plots that can be further manipulated. threejs command if it exists at all should do something like set up a low-level threejs scene that can be tweaked as advanced users please. Presumably, it is possible to just pass some HTML/JavaScript code that will be inserted into generated files?

[novoselt]

File-wise: perhaps instead of raw string it is possible to have template_three.js file that will be read/cached by the Python function? Perhaps with template_three.js.html to further wrap it into a standalone page. One of the advantages for development - syntax highlighting of this long template.

[novoselt]

So it seems that at the moment opacity is ignored and line thickness is not taken into account - is it possible to implement these?

Also when I scale the image text grows/shrinks and then "becomes normal again" - is it possible to always keep it the same size throughout the transition?

[novoselt]

What about embedding the resulting plots into web-page, i.e. how easy it is for someone-not-really-knowing-anything to take a plot from Sage and have it running on their web-page? (No using SageMathCell, just having the three.js stuff properly saved/inserted somewhere.)

[paulmasson]

Replying to novoselt:

What about embedding the resulting plots into web-page, i.e. how easy it is for someone-not-really-knowing-anything to take a plot from Sage and have it running on their web-page? (No using SageMathCell, just having the three.js stuff properly saved/inserted somewhere.)

The entire aim is to have a self-contained HTML file with everything, all geometric data and the JavaScript to process it. Then it's simply a matter of adding an iframe to a web page and setting its src attribute to the HTML file. Easy peasy!

[paulmasson]

Replying to novoselt:

So it seems that at the moment opacity is ignored and line thickness is not taken into account - is it possible to implement these?

Opacity should be simple. Line thickness can be included, but will not be consistent across operating systems because of a limitation in Microsoft's implementation of WebGL.

Also when I scale the image text grows/shrinks and then "becomes normal again" - is it possible to always keep it the same size throughout the transition?

Thought I had this figured out. For a plot with the origin at the center it behaves as you expect, but not when the center is displaced. Will definitely work on this.

[novoselt]

Replying to paulmasson:

Line thickness can be included, but will not be consistent across operating systems because of a limitation in Microsoft's implementation of WebGL.

I consider this to be a major flaw, no matter whose fault it is - on the one hand it is nice to use different thicknesses and on the other - single pixel width typically looks bad when used with projectors... Are there any sensible workarounds? Like text seems to be scaled and then scaled back - can it be done with lines too?

[paulmasson]

Replying to novoselt:

We most definitely want this in, so please keep working!!! Interface-wise let's stick to show for the actual showing of stuff and plot/plot3d for producing plots that can be further manipulated. threejs command if it exists at all should do something like set up a low-level threejs scene that can be tweaked as advanced users please.

A scene in Sage is a collection of Graphics3d objects. Three.js, like Jmol/JSmol, is merely a way to render the scene. I don't see the use for command to set up a separate Three.js scene from scratch.

Until this Three.js viewer is integrated into the Rich Output backend, I don't have a way to display the scene without a command other than show, which will default to Jmol/JSmol. That can change later once an initial version is working acceptably. I've spent enough time reading the Rich Output backend to know where to make those changes, and at that point show can then be set to default to a Three.js viewer if desired. For now I need the separate command!

Presumably, it is possible to just pass some HTML/JavaScript code that will be inserted into generated files?

See the next comment for this.

[novoselt]

No problem with having a separate command now, but what I meant is - let's not introduce and then deprecate it in Sage, so using rich output should be done on this ticket as well.

[paulmasson]

Replying to novoselt:

File-wise: perhaps instead of raw string it is possible to have template_three.js file that will be read/cached by the Python function? Perhaps with template_three.js.html to further wrap it into a standalone page. One of the advantages for development - syntax highlighting of this long template.

I can only think of two ways to communicate data from Python to JavaScript at the command line: either with the Python-formatted string I'm using, or by appending data to a URL as a query string and processing it from there. This second way leads to monstrous URLs that can be bookmarked but not saved as stand-alone files. With what I'm doing all of the data is embedded in the HTML file: saving the file saves the entire scene.

On the server you have other options for processing data, but running something like that at the command line seems to me to be massive overkill. If I'm missing something in your comment, please let me know a better way to transfer the data to the browser.

Also, the raw string is not proper JavaScript because all curly brackets are doubled to become literals during Python formatting. Saving that as a separate file would produce parsing errors.

[novoselt]

Sorry I was not clear again: what I meant is take your current template, save it as js file in the same Sage source folder, then in Python code open this file, read it as string, and do the same processing as what you do now. So it will not affect the end result for the user, just, IMHO, makes it easier to maintain this template inside of Sage.

[paulmasson]

Replying to novoselt:

Replying to paulmasson:

Line thickness can be included, but will not be consistent across operating systems because of a limitation in Microsoft's implementation of WebGL.

I consider this to be a major flaw, no matter whose fault it is - on the one hand it is nice to use different thicknesses and on the other - single pixel width typically looks bad when used with projectors... Are there any sensible workarounds? Like text seems to be scaled and then scaled back - can it be done with lines too?

Text is done on an HTML canvas, so that's completely different from WebGL lines. There are workarounds, but I'd have to think about it more and then would process lines the same way for all browsers.

[paulmasson]

Replying to novoselt:

Sorry I was not clear again: what I meant is take your current template, save it as js file in the same Sage source folder, then in Python code open this file, read it as string, and do the same processing as what you do now. So it will not affect the end result for the user, just, IMHO, makes it easier to maintain this template inside of Sage.

When the Python part of this file is integrated with the Rich Output backend, then all that will be left in this file will be the template, so sure. But again, this is not proper JavaScript because of the curly bracket doubling.

[novoselt]

Ah, and that's because you want to use .format(..) with this string. An alternative is to use %s substitution if it makes sense or just regular string replacement, but if you prefer doubling so be it since you are doing the actual work ;-)

[kcrisman]

Just wanted to say this sounds like a great discussion, keep it up! It would be great to have something reliable. Also you may want to check out how this looks/works in the Jupyter notebook as well as sagenb.

[kcrisman]

(I assume it will be fine, just mentioning.)

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​f4b1c03

Move template to separate file

[paulmasson]

Replying to novoselt:

Ah, and that's because you want to use .format(..) with this string. An alternative is to use %s substitution if it makes sense or just regular string replacement, but if you prefer doubling so be it since you are doing the actual work ;-)

Should have thought of string replacement! Template now separate. Much preferable to have proper JavaScript in it.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​df51bde	Update initial camera position
​4f7075d	Fix label scaling

[paulmasson]

Replying to paulmasson:

Replying to novoselt:

Also when I scale the image text grows/shrinks and then "becomes normal again" - is it possible to always keep it the same size throughout the transition?

Thought I had this figured out. For a plot with the origin at the center it behaves as you expect, but not when the center is displaced. Will definitely work on this.

This should be fixed now.

[egourgoulhon]

Replying to paulmasson:

That would include options for setting axes labels, setting digits after the decimal in labels, turning off axes labels altogether, turning off the bounding box and setting an explicit aspect ratio in all directions. Let me know what other options would be interesting.

It would be nice to have some (customizable) ticks along the bounding box, but this is probably somewhat tricky and should be the topic of another ticket.

Besides, what about text3d?

At the moment, when running threejs from the Jupyter notebook, the 3d plot is rendered in another tab of the browser. Could it be embedded in the notebook instead? (maybe this is related to the Rich Output issue).

Thanks again for your work on this!

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​62e7a8b

Integrate with IPython command line

[paulmasson]

Basic integration with the backend for the IPython command line has been added, and the usage has changed accordingly. This was important to understand how options are passed through the backend. Integration with notebooks will be added after basic display options are in place.

[paulmasson]

Replying to egourgoulhon:

Replying to paulmasson:

That would include options for setting axes labels, setting digits after the decimal in labels, turning off axes labels altogether, turning off the bounding box and setting an explicit aspect ratio in all directions. Let me know what other options would be interesting.

It would be nice to have some (customizable) ticks along the bounding box, but this is probably somewhat tricky and should be the topic of another ticket.

Indeed!

Besides, what about text3d?

This object does not have a json_repr and that would be overkill anyway. I can easily add optional text labels like those on the frame, but would need to think about how to automatically extract text3d from other Graphics3d objects.

At the moment, when running threejs from the Jupyter notebook, the 3d plot is rendered in another tab of the browser. Could it be embedded in the notebook instead? (maybe this is related to the Rich Output issue).

It can certainly be embedded, and that is precisely dependent on integration with the Rich Output backend. To be done.

Thanks again for your work on this!

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​a93418a	Implement basic options
​4f2b9f1	Update temporary threejs() command

[paulmasson]

I've now implement several basic display options:

frame (bool) display bounding box or not

aspect_ratio (list) individual aspect multipliers for each axis

axes_labels (list) labels to display. If set to false, all labels are removed.

decimals (integer) decimal points in labels

opacity (float) overall opacity for surfaces. Currently set for the entire scene.

I've also updated the temporary threejs() command so that it has the new options. This command will be maintained until integration with both notebook backends is complete.

[egourgoulhon]

I've tried the display options: they work well, except for aspect_ratio:

threejs(icosahedron(), aspect_ratio=[0.5, 1., 0.8])

returns

TypeError: 0.500000000000000 is not JSON serializable

[egourgoulhon]

May I ask about the status of this? As I understand, except for the aspect_ratio option and the Rich Output backend, this is almost ready. It would be so nice if this could be shipped with Sage 7.5!

[was]

I somehow just looked at this for a few minutes -- take or leave these comments. Feel free to ignore them...

The first thing I see (in ​https://git.sagemath.org/sage.git/tree/src/sage/plot/plot3d/threejs_template.html?id=67930e843d29652f143c67329aaf32be4ab120a8) is:

<script src=http://rawgit.com/mrdoob/three.js/r80/build/three.js></script>
<script src=http://rawgit.com/mrdoob/three.js/r80/examples/js/controls/OrbitControls.js></script>

A concern is that this won't work offline -- 3d graphics will just be completely broken without an external internet connection. Also, this is making 3d graphics display in Sage depend on "some random site" (rawgit.com) which says on their page: "The catch: this is a free service, so there are no uptime or support guarantees."...

This provides absolutely no Jupyter notebook integration at all as far as I can tell. It's just creating a single standalone local website for the image and popping that up in the users browser. If you do something more serious that does try to integrate with Jupyter, you might find it is a lot of work to get Chrome with more than about 10+ 3d plots on the same page.. That was a big problem when I implemented WebGL based 3d graphics for SageMathCloud?, which involved quite a bit of work (involving great care with the renderer, swapping things out with static png's etc.). When you're just trying to get a demo working you don't worry about such scale. However, if you're teaching, you can easily have many plots in one notebook. Anyway, this is one reason that the SMC Javascript is longer and more complicated.

Another question is how much of 3d plot rendering have you actually implemented? For example, I recently added arrowheads to lines to SMC, since I had missed those and you expect them when plotting 3d vector fields. I don't see any code in threejs_template.html for that.

I guess you just only support WebGL, even though three.js can support canvas too.... Maybe that's fine these days, but again supporting both is something I put a lot of work into.

The SMC implementation:

• client side -- ​https://github.com/sagemathinc/smc/blob/master/src/smc-webapp/3d.coffee
• server side -- ​https://github.com/sagemathinc/smc/blob/master/src/smc_sagews/smc_sagews/graphics.py

[kcrisman]

Great comments, especially the offline bit.

[paulmasson]

Replying to was:

A concern is that this won't work offline -- 3d graphics will just be completely broken without an external internet connection.

This is easily fixed by adding a second pair of script tags pointing to a local source. Since Three.js does not currently download during the build process, adding this feature will have to change that and is more appropriate for another ticket.

Also, this is making 3d graphics display in Sage depend on "some random site" (rawgit.com) which says on their page: "The catch: this is a free service, so there are no uptime or support guarantees."...

Rawgit.com is hardly some random site for GitHub people. That being said it's irrelevant where the code is hosted as long as it is available somewhere. The intent is to make the interactive image as portable as a PNG, so it can't depend entirely on one's local installation: an external CDN link is vital.

This provides absolutely no Jupyter notebook integration at all as far as I can tell. It's just creating a single standalone local website for the image and popping that up in the users browser.

The process here of creating 3D images exactly parallels that of 2D plots: a file is generated, saved to disc and displayed in the best possible viewer as determined by the rich output backend. It's not a local website, it's a file that can be saved and used elsewhere as desired, exactly as for static 2D plots.

If you do something more serious that does try to integrate with Jupyter, you might find it is a lot of work to get Chrome with more than about 10+ 3d plots on the same page.. That was a big problem when I implemented WebGL based 3d graphics for SageMathCloud?, which involved quite a bit of work (involving great care with the renderer, swapping things out with static png's etc.).

I'm well aware of the limitations of multiple WebGL contexts in a single web page. The real way to handle this is using scissoring on a single renderer: I wrote an ​example for the Three.js repository to do just that. Since this approach is not immediately modular, the fallback is to manage iframe content as it scrolls into view. While I was figuring out scissoring, a coding friend of mine ​explored that very subject to ​good effect, so we have an available resource for dealing with this issue as well. It's also a topic for another ticket, since it would require modifying notebook behavior. I can't control all of that in the process of creating stand-alone files. The motivation here is to bring Three.js to the command line interface first.

Another question is how much of 3d plot rendering have you actually implemented? For example, I recently added arrowheads to lines to SMC, since I had missed those and you expect them when plotting 3d vector fields. I don't see any code in threejs_template.html for that.

The code will currently render anything that returns a json_repr. This includes the arrow graphics primitive, which appears just fine, but not for example text3d. 3D vector fields don't have arrow heads in Sage 7.4 anyway, so that is something that can be added on another ticket.

I guess you just only support WebGL, even though three.js can support canvas too.... Maybe that's fine these days, but again supporting both is something I put a lot of work into.

This is also easily fixed by testing rendering capabilities, but I'd rather look forward for the initial version.

[paulmasson]

Replying to egourgoulhon:

May I ask about the status of this? As I understand, except for the aspect_ratio option and the Rich Output backend, this is almost ready. It would be so nice if this could be shipped with Sage 7.5!

Eric, there's a bit more work to be done:

1) All numeric input parameters need to be made JSON serializable. This is easy to do.

2) The Three.js Geometry that I used for convenience needs to be replaced with BufferGeometry. This will improve use of available memory and avoid possible browser issues, as well as prepare for stability in notebooks. This is straightforward.

3) The code used for line objects needs to be completely rewritten. There is a hardware driver limitation on Windows machines that prevents rendering of line thickness in WebGL that is not going away soon, and I'm still thinking about the best way around this. Andrey certainly won't approve this ticket without line thickness rendering decently across hardware platforms, and I agree with him on that.

4) Notebook integration needs to be added and tested. Since I am not familiar with the details of notebooks, this may not be straightforward without input from those more familiar. Adding a few Three.js files to a notebook page should be easy, but more than that may require modifying how the notebook dynamically handles iframe content. That might also be better dealt with on a separate ticket.

I've been distracted in the last couple weeks with trying to transpile Sage libraries with Emscripten for use directly in the browser, but since that's more work that I thought it would be I can set it aside for awhile and get back to this!

[egourgoulhon]

Replying to paulmasson:

Thanks for your answers.

3) The code used for line objects needs to be completely rewritten. There is a hardware driver limitation on Windows machines that prevents rendering of line thickness in WebGL that is not going away soon, and I'm still thinking about the best way around this. Andrey certainly won't approve this ticket without line thickness rendering decently across hardware platforms, and I agree with him on that.

I would be on a different tone here: as long as three.js is not Sage's default 3D viewer, I see no reason to defer its use for Linux and MacOS users, simply because Windows is limited. When decision is taken to make three.js the default viewer, it's of course a different matter. So IMHO the Windows line thickness issue could be postponed to another ticket.

I've been distracted in the last couple weeks with trying to transpile Sage libraries with Emscripten for use directly in the browser, but since that's more work that I thought it would be I can set it aside for awhile and get back to this!

Thanks!

[slelievre]

Replying to egourgoulhon:

Replying to paulmasson:

Thanks for your answers.

3) The code used for line objects needs to be completely rewritten. There is a hardware driver limitation on Windows machines that prevents rendering of line thickness in WebGL that is not going away soon, and I'm still thinking about the best way around this. Andrey certainly won't approve this ticket without line thickness rendering decently across hardware platforms, and I agree with him on that.

I would be on a different tone here: as long as three.js is not Sage's default 3D viewer, I see no reason to defer its use for Linux and MacOS users, simply because Windows is limited. When decision is taken to make three.js the default viewer, it's of course a different matter. So IMHO the Windows line thickness issue could be postponed to another ticket.

True, Windows line thickness could be its own ticket, and making three.js the default viewer could be another ticket depending on it.

I've been distracted in the last couple weeks with trying to transpile Sage libraries with Emscripten for use directly in the browser, but since that's more work that I thought it would be I can set it aside for awhile and get back to this!

Thanks!

Excellent. A recent ​Ask Sage question about tick marks on the frame of 3d plots points to the timeliness of this.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​1dd3f80	Fix points background
​0fea750	Fix JSON serialization error

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​53d6dec	Minor edit
​cabe3ee	Add basic Jupyter notebook support
​0e19bfc	Add basic Sage notebook support
​46dcb96	Improvements to labels

[paulmasson]

Turns out the BufferGeometry isn't necessary for getting this working in notebooks. I've added some basic integration for both notebook types parallel to how JSmol is embedded in each.

Caveat: WebGL is limited to 16 active contexts at a time, so while all the data is in the notebooks the figures may not be active until the cell is reevaluated. I have a basic idea of how to fix this in the future, but it would require a modification to the notebooks themselves which would be a separate ticket.

I haven't worked on the line thickness issue yet.

[egourgoulhon]

Thank you for all these improvements! It's nice to have viewer='threejs' among the show options!

There is an issue when plotting the sum of two objects that are themselves sums: only the first object is shown:

plot1 = line([(0,0,0), (0,1,0)]) + line([(0,1,0), (1,0,0)])
plot2 = line([(0,0,1), (0,1,1)]) + line([(0,1,1), (1,0,1)])
show(plot1 + plot2, viewer='threejs')  # only plot1 is shown
show(plot2 + plot1, viewer='threejs')  # only plot2 is shown

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​f51c4cc

Flatten potentially nested Graphics3dGroup

[paulmasson]

Replying to egourgoulhon:

Thank you for all these improvements! It's nice to have viewer='threejs' among the show options!

There is an issue when plotting the sum of two objects that are themselves sums: only the first object is shown:

plot1 = line([(0,0,0), (0,1,0)]) + line([(0,1,0), (1,0,0)])
plot2 = line([(0,0,1), (0,1,1)]) + line([(0,1,1), (1,0,1)])
show(plot1 + plot2, viewer='threejs')  # only plot1 is shown
show(plot2 + plot1, viewer='threejs')  # only plot2 is shown

Good catch! Should be fixed now.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​e978ff8

Remove temporary threejs() command

[paulmasson]

The temporary threejs() command is no longer needed and has been removed.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​5ed849e	Basic documentation for threejs viewer
​4088310	Add option for drawing axes
​1267458	Turn off axes labels with frame

[egourgoulhon]

Thanks for these changes. I've tested the latest version with plots of charts, vector fields and curves on the 2-sphere. Everything works well as you can see on ​this notebook.

Another issue with sums: the option opacity (and maybe other options) is propagated to all objects. For instance in

show(cube() + sphere((2,0,0), opacity=0.2), viewer='threejs') 

the cube is displayed with an opacity of 0.2.

There are also some missing doctests, as revealed by sage -coverage src/sage/plot/plot3d/base.pyx:

Missing doctests:
     * line 344: def _rich_repr_threejs(self, **kwds)

[kcrisman]

The propagation may be related to #10657 though that is about arrays and not sums - but there may be some similar lacking logic.

[egourgoulhon]

Replying to kcrisman:

The propagation may be related to #10657 though that is about arrays and not sums - but there may be some similar lacking logic.

In any case, this is somehow related to the three.js viewer, since neither jmol nor tachyon have this issue.

[paulmasson]

Replying to egourgoulhon:

Another issue with sums: the option opacity (and maybe other options) is propagated to all objects. For instance in

show(cube() + sphere((2,0,0), opacity=0.2), viewer='threejs') 

the cube is displayed with an opacity of 0.2.

Currently the code is setting global values for all optional keywords and this should of course change for opacity and thickness. The behavior you're seeing is because an option set in the _extra_kwds for one graph propagates up to the corresponding dictionary for the group, with the last occurrence of a setting taking precedence over previous settings.

I'd like to keep the option of a global setting for opacity and thickness and extract the settings for each component graph as an override, if that sounds reasonable.

One other question is what do to with the remaining settings, which I'm assuming should be global. Leave the default behavior that the last graph sets them all or try to change the existing behavior for graphics groups?

Also, should aspect_ratio be settable for each graph? That doesn't make much sense to me but would anyone expect that? The code for that would get messy.

[kcrisman]

If you're asking about summing several objects in one graph and them having different aspect ratios, I would definitely say no. I think that somewhere in the 2d code the last explicit aspect ratio is the one used, and this might even be documented. By the way, I'll note that in experimenting just now I couldn't get "last explicit aspect ratio" less than one to be recognized, only in single graphs...

[egourgoulhon]

Replying to kcrisman:

If you're asking about summing several objects in one graph and them having different aspect ratios, I would definitely say no.

+1

Replying to paulmasson:

I'd like to keep the option of a global setting for opacity and thickness and extract the settings for each component graph as an override, if that sounds reasonable.

IMHO, one should distinguish two kinds of options:

• those that are inherently global, like aspect_ratio, axes_labels, etc.
• those that pertain to individual objects, like opacity, thickness, etc.

I would vote for not propagating the "individual" options to all objects in a sum. Imagine for instance a plot with a lot of lines with the default thickness. Then one adds a line of thickness 3 and suddenly, all lines appear with that thickness. Even if documented, this is most surprising to the user. Being obliged to specify thickness=1 for all the lines of the first group to overcome this would be cumbersome and somehow would contradict the concept of default value. One could argue for a new option, e.g. global_thickness, to force all individual objects to be drawn with a given thickness, but this is clearly beyond the scope of this ticket.

Just for curiosity: how is it that, in the current settings, Jmol and Tachyon treat opacity in a sum as a genuine individual option, contrary to the three.js viewer? (note also that the three.js viewer of SMC behaves in the same way as Jmol and Tachyon).

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​202278b

Add missing doctest

[paulmasson]

Because of how the individual opacities/thicknesses propagate upward, my idea of a simple global override isn't possible. That would require an additional keyword as Eric pointed out, so I'll let it go for now. Only individual opacities/thicknesses will be set on graphs.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​dd5e63e

Set opacity by individual plot

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​191b7ae

Remove negative zero in labels

[paulmasson]

Opacity issue should now be fixed, along with an irritating negative zero that appeared in the labels of Eric's test notebook.

[egourgoulhon]

Replying to paulmasson:

Opacity issue should now be fixed,

It seems that there is still an issue with opacity:

show(cube() + sphere((2,0,0), opacity=0.2), viewer='threejs')

draws the sphere with an opacity of 1.

Besides, in the same plot, the lower bound of the frame box x-axis is displayed as -1, while it should be -0.5 (since -0.5 is the cube's min(x)). Maybe a round-off issue?

along with an irritating negative zero that appeared in the labels of Eric's test notebook.

This one is fixed indeed. Thanks!

[paulmasson]

Replying to egourgoulhon:

Besides, in the same plot, the lower bound of the frame box x-axis is displayed as -1, while it should be -0.5 (since -0.5 is the cube's min(x)). Maybe a round-off issue?

This is an explicit round-off in the JavaScript: the option decimals for the number of decimal points in labels defaults to zero. I thought that decimals might be a useful option, for example when the bounding box returns an irrational number. Either the decimals option can be removed entirely or only applied when explicity set.

The number in the label with axes labels is currently the average of the two bounding limits. If decimals is removed that number would show an unexpected value when not close to an integer. That's why the -0 was turning up in your notebook: the number before rounding was a bit less than zero.

The opacity issue for different shapes is occurring because _extra_kwds is not being set explicitly for all different paths to IndexFaceSet, which is the underlying class. This will take a bit of tracking...

[egourgoulhon]

Replying to paulmasson:

Replying to egourgoulhon:

Besides, in the same plot, the lower bound of the frame box x-axis is displayed as -1, while it should be -0.5 (since -0.5 is the cube's min(x)). Maybe a round-off issue?

This is an explicit round-off in the JavaScript: the option decimals for the number of decimal points in labels defaults to zero. I thought that decimals might be a useful option, for example when the bounding box returns an irrational number. Either the decimals option can be removed entirely or only applied when explicity set.

IMHO, it's a very usefull option and it should be maintained. Could the default be set to 1? This would solve the above issue (i.e. x_min appears as -0.5).

The number in the label with axes labels is currently the average of the two bounding limits. If decimals is removed that number would show an unexpected value when not close to an integer. That's why the -0 was turning up in your notebook: the number before rounding was a bit less than zero.

Even in the current settings, there seems to be some issue with that: considering again the example of comment:90 with decimals=2, we get the label x=1.25, while it should be x=1.75.

The opacity issue for different shapes is occurring because _extra_kwds is not being set explicitly for all different paths to IndexFaceSet, which is the underlying class. This will take a bit of tracking...

Do you think this is reasonable for the current ticket?

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​15ccb33	Default decimals to 2
​10e0766	Add extra keywords to parametric surface
​898a554	Add extra keywords to implicit surface

[paulmasson]

Replying to egourgoulhon:

Replying to paulmasson:

Replying to egourgoulhon:

Even in the current settings, there seems to be some issue with that: considering again the example of comment:90 with decimals=2, we get the label x=1.25, while it should be x=1.75.

We want the middle label to show the point halfway between the two ends: that's 1.25, not 1.75. I've defaulted decimals to 2 for now so we can move forward.

The opacity issue for different shapes is occurring because _extra_kwds is not being set explicitly for all different paths to IndexFaceSet, which is the underlying class. This will take a bit of tracking...

Do you think this is reasonable for the current ticket?

I think I've found the minimal changes necessary to get this to work. The _extra_kwds for ParametricSurface (which is used for sphere()) and ImplicitSurface were both empty when their respective json_reprs were called, so I set them both explicitly in the __init__ functions. I think this is a harmless change, since it just duplicates what is done outside the classes with instances of geometries dependent on them, and it certainly gets things working right now. If it causes problems down the line we'll have to rethink the entire json_repr structure and that would certainly be another ticket.

[egourgoulhon]

Replying to paulmasson:

Replying to egourgoulhon:

Even in the current settings, there seems to be some issue with that: considering again the example of comment:90 with decimals=2, we get the label x=1.25, while it should be x=1.75.

We want the middle label to show the point halfway between the two ends: that's 1.25, not 1.75.

Let me insist: since xmin=-0.5 and xmax=3.0, the half-way is x=1.75.

I've defaulted decimals to 2 for now so we can move forward.

OK, thanks.

I think I've found the minimal changes necessary to get this to work. The _extra_kwds for ParametricSurface (which is used for sphere()) and ImplicitSurface were both empty when their respective json_reprs were called, so I set them both explicitly in the __init__ functions. I think this is a harmless change, since it just duplicates what is done outside the classes with instances of geometries dependent on them, and it certainly gets things working right now. If it causes problems down the line we'll have to rethink the entire json_repr structure and that would certainly be another ticket.

Very good. The opacity option works well now!

By the way, what about thickness? It does not seem to be effective at the moment, even on a Linux computer (cf. comment:69):

show(line([(0,0,0), (1,1,1)]) + line([(1,0,0), (1,1,1)], thickness=4), 
     viewer='threejs')

displays two lines of thickness 1, while replacing 'threejs' by 'jmol' or 'tachyon' shows correctly the second line thicker than the first one.

[egourgoulhon]

Replying to egourgoulhon:

Very good. The opacity option works well now!

Well, not completely: in the example

show(cube(opacity=0.2) + sphere((2,0,0)), viewer='threejs')

the sphere is totally hidden by the cube. Again viewer='jmol' works fine in this case.

[paulmasson]

Replying to egourgoulhon:

Replying to egourgoulhon:

Very good. The opacity option works well now!

Well, not completely: in the example

show(cube(opacity=0.2) + sphere((2,0,0)), viewer='threejs')

the sphere is totally hidden by the cube. Again viewer='jmol' works fine in this case.

I'm not understanding the problem here: this example looks fine to me. The default axes in Three.js are rotated relative to Jmol but that's the only difference I see.

[egourgoulhon]

Replying to paulmasson:

the sphere is totally hidden by the cube. Again viewer='jmol' works fine in this case.

I'm not understanding the problem here: this example looks fine to me. The default axes in Three.js are rotated relative to Jmol but that's the only difference I see.

If you rotate the figure to put the cube in front of the sphere, you cannot see the sphere through it, i.e. the cube is fully opaque:

On the contrary, with jmol, you can see the sphere through the cube:

[egourgoulhon]

Note that if you permute the cube and the sphere in the graphic sum, i.e. run

show(sphere((2,0,0)) + cube(opacity=0.2), viewer='threejs')

it works well (the output is similar to the jmol one above).

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​2c33155

Add line thickness to extra keywords

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​e1f8460

Fix transparency issue

[paulmasson]

Replying to egourgoulhon:

Replying to paulmasson:

the sphere is totally hidden by the cube. Again viewer='jmol' works fine in this case.

I'm not understanding the problem here: this example looks fine to me. The default axes in Three.js are rotated relative to Jmol but that's the only difference I see.

If you rotate the figure to put the cube in front of the sphere, you cannot see the sphere through it, i.e. the cube is fully opaque:

Got it! Should be fixed now.

[paulmasson]

Replying to egourgoulhon:

Replying to paulmasson:

Replying to egourgoulhon:

By the way, what about thickness? It does not seem to be effective at the moment, even on a Linux computer (cf. comment:69):

The keyword thickness is missing from _extra_kwds for objects created with line3d but not strangely enough for parametric_plot3d which calls line3d: a quirk of keyword arguments. I've added it explicitly for the purposes of this ticket.

A better way to handle this situation is to define json_repr for Line and Point just as it already exists for IndexFaceSet. That would require a complete rewrite of _rich_repr_threejs and I'd rather do that on a separate ticket, so hopefully the simple change to line3d is sufficient for a first version.

[paulmasson]

Replying to egourgoulhon:

Replying to paulmasson:

Replying to egourgoulhon: We want the middle label to show the point halfway between the two ends: that's 1.25, not 1.75.

Let me insist: since xmin=-0.5 and xmax=3.0, the half-way is x=1.75.

If the lower endpoint were xmin=0 the midpoint would be 1.5, right? If the lower endpont moves up to +.5 then I agree the midpoint would be 1.75, but if the lower endpoint moves below zero to -.5 then the midpoint moves below 1.5 to 1.25.

[paulmasson]

Replying to slelievre:

Replying to egourgoulhon:

Replying to paulmasson:

Thanks for your answers.

3) The code used for line objects needs to be completely rewritten. There is a hardware driver limitation on Windows machines that prevents rendering of line thickness in WebGL that is not going away soon, and I'm still thinking about the best way around this. Andrey certainly won't approve this ticket without line thickness rendering decently across hardware platforms, and I agree with him on that.

I would be on a different tone here: as long as three.js is not Sage's default 3D viewer, I see no reason to defer its use for Linux and MacOS users, simply because Windows is limited. When decision is taken to make three.js the default viewer, it's of course a different matter. So IMHO the Windows line thickness issue could be postponed to another ticket.

True, Windows line thickness could be its own ticket, and making three.js the default viewer could be another ticket depending on it.

In the process of fixing a line thickness problem, I came across an existing keyword radius for drawing lines. This already solves the problem of drawing thicker lines since they are rendered as cylindrical segments.

Line thickness in WebGL is very hardware dependent even apart from the Windows problem. It will max out around 10 on Mac OS X, with higher values not having any effect. There's no problem leaving linethickness in place for those who want to use it, but the radius option is perhaps better and works already.

[egourgoulhon]

Replying to paulmasson:

If the lower endpoint were xmin=0 the midpoint would be 1.5, right? If the lower endpont moves up to +.5 then I agree the midpoint would be 1.75, but if the lower endpoint moves below zero to -.5 then the midpoint moves below 1.5 to 1.25.

Oups... you are perfectly right! Sorry for the confusion...

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​6ee4d31

Document radius option for lines

[egourgoulhon]

Replying to paulmasson:

If you rotate the figure to put the cube in front of the sphere, you cannot see the sphere through it, i.e. the cube is fully opaque:

Got it! Should be fixed now.

Indeed! Thanks!

[egourgoulhon]

Thanks for the radius and thickness options! IMHO this is very close to positive review. A few last points, maybe some of them can be defered to another ticket:

• The documentation about the use of threejs in the 3D Graphics section of the reference manual is rather poor. It would be nice to have an entry (even a small one) in the "Backends" subsection (for the time being there is only one such entry: "The Tachyon 3D Ray Tracer"), in particular to document options like decimals, which are specific to threejs.
• As discussed in comment:63, an internet connection is required (by src/sage/plot/plot3d/threejs_template.html) to access to the files ​three.js and ​OrbitControls.js. Apparently these files are released under a MIT license. Is it possible/meaningful to integrate a copy of them in Sage's sources files, so that the threejs viewer can be used off-line?
• What about text3d, which seems to be the last major missing functionality?. Would this require another ticket?
• The save method of 3D graphic objects, which generates a static png image, does not accept the option viewer='threejs':

  sphere().save('figure.png', viewer='jmol')     # OK
  sphere().save('figure.png', viewer='tachyon')  # OK
  sphere().save('figure.png', viewer='threejs') 
  ValueError: cannot use viewer=threejs to render image
  

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​8e5627b	Update doctest to remove long line
​33fcccf	JSON cleanup
​97c7435	Add basic text3d support
​b32d3ae	Documentation clarifications

[paulmasson]

Replying to egourgoulhon:

• The documentation about the use of threejs in the 3D Graphics section of the reference manual is rather poor. It would be nice to have an entry (even a small one) in the "Backends" subsection (for the time being there is only one such entry: "The Tachyon 3D Ray Tracer"), in particular to document options like decimals, which are specific to threejs.

The tachyon entry is there because its class is a separate Python file. I could make a separate file for Three.js but it won't have anything but documentation and examples, since all of the code is in Graphics3d._rich_repr_threejs.

• As discussed in comment:63, an internet connection is required (by src/sage/plot/plot3d/threejs_template.html) to access to the files ​three.js and ​OrbitControls.js. Apparently these files are released under a MIT license. Is it possible/meaningful to integrate a copy of them in Sage's sources files, so that the threejs viewer can be used off-line?

This is a planned feature and there is a standard ​method for switching to local JavaScript when there is no connection. I don't want to include it on this ticket because it will require a modification to the Sage build process to download the two files. I haven't made that sort of change yet and will want feedback from Volker as to the best location for the files to be accessed by both types of existing notebooks.

• What about text3d, which seems to be the last major missing functionality?. Would this require another ticket?

I've added basic support for this, with the caveat that it only works when text3d is not the only object viewed. This is because text3d is a packaged in a TransformationGroup and the process of flattening the input mangles the text location stored in the property _trans. The current behavior appears to work like Jmol but I'm not completely happy with it. The text3d object modifies the bounding box for the entire GraphicsGroup3d, so the text often ends up sitting on the frame. A future feature would be to add a labels global option that would be an array of text objects that could be placed anywhere, even outside the frame.

• The save method of 3D graphic objects, which generates a static png image, does not accept the option viewer='threejs':

  sphere().save('figure.png', viewer='jmol')     # OK
  sphere().save('figure.png', viewer='tachyon')  # OK
  sphere().save('figure.png', viewer='threejs') 
  ValueError: cannot use viewer=threejs to render image
  

Jmol and Tachyon are their own renderers, so they are capable of producing preview images. The rendering of Three.js occurs entirely in the browser, so this Python method is never going to work for it. What I can add later is a right-context menu for the HTML page that will save image data to a file. That would best be done as a separate ticket.

[egourgoulhon]

Replying to paulmasson:

Replying to egourgoulhon:

• The documentation about the use of threejs in the 3D Graphics section of the reference manual is rather poor. It would be nice to have an entry (even a small one) in the "Backends" subsection (for the time being there is only one such entry: "The Tachyon 3D Ray Tracer"), in particular to document options like decimals, which are specific to threejs.

The tachyon entry is there because its class is a separate Python file. I could make a separate file for Three.js but it won't have anything but documentation and examples, since all of the code is in Graphics3d._rich_repr_threejs.

OK, but note that one can set up a pure documentation file, with only docstrings and no Python code; an example is src/sage/plot/plot3d/examples.py. Maybe you should just add a few lines to that file.

• As discussed in comment:63, an internet connection is required (by src/sage/plot/plot3d/threejs_template.html) to access to the files ​three.js and ​OrbitControls.js. Apparently these files are released under a MIT license. Is it possible/meaningful to integrate a copy of them in Sage's sources files, so that the threejs viewer can be used off-line?

This is a planned feature and there is a standard ​method for switching to local JavaScript when there is no connection. I don't want to include it on this ticket because it will require a modification to the Sage build process to download the two files. I haven't made that sort of change yet and will want feedback from Volker as to the best location for the files to be accessed by both types of existing notebooks.

OK very good.

I've added basic support for this, with the caveat that it only works when text3d is not the only object viewed. This is because text3d is a packaged in a TransformationGroup and the process of flattening the input mangles the text location stored in the property _trans. The current behavior appears to work like Jmol but I'm not completely happy with it. The text3d object modifies the bounding box for the entire GraphicsGroup3d, so the text often ends up sitting on the frame. A future feature would be to add a labels global option that would be an array of text objects that could be placed anywhere, even outside the frame.

OK, thank you very much for the addition of text3d!

Jmol and Tachyon are their own renderers, so they are capable of producing preview images. The rendering of Three.js occurs entirely in the browser, so this Python method is never going to work for it. What I can add later is a right-context menu for the HTML page that will save image data to a file. That would best be done as a separate ticket.

OK fine.

Playing with the latest version, I've noticed an issue with point3d: running

show(cube() + point3d((0,0,1)), viewer='threejs')

results in a frame box that is too high: z_max = 2, whereas it should be 1. With Jmol or Tachyon, the frame box is fine.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​d329b81

Remove moveBoundsOffPoint

[paulmasson]

Replying to egourgoulhon:

Replying to paulmasson:

Replying to egourgoulhon:

OK, but note that one can set up a pure documentation file, with only docstrings and no Python code; an example is src/sage/plot/plot3d/examples.py. Maybe you should just add a few lines to that file.

I have a much better idea for this. I'll work on it tomorrow.

Playing with the latest version, I've noticed an issue with point3d: running

show(cube() + point3d((0,0,1)), viewer='threejs')

results in a frame box that is too high: z_max = 2, whereas it should be 1. With Jmol or Tachyon, the frame box is fine.

The original commit had a function to move points off the bounding frame to help me determine that the points were being rendered. Since this is unexpected behavior, I've removed that function.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​034029a	Standardize indentation
​5d22cf0	Remove JS eval()
​98102b5	Move documentation to separate file

[paulmasson]

Documentation is now in a separate file and can be accessed easily from a link in the "Backends" section of the index. I've also added a couple live examples for the HTML version. I'll add more later after other fixes/features are addressed on future tickets, particularly making the viewer work offline.

I also made some changes to remove the JavaScript eval function from the template. I had it there for convenience but don't want an insecure method in the final version.

[egourgoulhon]

Thanks a lot for all these changes! The documentation looks very nice. As revealed by the patchbot, there are however 2 doctest errors in src/doc/en/reference/plot3d/threejs.rst (I could reproduce those on my computer). Once this is fixed, I would go for a positive review.

PS: I've updated the ​notebook about plotting fields on the 2-sphere, which works very well (note that since Sage 7.5.beta4, you do no longer need to install SageManifolds to run it).

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​b0b2c14

Fix backend for doctests

[paulmasson]

Replying to egourgoulhon:

As revealed by the patchbot, there are however 2 doctest errors in src/doc/en/reference/plot3d/threejs.rst

Done.

[egourgoulhon]

Thank you very much for your work. This is a great enhancement for Sage!

[kcrisman]

I just asked a few dumb questions, so removing name - but nice work!!!

[tmonteil]

There is a threejs (optional) package in Sage already. Do you really need to fetch files from a CDN (without user prior consent), and not those provided by the package ? What would be missing ?

[dimpase]

see ​https://groups.google.com/d/msg/sage-release/__wlsF1jv_Y/VQc35Pf7CAAJ :

         from sage.env import SAGE_SRC 
         filename = os.path.join(SAGE_SRC, 'sage', 
                                 'plot', 'plot3d', 'threejs_template.html') 
         f = open(filename, 'r') 
         html = f.read() 
         f.close() 

is bad, as SAGE_SRC should not be used at runtime: all these files should be installed in SAGE_LOCAL, oe whatever the right place is.

Matthias and Jeroen know more on how this should be properly set up.

[tmonteil]

For this, you should put the threejs_template.html file in some SAGE_ROOT/src/ext/threejs/ directory (or replace threejs by something more appropriate if you think it is a good idea). Then it will be automatically copied to SAGE_ROOT/local/share/sage/ext/threejs/, and you should access it with os.path.join(SAGE_EXTCODE, 'threejs', 'threejs_template.html') because some distros split the stuff and do not have such thing as SAGE_ROOT.

[tmonteil]

Follow-up : #22014

[slelievre]

Follow-up at #32560 regarding auto-scaling-down the z direction when aspect ratio is [1, 1, 1].