It all started out when I stumbled across this YouTube channel: https://www.youtube.com/@henryseg/videos Henry Segerman has some amazing 3D printed curiosities, and I began to ponder how to create some of them using OpenSCAD. Among Henry's videos is this walk through of a geometry exhibit: https://www.youtube.com/watch?v=1FUMJPjPSgQ Near the end, we come to the "projection from 4 space into 3 space of a rotating hypercube zoetrope".  Fascinating.  I tried, but could not find, all of the 3D models that were required for this, so one thing I am curious about is whether we could compute these using OpenSCAD. Kevin Holmes has taken zoetropes to an entirely new level: https://www.youtube.com/@n0f8r/videos If you look over his videos thoroughly, the complexity and enormity of his work is stunning.  I asked him whether he had considered creating a platter as a single huge 3D print.  He prints everything in resin, hand paints them, and then assembles the platter.  I am more lazy: I want to do the work up front and then make a single print on my Prusa XL.  His point is that the resolution available from a regular FDM printer would not do justice to his work.  Probably true. So, in the end, my quest is to calculate the 3D representations of the rotating hypercube and create a single print zoetrope platter compatible with Kevin's display. I hope that you find some of this to be interesting, if not inspiring. Jon -- This email has been checked for viruses by AVG antivirus software. www.avg.com

...Near the end, we come to the "projection from 4 space into 3 space of a rotating hypercube zoetrope"... Well, the 4th dimension is just the time axis. Your OpenSCAD model of watever, needs the t$ variable which does the transformation for each "picture" of your model, cordinated with the rotate that places them along the rim. Easy to say, a little harder to code ;-) lør. 22. jun. 2024 18.51 skrev Jon Bondy via Discuss < discuss@lists.openscad.org>: > It all started out when I stumbled across this YouTube channel: > > https://www.youtube.com/@henryseg/videos > > Henry Segerman has some amazing 3D printed curiosities, and I began to > ponder how to create some of them using OpenSCAD. > > Among Henry's videos is this walk through of a geometry exhibit: > > https://www.youtube.com/watch?v=1FUMJPjPSgQ > > Near the end, we come to the "projection from 4 space into 3 space of a > rotating hypercube zoetrope". Fascinating. I tried, but could not > find, all of the 3D models that were required for this, so one thing I > am curious about is whether we could compute these using OpenSCAD. > > Kevin Holmes has taken zoetropes to an entirely new level: > > https://www.youtube.com/@n0f8r/videos > > If you look over his videos thoroughly, the complexity and enormity of > his work is stunning. I asked him whether he had considered creating a > platter as a single huge 3D print. He prints everything in resin, hand > paints them, and then assembles the platter. I am more lazy: I want to > do the work up front and then make a single print on my Prusa XL. His > point is that the resolution available from a regular FDM printer would > not do justice to his work. Probably true. > > So, in the end, my quest is to calculate the 3D representations of the > rotating hypercube and create a single print zoetrope platter compatible > with Kevin's display. > > I hope that you find some of this to be interesting, if not inspiring. > > Jon > > > -- > This email has been checked for viruses by AVG antivirus software. > www.avg.com > _______________________________________________ > OpenSCAD mailing list > To unsubscribe send an email to discuss-leave@lists.openscad.org >

Uh, no, the 4th dimension is not time in this example. It seems like if you can define what you want to do exactly here it should be a very simple thing. A hypercube is an object in four spatial dimensions formed from eight cubes. It's very easy to construct the coordinates of a basic hypercube. So you can construct the points and faces. You can then build the 4d rotation matrix to rotate it some way you like. This would be parameterized over a rotation angle, which would correspond to the time dimension. You apply the 4d rotation matrix to vertices and follow with a projection to 3d (presumably just discarding the 4th point). The main question mark is what, exactly, are the faces you are trying to construct? A 3d projection of a hypercube is going to mostly intersect itself and won't be a very interesting object. It seems like maybe you actually want a wireframe? Probably easier to make a wireframe by projecting edges from 4d to 3d and then building the shape around that. On Sat, Jun 22, 2024 at 12:59 PM Michael Möller via Discuss < discuss@lists.openscad.org> wrote: > ...Near the end, we come to the "projection from 4 space into 3 space of a > rotating hypercube zoetrope"... > > Well, the 4th dimension is just the time axis. Your OpenSCAD model of > watever, needs the t$ variable which does the transformation for each > "picture" of your model, cordinated with the rotate that places them along > the rim. > > Easy to say, a little harder to code ;-) > > lør. 22. jun. 2024 18.51 skrev Jon Bondy via Discuss < > discuss@lists.openscad.org>: > >> It all started out when I stumbled across this YouTube channel: >> >> https://www.youtube.com/@henryseg/videos >> >> Henry Segerman has some amazing 3D printed curiosities, and I began to >> ponder how to create some of them using OpenSCAD. >> >> Among Henry's videos is this walk through of a geometry exhibit: >> >> https://www.youtube.com/watch?v=1FUMJPjPSgQ >> >> Near the end, we come to the "projection from 4 space into 3 space of a >> rotating hypercube zoetrope". Fascinating. I tried, but could not >> find, all of the 3D models that were required for this, so one thing I >> am curious about is whether we could compute these using OpenSCAD. >> >> Kevin Holmes has taken zoetropes to an entirely new level: >> >> https://www.youtube.com/@n0f8r/videos >> >> If you look over his videos thoroughly, the complexity and enormity of >> his work is stunning. I asked him whether he had considered creating a >> platter as a single huge 3D print. He prints everything in resin, hand >> paints them, and then assembles the platter. I am more lazy: I want to >> do the work up front and then make a single print on my Prusa XL. His >> point is that the resolution available from a regular FDM printer would >> not do justice to his work. Probably true. >> >> So, in the end, my quest is to calculate the 3D representations of the >> rotating hypercube and create a single print zoetrope platter compatible >> with Kevin's display. >> >> I hope that you find some of this to be interesting, if not inspiring. >> >> Jon >> >> >> -- >> This email has been checked for viruses by AVG antivirus software. >> www.avg.com >> _______________________________________________ >> OpenSCAD mailing list >> To unsubscribe send an email to discuss-leave@lists.openscad.org >> > _______________________________________________ > OpenSCAD mailing list > To unsubscribe send an email to discuss-leave@lists.openscad.org >

Jon, Here is some zoetrope work done using 3D resin printing by a professor and personal friend at Stanford. Although it's based on the golden ratio rather than hypercubes, it may also provide some inspiration if you've not seen it already. https://www.youtube.com/watch?v=B5p2A5mazEs Regards, Curt On 6/22/2024 9:50 AM, Jon Bondy via Discuss wrote: > It all started out when I stumbled across this YouTube channel: > > https://www.youtube.com/@henryseg/videos > > Henry Segerman has some amazing 3D printed curiosities, and I began to > ponder how to create some of them using OpenSCAD. > > Among Henry's videos is this walk through of a geometry exhibit: > > https://www.youtube.com/watch?v=1FUMJPjPSgQ > > Near the end, we come to the "projection from 4 space into 3 space of > a rotating hypercube zoetrope".  Fascinating.  I tried, but could not > find, all of the 3D models that were required for this, so one thing I > am curious about is whether we could compute these using OpenSCAD. > > Kevin Holmes has taken zoetropes to an entirely new level: > > https://www.youtube.com/@n0f8r/videos > > If you look over his videos thoroughly, the complexity and enormity of > his work is stunning.  I asked him whether he had considered creating > a platter as a single huge 3D print.  He prints everything in resin, > hand paints them, and then assembles the platter.  I am more lazy: I > want to do the work up front and then make a single print on my Prusa > XL.  His point is that the resolution available from a regular FDM > printer would not do justice to his work.  Probably true. > > So, in the end, my quest is to calculate the 3D representations of the > rotating hypercube and create a single print zoetrope platter > compatible with Kevin's display. > > I hope that you find some of this to be interesting, if not inspiring. > > Jon > >

Excellent video!  Thanks so much for telling us about it. Jon On 6/22/2024 9:16 PM, Curt McDowell wrote: > Jon, > > Here is some zoetrope work done using 3D resin printing by a professor > and personal friend at Stanford. Although it's based on the golden ratio > rather than hypercubes, it may also provide some inspiration if you've > not seen it already. > > https://www.youtube.com/watch?v=B5p2A5mazEs > > Regards, > Curt > > On 6/22/2024 9:50 AM, Jon Bondy via Discuss wrote: >> It all started out when I stumbled across this YouTube channel: >> >> https://www.youtube.com/@henryseg/videos >> >> Henry Segerman has some amazing 3D printed curiosities, and I began to >> ponder how to create some of them using OpenSCAD. >> >> Among Henry's videos is this walk through of a geometry exhibit: >> >> https://www.youtube.com/watch?v=1FUMJPjPSgQ >> >> Near the end, we come to the "projection from 4 space into 3 space of >> a rotating hypercube zoetrope".  Fascinating.  I tried, but could not >> find, all of the 3D models that were required for this, so one thing I >> am curious about is whether we could compute these using OpenSCAD. >> >> Kevin Holmes has taken zoetropes to an entirely new level: >> >> https://www.youtube.com/@n0f8r/videos >> >> If you look over his videos thoroughly, the complexity and enormity of >> his work is stunning.  I asked him whether he had considered creating >> a platter as a single huge 3D print.  He prints everything in resin, >> hand paints them, and then assembles the platter.  I am more lazy: I >> want to do the work up front and then make a single print on my Prusa >> XL.  His point is that the resolution available from a regular FDM >> printer would not do justice to his work.  Probably true. >> >> So, in the end, my quest is to calculate the 3D representations of the >> rotating hypercube and create a single print zoetrope platter >> compatible with Kevin's display. >> >> I hope that you find some of this to be interesting, if not inspiring. >> >> Jon >> >>