### Zoetropes

JB
Jon Bondy
Sat, Jun 22, 2024 4:50 PM

It all started out when I stumbled across this YouTube channel:

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:

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

Kevin Holmes has taken zoetropes to an entirely new level:

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

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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
MM
Michael Möller
Sat, Jun 22, 2024 4:58 PM

...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 <

It all started out when I stumbled across this YouTube channel:

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:

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

Kevin Holmes has taken zoetropes to an entirely new level:

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

--
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AM
Sat, Jun 22, 2024 5:24 PM

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 <

...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 <

It all started out when I stumbled across this YouTube channel:

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:

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

Kevin Holmes has taken zoetropes to an entirely new level:

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

To unsubscribe send an email to discuss-leave@lists.openscad.org

To unsubscribe send an email to discuss-leave@lists.openscad.org

CM
Curt McDowell
Sun, Jun 23, 2024 1:16 AM

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

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:

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:

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

Kevin Holmes has taken zoetropes to an entirely new level:

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

JJ
jon jonbondy.com
Sun, Jun 23, 2024 7:50 PM

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

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:

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:

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

Kevin Holmes has taken zoetropes to an entirely new level:

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