# Message #1242

From: Roice Nelson <roice3@gmail.com>

Subject: Re: [MC4D] Re: 3D-only rotations in MHT633

Date: Tue, 02 Nov 2010 20:11:39 -0500

Argh! Scratch the "assuming the camera is invisible" comment. I was

letting my rays get ahead of themselves and wrap back around to the viewer.

And profuse apologies for the extra spam.

To try to make this correction a useful post, let me mention that this

particular lapse came from me recalling portions of a very nice discussion

of this exact topic in Thurston’s "Three-Dimensional Geometry and Topology".

See "Example 1.4.2 (the three sphere from the inside)", starting on page

- The short two page discussion is visible in google

books<http://books.google.com/books?id=9kkuP3lsEFQC&printsec=frontcover&dq=Three+dimensional+geometry+and+topology&hl=en&ei=BbTQTKT2C8WAlAe2q529Bg&sa=X&oi=book_result&ct=result&resnum=1&ved=0CDIQ6AEwAA#v=onepage&q&f=false>,

and very readable :) I’ll make myself scarce now…

Cheers,

Roice

On Tue, Nov 2, 2010 at 7:39 PM, Roice Nelson <roice3@gmail.com> wrote:

> I realized that for a 3^4 "in sphere view", the 1C sticker would always

> block seeing further than the location that is antipodal to the camera in

> S3, regardless of shrink settings. So you could never see beyond that. You

> potentially could see beyond the antipode for the 4^4 though, assuming the

> camera is invisible anyway :) I still think an "in sphere" view might work

> well and would be interesting to play with…

>

> Roice

>

> On Tue, Nov 2, 2010 at 7:14 PM, Roice Nelson <roice3@gmail.com> wrote:

>

>>

>> On Tue, Nov 2, 2010 at 6:15 PM, Andrey <andreyastrelin@yahoo.com> wrote:

>>

>>> Roice,

>>> I’m not sure what you mean by "3D-only rotations". I see that navigation

>>> in S3 (in MC4D) and in H3 uses only one camera with 6 position/orientation

>>> parameters (+ some zoom parameters) like normal 3D navigation. For example,

>>> in MC4D you can’t freely navigate in projection space (look from center

>>> outside etc.) like you can, say, in MC7D.

>>>

>>

>> Sorry that wasn’t clear. By "3D-only rotations", I meant rotations which

>> are done after the H3 -> R3 projection, not before it. They are Euclidean

>> 3D rotations of the projected (3D) object, and are what Melinda was asking

>> for. These rotations would preserve the shape of 3D objects, unlike the

>> left-click dragging currently in MHT633. Does that help clarify?

>>

>> If you implement the ball model with the POV at the origin, your

>> left-click dragging should automatically result in the types of rotations I

>> was intending to describe.

>>

>>

>>> In MC4D we talk about "3D projection" because there are problems with

>>> real view in sphere: all rays from camera meet in opposite point of sphere

>>> and you can’t see farther than that point. It can be solved by a

>>> nonrealistic optics: say, rays are going by circles tangent to camera axis -

>>> or by intermediate projection, as done in MC4D.

>>>

>>

>> I think an "in sphere" view could work well for the 3^4. The image of the

>> furthest cube would cover the entire background and would be "inverted".

>> Depending on face/sticker shrink values, you wouldn’t be able to see past it

>> like you describe, but you could still see the entire puzzle and work with

>> it.

>>

>>

>>> Yes, it’s easy to convert view in MHT from real-view to Poincare ball

>>> (centered in POV). The only problem will be with the situation when camera

>>> is outside of the space. In that case we’ll need to recalculate "shift-left

>>> drag" operation (twist of camera or x-y pan): it will become sliding along

>>> some straight line. But I think that it’s not very difficult.

>>>

>>

>> Don’s tessellation applet <http://www.plunk.org/~hatch/HyperbolicApplet/>had to deal with the same problem of hyperbolic panning outside the model

>> boundary, so you might check out what he did there…

>>

>> seeya,

>> Roice

>>

>

>