Message #1241

From: Roice Nelson <>
Subject: Re: [MC4D] Re: 3D-only rotations in MHT633
Date: Tue, 02 Nov 2010 19:39:54 -0500

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…


On Tue, Nov 2, 2010 at 7:14 PM, Roice Nelson <> wrote:

> On Tue, Nov 2, 2010 at 6:15 PM, Andrey <> 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 <>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