Message #1239

From: Andrey <>
Subject: Re: 3D-only rotations in MHT633
Date: Tue, 02 Nov 2010 23:15:34 -0000

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.
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.
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.
I’ll think about introducing of this view model in the program.


— In, Roice Nelson <roice3@…> wrote:
> I wanted to chime in that I liked Melinda’s thoughts on this.
> This email is going to make the argument that the Poincare ball model would
> be the right place to offer 3D-only rotations. One would do the projection
> to the ball model, then allow the user to manipulate that post-projection as
> if it was a 3d object. Of course, you could also offer enhanced controls to
> do pre-projection H3 movements, leading to all the fun warping. Here is my
> reasoning for liking the ball model for this…
> First of all, it is the closest H3 analogue we have to the projection that
> MC4D uses.
> <digression as to why>
> MC4D is close to a stereographic projection of S3 objects. The vertices
> live in S3 and are stereographically projected. The edges are then
> connected up with straight Euclidean lines, living only slightly outside of
> S3 (in R4). The ball model of H3 is also a stereographic projection of a
> constant radius surface (see this
> page<>),
> so it is an analogous situation. One could even similarly connect up the
> stereographically projected vertices with straight lines, and I wonder what
> Euclidean dimensional space that original object might live in, if any…not
> R4!
> </digression as to why>
> But analogy closeness aside, the crux of why I think 3D rotations would fit
> in quite naturally with a ball model representation is the following:
> Consider that in the ball model, spheres centered at the origin are
> equidistant from the origin in both H3 space and projected space. So for a
> puzzle representation with the POV (lookat position) always at the origin, *a
> 3D rotation is also an H3 rotation*. Things work well in MC4D for the same
> reason, because the 3D rotations are also R4 rotations.
> When this is not the case, I can see why offering 3D-only rotations would be
> strange (either in the current "in space" view of MHT633 or if there was a
> similar "S3 in space" view for MC4D). Due to the 3D rotations not also
> being an H3 rotation, the user would be forced to mentally track two
> different sets of vectors, the 3D camera position and the H3 camera
> position. Here’s an example of what I mean… Say you’re at some location,
> then you 3D rotate around 180 degrees, then you want to do another H3
> movement, moving forward for example. It would be awkward to do so, unless
> you snapped back to a canonical 3D position first (your original location
> with no rotation). If you didn’t snap back, the forward H3
> movement would make you feel like you were moving backwards, as all the
> pieces rushed away from you. It seems like it could be easy to get lost.
> A final benefit of doing this with the ball model is that it is more overtly
> a model, which also leads to a naturalness in zooming around and studying it
> in the way Melinda describes. Hope I’m not being too off-topic or
> persistent with the ball model focus (though I can say I would be happy to
> help on such a feature, if Andrey ever desired that)…
> All the best,
> Roice