# Message #1372

From: Andrey <andreyastrelin@yahoo.com>

Subject: [MC4D] MS5D v0.11 uploaded [Re: MS5D v0.1]

Date: Sat, 29 Jan 2011 21:32:00 -0000

Hi Roice,

When I looked at my projection formulae, I found that they are equivalent to the simplest 3D projection:

Let corners of our puzzle are on the sphere (0,R). Define the position of camera by orthogonal basis (e_x,e_y,e_z,e_u,e_v) and one number r (-R<r<=R). Let P be the point on the sphere. It’s coordinates in the Camera basis are (x,y,z,u,v). Then screen coordinates will be (x/(z+r),y/(z+r)) - and u,v coordinates of the points are just ignored :)

I took large enough view angle (2 radians), and it gives fisheye effect, especially when r=R (it’s initial zoom level).

"Center" of 3D rotation is 2D plane u=v=0. Zoom is controlled by parameter r. Probably I could enter another Zoom (View Angle) or enable r>R (and show puzzle from the outside). When you zoom in, you get r -> -R, and only small part of the sphere becomes visible.

Now degrees of freedom.

Normal-Left: 3D rotations x-z and y-z

Normal-Right: Sliding z-u (up/down) and screen rotation x-y (left/right)

Shift-Left: 4D rotations x-u and y-u

Shift-Right: 4D (or 5D?) rotations x-v and y-v.

So the missing degrees of freedom are:

- alternative 5D sliding z-v
- 4D/5D rotation u-v.

I’ll slow down animation on the left (to 10s per twist, haha), but save right size fast - it will be used for full undo/redo animation as well, and we may want the smallest delays there.

My favorite now is 2/5 with only two types of pieces (4C and 5C). Probably it will be possible to solve full scrambed puzzle there.

Good luck!

Andrey