Message #2485

From: Eduard Baumann <baumann@mcnet.ch>
Subject: Re: [MC4D] Edge sets in MagicTile
Date: Thu, 15 Nov 2012 11:11:18 +0100

Thanks a lot.
Ed

—– Original Message —–
From: Roice Nelson
To: 4D_Cubing@yahoogroups.com
Sent: Thursday, November 15, 2012 6:44 AM
Subject: Re: [MC4D] Edge sets in MagicTile

Hi Ed,

Some inlines for you below.

On Wed, Nov 14, 2012 at 6:55 AM, Eduard wrote:

Aha.<br>
&lt;InitialEdgeSet&gt;1&#58;3&lt;/InitialEdgeSet&gt;<br>
does a restriction.<br>
How?

By default, all edges of the white tile are used for reflections. In the KQ example I gave, one edge set was encoding 7 copies. ‘InitialEdgeSet’ allows you to override using all of the edges at the start (it also references edges in a CCW 0-indexed fashion).

It’s confusing, because the "1:3" here means something different than "1:3" would in an ‘EdgeSet’ tag. In the former, it refers to the starting reflection of two different encoded copies. In the latter, it would refer to multiple reflections of one encoded copy. Not the cleanest, but I hope this makes sense.

I found this setting necessary for puzzles with asymmetrical colorings. I can’t remember now, but it might even have been the IRPs that first required it.

On Wed, Nov 14, 2012 at 6:45 AM, Eduard wrote:

KQ 24<br>
         &lt;EdgeSet&gt;3&#58;3&#58;3&lt;/EdgeSet&gt;<br>
            I see also 4&#58;4&#58;4 why ?

You are totally correct, and I glossed over this in the previous email. There is a setting, "UseMirroredEdgeSet", which is true by default. In the case of KQ, this means "3:3:3" also implicitly does the mirror reflections "4:4:4".

Before I said: "3:3:3" actually represents 4 reflections, applied in each of the 7 directions, encoding 7 copies.

But really: "3:3:3" actually represents 4 reflections, applied in each of the 7 directions and their mirrors, encoding 14 copies. So it is a very compact representation of a lot of isometries!

Apologies for confusion from me omitting this before. I had been trying to not throw too much out at once.

Are the sets valable for all edges of all colors ?

I wasn’t fully sure what you are asking, but I interpret it to mean "Do these sets apply equally to every tile?" The answer to that is no. The sets only apply to the white tile. They are used to calculate a set of isometries, which are then applied to all fundamental tiles. But their effect on the other tiles may be different (on less symmetrical puzzles anyway…on very symmetrical puzzles like KQ, all tiles end up behaving identically).

Since you are digging deep into this configuration, I will try to write up a page with fuller details, and a few more pictorial examples. I’ll try to work on this over the Thanksgiving holiday next week. Hopefully it will help you to be able to explore and find some cool new colorings!

Cheers,
Roice