The big mathematical news this month is that a polygon has been
discovered that will tile the plane but only aperiodically. Penrose
tiles achieve this with two tile types; it's been an open question for
decades whether you could do it with only one tile. Now someone has
announced the discovery of such a thing, so _obviously_ this
mathematically exciting tiling ought to be one of the Loopy grid
options!
The polygon, named a 'hat' by its discoverers, consists of the union
of eight cells of the 'Kites' periodic tiling that Loopy already
implements. So all the vertex coordinates of the whole tiling are
vertices of the Kites grid, which makes handling the coordinates in an
exact manner a lot easier than Penrose tilings.
What's _harder_ than Penrose tilings is that, although this tiling can
be generated by a vaguely similar system of recursive expansion, the
expansion is geometrically distorting, which means you can't easily
figure out which tiles can be discarded early to save CPU. Instead
I've come up with a completely different system for generating a patch
of tiling, by using a hierarchical coordinate system to track a
location within many levels of the expansion process without ever
simulating the process as a whole. I'm really quite pleased with that
technique, and am tempted to try switching the Penrose generator over
to it too - except that we'd have to keep the old generator around to
stop old game ids being invalidated, and also, I think it would be
slightly trickier without an underlying fixed grid and without
overlaps in the tile expansion system.
However, before coming up with that, I got most of the way through
implementing the more obvious system of actually doing the expansions.
The result worked, but was very slow (because I changed approach
rather than try to implement tree-pruning under distortion). But the
code was reusable for two other useful purposes: it generated the
lookup tables needed for the production code, and it also generated a
lot of useful diagrams. So I've committed it anyway as a supporting
program, in a new 'aux' source subdirectory, and in aux/doc is a
writeup of the coordinate system's concepts, with all those diagrams.
(That's the kind of thing I'd normally put in a huge comment at the
top of the file, but doing all those diagrams in ASCII art would be
beyond miserable.)
From a gameplay perspective: the hat polygon has 13 edges, but one of
them has a vertex of the Kites tiling in the middle, and sometimes two
other tile boundaries meet at that vertex. I've chosen to represent
every hat as having degree 14 for Loopy purposes, because if you only
included that extra vertex when it was needed, then people would be
forever having to check whether this was a 13-hat or a 14-hat and it
would be nightmarish to play.
Even so, there's a lot of clicking involved to turn all those fiddly
individual edges on or off. This grid is noticeably nicer to play in
'autofollow' mode, by setting LOOPY_AUTOFOLLOW in the environment to
either 'fixed' or 'adaptive'. I'm tempted to make 'fixed' the default,
except that I think it would confuse players of ordinary square Loopy!
Every grid shape has its own limit, so this involved adding a new
interface between loopy.c and grid.c. The limits are based on ensuring
that the co-ordinate system of the grid doesn't overflow INT_MAX and
neither do the lengths of the face and dot arrays.
Though now I come to look at it I think the actual limits of grid.c are
much lower. Hmm.
A grid based on dodecagons with square symmetry. In between dodecagons
there are 4 triangles around 1 square, which resembles a compass rose.
https://en.wikipedia.org/wiki/3-4-3-12_tiling
Regular hexagons and equilateral triangles in strict alternation, with
two of each interleaved around each vertex.
https://en.wikipedia.org/wiki/Trihexagonal_tiling
Thanks to Michael Quevillon for the patch.
Officially known as the '3-4-6-12 tiling', according to, e.g.,
https://en.wikipedia.org/wiki/3-4-6-12_tiling .
Thanks to Michael Quevillon for contributing this patch (and for
choosing a less hard-to-remember name for the tiling :-).
puzzle backend function which ought to have it, and propagate those
consts through to per-puzzle subroutines as needed.
I've recently had to do that to a few specific parameters which were
being misused by particular puzzles (r9657, r9830), which suggests
that it's probably a good idea to do the whole lot pre-emptively
before the next such problem shows up.
[originally from svn r9832]
[r9657 == 3b250baa02a7332510685948bf17576c397b8ceb]
[r9830 == 0b93de904a98f119b1a95d3a53029f1ed4bfb9b3]
to add two kinds of Penrose tiling to the grid types supported by
Loopy.
This has involved a certain amount of infrastructure work, because of
course the whole point of Penrose tilings is that they don't have to
be the same every time: so now grid.c has grown the capacity to
describe its grids as strings, and reconstitute them from those string
descriptions. Hence a Penrose Loopy game description consists of a
string identifying a particular piece of Penrose tiling, followed by
the normal Loopy clue encoding.
All the existing grid types decline to provide a grid description
string, so their Loopy game descriptions have not changed encoding.
[originally from svn r9159]
part that converts from abstract grid coordinates into screen
coordinates. This should speed up window-resizing by eliminating
pointless reiteration of the complicated part of the algorithm: now
when a game_drawstate is renewed, only the conversion into screen
coordinates has to be redone.
[originally from svn r9157]
overly complicated algorithm that uses it to home in on the grid edge
closest to a mouse click. That algorithm is being stressed beyond its
limit by the new grid type, and it's unnecessary anyway given that no
sensibly sized puzzle grid is going to be big enough to make it
prohibitively expensive just to do the trivial approach of iterating
over all edges and finding the closest of the eligible ones.
[originally from svn r9108]
on Windows at all?! Fix some departures from the C standard, mostly
declaring variables after a statement has already been issued in the
same block. MSVC is picky about this where gcc is forgiving, and TBH
I'd change the latter given the choice.
[originally from svn r8166]
Lambrou. Now capable of handling triangular and hexagonal grids as
well as square ones, and then a number of semiregular plane tilings
and duals of semiregular ones. In fact, most of the solver code
supports an _arbitrary_ planar graph (well, provided both the graph
and its dual have no self-edges), so it could easily be extended
further with only a little more effort.
[originally from svn r8162]
