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1996-04-08
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X-BASED HEXAGONS
================ Hexagons X widget, V5.3
It has been tested on the following platforms:
HP 3xx & 700 HP-UX 9.0x X11R5
Sun4, SPARC SunOS 4.1.3 X11R4
Sun4, SPARC SunOS 5.4 X11R5
PC, 486 Linux 1.0.9 X11R5
PC, 486 Linux 1.2.8 X11R6(*)
* Keypad may not work, since various keycodes may not be defined
by default. Check that "KP_1 - KP_9, Home, Up, Prior, Left,
Begin, Right, End, Down, Next" are defined towards the end of
/usr/lib/X11/etc/xmodmap.std . If not defined
cp /usr/lib/X11/etc/xmodmap.std /usr/lib/X11/xinit/.Xmodmap
and then motify this or create your own at ${HOME}/.Xmodmap .
You should just have to uncomment them (get rid of some '!').
If yours is not in this list, please let me know -- thanks. The
most updated source could be found on ftp.x.org under
/contrib/games/puzzles.
HOW TO BUILD?
It should be easy. Edit the Imakefile (or Makefile.std, see below)
for appropriate settings of variable SCOREFILE, then do:
xmkmf
make
xhexagons [motif version will be xmhexagons]
Note: if you don't have 'xmkmf' or the "Makefile" it generates
doesn't work well, edit Makefile.std for appropriate settings for
XINCLUDEPATH and XLIBPATH, then try:
make -f Makefile.std
xhexagons
or if you have Motif, uncomment appropriate sections, then try:
make -f Makefile.std all.xm
xmhexagons
You should have Hexagons.ad copied to $(HOME)/Hexagons or
/usr/lib/X11/app-defaults/Hexagons to run, especially if the background
is similar to one of the faces. Edit this file for your preferences.
You might want to move xhexagons into /usr/bin/X11 (or wherever your
X binaries are).
You might also want to move xhexagons.man to /usr/man/man6/xhexagons.6
ANYTHING SPECIAL IN USING?
Click on the left mouse button to move tile. If in corners mode,
a free tile will not move until released on a space.
Click on the right mouse button if you want to randomize the puzzle.
Also 'R' or 'r' does the same thing. One must double click on
the right mouse button if the puzzle is being worked on.
'I' or 'i' to increase or move up the number of hexagons.
'D' or 'd' to decrease or move down the number of hexagons.
'C' or 'c' to toggle corners mode. (Default is on).
'S' or 's' to auto-solve. Unfortunately, its unimplemented.
'U' or 'u' to undo last move.
'G' or 'g' to get a saved puzzle.
'W' or 'w' to write or save a puzzle.
'Q', 'q', or Control-C to kill program.
Key pad is defined for Hexagons as:
7 9
^
4 < > 6
v
1 3
Tiles can also be moved by the keypad,
KP_7=>TopLeft KP_9=>TopRight
KP=>Left KP_6=>Right
KP_1=>BottomLeft KP_3=>BottomRight
In corners mode, one can only move one tile at a time. The only
tiles that can be moved are the tile(s) next to both spaces. In the
other mode, one can move more than one tile at a time and one is
not constrained by parity.
The title is in the following format (non-motif version):
xhexagons: <size> @ (<Number of moves>/\
{<Record number of moves>|NEVER|PRACTICE}) - <Comment>
{<Record...}: puzzle is either in practice mode or record mode
In record mode, if there is no record of the current puzzle, it
displays "NEVER".
If you were looking for a auto-solver, sorry.
Keep in mind that Hexagons is a widget that can be simply stuck in
other X programs. (If you find a use for this, let me know).
Refer to the man page for detailed command line options.
If you want further information on puzzles, I'll be glad :-) to send
it to you.
SAVE FORMAT
The format is not standard. The reason is that this is simple to
produce and I do not know what the standard is. The format will
probably change to become more readable.
size: number of tiles in a row
corners: 0 false, 1 true hexagon corners
moves: 0-MAXINT
startingPosition: array where 0 is the empty space for the HIGH hexagon
and -1 is the empty space for the LOW hexagon.
This is then followed by the moves
move #: direction
Direction is represented as 0 upper right, 1 right, 2 lower right,
3 lower left, 4 left, and 5 upper left.
Caution: the program may crash on corrupted input.
MATHEMATICAL BASIS
Lets start out with a triangle of hexagons for simplicity's sake
and then expand these ideas to a hexagon of hexagons
Assuming it is a triangle of i hexagons in each row and the
numbering starts from 1.
Corner 1-> 1
2-> i(i+1)/2 - i + 1
3-> i(i+1)/2
Center ->i%3 =>
1: (2i'-1)*(2i')/2-i'+1 where i'= (i+2)/3
default: None
Max_Width -> i * 3^(1/2) units
Max_Height -> (3/2)i+(1/2) units
Start -> x= i * 3^(1/2)/2 units
y=0
fin=i
step=i
Next -> (n==fin) =>
true: x+= -3^(1/2) * (2 * step - 1)/2 units; y+=3/2 units;
step++; fin+=step
default: x+= 3^(1/2) units
Same row? -> (m'==n') where s'=(1+sqrt_trunc(1+8*(s - 1)))/2 {k}
i.e. s = s'(s'-1)/2
Same trbl? -> (m-1)-m'(m'-1)/2 == (n-1)-n'(n'-1)/2 {i}
Same tlbr? -> (m'+1)m'/2-m == (n'+1)n'/2-n {j}
Now assuming it is a hexagon of i hexagons in each row and
the numbering starts from 1.
Corner 1-> 1
2-> i
3-> Center - i + 1
4-> Center + i - 1
5-> 3i(i-1) - i + 2
6-> 3i(i-1) + 1
Center -> 3i(i-1)/2 + 1
Max_Width -> (2i-1) * 3^(1/2) units
Max_Height -> 3i-1 units
Start -> x= i * 3^(1/2)/2 units
y=0
fin=i
step=i
Next -> (n<=center) =>
true: (n==fin)
true: x+= -3^(1/2) * (2 * step - 1)/2 units; y+=3/2 units;
step++; fin+=step
default: x+= 3^(1/2) units
default: (n==fin)
true: step--; x+= -3^(1/2) * (2 * step - 1)/2 units;
y+=3/2 units; fin+=step
default: x+= 3^(1/2) units
Same row? -> (m'==n') {k} where (s<=center) =>
true: s' = (1+sqrt_trunc(1+8*(s+i*(i-1)/2)))/2-i
i.e. s = s'*(2s'-1)-(i)(i-1)/2
default: s' = 3*i-2-(1+sqrt_trunc(1+8*(3i(i-1)+1+i*(i-1)/2-s)))/2)
Same trbl? -> (m''==n'') {i} where (s<=center) =>
true: s'' = (s+i*(i-1)/2)-(s'+i)*(s'+i-1)/2
default: s'' = 2*i-2-(3i(i-1)+i*(i-1)/2-s-(3*i-s'-2)*(3*i-s'-3)/2)
Same tlbr? -> (m''==n'') {j} where (s<=center) =>
true: s'' = -1-((s+i*(i-1)/2)-(s'+i+1)*(s'+i)/2)
default: s'' = 2*i-1+(3i(i-1)+i*(i-1)/2-s-(3*i-s'-1)*(3*i-s'-2)/2)
FOUND A BUG?
Send bugs reports and fixes to the author. For bugs, please include
as much information as to their location as possible, since I may not
have the resources to duplicate the them.
David Albert Bagley, bagleyd@hertz.njit.edu
HISTORY
[Apr 08, 96] V5.3: Minor changes.
[Jan 31, 96] V5.2: If corners mode, a tile is now moved by a more
intuitive drag and drop approach. Tiles will invert,
when selected. Now using dynamic allocation, so there
is no maximum size.
[Dec 15, 95] V5.1: Minor updates, RNG for 32/64 bit, border color
to make faces look more realistic.
[Oct 01, 95] V5.0: Xt/Motif, your choice.
[May 16, 95] V4.10: Warnings removed from Sun's cc and lint and now
include a random number generator.
[Mar 13, 95] V4.5: Removed lint warnings and added a VMS make.com .
[Nov 11, 94] V4.4: Conservative guess for random number generator.
[Nov 02, 94] V4.3: Now allows undos, saves, and recalls.
[Aug 23, 94] V4.2: Switched left and middle buttons on the mouse to
have up and down consistent with vi's "j", "k" keys.
[Jun 28, 94] V4.1: Can accommodate a auto-solver.
[Jun 07, 94] V4.0: Xt version.
I got some good ideas from oclock.
[Apr 01, 93] V3.0: Motif version.
I got some good ideas from Douglas A. Young's
book: "The X Window System Programming and Applications
with Xt OSF/Motif Edition", particularly his dial widget.
I got some good ideas on presentation from Q. Zhao's
tetris.
[Jan 07, 92] V2.0: XView version.
[Sep 06, 91] V1.0: SunView version.