www.gusucode.com > demos工具箱matlab源码程序 > demos/soma.m
function soma(Action)
%SOMA display precomputed solutions to Piet Hein's soma cube
% A solution is represented by a vector of locations within
% the 3x3 cube, 1 being lower left front, 27 being upper right back.
% This gui allows the user to look at one solution at a time.
% W. M. McKeeman
% Copyright 1984-2014 The MathWorks, Inc.
switch nargin,
case 0,
LocalInitFig
case 1,
fig = gcf;
Data = get(fig,'UserData');
switch Action,
case 'Info',
ttlStr = mfilename;
hlpStr1 = ...
{' The soma cube is a puzzle consisting of seven pieces that '
' can be assembled into a 3x3x3 cube. It is a special case of '
' space-filling puzzles. '
' '
' The seven pieces of the soma cube are all pieces that can be '
' made by gluing four or less cubes together at their faces, '
' producing a piece with an inside corner. That is, three '
' cubes forming a "V" are included but three cubes making an '
' "I" are excluded. '
' '
' The seven pieces are named V L T Z S R Y, all but S and R '
' approximating the shape of the assembled cubes. The S piece '
' is "screw shaped" and the R piece is its reflection. The R '
' piece is a "right-handed screw". Pictures of these pieces are'
' displayed when soma.m runs. '
' '
' There are 240 unique ways to assemble the 7 pieces into a '
' 3x3x3 cube, discounting reflections and rotations. '
' '};
hlpStr2 = ...
{' The combinatorics of brute force computation are on the '
' order of 100^7, since each piece can fit into the cube in '
' about 100 different ways. Fortunately, there are some '
' theories which reduce the computation to a feasible task. '
' '
' The simplest theorem involves examining the 8 vertices of the'
' completed solution. The V Z S R Y pieces can occupy at most '
' 1 of these 8 vertices. The T piece can touch 2 or 0 '
' vertices, and the L piece can touch 2, 1 or 0. If you add '
' up the maximum number of vertices touchable by the pieces, '
' it comes out to 1+2+2+1+1+1+1=9. Therefore, exactly one '
' piece contributes 1 less than its maximum. That cannot be T,'
' because it cannot touch 1 vertex. One concludes that T '
' always touches 2 vertices, and therefore is always in exactly'
' the same position in the finished cube (after rotation). The'
' soma cube is really only a 6 piece puzzle! '
' '};
hlpStr3 = ...
{' A more general theorem accounts for classes VEFC, standing '
' for the 8 Vertices, 12 Edges, 6 Faces and 1 Center. Any '
' solution has to fill each of the VEFC classes exactly. To '
' carry out the analysis, first classify the pieces themselves '
' by VEFC. V, for example, can be 1200, meaning 1 vertex, 2 '
' edges, 0 faces and 0 centers. The sum of the VEFC vectors '
' has to add up to 8 12 6 1, and therefore the search can be '
' restricted to class of piece positions for which the VEFC sum'
' holds. This leads to 11 combinations of piece position '
' classes, for which the combinatoric is more like 10^7, which '
' can be computed in about an hour. '
' '
' This program could be modified to solve other objects that '
' can be built out of the 7 pieces (commercial puzzles come '
' with dozens of suggestions), or to solve puzzles made of '
' other pieces (The double soma cube consists of L T Z S R Y '
' plus two length 4 "I" pieces plus 2 size 4 "O" pieces gives '
' 24+24+4+4+4+4=64, making a 4x4x4 cube possible). The eight '
' queens problem can be thought of as filling a space '
' consisting of rows, columns and diagonals of the chessboard '
' (8+8+14+14) where each queen takes a row, a column and two '
' diagonals. '};
helpwin(cat(1,hlpStr1, hlpStr2, hlpStr3), ttlStr);
case 'Next',
if Data.sn < 240,
Data.sn = Data.sn+1;
else
Data.sn = 1;
end
set(Data.pn,'string',getString(message('MATLAB:demos:soma:LabelNOf240',num2str(Data.sn))));
Data.sol = Data.sols(Data.sn,:);
LocalRepaint(Data)
set(fig,'UserData',Data);
case 'Previous',
if Data.sn > 1,
Data.sn = Data.sn-1;
else
Data.sn = 240;
end
set(Data.pn,'string',getString(message('MATLAB:demos:soma:LabelNOf240',num2str(Data.sn))));
Data.sol = Data.sols(Data.sn,:);
LocalRepaint(Data)
set(fig,'UserData',Data);
case 'Close',
delete(gcf)
case 'RotateXY',
Data.sol = LocalRXY(Data.sol);
LocalRepaint(Data)
set(fig,'UserData',Data);
case 'RotateYZ',
Data.sol = LocalRYZ(Data.sol);
LocalRepaint(Data)
set(fig,'UserData',Data);
otherwise,
error('MATLAB:soma:NoInputs','%s',...
getString(message('MATLAB:demos:soma:NoInputs')));
end % switch
otherwise,
error('MATLAB:soma:NoInputs','%s',...
getString(message('MATLAB:demos:soma:NoInputs')));
end % switch
%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% LocalRepaint %%%%%
%%%%%%%%%%%%%%%%%%%%%%%%
function LocalRepaint(Data)
% FUNCTION: LocalRepaint
% PURPOSE: callback to repaint the soma cube
% METHOD: run from stage4.m
% facelet -- cubie correlation
% R L T R L T R L T
face = [1 1 19 10 10 22 19 19 25,...
2 4 20 11 13 23 20 22 26,...
3 7 21 12 16 24 21 25 27];
% the standard VLTZSRY order of display, 3 V, 4 L, etc.
% r g b
purple = [.4 0 .6]; % V -- piece colors
blue = [0 0 1]; % L
green = [0 1 .2]; % T
yellow = [1 1 0]; % Z
orange = [.9 .5 0]; % S
red = [1 0 0]; % R
violet = [1 0 1]; % Y
white = [1 1 1]; % empty
pc = [purple; purple; purple
blue; blue; blue; blue
green; green; green; green
yellow; yellow; yellow; yellow
orange; orange; orange; orange
red; red; red; red
violet; violet; violet; violet];
for c = 1:27
soltn = Data.sol(c);
set(Data.squarelet(soltn), 'facecolor', pc(c,:));
for d = 1:27
if soltn == face(d)
set(Data.trp(d), 'facecolor', pc(c,:));
end
end
end
%%%%%%%%%%%%%%%%%%%%
%%%%% LocalRXY %%%%%
%%%%%%%%%%%%%%%%%%%%
function newp = LocalRXY(oldp)
% FUNCTION: LocalRXY
% PURPOSE: rotate a cube in the xy plane
tx = [ 3 6 9 2 5 8 1 4 7,...
12 15 18 11 14 17 10 13 16,...
21 24 27 20 23 26 19 22 25];
newp = tx(oldp);
%%%%%%%%%%%%%%%%%%%%
%%%%% LocalRYZ %%%%%
%%%%%%%%%%%%%%%%%%%%
function newp = LocalRYZ(oldp)
% FUNCTION: LocalRYZ
% PURPOSE: rotate a cube in the xy plane
tx = [7 8 9 16 17 18 25 26 27,...
4 5 6 13 14 15 22 23 24,...
1 2 3 10 11 12 19 20 21]; % rotation y to z
newp = tx(oldp);
%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% LocalInitFig %%%%%
%%%%%%%%%%%%%%%%%%%%%%%%
function LocalInitFig
cubie = [0 0; 0 1; 1 1; 1 0; 0 0]; % to draw a little square
% physical layout of cubies to form sliced display of 3x3 cube
cube = [0 0; 1 0; 2 0; 0 1; 1 1; 2 1; 0 2; 1 2; 2 2
4 0; 5 0; 6 0; 4 1; 5 1; 6 1; 4 2; 5 2; 6 2
8 0; 9 0; 10 0; 8 1; 9 1; 10 1; 8 2; 9 2; 10 2];
% r g b
purple = [.4 0 .6]; % V -- piece colors
blue = [0 0 1]; % L
green = [0 1 .2]; % T
yellow = [1 1 0]; % Z
orange = [.9 .5 0]; % S
red = [1 0 0]; % R
violet = [1 0 1]; % Y
white = [1 1 1]; % empty
v = [1 0; 0 0; 0 1]; % to draw a V
l = [v; 0 2]; % add a cubie and get an L
t = [0 1; 1 1; 2 1; 1 0]; % to draw a T
z = [0 1; 1 1; 1 0; 2 0]; % to draw a Z
s = [v; 1.2 .2]; % add a cubie and get an S
r = [v; .2 1.2]; % add a cubie and get an R
y = [v; .2 .2]; % add a cubie and get a Y
xv = cubie(:,1); % x vector to drive patch()
yv = cubie(:,2); % y vector to drive patch()
backcolor = [1 1 1]; % white
backcolor = [.8 .8 .8]; % grey
screenpos = 300; % about the middle
screenx = 700; % about half
screeny = 500; % about half
axescolor = [1 1 1];
figh = figure(...
'Color' , backcolor,...
'NumberTitle','off', ...
'Toolbar', 'none', ...
'CloseRequestFcn','soma Close', ...
'Name' , getString(message('MATLAB:demos:soma:TitleSomaCubeSolutions')));
ax2 = axes(...
'Units' , 'normalized',...
'Position', [0.05 .05 0.7 0.25] ,...
'Color' , axescolor);
axis([0 1 0 1]);
set(gca,'XTick',[],'YTick',[]);
text(.5,.5,{getString(message('MATLAB:demos:soma:LabelSomaCube'));' '; ...
getString(message('MATLAB:demos:soma:LabelLongDescription'))}, ...
'HorizontalAlignment','center', ...
'color', 'black');
ax = axes(...
'Units' , 'normalized',...
'Position', [0.05 .3 0.7 0.7] ,...
'Color' , axescolor);
axis image ;
axis([0 1 0 .6]);
set(gca,'XTick',[],'YTick',[]);
buttonx = .80;
buttony = .95;
buttonwidth = 0.15;
buttonheight = 0.08;
spacing = 0.03;
sn = 1;
% following are the active elements for user control
uicontrol(figh,... % decrement solution selection
'Style' , 'frame',...
'Units' , 'normalized',...
'Position', [buttonx-0.01,0.05,buttonwidth+0.02,0.9]);
pt = uicontrol(figh,... % slider title
'Style', 'text',...
'String', getString(message('MATLAB:demos:soma:LabelSolutionNumber')),...
'Units', 'normalized',...
'Position',[buttonx,buttony-buttonheight-spacing, ...
buttonwidth,buttonheight]);
pn = uicontrol(figh,... % visible solution number
'Style', 'text',...
'String', getString(message('MATLAB:demos:soma:LabelNOf240',num2str(1))),...
'Units', 'normalized',...
'Position',[buttonx, buttony-2*buttonheight-spacing, ...
buttonwidth,buttonheight]);
decr = uicontrol(figh,... % decrement solution selection
'Style' , 'pushbutton',...
'Units' , 'normalized',...
'String' , getString(message('MATLAB:demos:shared:LabelPrevious')),...
'Position',[buttonx, buttony-3*buttonheight-2*spacing, ...
buttonwidth,buttonheight], ...
'Callback', 'soma Previous');
incr = uicontrol(figh,... % increment solution selection
'Style' , 'pushbutton',...
'Units' , 'normalized',...
'String' , getString(message('MATLAB:demos:shared:LabelNext')),...
'Position',[buttonx, buttony-4*buttonheight-3*spacing, ...
buttonwidth,buttonheight], ...
'Callback', 'soma Next');
pq = uicontrol(figh ,... % the [quit] button
'Style' , 'pushbutton',...
'Units' , 'normalized',...
'String' , getString(message('MATLAB:demos:shared:LabelClose')),...
'Position' , [buttonx, 0.05+spacing,buttonwidth,buttonheight],...
'Callback' ,'soma Close');
pq = uicontrol(figh ,... % the info button
'Style' , 'pushbutton',...
'Units' , 'normalized',...
'String' , getString(message('MATLAB:demos:shared:LabelInfo')),...
'Position' , [buttonx, 0.05+2*spacing+buttonheight, ...
buttonwidth,buttonheight],...
'Callback' ,'soma Info');
rot1 = uicontrol(figh,... % rotate solution xy
'Style', 'pushbutton',...
'Units', 'normalized',...
'String', getString(message('MATLAB:demos:soma:LabelRotateRight')),...
'Position', [.575, .72, .15, .08],...
'Callback','soma RotateXY');
rot2 = uicontrol(figh,... % rotate solution yz
'Style', 'pushbutton',...
'Units', 'normalized',...
'Position', [.44, .58, .15, .08],...
'String', getString(message('MATLAB:demos:soma:LabelRotateDown')),...
'Callback', 'soma RotateYZ');
sqsize = 0.03; % edge of a squarelet
dy3 = 1; % y posit for sample title
dy2 = dy3+1; % y posit for name of sample
dy = dy2+1; % y posit for sample pieces
dx = 4; % x posit for sample pieces
text('position', [dx+.5 dy2]*sqsize, 'string', 'V', 'color', 'black');
for c = 1:3 % paint a sample V
xx = xv+v(c,1)+dx;
yy = yv+v(c,2)+dy;
pv = patch(xx*sqsize, yy*sqsize, purple);
end
dx = dx + 4;
text('position', [dx+.5 dy2]*sqsize, 'string', 'L', 'color', 'black');
for c = 1:4 % paint a sample L
xx = xv+l(c,1)+dx;
yy = yv+l(c,2)+dy;
ph = patch(xx*sqsize, yy*sqsize, blue);
end
dx = dx + 4;
text('position', [dx+1 dy2]*sqsize, 'string', 'T', 'color', 'black');
for c = 1:4 % paint a sample T
xx = xv+t(c,1)+dx;
yy = yv+t(c,2)+dy;
pt = patch(xx*sqsize, yy*sqsize, green);
end
dx = dx + 4;
text('position', [dx+1 dy2]*sqsize, 'string', 'Z', 'color', 'black');
for c = 1:4 % paint a sample Z
xx = xv+z(c,1)+dx;
yy = yv+z(c,2)+dy;
pz = patch(xx*sqsize, yy*sqsize, yellow);
end
dx = dx + 4;
text('position', [dx+.5 dy2]*sqsize, 'string', 'S', 'color', 'black');
for c = 1:4 % paint a sample S
xx = xv+s(c,1)+dx;
yy = yv+s(c,2)+dy;
ps = patch(xx*sqsize, yy*sqsize, orange);
end
dx = dx + 4;
text('position', [dx+.5 dy2]*sqsize, 'string', 'R', 'color', 'black');
for c = 1:4 % paint a sample R
xx = xv+r(c,1)+dx;
yy = yv+r(c,2)+dy;
pr = patch(xx*sqsize, yy*sqsize, red);
end
dx = dx + 4;
text('position', [dx+.5 dy2]*sqsize, 'string', 'Y', 'color', 'black');
for c = 1:4 % paint a sample Y
xx = xv+y(c,1)+dx;
yy = yv+y(c,2)+dy;
py = patch(xx*sqsize, yy*sqsize, violet);
end
text('position', [14.5 dy3]*sqsize,...
'string', getString(message('MATLAB:demos:soma:LabelSomaCubePieces')),...
'color', 'black');
% paint an empty solution in three layers
% cube(i,1) is a sequence of x positions outlining squarelet i [1:27]
% cube(i,2) is a sequence of y positions outlining squarelet 1 [1:27]
for c = 1:27 % cycle through cubies
xx = xv+cube(c,1)+5; % x trace for cubie c
yy = yv+cube(c,2)+12; % y trace + move image up 6
squarelet(c) = patch(xx*sqsize, yy*sqsize, white);
end
% paint an empty cube in 3 d
c = cos(pi/6); % 30 degrees
s = sin(pi/6);
x1 = [0 c c 0 0]; % trace a facelet on right
y1 = [0 s c+s c 0];
x2 = -x1; % trace a facelet on left
x3 = [0 c 0 -c 0]; % trace a facelet on top
y3 = [ 0 s 2*s s 0]+3*c;
dx3 = 22; % place 3d image on screen
dy3 = 11;
x1 = x1 + dx3;
x2 = x2 + dx3;
x3 = x3 + dx3;
y1 = y1 + dy3;
y3 = y3 + dy3;
k = 1; % 27 visible facelets
for x = 0:2
for y = 0:2
px = x1+x*c;
py = y1+y*c+x*s;
trp(k) = patch(px*sqsize, py*sqsize, [1 1 1]); % on right R
k = k + 1;
px = x2-x*c;
trp(k) = patch(px*sqsize, py*sqsize, [1 1 1]); % on left L
k = k + 1;
px = x3+x*c-y*c;
py = y3+y*s+x*s;
trp(k) = patch(px*sqsize, py*sqsize, [1 1 1]); % on top T
k = k + 1;
end
end
gox = 11*sqsize;
goy = .48;
line1 = text(gox, goy,'',...
'HorizontalAlignment','center', ...
'color', 'black', ...
'String',getString(message('MATLAB:demos:soma:LabelSolutionInThreeLayers')));
line2 = text(.5, .58,...
getString(message('MATLAB:demos:soma:TitleSolutionsForTheSomaCubePuzzleOfPietHein')),...
'HorizontalAlignment','center', ...
'color', 'black');
layerx = .15;
layery = .32;
lw = sqsize*4;
line3 = text(layerx+.005, layery, getString(message('MATLAB:demos:soma:LabelBottom')), 'color', 'black');
line4 = text(layerx+lw+.01, layery, getString(message('MATLAB:demos:soma:LabelMiddle')), 'color', 'black');
line5 = text(layerx+2*lw+.025, layery, getString(message('MATLAB:demos:soma:LabelTop')), 'color', 'black');
Patches = findobj(figh,'Type','patch');
Data.pn = pn;
Data.sn = sn;
Data.sols = somasols;
Data.sol = Data.sols(1,:);
Data.squarelet = squarelet;
Data.trp = trp;
set(figh,'UserData',Data);
LocalRepaint(Data)