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# (C)2007-2008 by Marc Roeder,
# distribute under the terms of the GPL version 2.0 or later
LoadPackage("hapcryst");
####
# Adjust these variables, if needed:
#
JAVAVIEW_PROGRAM:=Filename(DirectoriesSystemPrograms(),"javaview");
#JAVAVIEW_OUTPUT_DIR:=Directory("~/flatManifolds3d/tmp");
JAVAVIEW_OUTPUT_DIR:=DirectoryTemporary();
PRECISION:=9;
## PRECISION is the number of digits after the first non- zero digit
## after the comma.
## If your polytope looks too strange, increase this number.
JAVAVIEW_WRAPPER_FILE:=Filename(DirectoriesPackageLibrary("hapcryst","examples"),"javaviewwrapper.txt");
ReadPackage("hapcryst","examples/orbitcoloring.gap");
############
### The following 3-dimensional space groups are Bieberbach.
### So you might try viewFundamentalDomain for those:
bieberbachlist:=[ 1, 4, 7, 9, 19, 33, 34, 76, 142, 165 ];
#############################################################################
##
## PLEASE READ THIS:
##
## to get a picture of a fundamental domain of a 3-dimensional Bieberbach
## group, just type
## viewFundamentalDomain([a,b,c],n);
## with a,b,c rational numbers and n a number from the bieberbachlist.
##
## or type
## viewTessellation([a,b,c],n);
## to get a part of the tessellation defined by the fundamental domain.
## The shown geometry contains hidden parts. Look at "Inspector>Display"
## The neighbouring parts are named by the face of the original fundamental
## cell they touch. You can view the names by making the fundamental domain
## "FD" active and tick the box at "Method>Show>Show Element Names".
##
## Use "Inspector>Camera" to zoom in and out.
#############################################################################
##
## This function takes a fundamental domain and colors the faces.
## It also calculates a set of images under <maps> and generates a
## JavaView file containing all that.
##
writeFundamentalDomainAndImages:=function(poly,maps,group,point,groupnr)
local startpointstring, filename, vertexonlypoly, abstract,
title, detail, data, outputfile;
startpointstring:=ReplacedString(JoinStringsWithSeparator(List(point,String),"_"),"/",".");
filename:=Concatenation([numberWithLeadingZeros(groupnr,3),
"__",
startpointstring]);
vertexonlypoly:=CreatePolymakeObjectFromFile(JAVAVIEW_OUTPUT_DIR,Concatenation(filename,".poly"));
ClearPolymakeObject(vertexonlypoly);
AppendVertexlistToPolymakeObject(vertexonlypoly,Polymake(poly,"VERTICES"));
Unbind(vertexonlypoly);
abstract:="Fundamental cell of cystallographic group ";
Append(abstract,String(groupnr));
title:=Concatenation("FD ",String(groupnr));
detail:="This is the fundamental cell of the crystallographic group number ";
Append(detail,String(groupnr));
Append(detail," from GAPs crystallographic groups library.\n The orbits are colored in each dimension.\n");
Append(detail,"Starting point for Dirichlet-Voronoi: ");
Append(detail,String(point));
Append(detail,".\nOutput precision: ");
Append(detail,String(PRECISION));
Append(detail," (this is the number of digits after the first non-zero entry after the point.");
Append(detail,"\nGenerated using the GAP packages HAPcryst and polymake as well as the computational geometry package polymake.");
data:=javaviewDatastring(poly,maps,group,PRECISION);
Append(filename,".jvx");
outputfile:= OutputTextFile(Filename(JAVAVIEW_OUTPUT_DIR,filename), false );
WriteAll(outputfile,
javaviewWrappedDatastring(
title,
abstract,
detail,
data,
JAVAVIEW_WRAPPER_FILE)
);
CloseStream(outputfile);
return Filename(JAVAVIEW_OUTPUT_DIR,filename);
end;
#############################################################################
##
## This just generates the fundamental domain and writes a JavaView file for it
##
writeFundamentalDomain:=function(poly,group,point,groupnr)
return writeFundamentalDomainAndImages(poly,[IdentityMat(4)],group,point,groupnr);
end;
#############################################################################
##
##
generateFundamentalDomain:=function(point,groupnr)
local group, poly, filename,vo;
group:=SpaceGroup(3,groupnr);
# poly:=FundamentalDomainStandardSpaceGroup(point,group);
poly:=FundamentalDomainBieberbachGroupNC(point,group);
if not IsFundamentalDomainStandardSpaceGroup(poly,group)
then
Error("failed generating fundamental domain");
fi;
filename:=writeFundamentalDomain(poly,group,point,groupnr);
return filename;
end;
viewFundamentalDomain:=function(point,groupnr)
local filename;
filename:=generateFundamentalDomain(point,groupnr);
Exec(Concatenation([JAVAVIEW_PROGRAM," ",filename]));
return filename;
end;
generateTessellationFromPolytope:=function(point,poly,groupnr)
local group, facets, vertices, orbitdecomp, maps, facet,
orbit, otherfacet, filename;
group:=SpaceGroup(3,groupnr);
Polymake(poly,"FACETS VERTICES_IN_FACETS FACE_LATTICE");
facets:=Polymake(poly,"VERTICES_IN_FACETS");
vertices:=Polymake(poly,"VERTICES");
orbitdecomp:=edgeOrbitDecomposition(facets,vertices,group);
maps:=[IdentityMat(4)];
for facet in facets
do
orbit:=First(orbitdecomp,o->facet in o);
otherfacet:=First(orbit,f->f<>facet);
Add(maps,RepresentativeActionOnRightOnSets(group,Set(otherfacet,i->vertices[i]),Set(facet,i->vertices[i])));
od;
filename:=writeFundamentalDomainAndImages(poly,maps,group,point,groupnr);
return filename;
end;
generateTessellation:=function(point,groupnr)
local group, poly, filename;
group:=SpaceGroup(3,groupnr);
# poly:=FundamentalDomainStandardSpaceGroup(point,group);
poly:=FundamentalDomainBieberbachGroupNC(point,group);
filename:=generateTessellationFromPolytope(point,poly,groupnr);
return filename;
end;
viewTessellation:=function(point,groupnr)
local filename;
filename:=generateTessellation(point,groupnr);
Exec(Concatenation([JAVAVIEW_PROGRAM," ",filename]));
return filename;
end;
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