dolfin team mailing list archive
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dolfin team
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Mailing list archive
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Message #18018
Re: Merge request for some sandbox stuff
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To:
Anders Logg <logg@xxxxxxxxx>
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From:
Andre Massing <massing@xxxxxxxxx>
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Date:
Tue, 6 Apr 2010 18:44:03 +0200
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Cc:
DOLFIN Mailing List <dolfin@xxxxxxxxxxxxxxxxxxx>
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In-reply-to:
<20100406155011.GZ6930@olorin>
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Organization:
Simula Research Laboratory
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User-agent:
KMail/1.13.1 (Linux/2.6.31.4-centrino-duo; KDE/4.4.1; x86_64; ; )
On Tuesday 6. April 2010 17.50.13 Anders Logg wrote:
> Could you publish your sandbox branch?
It is published under
lp:~massing/dolfin/sandbox_branch
but bzr crashed while I was pushing it, great. Checked it, everything seems
to be there. Something seems to be wrong with launchpad server, my mails
needed half a day to be delivered.
>
> I think we should just merge published sandbox branches without (or
> with minimal) review, but it's good to use the possibility of
> publishing branches on Launchpad + I need to practice how to
> review/approve/merge branches on Launchpad. I've never done it before.
>
> --
> Anders
>
> On Tue, Apr 06, 2010 at 11:25:07AM +0200, Andre Massing wrote:
> > Hi!
> >
> > While I am working on a implementation of Nitsche methods for overlapping
> > meshes in DOLFIN I produce some sand, which might be nice to be added to
> > the sandbox :) It contains among other things some prototypes for
> > building a complete intersection map for two overlapping meshes (which
> > cells/facets are covered by which cells/facest) and for barycenter
> > quadrature formulas on arbitrary polyhedrons and polygons
> > (unfortunately just for the 3D case, up to now).
> >
> > Kind regards,
> > Andre
> >
> > # Bazaar merge directive format 2 (Bazaar 0.90)
> > # revision_id: massing@xxxxxxxxx-20100406091417-ogh30d38n95eh5cq
> > # target_branch: bzr+ssh://bazaar.launchpad.net/~dolfin-\
> > # core/dolfin/sandbox/
> > # testament_sha1: 74c2e1fd30a903bacbd8c50606cb683173e73813
> > # timestamp: 2010-04-06 11:15:17 +0200
> > # base_revision_id: logg@xxxxxxxxx-20100226124738-bk9jlyb9voycqbwa
> > #
> > # Begin patch
> > === renamed directory 'cgal' => 'nitsche_method'
> > === added directory 'nitsche_method/data'
> > === added directory 'nitsche_method/data/meshes'
> > === added file 'nitsche_method/data/meshes/rotator.xml'
> > --- nitsche_method/data/meshes/rotator.xml 1970-01-01 00:00:00 +0000
> > +++ nitsche_method/data/meshes/rotator.xml 2010-03-16 14:39:09 +0000
> > @@ -0,0 +1,402 @@
> > +<?xml version="1.0" encoding="UTF-8"?>
> > +
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> > + <entity index="36" value="792"/>
> > + <entity index="37" value="833"/>
> > + <entity index="38" value="793"/>
> > + <entity index="39" value="834"/>
> > + <entity index="40" value="794"/>
> > + <entity index="41" value="835"/>
> > + <entity index="42" value="795"/>
> > + <entity index="43" value="836"/>
> > + <entity index="44" value="796"/>
> > + <entity index="45" value="837"/>
> > + <entity index="46" value="797"/>
> > + <entity index="47" value="838"/>
> > + <entity index="48" value="839"/>
> > + <entity index="49" value="840"/>
> > + <entity index="50" value="841"/>
> > + <entity index="51" value="801"/>
> > + <entity index="52" value="842"/>
> > + <entity index="53" value="802"/>
> > + <entity index="54" value="843"/>
> > + <entity index="55" value="803"/>
> > + <entity index="56" value="844"/>
> > + <entity index="57" value="804"/>
> > + <entity index="58" value="845"/>
> > + <entity index="59" value="805"/>
> > + <entity index="60" value="846"/>
> > + <entity index="61" value="806"/>
> > + <entity index="62" value="847"/>
> > + <entity index="63" value="807"/>
> > + <entity index="64" value="848"/>
> > + <entity index="65" value="808"/>
> > + <entity index="66" value="849"/>
> > + <entity index="67" value="809"/>
> > + <entity index="68" value="850"/>
> > + <entity index="69" value="872"/>
> > + <entity index="70" value="871"/>
> > + <entity index="71" value="873"/>
> > + <entity index="72" value="874"/>
> > + <entity index="73" value="875"/>
> > + <entity index="74" value="876"/>
> > + <entity index="75" value="877"/>
> > + <entity index="76" value="878"/>
> > + <entity index="77" value="879"/>
> > + <entity index="78" value="880"/>
> > + <entity index="79" value="881"/>
> > + <entity index="80" value="882"/>
> > + <entity index="81" value="883"/>
> > + <entity index="82" value="884"/>
> > + <entity index="83" value="885"/>
> > + <entity index="84" value="886"/>
> > + <entity index="85" value="887"/>
> > + <entity index="86" value="888"/>
> > + <entity index="87" value="889"/>
> > + <entity index="88" value="890"/>
> > + <entity index="89" value="891"/>
> > + <entity index="90" value="922"/>
> > + <entity index="91" value="921"/>
> > + <entity index="92" value="923"/>
> > + <entity index="93" value="963"/>
> > + <entity index="94" value="962"/>
> > + <entity index="95" value="964"/>
> > + <entity index="96" value="1004"/>
> > + <entity index="97" value="1003"/>
> > + <entity index="98" value="1005"/>
> > + <entity index="99" value="1045"/>
> > + <entity index="100" value="1044"/>
> > + <entity index="101" value="1046"/>
> > + <entity index="102" value="1086"/>
> > + <entity index="103" value="1085"/>
> > + <entity index="104" value="1087"/>
> > + <entity index="105" value="1127"/>
> > + <entity index="106" value="1126"/>
> > + <entity index="107" value="1128"/>
> > + <entity index="108" value="1168"/>
> > + <entity index="109" value="1167"/>
> > + <entity index="110" value="1169"/>
> > + <entity index="111" value="1209"/>
> > + <entity index="112" value="1208"/>
> > + <entity index="113" value="1210"/>
> > + <entity index="114" value="1250"/>
> > + <entity index="115" value="1249"/>
> > + <entity index="116" value="1251"/>
> > + </meshfunction>
> > + </data_entry>
> > + </data>
> > + </mesh>
> > +</dolfin>
> >
> > === added file 'nitsche_method/data/meshes/rotor_cavity.geo'
> > --- nitsche_method/data/meshes/rotor_cavity.geo 1970-01-01 00:00:00 +0000
> > +++ nitsche_method/data/meshes/rotor_cavity.geo 2010-03-16 14:39:09
+0000
> > @@ -0,0 +1,82 @@
> > +//This file defines start geometry for the driven rotor in the cavity
> > problem. +
> > +lb = 0.5;
> > +lc = 0.3;
> > +
> > +// This variable can then be used in the definition of Gmsh's simplest
> > +// `elementary entity', a `Point'. A Point is defined by a list of
> > +// four numbers: three coordinates (X, Y and Z), and a characteristic
> > +// length (lc) that sets the target element size at the point:
> > +
> > +//Cavity geometry
> > +H = 2.0;
> > +
> > +Point(1) = {-H, -H, 0, lb};
> > +Point(2) = {H, -H, 0, lb};
> > +Point(3) = {H, H, 0, lb};
> > +Point(4) = {-H, H, 0, lb};
> > +
> > +Line(1) = {1, 2};
> > +Line(2) = {2, 3};
> > +Line(3) = {3, 4};
> > +Line(4) = {4, 1};
> > +
> > +Line Loop(5) = {1,2,3,4};
> > +
> > +//Physical Point(1) = {1,2,3,4};
> > +//Physical Line(1) = {5};
> > +
> > +
> > +//Rotor geometry
> > +h = 0.1;
> > +l = 1.0;
> > +
> > +//Point(5) = {-h,-h,0,lc};
> > +//Point(6) = {h,-h,0,lc};
> > +//Point(7) = {h,h,0,lc};
> > +//Point(8) = {-h,h,0,lc};
> > +//
> > +//Line(6) = {5,6};
> > +//Line(7) = {6,7};
> > +//Line(8) = {7,8};
> > +//Line(9) = {8,5};
> > +//
> > +//Line Loop(10) = {6,7,8,9};
> > +//Plane Surface(101) = {10};
> > +//Plane Surface(100) = {10};
> > +//Plane Surface(200) = {5,10};
> > +
> > +Point(5) = {h,h,0,lc};
> > +Point(6) = {h,l,0,lc};
> > +Point(7) = {-h,l,0,lc};
> > +Point(8) = {-h,h,0,lc};
> > +Point(9) = {-l,h,0,lc};
> > +Point(10) = {-l,-h,0,lc};
> > +Point(11) = {-h,-h,0,lc};
> > +Point(12) = {-h,-l,0,lc};
> > +Point(13) = {h,-l,0,lc};
> > +Point(14) = {h,-h,0,lc};
> > +Point(15) = {l,-h,0,lc};
> > +Point(16) = {l,h,0,lc};
> > +
> > +Line(6) = {5,6};
> > +Line(7) = {6,7};
> > +Line(8) = {7,8};
> > +Line(9) = {8,9};
> > +Line(10) = {9,10};
> > +Line(11) = {10,11};
> > +Line(12) = {11,12};
> > +Line(13) = {12,13};
> > +Line(14) = {13,14};
> > +Line(15) = {14,15};
> > +Line(16) = {14,15};
> > +Line(17) = {15,16};
> > +Line(18) = {16,5};
> > +
> > +Line Loop(19) = {6,7,8,9,10,11,12,13,14,15,16,17,18};
> > +
> > +//Physical Point(2) = {6,7,8,9,10,11,12,13,14,15,16,17,18};
> > +//Physical Line(2) = {19};
> > +
> > +Plane Surface(100) = {19};
> > +Plane Surface(101) = {5,19};
> >
> > === added directory 'nitsche_method/entity_intersection'
> > === added file 'nitsche_method/entity_intersection/SConstruct'
> > --- nitsche_method/entity_intersection/SConstruct 1970-01-01 00:00:00
> > +0000 +++ nitsche_method/entity_intersection/SConstruct 2010-02-10
> > 03:14:09 +0000 @@ -0,0 +1,16 @@
> > +# This is an example of a simple SConstruct file for building
> > +# programs against DOLFIN. To build this demo, just type 'scons'.
> > +
> > +import os, commands
> > +
> > +# Get compiler from pkg-config
> > +compiler = commands.getoutput('pkg-config --variable=compiler dolfin')
> > +
> > +# Create a SCons Environment based on the main os environment
> > +env = Environment(ENV=os.environ, CXX=compiler)
> > +
> > +# Get compiler flags from pkg-config
> > +env.ParseConfig('pkg-config --cflags --libs dolfin')
> > +
> > +#env.Program(['tetrahedron_triangle_intersection_test.cpp'])
> > +env.Program(['primitive_intersector_test.cpp'])
> >
> > === added file
> > 'nitsche_method/entity_intersection/primitive_intersector_test.cpp' ---
> > nitsche_method/entity_intersection/primitive_intersector_test.cpp
1970-0
> > 1-01 00:00:00 +0000 +++
> > nitsche_method/entity_intersection/primitive_intersector_test.cpp
2010-0
> > 3-05 23:36:16 +0000 @@ -0,0 +1,40 @@
> > +//
> > ========================================================================
> > ============= +//
> > +// Copyright (C) 2010-02-10 André Massing
> > +// Licensed under the GNU LGPL Version 2.1.
> > +//
> > +// Modified by André Massing, 2010
> > +//
> > +// First added: 2010-02-10
> > +// Last changed: 2010-02-22
> > +//
> > +//Author: André Massing (am), massing@xxxxxxxxx
> > +//Company: Simula Research Laboratory, Fornebu, Norway
> > +//
> > +//
> > ========================================================================
> > ============= +
> > +#include <dolfin/mesh/dolfin_mesh.h>
> > +#include <iostream>
> > +
> > +using namespace dolfin;
> > +
> > +int main ()
> > +{
> > + UnitCube cube(3,3,2);
> > + cout <<"Total number of cells in Cube:" << cube.num_cells() <<endl;
> > +
> > + UnitSphere sphere(3);
> > + cout <<"Total number of cells in Sphere:" << sphere.num_cells()
> > <<endl; +
> > + for (CellIterator cube_cell(cube); !cube_cell.end(); ++cube_cell)
> > + {
> > + for (CellIterator sphere_cell(cube); !sphere_cell.end();
> > ++sphere_cell) + {
> > + if (PrimitiveIntersector::do_intersect(*cube_cell, *sphere_cell))
> > + std::cout <<"Cell number " << cube_cell->index() << " intersects with
"
> > + <<"Cell number " << sphere_cell->index() << std::endl;
> > + }
> > + }
> > +
> > + return 0;
> > +}
> >
> > === added directory 'nitsche_method/integration_on_complex_domains'
> > === added directory
> > 'nitsche_method/integration_on_complex_domains/gauss_projection_green'
> > === added file
> > 'nitsche_method/integration_on_complex_domains/gauss_projection_green/Ba
> > ryCenterQuadrature.cpp' ---
> > nitsche_method/integration_on_complex_domains/gauss_projection_green/Bar
> > yCenterQuadrature.cpp 1970-01-01 00:00:00 +0000 +++
> > nitsche_method/integration_on_complex_domains/gauss_projection_green/Bar
> > yCenterQuadrature.cpp 2010-04-01 10:43:19 +0000 @@ -0,0 +1,270 @@
> > +//
> > ========================================================================
> > ============= +//
> > +// Copyright (C) 2010-03-17 André Massing
> > +// Licensed under the GNU LGPL Version 2.1.
> > +//
> > +// Modified by André Massing, 2010
> > +//
> > +// First added: 2010-03-17
> > +// Last changed: 2010-04-01
> > +//
> > +//Author: André Massing (am), massing@xxxxxxxxx
> > +//Company: Simula Research Laboratory, Fornebu, Norway
> > +//Remark: This is an adapted version of Brian Mirtichs original C code
> > for +//computin polyhedral mass properties, which can be found at
> > <web-address> +//
> > ========================================================================
> > ============= +
> > +#include "BaryCenterQuadrature.h"
> > +#include <math.h>
> > +
> > +#define X 0
> > +#define Y 1
> > +#define Z 2
> > +#define SQR(x) ((x)*(x))
> > +#define CUBE(x) ((x)*(x)*(x))
> > +
> > +
> > +using std::sqrt;
> > +using namespace dolfin;
> > +
> > +
> > +void BaryCenterQuadrature::compute_quadrature_rule(const
> > Nef_polyhedron_3 & polyhedron) +{
> > + //coordinates of the bary center
> > + double bary_center [3] = {0,0,0};
> > +
> > + _weight = 0;
> > +
> > + //determine if polyhedron has a non vanishing 3d measure.
> > + //This requires to have volumes marked with one.
> > + bool has_volume = false;
> > + Nef_polyhedron_3::Volume_const_iterator vi;
> > + CGAL_forall_volumes(vi,polyhedron)
> > + {
> > + std::cout <<"vi->mark: " << vi->mark() <<std::endl;
> > + if(vi->mark())
> > + {
> > + has_volume = true;
> > + break;
> > + }
> > + }
> > +
> > + //variables needing during the computation
> > + //components of surface normal
> > + double nx, ny, nz;
> > + double normal [3] = {0,0,0};
> > +
> > + //start and end point of the edge
> > + double source[3] = {0,0,0};
> > + double target[3] = {0,0,0};
> > +
> > + //permutation of the coordinates X,Y,Z
> > + int A,B,C;
> > +
> > + std::cout <<" Number of volumes :" << polyhedron.number_of_volumes()
> > << std::endl; + std::cout << "Outer iteration along faces, next f \n";
> > + std::cout <<"++++++++++++++++++++++++++++++++++++++++" << std::endl;
> > +
> > + std::cout << "Polyhedron is 2d Manifold: " <<
> > const_cast<Nef_polyhedron_3 &>(polyhedron).is_simple() << std::endl; +
> > + for(Nef_polyhedron_3::Halffacet_const_iterator f =
> > polyhedron.halffacets_begin (), + end = polyhedron.halffacets_end();
> > + f != end; ++f)
> > + {
> > + if (f->incident_volume()->mark() || (!has_volume && f->is_twin()))
> > + {
> > + //compute best projection direction.
> > + //get normal of the surface and the offset
> > + //FIXME: check right orientation
> > + Plane_3 face_plane = f->plane();
> > + Vector_3 test_normal = face_plane.orthogonal_vector();
> > + nx = CGAL::to_double(face_plane.a());
> > + ny = CGAL::to_double(face_plane.b());
> > + nz = CGAL::to_double(face_plane.c());
> > +
> > + double normal_length = sqrt(nx*nx + ny*ny + nz*nz);
> > + normal[0] = nx/normal_length;
> > + normal[1] = ny/normal_length;
> > + normal[2] = nz/normal_length;
> > +
> > + nx = fabs(nx);
> > + ny = fabs(ny);
> > + nz = fabs(nz);
> > +
> > + //Choose permutation to get best conditioned projection
> > direction. + if (nx > ny && nx > nz)
> > + C = X;
> > + else
> > + C = (ny > nz) ? Y : Z;
> > + A = (C + 1) % 3;
> > + B = (A + 1) % 3;
> > +
> > + //begin compute the face integrals
> > + //begin compute the projection integrals
> > + double a0, a1, da;
> > + double b0, b1, db;
> > + double a0_2, b0_2;
> > + double a0_3, b0_3;
> > + double a0_4, b0_4;
> > + double a1_2, b1_2;
> > + double C1, Ca, Caa, Cb, Cbb, Cab;
> > + double Kab;
> > + double P1, Pa, Pb, Paa, Pbb, Pab;
> > + P1 = Pa = Pb = Paa = Pab = Pbb = 0.0;
> > + double Fa, Fb, Fc, Faa, Fbb, Fcc;
> > +
> > + for(Nef_polyhedron_3::Halffacet_cycle_const_iterator fc =
> > f->facet_cycles_begin(); + fc != f->facet_cycles_end(); ++fc)
> > + {
> > + //exclude a SHalfloops (whatever this is)
> > + if ( fc.is_shalfedge() )
> > + {
> > + Nef_polyhedron_3::SHalfedge_const_handle h = fc;
> > + Nef_polyhedron_3::SHalfedge_around_facet_const_circulator hc(h);
> > + Nef_polyhedron_3::SHalfedge_around_facet_const_circulator he(hc);
> > + CGAL_For_all(hc,he)
> > + {
> > + std::cout <<"----------------------------------------" <<
> > std::endl; +
> > + Nef_polyhedron_3::SVertex_const_handle v = hc->source();
> > +
> > + const Point_3 & source_point(v->source()->point());
> > + const Point_3 & target_point(v->target()->point());
> > + std::cout <<"Source point " << source_point << std::endl;
> > + std::cout <<"Target point " << target_point <<std::endl;
> > +
> > + source[0] = CGAL::to_double(source_point.x());
> > + source[1] = CGAL::to_double(source_point.y());
> > + source[2] = CGAL::to_double(source_point.z());
> > +
> > + target[0] = CGAL::to_double(target_point.x());
> > + target[1] = CGAL::to_double(target_point.y());
> > + target[2] = CGAL::to_double(target_point.z());
> > +
> > + a0 = source[A];
> > + b0 = source[B];
> > + a1 = target[A];
> > + b1 = target[B];
> > +
> > + da = a1 - a0;
> > + db = b1 - b0;
> > +
> > + a0_2 = a0 * a0;
> > + a0_3 = a0_2 * a0;
> > + a0_4 = a0_3 * a0;
> > + a1_2 = a1 * a1;
> > + b0_2 = b0 * b0;
> > + b0_3 = b0_2 * b0;
> > + b0_4 = b0_3 * b0;
> > + b1_2 = b1 * b1;
> > +
> > + C1 = a1 + a0;
> > + Ca = a1*C1 + a0_2;
> > + Caa = a1*Ca + a0_3;
> > + Cb = b1*(b1 + b0) + b0_2;
> > + Cbb = b1*Cb + b0_3;
> > + Cab = 3*a1_2 + 2*a1*a0 + a0_2;
> > + Kab = a1_2 + 2*a1*a0 + 3*a0_2;
> > +
> > + P1 += db*C1;
> > + Pa += db*Ca;
> > + Paa += db*Caa;
> > + Pb += da*Cb;
> > + Pbb += da*Cbb;
> > + Pab += db*(b1*Cab + b0*Kab);
> > + }
> > + std::cout <<"----------------------------------------" <<
std::endl;
> > + }
> > + }
> > +
> > + P1 /= 2.0;
> > + Pa /= 6.0;
> > + Paa /= 12.0;
> > + Pb /= -6.0;
> > + Pbb /= -12.0;
> > + Pab /= 24.0;
> > +
> > + info("P1 : %e",P1);
> > + info("Pa : %e",Pa);
> > + info("Paa : %e",Paa);
> > + info("Pb : %e",Pb);
> > + info("Pbb : %e",Pbb);
> > + info("Pab : %e",Pab);
> > +
> > + double k1, k2, k3;
> > + k1 = 1 / normal[C]; k2 = k1 * k1; k3 = k2 * k1;
> > + double w = CGAL::to_double(face_plane.d())/normal_length ;
> > + info("Normal[0] : %e ", normal[0]);
> > + info("Normal[1] : %e ", normal[1]);
> > + info("Normal[2] : %e ", normal[2]);
> > + info("w : %e ", w);
> > +
> > + Fa = k1 * Pa;
> > + Fb = k1 * Pb;
> > + Fc = -k2 * (normal[A]*Pa + normal[B]*Pb + w*P1);
> > +
> > + //debug
> > + Faa = k1 * Paa;
> > + Fbb = k1 * Pbb;
> > + Fcc = k3 * (SQR(normal[A])*Paa + 2*normal[A]*normal[B]*Pab +
> > SQR(normal[B])*Pbb + + w*(2*(normal[A]*Pa + normal[B]*Pb) +
w*P1));
> > +
> > + info("Fa : %e",Fa);
> > + info("Fb : %e",Fb);
> > + info("Fc : %e",Fc);
> > + info("Faa : %e",Faa);
> > + info("Fbb : %e",Fbb);
> > + info("Fcc : %e",Fcc);
> > + //end computation face integrals
> > +
> > + if (has_volume)
> > + {
> > + double contribution = (normal[X] * ((A == X) ? Fa : ((B == X) ? Fb :
> > Fc))); + info("Contribution: %e", contribution);
> > + info("Normal[X]: %e", normal[X]);
> > + info("A: %d", A);
> > + info("B: %d", B);
> > + info("C: %d", C);
> > + _weight += normal[X] * ((A == X) ? Fa : ((B == X) ? Fb : Fc));
> > + info("Volume: %e", _weight);
> > +
> > + bary_center[A] += normal[A] * Faa;
> > + bary_center[B] += normal[B] * Fbb;
> > + bary_center[C] += normal[C] * Fcc;
> > + }
> > + else
> > + {
> > + info("No volume: P1 is %e",P1);
> > + info("No volume: normal[C] is %e", normal[C]);
> > + //does not work yet
> > + //@todo does not work yet.
> > + _weight += -P1/normal[C];
> > + info("No volume: weight is %e", _weight);
> > + info("Fa : %e",Fa);
> > + info("Fb : %e",Fb);
> > + info("Fc : %e",Fc);
> > + bary_center[A] += -Fa;
> > + bary_center[B] += -Fb;
> > + bary_center[C] += -Fc;
> > + }
> > + }
> > + }
> > +
> > + //applies also if polyhedron has no no volume, since
> > + //we no iterating two times (each halffacet).
> > + if (has_volume)
> > + {
> > + bary_center[X] /= (2*_weight);
> > + bary_center[Y] /= (2*_weight);
> > + bary_center[Z] /= (2*_weight);
> > + }
> > + else
> > + {
> > + bary_center[X] /= _weight;
> > + bary_center[Y] /= _weight;
> > + bary_center[Z] /= _weight;
> > + }
> > +
> > + //use these later directly.
> > + _point = Point(3,bary_center);
> > +}
> >
> > === added file
> > 'nitsche_method/integration_on_complex_domains/gauss_projection_green/Ba
> > ryCenterQuadrature.h' ---
> > nitsche_method/integration_on_complex_domains/gauss_projection_green/Bar
> > yCenterQuadrature.h 1970-01-01 00:00:00 +0000 +++
> > nitsche_method/integration_on_complex_domains/gauss_projection_green/Bar
> > yCenterQuadrature.h 2010-04-01 10:43:19 +0000 @@ -0,0 +1,69 @@
> > +//
> > ========================================================================
> > ============= +//
> > +// Copyright (C) 2010-03-17 André Massing
> > +// Licensed under the GNU LGPL Version 2.1.
> > +//
> > +// Modified by André Massing, 2010
> > +//
> > +// First added: 2010-03-17
> > +// Last changed: 2010-03-30
> > +//
> > +//Author: André Massing (am), massing@xxxxxxxxx
> > +//Company: Simula Research Laboratory, Fornebu, Norway
> > +//
> > +//
> > ========================================================================
> > ============= +
> > +#ifndef __BARYCENTERQUADRATURE_H
> > +#define __BARYCENTERQUADRATURE_H
> > +
> > +#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
> > +
> > +#include <CGAL/Nef_polyhedron_3.h>
> > +#include <CGAL/Polyhedron_3.h>
> > +
> > +#include <dolfin/mesh/Point.h>
> > +
> > +namespace dolfin {
> > +
> > + typedef CGAL::Exact_predicates_exact_constructions_kernel Kernel;
> > + typedef CGAL::Polyhedron_3<Kernel> Polyhedron_3;
> > + typedef CGAL::Nef_polyhedron_3<Kernel> Nef_polyhedron_3;
> > + typedef Nef_polyhedron_3::Point_3 Point_3;
> > + typedef Nef_polyhedron_3::Plane_3 Plane_3;
> > + typedef Nef_polyhedron_3::Vector_3 Vector_3;
> > +
> > + ///This class computes the barycenter of an arbitrary polyhedron or
> > + ///polygon and therefore allows for bary center quadrature on complex
> > + ///polyhedrons. Note: barycenter quadrature is exact for polynom deg
> > <= 1. + class BaryCenterQuadrature {
> > +
> > + public:
> > +
> > + BaryCenterQuadrature() : _weight(0), _point(0,0,0), _length(1) {}
> > +
> > + ///@todo split the ugly implementation up into some subroutines and
> > removes + //all the macro etc stuff. Make also working polyhedrons
> > which are + //degenerated.
> > + void compute_quadrature_rule(const Nef_polyhedron_3 & polyhedron);
> > +
> > + //return pointer
> > + ///Gives the points for the last computed Polyhedron.
> > + Point * points() {return &_point;}
> > + ///Gives the weights for the last computed Polyhedron.
> > + double * weights() {return &_weight; }
> > +
> > + ///Number of quadrature points/weights.
> > + uint length() {return _length;}
> > +
> > + private:
> > +
> > + double _weight;
> > + Point _point;
> > + uint _length;
> > +
> > +
> > + };
> > +
> > +}
> > +
> > +#endif // ----- #ifndef __BARYCENTERQUADRATURE_H -----
> >
> > === added file
> > 'nitsche_method/integration_on_complex_domains/gauss_projection_green/RE
> > ADME' ---
> > nitsche_method/integration_on_complex_domains/gauss_projection_green/REA
> > DME 1970-01-01 00:00:00 +0000 +++
> > nitsche_method/integration_on_complex_domains/gauss_projection_green/REA
> > DME 2010-03-18 18:15:26 +0000 @@ -0,0 +1,146 @@
> > +1. OVERVIEW
> > +
> > + This code accompanies the paper:
> > +
> > + Brian Mirtich, "Fast and Accurate Computation of
> > + Polyhedral Mass Properties," journal of graphics
> > + tools, volume 1, number 2, 1996.
> > +
> > + It computes the ten volume integrals needed for
> > + determining the center of mass, moments of
> > + inertia, and products of inertia for a uniform
> > + density polyhedron. From this information, a
> > + body frame can be computed.
> > +
> > + To compile the program, use an ANSI compiler, and
> > + type something like
> > +
> > + % cc volInt.c -O2 -lm -o volInt
> > +
> > +
> > + Revision history
> > +
> > + 26 Jan 1996 Program creation.
> > +
> > + 3 Aug 1996 Corrected bug arising when polyhedron density
> > + is not 1.0. Changes confined to function main().
> > + Thanks to Zoran Popovic for catching this one.
> > +
> > +
> > +
> > +2. POLYHEDRON GEOMETRY FILES
> > +
> > + The program reads a data file specified on the
> > + command line. This data file describes the
> > + geometry of a polyhedron, and has the following
> > + format:
> > +
> > + N
> > +
> > + x_0 y_0 z_0
> > + x_1 y_1 z_1
> > + .
> > + .
> > + .
> > + x_{N-1} y_{N-1} z_{N-1}
> > +
> > + M
> > +
> > + k1 v_{1,1} v_{1,2} ... v_{1,k1}
> > + k2 v_{2,1} v_{2,2} ... v_{2,k2}
> > + .
> > + .
> > + .
> > + kM v_{M,1} v_{M,2} ... v_{M,kM}
> > +
> > +
> > + where:
> > + N number of vertices on polyhedron
> > + x_i y_i z_i x, y, and z coordinates of ith vertex
> > + M number of faces on polyhedron
> > + ki number of vertices on ith face
> > + v_{i,j} jth vertex on ith face
> > +
> > + In English:
> > +
> > + First the number of vertices are specified. Next
> > + the vertices are defined by listing the 3
> > + coordinates of each one. Next the number of faces
> > + are specified. Finally, the faces themselves are
> > + specified. A face is specified by first giving
> > + the number of vertices around the polygonal face,
> > + followed by the (integer) indices of these
> > + vertices. When specifying indices, note that
> > + they must be given in counter-clockwise order
> > + (when looking at the face from outside the
> > + polyhedron), and the vertices are indexed from 0
> > + to N-1 for a polyhedron with N faces.
> > +
> > + White space can be inserted (or not) as desired.
> > + Three example polyhedron geometry files are included:
> > +
> > + cube A cube, 20 units on a side, centered at
> > + the origin and aligned with the coordinate axes.
> > +
> > + tetra A tetrahedron formed by taking the convex
> > + hull of the origin, and the points (5,0,0),
> > + (0,4,0), and (0,0,3).
> > +
> > + icosa An icosahedron with vertices lying on the unit
> > + sphere, centered at the origin.
> > +
> > +
> > +
> > +3. RUNNING THE PROGRAM
> > +
> > + Simply type,
> > +
> > + % volInt <polyhedron geometry filename>
> > +
> > + The program will read in the geometry of the
> > + polyhedron, and the print out the ten volume
> > + integrals.
> > +
> > + The program also computes some of the mass
> > + properties which may be inferred from the volume
> > + integrals. A density of 1.0 is assumed, although
> > + this may be changed in function main(). The
> > + center of mass is computed as well as the inertia
> > + tensor relative to a frame with origin at the
> > + center of mass. Note, however, that this matrix
> > + may not be diagonal. If not, a diagonalization
> > + routine must be performed, to determine the
> > + orientation of the true body frame relative to
> > + the original model frame. The Jacobi method
> > + works quite well (see Numerical Recipes in C by
> > + Press, et. al.).
> > +
> > +
> > +
> > +4. DISCLAIMERS
> > +
> > + 1. The volume integration code has been written
> > + to match the development and algorithms presented
> > + in the paper, and not with maximum optimization
> > + in mind. While inherently very efficient, a few
> > + more cycles can be squeezed out of the algorithm.
> > + This is left as an exercise. :)
> > +
> > + 2. Don't like global variables? The three
> > + procedures which evaluate the volume integrals
> > + can be combined into a single procedure with two
> > + nested loops. In addition to providing some
> > + speedup, all of the global variables can then be
> > + made local.
> > +
> > + 3. The polyhedron data structure used by the
> > + program is admittedly lame; much better schemes
> > + are possible. The idea here is just to give the
> > + basic integral evaluation code, which will have
> > + to be adjusted for other polyhedron data
> > + structures.
> > +
> > + 4. There is no error checking for the input
> > + files. Be careful. Note the hard limits
> > + #defined for the number of vertices, number of
> > + faces, and number of vertices per faces.
> >
> > === added file
> > 'nitsche_method/integration_on_complex_domains/gauss_projection_green/SC
> > onstruct' ---
> > nitsche_method/integration_on_complex_domains/gauss_projection_green/SCo
> > nstruct 1970-01-01 00:00:00 +0000 +++
> > nitsche_method/integration_on_complex_domains/gauss_projection_green/SCo
> > nstruct 2010-04-02 18:46:57 +0000 @@ -0,0 +1,22 @@
> > +import os, commands
> > +
> > +# Import("cppunitCfg")
> > +
> > +# Get compiler from pkg-config
> > +compiler = commands.getoutput('pkg-config --variable=compiler dolfin')
> > +
> > +# Create a SCons Environment based on the main os environment
> > +env = Environment(ENV=os.environ, CXX=compiler)
> > +
> > +env.Append(CXXFLAGS = '-ggdb')
> > +
> > +# Get compiler flags from pkg-config
> > +env.ParseConfig('pkg-config --cflags --libs dolfin')
> > +
> > +#Program
> > +env.Program('quadrature_test',['BaryCenterQuadrature.cpp','main.cpp'])
> > +env.Program('iteration_tetrahedron.cpp')
> > +env.Program('iteration_tetrahedron_2.cpp')
> > +
> > +env.Append(LIBS='-lcppunit')
> > +env.Program('unittest',['BaryCenterQuadrature.cpp','test.cpp'])
> >
> > === added file
> > 'nitsche_method/integration_on_complex_domains/gauss_projection_green/al
> > ut_snippet.cpp' ---
> > nitsche_method/integration_on_complex_domains/gauss_projection_green/alu
> > t_snippet.cpp 1970-01-01 00:00:00 +0000 +++
> > nitsche_method/integration_on_complex_domains/gauss_projection_green/alu
> > t_snippet.cpp 2010-03-18 18:15:26 +0000 @@ -0,0 +1,96 @@
> > +//
> > ========================================================================
> > ============= +//
> > +// Copyright (C) 2010-02-17 André Massing
> > +// Licensed under the GNU LGPL Version 2.1.
> > +//
> > +// Modified by André Massing, 2010
> > +//
> > +// First added: 2010-02-17
> > +// Last changed: 2010-02-17
> > +//
> > +//Author: André Massing (am), massing@xxxxxxxxx
> > +//Company: Simula Research Laboratory, Fornebu, Norway
> > +//
> > +//
> > ========================================================================
> > ============= +
> > +
> > +struct
> > +{
> > + Point_3 p1, p2, p3;
> > +}triangle;
> > +
> > +class Shell_explorer
> > +{
> > + bool first;
> > + const Nef_polyhedron& N;
> > + vector<triangle> m_triangle_list;
> > +
> > +public:
> > + Shell_explorer(const Nef_polyhedron& N_)
> > + : first(true), N(N_) {}
> > +
> > + void visit(Vertex_const_handle v){}
> > + void visit(Halfedge_const_handle ){}
> > + void visit(Halffacet_const_handle facet)
> > + {
> > + for (Halffacet_cycle_const_iterator it =
> > +facet->facet_cycles_begin(); it != facet->facet_cycles_end(); it++)
> > + {
> > + SHalfedge_const_handle se = SHalfedge_const_handle(it);
> > + CGAL_assertion(se!=0);
> > + SHalfedge_around_facet_const_circulator hc_start(se);
> > + SHalfedge_around_facet_const_circulator hc_end(hc_start);
> > + vector <Point_3> vertices;
> > + int count = 0;
> > + CGAL_For_all(hc_start,hc_end)
> > + {
> > + SVertex_const_handle svert = hc_start->source();
> > + Point_3 vpoint = svert->center_vertex()->point();
> > + vertices.push_back(vpoint);
> > + }
> > + for (int i=0; i<vertices.size()-2; i++)
> > + {
> > + triangle t;
> > + t.p1 = vertices[0];
> > + t.p3 = vertices[i+1];
> > + t.p2 = vertices[i+2];
> > + m_triangle_list.push_back(t);
> > + }
> > +
> > + }
> > + }
> > + void visit(SHalfedge_const_handle ) {}
> > + void visit(SHalfloop_const_handle ) {}
> > + void visit(SFace_const_handle sf) {}
> > +
> > + vector<triangle>getTriangleList()
> > + {
> > + vector<triangle> templist;
> > + for (int i=0; i<m_triangle_list.size(); i++)
> > + templist.push_back(m_triangle_list[i]);
> > + m_triangle_list.clear();
> > + return templist;
> > + }
> > + void reset_minimal_vertex() { first = true; }
> > +};
> > +
> > +Usage:
> > +void main()
> > +{
> > + Nef_polyhedron nPoly;
> > + Volume_const_iterator c;
> > + Shell_explorer SE(nPoly);
> > +
> > + CGAL_forall_volumes(c,nPoly)
> > + {
> > + Shell_entry_const_iterator it;
> > + int shellcount = 0;
> > + vector <triangle> temp;
> > + CGAL_forall_shells_of(it,c)
> > + {
> > + SE.reset_minimal_vertex();
> > + entrypaths.visit_shell_objects(SFace_const_handle(it),SE);
> > + vector<triangle> tris = SE.getTriangleList();
> > + }
> > + }
> > +}
> >
> > === added file
> > 'nitsche_method/integration_on_complex_domains/gauss_projection_green/cu
> > be' ---
> > nitsche_method/integration_on_complex_domains/gauss_projection_green/cub
> > e 1970-01-01 00:00:00 +0000 +++
> > nitsche_method/integration_on_complex_domains/gauss_projection_green/cub
> > e 2010-03-18 18:15:26 +0000 @@ -0,0 +1,21 @@
> > +8
> > +
> > +-10 -10 -10
> > ++10 -10 -10
> > ++10 +10 -10
> > +-10 +10 -10
> > +-10 -10 +10
> > ++10 -10 +10
> > ++10 +10 +10
> > +-10 +10 +10
> > +
> > +6
> > +
> > +4 0 3 2 1
> > +4 4 5 6 7
> > +4 0 1 5 4
> > +4 6 2 3 7
> > +4 1 2 6 5
> > +4 0 4 7 3
> > +
> > +
> >
> > === added file
> > 'nitsche_method/integration_on_complex_domains/gauss_projection_green/ic
> > osa' ---
> > nitsche_method/integration_on_complex_domains/gauss_projection_green/ico
> > sa 1970-01-01 00:00:00 +0000 +++
> > nitsche_method/integration_on_complex_domains/gauss_projection_green/ico
> > sa 2010-03-18 18:15:26 +0000 @@ -0,0 +1,38 @@
> > +12
> > +
> > ++0.00000000 +0.00000000 +1.00000000
> > ++0.00000000 +0.00000000 -1.00000000
> > ++0.89442719 +0.00000000 +0.44721360
> > ++0.27639320 +0.85065081 +0.44721360
> > +-0.72360680 +0.52573111 +0.44721360
> > +-0.72360680 -0.52573111 +0.44721360
> > ++0.27639320 -0.85065081 +0.44721360
> > ++0.72360680 +0.52573111 -0.44721360
> > +-0.27639320 +0.85065081 -0.44721360
> > +-0.89442719 +0.00000000 -0.44721360
> > +-0.27639320 -0.85065081 -0.44721360
> > ++0.72360680 -0.52573111 -0.44721360
> > +
> > +20
> > +
> > +3 6 11 2
> > +3 3 2 7
> > +3 7 2 11
> > +3 0 2 3
> > +3 0 6 2
> > +3 10 1 11
> > +3 1 7 11
> > +3 10 11 6
> > +3 8 7 1
> > +3 8 3 7
> > +3 5 10 6
> > +3 5 6 0
> > +3 4 3 8
> > +3 4 0 3
> > +3 9 8 1
> > +3 9 1 10
> > +3 4 5 0
> > +3 9 10 5
> > +3 9 5 4
> > +3 9 4 8
> > +
> >
> > === added file
> > 'nitsche_method/integration_on_complex_domains/gauss_projection_green/it
> > eration_tetrahedron.cpp' ---
> > nitsche_method/integration_on_complex_domains/gauss_projection_green/ite
> > ration_tetrahedron.cpp 1970-01-01 00:00:00 +0000 +++
> > nitsche_method/integration_on_complex_domains/gauss_projection_green/ite
> > ration_tetrahedron.cpp 2010-03-25 23:33:08 +0000 @@ -0,0 +1,58 @@
> > +#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
> > +#include <CGAL/Nef_polyhedron_3.h>
> > +#include <CGAL/Polyhedron_3.h>
> > +
> > +typedef CGAL::Exact_predicates_exact_constructions_kernel Kernel;
> > +typedef CGAL::Polyhedron_3<Kernel> Polyhedron_3;
> > +typedef CGAL::Nef_polyhedron_3<Kernel> Nef_polyhedron_3;
> > +typedef Nef_polyhedron_3::Point_3 Point_3;
> > +
> > +int main()
> > +{
> > +
> > + Point_3 a(1.0, 0.0, 0.0);
> > + Point_3 b(0.0, 1.0, 0.0);
> > + Point_3 c(0.0, 0.0, 1.0);
> > + Point_3 d(0.0, 0.0, 0.0);
> > +
> > + //Build a tetrahedron
> > + Polyhedron_3 P;
> > + P.make_tetrahedron(a,b,c,d);
> > + Nef_polyhedron_3 NP(P);
> > +
> > + std::cout << "Iteration along face ...\n";
> > + int face_counter = 0;
> > + for(Nef_polyhedron_3::Halffacet_const_iterator f = NP.halffacets_begin
> > (), + end = NP.halffacets_end();
> > + f != end;
> > + ++f)
> > + {
> > + if(f->is_twin())
> > + continue;
> > + std::cout <<"########################################" << std::endl;
> > + std::cout << "Face number " << face_counter++ << std::endl;
> > + for(Nef_polyhedron_3::Halffacet_cycle_const_iterator fc =
> > f->facet_cycles_begin(), + cycles_end = f->facet_cycles_end();
> > + fc != cycles_end;
> > + ++fc)
> > + {
> > + if ( fc.is_shalfedge() )
> > + {
> > + std::cout <<"Edge consist of points: " << std::endl;
> > + Nef_polyhedron_3::SHalfedge_const_handle se = fc;
> > + Nef_polyhedron_3::SHalfedge_around_facet_const_circulator hc(se);
> > + Nef_polyhedron_3::SHalfedge_around_facet_const_circulator he(hc);
> > + CGAL_For_all(hc,he)
> > + {
> > + Nef_polyhedron_3::SVertex_const_handle v = hc->source();
> > +// Nef_polyhedron_3::Halfedge_const_handle v = hc->source();
> > + const Point_3 & source_point(v->source()->point());
> > + const Point_3 & target_point(v->target()->point());
> > + std::cout <<"Source point " << source_point << std::endl;
> > + std::cout <<"Target point " << target_point <<std::endl;
> > + }
> > + }
> > + }
> > + }
> > + return 0;
> > +}
> >
> > === added file
> > 'nitsche_method/integration_on_complex_domains/gauss_projection_green/it
> > eration_tetrahedron_2.cpp' ---
> > nitsche_method/integration_on_complex_domains/gauss_projection_green/ite
> > ration_tetrahedron_2.cpp 1970-01-01 00:00:00 +0000 +++
> > nitsche_method/integration_on_complex_domains/gauss_projection_green/ite
> > ration_tetrahedron_2.cpp 2010-04-01 10:43:19 +0000 @@ -0,0 +1,140 @@
> > +#include<vector>
> > +
> > +#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
> > +#include <CGAL/Nef_polyhedron_3.h>
> > +#include <CGAL/Polyhedron_3.h>
> > +#include <CGAL/Gmpz.h>
> > +#include <CGAL/Homogeneous.h>
> > +
> > +typedef CGAL::Exact_predicates_exact_constructions_kernel Kernel;
> > +typedef CGAL::Polyhedron_3<Kernel> Polyhedron_3;
> > +typedef CGAL::Nef_polyhedron_3<Kernel> Nef_polyhedron_3;
> > + typedef Nef_polyhedron_3::Vector_3 Vector_3;
> > +typedef Nef_polyhedron_3::Point_3 Point_3;
> > +typedef Nef_polyhedron_3::Vertex_const_handle Vertex_const_handle;
> > +typedef Nef_polyhedron_3::Halfedge_const_handle Halfedge_const_handle;
> > +typedef Nef_polyhedron_3::Halffacet_const_handle Halffacet_const_handle;
> > +typedef Nef_polyhedron_3::Halffacet_cycle_const_iterator
> > Halffacet_cycle_const_iterator; +typedef
> > Nef_polyhedron_3::SHalfedge_const_handle SHalfedge_const_handle;
> > +typedef Nef_polyhedron_3::SHalfedge_around_facet_const_circulator
> > SHalfedge_around_facet_const_circulator; +typedef
> > Nef_polyhedron_3::SHalfloop_const_handle SHalfloop_const_handle;
> > +typedef Nef_polyhedron_3::SFace_const_handle SFace_const_handle;
> > +typedef Nef_polyhedron_3::Volume_const_iterator Volume_const_iterator;
> > +typedef Nef_polyhedron_3::Shell_entry_const_iterator
> > Shell_entry_const_iterator; +
> > +typedef std::vector<Nef_polyhedron_3> PolyhedronList;
> > +typedef PolyhedronList::const_iterator PolyhedronListIterator;
> > +
> > +class Shell_explorer
> > +{
> > + const Nef_polyhedron_3 & N;
> > +
> > +public:
> > + Shell_explorer(const Nef_polyhedron_3 & N_)
> > + : N(N_) {}
> > +
> > + void visit(Vertex_const_handle v) {}
> > + void visit(Halfedge_const_handle ){}
> > + void visit(Halffacet_const_handle facet)
> > + {
> > + std::cout << "Visting faces ..." << std::endl;
> > + std::cout <<"++++++++++++++++++++++++++++++++++++++++" << std::endl;
> > + Vector_3 test_normal = facet->plane().orthogonal_vector();
> > + std::cout <<"Normal vector of the plane is " << test_normal
> > <<std::endl; +
> > + for (Halffacet_cycle_const_iterator it =
> > + facet->facet_cycles_begin(); it != facet->facet_cycles_end(); it++)
> > + {
> > + std::cout << "Visting Edges ..." << std::endl;
> > + std::cout <<"----------------------------------------" <<
> > std::endl; + Nef_polyhedron_3::SHalfedge_const_handle h = it;
> > + Nef_polyhedron_3::SHalfedge_around_facet_const_circulator hc(h),
> > he(hc); + CGAL_For_all(hc,he)
> > + {
> > + Nef_polyhedron_3::SVertex_const_handle v = hc->source();
> > + const Nef_polyhedron_3::Point_3& source = v->source()->point();
> > + const Nef_polyhedron_3::Point_3& target = v->target()->point();
> > + std::cout <<"Source :" <<source <<std::endl;
> > + std::cout <<"Target :" <<target <<std::endl;
> > + }
> > + }
> > + }
> > + void visit(SHalfedge_const_handle ) {}
> > + void visit(SHalfloop_const_handle ) {}
> > + void visit(SFace_const_handle sf) {}
> > +
> > +};
> > +
> > +int main()
> > +{
> > + Point_3 a1(1.0, 0.0, 0.0);
> > + Point_3 b1(0.0, 1.0, 0.0);
> > + Point_3 c1(0.0, 0.0, 1.0);
> > + Point_3 d1(0.0, 0.0, 0.0);
> > +
> > + Point_3 a2(-1.0, 0.0, 0.0);
> > + Point_3 b2(0.0, 1.0, 0.0);
> > + Point_3 c2(0.0, 0.0, 1.0);
> > + Point_3 d2(0.0, 0.0, 0.0);
> > +
> > + Point_3 a3(1.0, 0.0, 0.0);
> > + Point_3 b3(0.0, -1.0, 0.0);
> > + Point_3 c3(0.0, 0.0, 1.0);
> > + Point_3 d3(0.0, 0.0, 0.0);
> > +
> > + Point_3 a4(-1.0, 0.0, 0.0);
> > + Point_3 b4(0.0, -1.0, 0.0);
> > + Point_3 c4(0.0, 0.0, 1.0);
> > + Point_3 d4(0.0, 0.0, 0.0);
> > +
> > + Point_3 A(2.0, 1.0, 1.0);
> > + Point_3 B(1.0, 2.0, 1.0);
> > + Point_3 C(1.0, 1.0, 2.0);
> > + Point_3 D(1.0, 1.0, 1.0);
> > +
> > + //Build a point tetrahedron
> > + Polyhedron_3 P1;
> > + P1.make_triangle(a1,b1,c1);
> > + Nef_polyhedron_3 N1(P1);
> > +
> > + Polyhedron_3 P2;
> > + P2.make_tetrahedron(a2,b2,c2,d2);
> > + Nef_polyhedron_3 N2(P2);
> > +
> > + Polyhedron_3 P3;
> > + P3.make_tetrahedron(a3,b3,c3,d3);
> > + Nef_polyhedron_3 N3(P3);
> > +
> > + Polyhedron_3 P4;
> > + P4.make_tetrahedron(a4,b4,c4,d4);
> > + Nef_polyhedron_3 N4(P4);
> > +
> > + PolyhedronList polyhedrons;
> > +
> > + polyhedrons.push_back(N1);
> > + polyhedrons.push_back(N2);
> > +
> > + //Build a point tetrahedron
> > + for (PolyhedronListIterator pi = polyhedrons.begin(), end =
> > polyhedrons.end(); + pi != end; ++pi)
> > + {
> > + Volume_const_iterator vi;
> > + Shell_explorer SE(*pi);
> > +
> > + std::cout <<"Next polyhedron:\n"
> > + << "##############################" <<std::endl;
> > + int ic = 0;
> > + CGAL_forall_volumes(vi,*pi)
> > + {
> > + std::cout << "Volume " << ic++ << " has mark " << vi->mark()<<
> > std::endl; +
> > + Shell_entry_const_iterator it;
> > + CGAL_forall_shells_of(it,vi)
> > + {
> > + pi->visit_shell_objects(SFace_const_handle(it),SE);
> > + }
> > + std::cout << "\n\n";
> > + }
> > + }
> > + return 0;
> > +}
> >
> > === added file
> > 'nitsche_method/integration_on_complex_domains/gauss_projection_green/ma
> > in.cpp' ---
> > nitsche_method/integration_on_complex_domains/gauss_projection_green/mai
> > n.cpp 1970-01-01 00:00:00 +0000 +++
> > nitsche_method/integration_on_complex_domains/gauss_projection_green/mai
> > n.cpp 2010-04-01 10:43:19 +0000 @@ -0,0 +1,190 @@
> > +//
> > ========================================================================
> > ============= +//
> > +// Copyright (C) 2010-03-19 André Massing
> > +// Licensed under the GNU LGPL Version 2.1.
> > +//
> > +// Modified by André Massing, 2010
> > +//
> > +// First added: 2010-03-19
> > +// Last changed: 2010-03-31
> > +//
> > +//Author: André Massing (am), massing@xxxxxxxxx
> > +//Company: Simula Research Laboratory, Fornebu, Norway
> > +//
> > +//
> > ========================================================================
> > ============= +
> > +#include "BaryCenterQuadrature.h"
> > +#include <dolfin.h>
> > +
> > +#include <iostream>
> > +#include<vector>
> > +
> > +using namespace dolfin;
> > +
> > +typedef std::vector<Nef_polyhedron_3> PolyhedronList;
> > +typedef PolyhedronList::const_iterator PolyhedronListIterator;
> > +
> > +
> > +using namespace dolfin;
> > +
> > +int main()
> > +{
> > +
> > + Point_3 e0(0.0, 0.0, 0.0);
> > +
> > + Point_3 e1(1.0, 0.0, 0.0);
> > + Point_3 e2(0.0, 1.0, 0.0);
> > + Point_3 e3(0.0, 0.0, 1.0);
> > +
> > + Point_3 _e1(-1.0, 0.0, 0.0);
> > + Point_3 _e2(0.0, -1.0, 0.0);
> > + Point_3 _e3(0.0, 0.0, -1.0);
> > +
> > + Point_3 A(2.0, 1.0, 1.0);
> > + Point_3 B(1.0, 2.0, 1.0);
> > + Point_3 C(1.0, 1.0, 2.0);
> > + Point_3 D(1.0, 1.0, 1.0);
> > +
> > + //Create tetrahedrons with unit vectors
> > + Polyhedron_3 P1;
> > + P1.make_tetrahedron(e0,e1,e2,e3);
> > + Nef_polyhedron_3 N1(P1);
> > +
> > + Polyhedron_3 P2;
> > + P2.make_tetrahedron(e0,_e1,e2,e3);
> > + Nef_polyhedron_3 N2(P2);
> > +
> > + Polyhedron_3 P3;
> > + P3.make_tetrahedron(e0,e1,_e2,e3);
> > + Nef_polyhedron_3 N3(P3);
> > +
> > + Polyhedron_3 P4;
> > + P4.make_tetrahedron(e0,_e1,_e2,e3);
> > + Nef_polyhedron_3 N4(P4);
> > +
> > + Polyhedron_3 P5;
> > + P5.make_tetrahedron(e0,e1,e2,_e3);
> > + Nef_polyhedron_3 N5(P5);
> > +
> > + Polyhedron_3 P6;
> > + P6.make_tetrahedron(e0,_e1,e2,_e3);
> > + Nef_polyhedron_3 N6(P6);
> > +
> > + Polyhedron_3 P7;
> > + P7.make_tetrahedron(e0,e1,_e2,_e3);
> > + Nef_polyhedron_3 N7(P7);
> > +
> > + Polyhedron_3 P8;
> > + P8.make_tetrahedron(e0,_e1,_e2,_e3);
> > + Nef_polyhedron_3 N8(P8);
> > +
> > + //Create triangles
> > + Polyhedron_3 P9;
> > + P9.make_triangle(e0,e1,e2);
> > + Nef_polyhedron_3 N9(P9);
> > +
> > + Polyhedron_3 P10;
> > + P10.make_triangle(e0,e1,e3);
> > + Nef_polyhedron_3 N10(P10);
> > +
> > + Polyhedron_3 P11;
> > + P11.make_triangle(e0,e2,e3);
> > + Nef_polyhedron_3 N11(P11);
> > +
> > + Polyhedron_3 P12;
> > + P12.make_triangle(e1,e2,e3);
> > + Nef_polyhedron_3 N12(P12);
> > +
> > + Polyhedron_3 P13;
> > + P13.make_triangle(e0,_e1,e2);
> > + Nef_polyhedron_3 N13(P13);
> > +
> > + Polyhedron_3 P14;
> > + P14.make_triangle(e0,_e1,e3);
> > + Nef_polyhedron_3 N14(P14);
> > +
> > + Polyhedron_3 P15;
> > + P15.make_triangle(e0,e2,e3);
> > + Nef_polyhedron_3 N15(P15);
> > +
> > + Polyhedron_3 P16;
> > + P16.make_triangle(_e1,e2,e3);
> > + Nef_polyhedron_3 N16(P16);
> > +
> > + PolyhedronList polyhedrons;
> > + PolyhedronList polygons;
> > +
> > + //single polyhedrons
> > + polyhedrons.push_back(N1);
> > + polyhedrons.push_back(N2);
> > + polyhedrons.push_back(N3);
> > + polyhedrons.push_back(N4);
> > + polyhedrons.push_back(N5);
> > + polyhedrons.push_back(N6);
> > + polyhedrons.push_back(N7);
> > + polyhedrons.push_back(N8);
> > +
> > + //combined tetrehedrons
> > + polyhedrons.push_back(N1 + N2);
> > + polyhedrons.push_back(N1 + N2 + N3);
> > + polyhedrons.push_back(N1 + N2 + N3 + N4);
> > +
> > + polyhedrons.push_back(N5 + N6);
> > + polyhedrons.push_back(N5 + N6 + N7);
> > + polyhedrons.push_back(N5 + N6 + N7 + N9);
> > +
> > + polyhedrons.push_back(N1 + N2 + N3 + N4 + N5 + N6 + N7 + N4);
> > +
> > + //polygons
> > + polygons.push_back(N9);
> > + polygons.push_back(N10);
> > + polygons.push_back(N11);
> > + polygons.push_back(N12);
> > + polygons.push_back(N13);
> > + polygons.push_back(N14);
> > + polygons.push_back(N15);
> > + polygons.push_back(N16);
> > +
> > + //combined polygons
> > + polygons.push_back(N9 + N10);
> > + polygons.push_back(N9 + N10 + N11);
> > + polygons.push_back(N9 + N10 + N11 + N12);
> > +
> > + polygons.push_back(N13 + N14);
> > + polygons.push_back(N13 + N14 + N15);
> > + polygons.push_back(N13 + N14 + N15 + N16);
> > +
> > + polygons.push_back(N9 + N10 + N11 + N12 + N13 + N14 + N15 + N12);
> > +
> > + BaryCenterQuadrature quadrature_rule;
> > +
> > + int counter = 0;
> > + std::cout << "Quadrature rule for Polyhdrons\n" ;
> > + std::cout <<"------------------------------\n";
> > + for (PolyhedronListIterator pi = polyhedrons.begin(), end =
> > polyhedrons.end(); + pi != end; ++pi)
> > + {
> > + cout <<"Next polyhedron: " << ++counter << endl
> > + << "##############################" <<endl;
> > + quadrature_rule.compute_quadrature_rule(*pi);
> > + cout <<"Volume: " << *(quadrature_rule.weights()) <<endl;
> > + cout <<"Barycenter: "
> > + << quadrature_rule.points()[0] << endl <<endl;
> > + }
> > +
> > + counter = 0;
> > + std::cout << "Quadrature rule for Polygons\n" ;
> > + std::cout <<"------------------------------\n";
> > + for (PolyhedronListIterator pi = polygons.begin(), end =
> > polygons.end(); + pi != end; ++pi)
> > + {
> > + cout <<"Next polygons: " << ++counter << endl
> > + << "##############################" <<endl;
> > + quadrature_rule.compute_quadrature_rule(*pi);
> > + cout <<"Volume: " << *(quadrature_rule.weights()) <<endl;
> > + cout <<"Barycenter: "
> > + << quadrature_rule.points()[0] << endl <<endl;
> > + }
> > +
> > + return 0;
> > +}
> >
> > === added file
> > 'nitsche_method/integration_on_complex_domains/gauss_projection_green/ma
> > rtin_baeker_snippet.cpp' ---
> > nitsche_method/integration_on_complex_domains/gauss_projection_green/mar
> > tin_baeker_snippet.cpp 1970-01-01 00:00:00 +0000 +++
> > nitsche_method/integration_on_complex_domains/gauss_projection_green/mar
> > tin_baeker_snippet.cpp 2010-03-18 18:15:26 +0000 @@ -0,0 +1,93 @@
> > +//
> > ========================================================================
> > ============= +//
> > +// Copyright (C) 2010-02-17 André Massing
> > +// Licensed under the GNU LGPL Version 2.1.
> > +//
> > +// Modified by André Massing, 2010
> > +//
> > +// First added: 2010-02-17
> > +// Last changed: 2010-02-17
> > +//
> > +//Author: André Massing (am), massing@xxxxxxxxx
> > +//Company: Simula Research Laboratory, Fornebu, Norway
> > +//
> > +//
> > ========================================================================
> > ============= +
> > + for(Nef_polyhedron::Halffacet_const_iterator
> > + f = Cube.halffacets_begin (),
> > + end = Cube.halffacets_end();
> > + f != end; ++f)
> > + {
> > + if(f->is_twin()) continue;
> > + std::cout << "Outer iteration, next f \n";
> > + for(Nef_polyhedron::Halffacet_cycle_const_iterator
> > + fc = f->facet_cycles_begin(),
> > + end = f->facet_cycles_end();
> > + fc != end; ++fc)
> > + {
> > + std::cout << "Inner iteration, next fc \n";
> > + if ( fc.is_shalfedge() )
> > + {
> > + std::cout << "Halfedge consists of points \n";
> > +
> > + Nef_polyhedron::SHalfedge_const_handle h = fc;
> > + Nef_polyhedron::SHalfedge_around_facet_const_circulator hc(h),
> > he(hc); + CGAL_For_all(hc,he)
> > + { // all vertex coordinates in facet cycle
> > + Nef_polyhedron::SVertex_const_handle v = hc->source();
> > + const Nef_polyhedron::Point_3& point = v->source()->point();
> > + std::cout << "p: " << CGAL::to_double(point.x()) << " " <<
> > + CGAL::to_double(point.y()) << " " <<
> > + CGAL::to_double(point.z()) << std::endl;
> > +
> > + }
> > +
> > + }
> > + }
> > +
> > + }
> > +
> > + // Alternative to iterating over halfedges:
> > +// Nef_polyhedron::Halfedge_const_iterator e =
> > Cube.halfedges_begin(); +// CGAL_forall_halfedges(e,Cube) {
> > +
> > +
> > + for(Nef_polyhedron::Halfedge_const_iterator
> > + e = Cube.halfedges_begin(),
> > + end = Cube.halfedges_end();
> > + e != end; ++e)
> > + {
> > + const Nef_polyhedron::Vertex_const_handle& s = e->source();
> > + const Nef_polyhedron::Vertex_const_handle& t = e->twin()->source();
> > + const Nef_polyhedron::Point_3& a = s->point();
> > + const Nef_polyhedron::Point_3& b = t->point();
> > + std::cout << "From a: " << CGAL::to_double(a.x()) << " " <<
> > + CGAL::to_double(a.y()) << " " <<
> > + CGAL::to_double(a.z()) << " to b: " <<
> > + CGAL::to_double(b.x()) << " " <<
> > + CGAL::to_double(b.y()) << " " <<
> > + CGAL::to_double(b.z()) <<std::endl;
> > + typedef Nef_polyhedron::Object_handle Object_handle;
> > + typedef Nef_polyhedron::Vertex_const_handle Vertex_const_handle;
> > + Vertex_const_handle v;
> > + Object_handle o = Cube.locate(a);
> > + if(CGAL::assign(v,o))
> > + std::cout << " a is a vertex" << std::endl;
> > + else
> > + std::cout << " a is not a vertex" << std::endl;
> > + }
> > +
> > +// Nef_polyhedron::Vertex_const_iterator v;
> > +
> > +// CGAL_forall_vertices(v, Cube.sncp())
> > + for(Nef_polyhedron::Vertex_const_iterator
> > + v = Cube.vertices_begin(),
> > + end = Cube.vertices_end();
> > + v != end; ++v)
> > + {
> > + const Nef_polyhedron::Point_3& a = v->point();
> > + std::cout << "Vertex: " << CGAL::to_double(a.x()) << " " <<
> > + CGAL::to_double(a.y()) << " " <<
> > + CGAL::to_double(a.z()) << std::endl;
> > +
> > + }
> >
> > === added file
> > 'nitsche_method/integration_on_complex_domains/gauss_projection_green/te
> > st.cpp' ---
> > nitsche_method/integration_on_complex_domains/gauss_projection_green/tes
> > t.cpp 1970-01-01 00:00:00 +0000 +++
> > nitsche_method/integration_on_complex_domains/gauss_projection_green/tes
> > t.cpp 2010-04-02 22:47:40 +0000 @@ -0,0 +1,598 @@
> > +//
> > ========================================================================
> > ============= +//
> > +// Copyright (C) 2010-04-01 André Massing
> > +// Licensed under the GNU LGPL Version 2.1.
> > +//
> > +// Modified by André Massing, 2010
> > +//
> > +// First added: 2010-04-01
> > +// Last changed: 2010-04-03
> > +//
> > +//Author: André Massing (am), massing@xxxxxxxxx
> > +//Company: Simula Research Laboratory, Fornebu, Norway
> > +//
> > +//Description: Unittest for BaryCenterQuadrature.
> > ========================================================================
> > ============= +
> > +#include<vector>
> > +#include <iostream>
> > +
> > +#include <dolfin.h>
> > +#include <dolfin/common/unittest.h>
> > +
> > +#include <CGAL/Nef_polyhedron_3.h>
> > +#include "BaryCenterQuadrature.h"
> > +
> > +using namespace dolfin;
> > +
> > +typedef Nef_polyhedron_3::Aff_transformation_3 Aff_transformation_3;
> > +
> > +typedef std::vector<Nef_polyhedron_3> PolyhedronList;
> > +typedef PolyhedronList::const_iterator PolyhedronListIterator;
> > +
> > +typedef std::vector<int> IntList;
> > +typedef std::vector<int>::const_iterator IntListIterator;
> > +typedef std::vector<double> DoubleList;
> > +typedef std::vector<double>::const_iterator DoubleListIterator;
> > +typedef std::vector<Point> PointList;
> > +typedef std::vector<Point>::const_iterator PointListIterator;
> > +
> > +class BaryCenter : public CppUnit::TestFixture
> > +{
> > + CPPUNIT_TEST_SUITE(BaryCenter);
> > + CPPUNIT_TEST(testSimplePolyhedrons);
> > + CPPUNIT_TEST(testSimplePolygons);
> > + CPPUNIT_TEST(testComplexPolyhedrons);
> > + CPPUNIT_TEST(testComplexPolygons);
> > + CPPUNIT_TEST_SUITE_END();
> > +
> > +
> > + void almost_equal_points(const Point & p1, const Point & p2, double
> > delta) + {
> > + CPPUNIT_ASSERT_DOUBLES_EQUAL(p1.x(),p2.x(),delta);
> > + CPPUNIT_ASSERT_DOUBLES_EQUAL(p1.y(),p2.y(),delta);
> > + CPPUNIT_ASSERT_DOUBLES_EQUAL(p1.z(),p2.z(),delta);
> > + }
> > +
> > + //Helper function to create reference polyhedrons.
> > + void add_test_polyhedron(const Point_3 & p1,
> > + const Point_3 & p2,
> > + const Point_3 & p3,
> > + const Point_3 & p4,
> > + PolyhedronList & polyhedrons
> > + )
> > + {
> > + Polyhedron_3 P;
> > + P.make_tetrahedron(p1,p2,p3,p4);
> > + Nef_polyhedron_3 N(P);
> > + polyhedrons.push_back(N);
> > + }
> > +
> > + void add_test_polyhedron(const Point_3 & p1,
> > + const Point_3 & p2,
> > + const Point_3 & p3,
> > + PolyhedronList & polyhedrons
> > + )
> > + {
> > + Polyhedron_3 P;
> > + P.make_triangle(p1,p2,p3);
> > + Nef_polyhedron_3 N(P);
> > + polyhedrons.push_back(N);
> > + }
> > +
> > + //Helper function to union disjoint polyhedrons and to compute the
> > volume and barycenter. + //Indices indicate which polyhedrons should be
> > unioned. No checks at all (index, disjointness etc) + //Computed
> > polyhedrons, volumes and barycenters will be append to the given list. +
> > void add_disjoint_polyhedrons(const IntList indices,
> > + PolyhedronList & polyhedrons,
> > + DoubleList & volumes,
> > + PointList & points)
> > + {
> > + double volume = 0;
> > + Point point(0,0,0);
> > + Nef_polyhedron_3 polyhedron;
> > +
> > + for (IntListIterator i = indices.begin(); i != indices.end(); ++i)
> > + {
> > + polyhedron += polyhedrons[*i];
> > + point += volumes[*i] * points[*i] ;
> > + volume += volumes[*i];
> > + }
> > + point /= volume;
> > +
> > + polyhedrons.push_back(polyhedron);
> > + volumes.push_back(volume);
> > + points.push_back(point);
> > + }
> > +
> > +
> > + void testSimplePolyhedrons()
> > + {
> > + //Create origin and unit vectors.
> > + Point_3 e0(0.0, 0.0, 0.0);
> > +
> > + Point_3 e1(1.0, 0.0, 0.0);
> > + Point_3 e2(0.0, 1.0, 0.0);
> > + Point_3 e3(0.0, 0.0, 1.0);
> > +
> > + Point_3 _e1(-1.0, 0.0, 0.0);
> > + Point_3 _e2(0.0, -1.0, 0.0);
> > + Point_3 _e3(0.0, 0.0, -1.0);
> > +
> > + //Create tetrahedrons with unit vectors and reference results.
> > + DoubleList reference_volumes;
> > + PointList reference_bary_centers;
> > + PolyhedronList reference_polyhedrons;
> > +
> > + add_test_polyhedron(e0,e1,e2,e3,reference_polyhedrons);
> > + reference_volumes.push_back(1.0/6.0);
> > + reference_bary_centers.push_back(Point(0.25,0.25,0.25));
> > +
> > + add_test_polyhedron(e0,_e1,e2,e3,reference_polyhedrons);
> > + reference_volumes.push_back(1.0/6.0);
> > + reference_bary_centers.push_back(Point(-0.25,0.25,0.25));
> > +
> > + add_test_polyhedron(e0,e1,_e2,e3,reference_polyhedrons);
> > + reference_volumes.push_back(1.0/6.0);
> > + reference_bary_centers.push_back(Point(0.25,-0.25,0.25));
> > +
> > + add_test_polyhedron(e0,_e1,_e2,e3,reference_polyhedrons);
> > + reference_volumes.push_back(1.0/6.0);
> > + reference_bary_centers.push_back(Point(-0.25,-0.25,0.25));
> > +
> > + add_test_polyhedron(e0,e1,e2,_e3,reference_polyhedrons);
> > + reference_volumes.push_back(1.0/6.0);
> > + reference_bary_centers.push_back(Point(0.25,0.25,-0.25));
> > +
> > + add_test_polyhedron(e0,_e1,e2,_e3,reference_polyhedrons);
> > + reference_volumes.push_back(1.0/6.0);
> > + reference_bary_centers.push_back(Point(-0.25,0.25,-0.25));
> > +
> > + add_test_polyhedron(e0,e1,_e2,_e3,reference_polyhedrons);
> > + reference_volumes.push_back(1.0/6.0);
> > + reference_bary_centers.push_back(Point(0.25,-0.25,-0.25));
> > +
> > + add_test_polyhedron(e0,_e1,_e2,_e3,reference_polyhedrons);
> > + reference_volumes.push_back(1.0/6.0);
> > + reference_bary_centers.push_back(Point(-0.25,-0.25,-0.25));
> > +
> > + //Add sum of polyhedrons
> > + IntList add_indices;
> > + add_indices.push_back(0);
> > +
> > + add_indices.push_back(1);
> > + add_disjoint_polyhedrons(add_indices,
> > + reference_polyhedrons,
> > + reference_volumes,
> > + reference_bary_centers);
> > +
> > + add_indices.push_back(2);
> > + add_disjoint_polyhedrons(add_indices,
> > + reference_polyhedrons,
> > + reference_volumes,
> > + reference_bary_centers);
> > +
> > + add_indices.push_back(3);
> > + add_disjoint_polyhedrons(add_indices,
> > + reference_polyhedrons,
> > + reference_volumes,
> > + reference_bary_centers);
> > +
> > + add_indices.push_back(4);
> > + add_disjoint_polyhedrons(add_indices,
> > + reference_polyhedrons,
> > + reference_volumes,
> > + reference_bary_centers);
> > +
> > + add_indices.push_back(5);
> > + add_disjoint_polyhedrons(add_indices,
> > + reference_polyhedrons,
> > + reference_volumes,
> > + reference_bary_centers);
> > +
> > + add_indices.push_back(6);
> > + add_disjoint_polyhedrons(add_indices,
> > + reference_polyhedrons,
> > + reference_volumes,
> > + reference_bary_centers);
> > +
> > + add_indices.push_back(7);
> > + add_disjoint_polyhedrons(add_indices,
> > + reference_polyhedrons,
> > + reference_volumes,
> > + reference_bary_centers);
> > +
> > + //Add translated version
> > + //Upper halfspace
> > + Nef_polyhedron_3 polyhedron = reference_polyhedrons[0];
> > + polyhedron.transform(Aff_transformation_3(CGAL::TRANSLATION,
> > Vector_3(1, 1, 1))); + reference_polyhedrons.push_back(polyhedron);
> > + reference_volumes.push_back(1.0/6.0);
> > + reference_bary_centers.push_back(Point(1.25,1.25,1.25));
> > +
> > + polyhedron = reference_polyhedrons[1];
> > + polyhedron.transform(Aff_transformation_3(CGAL::TRANSLATION,
> > Vector_3(-1, 1, 1))); + reference_polyhedrons.push_back(polyhedron);
> > + reference_volumes.push_back(1.0/6.0);
> > + reference_bary_centers.push_back(Point(-1.25,1.25,1.25));
> > +
> > + polyhedron = reference_polyhedrons[2];
> > + polyhedron.transform(Aff_transformation_3(CGAL::TRANSLATION,
> > Vector_3(1, -1, 1))); + reference_polyhedrons.push_back(polyhedron);
> > + reference_volumes.push_back(1.0/6.0);
> > + reference_bary_centers.push_back(Point(1.25,-1.25,1.25));
> > +
> > + polyhedron = reference_polyhedrons[3];
> > + polyhedron.transform(Aff_transformation_3(CGAL::TRANSLATION,
> > Vector_3(-1, -1, 1))); + reference_polyhedrons.push_back(polyhedron);
> > + reference_volumes.push_back(1.0/6.0);
> > + reference_bary_centers.push_back(Point(-1.25,-1.25,1.25));
> > +
> > + polyhedron = reference_polyhedrons[4];
> > + polyhedron.transform(Aff_transformation_3(CGAL::TRANSLATION,
> > Vector_3(1, 1, -1))); + reference_polyhedrons.push_back(polyhedron);
> > + reference_volumes.push_back(1.0/6.0);
> > + reference_bary_centers.push_back(Point(1.25,1.25,-1.25));
> > +
> > + polyhedron = reference_polyhedrons[5];
> > + polyhedron.transform(Aff_transformation_3(CGAL::TRANSLATION,
> > Vector_3(-1, 1, -1))); + reference_polyhedrons.push_back(polyhedron);
> > + reference_volumes.push_back(1.0/6.0);
> > + reference_bary_centers.push_back(Point(-1.25,1.25,-1.25));
> > +
> > + polyhedron = reference_polyhedrons[6];
> > + polyhedron.transform(Aff_transformation_3(CGAL::TRANSLATION,
> > Vector_3(1, -1, -1))); + reference_polyhedrons.push_back(polyhedron);
> > + reference_volumes.push_back(1.0/6.0);
> > + reference_bary_centers.push_back(Point(1.25,-1.25,-1.25));
> > +
> > + polyhedron = reference_polyhedrons[7];
> > + polyhedron.transform(Aff_transformation_3(CGAL::TRANSLATION,
> > Vector_3(-1, -1, -1))); +
> > reference_polyhedrons.push_back(polyhedron);
> > + reference_volumes.push_back(1.0/6.0);
> > + reference_bary_centers.push_back(Point(-1.25,-1.25,-1.25));
> > +
> > + //Add the disjoint union of the translated polyhedrons.
> > + add_indices.clear();
> > + add_indices.push_back(15);
> > +
> > + add_indices.push_back(16);
> > + add_disjoint_polyhedrons(add_indices,
> > + reference_polyhedrons,
> > + reference_volumes,
> > + reference_bary_centers);
> > +
> > + add_indices.push_back(17);
> > + add_disjoint_polyhedrons(add_indices,
> > + reference_polyhedrons,
> > + reference_volumes,
> > + reference_bary_centers);
> > +
> > + add_indices.push_back(18);
> > + add_disjoint_polyhedrons(add_indices,
> > + reference_polyhedrons,
> > + reference_volumes,
> > + reference_bary_centers);
> > +
> > + add_indices.push_back(19);
> > + add_disjoint_polyhedrons(add_indices,
> > + reference_polyhedrons,
> > + reference_volumes,
> > + reference_bary_centers);
> > +
> > + add_indices.push_back(20);
> > + add_disjoint_polyhedrons(add_indices,
> > + reference_polyhedrons,
> > + reference_volumes,
> > + reference_bary_centers);
> > +
> > + add_indices.push_back(21);
> > + add_disjoint_polyhedrons(add_indices,
> > + reference_polyhedrons,
> > + reference_volumes,
> > + reference_bary_centers);
> > +
> > + add_indices.push_back(22);
> > + add_disjoint_polyhedrons(add_indices,
> > + reference_polyhedrons,
> > + reference_volumes,
> > + reference_bary_centers);
> > +
> > + //Instantiate quadrature rule
> > + BaryCenterQuadrature quadrature_rule;
> > +
> > + //Check volume and barycenter for polyhedrons
> > + for (dolfin::uint i = 0; i < reference_polyhedrons.size(); ++i)
> > + {
> > + quadrature_rule.compute_quadrature_rule(reference_polyhedrons[i]);
> > + CPPUNIT_ASSERT_DOUBLES_EQUAL(reference_volumes[i],
> > + quadrature_rule.weights()[0], 1.0e-12);
> > + almost_equal_points(reference_bary_centers[i],
> > + quadrature_rule.points()[0], 1.0e-12);
> > + }
> > + }
> > +
> > + void testSimplePolygons()
> > + {
> > + //Create origin and unit vectors.
> > + Point_3 e0(0.0, 0.0, 0.0);
> > +
> > + Point_3 e1(1.0, 0.0, 0.0);
> > + Point_3 e2(0.0, 1.0, 0.0);
> > + Point_3 e3(0.0, 0.0, 1.0);
> > +
> > + Point_3 _e1(-1.0, 0.0, 0.0);
> > + Point_3 _e2(0.0, -1.0, 0.0);
> > + Point_3 _e3(0.0, 0.0, -1.0);
> > +
> > + //Create tetrahedrons with unit vectors and reference results.
> > + DoubleList reference_volumes;
> > + PointList reference_bary_centers;
> > + PolyhedronList reference_polyhedrons;
> > +
> > + //skew plane upper e3 plane
> > + add_test_polyhedron(e1,e2,e3,reference_polyhedrons);
> > + //todo find exact values
> > + reference_volumes.push_back(8.660254e-01);
> > + reference_bary_centers.push_back(Point(1.0/3.0,1.0/3.0,1.0/3.0));
> > +
> > + add_test_polyhedron(_e1,e2,e3,reference_polyhedrons);
> > + //todo find exact values
> > + reference_volumes.push_back(8.660254e-01);
> > + reference_bary_centers.push_back(Point(-1.0/3.0,1.0/3.0,1.0/3.0));
> > +
> > + add_test_polyhedron(_e1,_e2,e3,reference_polyhedrons);
> > + //todo find exact values
> > + reference_volumes.push_back(8.660254e-01);
> > + reference_bary_centers.push_back(Point(-1.0/3.0,-1.0/3.0,1.0/3.0));
> > +
> > + add_test_polyhedron(e1,_e2,e3,reference_polyhedrons);
> > + //todo find exact values
> > + reference_volumes.push_back(8.660254e-01);
> > + reference_bary_centers.push_back(Point(1.0/3.0,-1.0/3.0,1.0/3.0));
> > +
> > + //skew plane lower -e3 plane
> > + add_test_polyhedron(e1,e2,_e3,reference_polyhedrons);
> > + //todo find exact values
> > + reference_volumes.push_back(8.660254e-01);
> > + reference_bary_centers.push_back(Point(1.0/3.0,1.0/3.0,-1.0/3.0));
> > +
> > + add_test_polyhedron(_e1,e2,_e3,reference_polyhedrons);
> > + //todo find exact values
> > + reference_volumes.push_back(8.660254e-01);
> > + reference_bary_centers.push_back(Point(-1.0/3.0,1.0/3.0,-1.0/3.0));
> > +
> > + add_test_polyhedron(_e1,_e2,_e3,reference_polyhedrons);
> > + //todo find exact values
> > + reference_volumes.push_back(8.660254e-01);
> > + reference_bary_centers.push_back(Point(-1.0/3.0,-1.0/3.0,-1.0/3.0));
> > +
> > + add_test_polyhedron(e1,_e2,_e3,reference_polyhedrons);
> > + //todo find exact values
> > + reference_volumes.push_back(8.660254e-01);
> > + reference_bary_centers.push_back(Point(1.0/3.0,-1.0/3.0,-1.0/3.0));
> > +
> > + //e1-e2 plane
> > + add_test_polyhedron(e0,e1,e2,reference_polyhedrons);
> > + reference_volumes.push_back(1.0/2.0);
> > + reference_bary_centers.push_back(Point(1.0/3.0,1.0/3.0,0.0));
> > +
> > + add_test_polyhedron(e0,_e1,e2,reference_polyhedrons);
> > + reference_volumes.push_back(1.0/2.0);
> > + reference_bary_centers.push_back(Point(-1.0/3.0,1.0/3.0,0.0));
> > +
> > + add_test_polyhedron(e0,_e1,_e2,reference_polyhedrons);
> > + reference_volumes.push_back(1.0/2.0);
> > + reference_bary_centers.push_back(Point(-1.0/3.0,-1.0/3.0,0.0));
> > +
> > + add_test_polyhedron(e0,e1,_e2,reference_polyhedrons);
> > + reference_volumes.push_back(1.0/2.0);
> > + reference_bary_centers.push_back(Point(1.0/3.0,-1.0/3.0,0.0));
> > +
> > + //e1-e3 plane
> > + add_test_polyhedron(e0,e1,e3,reference_polyhedrons);
> > + reference_volumes.push_back(1.0/2.0);
> > + reference_bary_centers.push_back(Point(1.0/3.0,0.0,1.0/3.0));
> > +
> > + add_test_polyhedron(e0,_e1,e3,reference_polyhedrons);
> > + reference_volumes.push_back(1.0/2.0);
> > + reference_bary_centers.push_back(Point(-1.0/3.0,0.0,1.0/3.0));
> > +
> > + add_test_polyhedron(e0,_e1,_e3,reference_polyhedrons);
> > + reference_volumes.push_back(1.0/2.0);
> > + reference_bary_centers.push_back(Point(-1.0/3.0,0.0,-1.0/3.0));
> > +
> > + add_test_polyhedron(e0,e1,_e3,reference_polyhedrons);
> > + reference_volumes.push_back(1.0/2.0);
> > + reference_bary_centers.push_back(Point(1.0/3.0,0.0,-1.0/3.0));
> > +
> > + //e2-e3 plane
> > + add_test_polyhedron(e0,e2,e3,reference_polyhedrons);
> > + reference_volumes.push_back(1.0/2.0);
> > + reference_bary_centers.push_back(Point(0.0,1.0/3.0,1.0/3.0));
> > +
> > + add_test_polyhedron(e0,_e2,e3,reference_polyhedrons);
> > + reference_volumes.push_back(1.0/2.0);
> > + reference_bary_centers.push_back(Point(0.0,-1.0/3.0,1.0/3.0));
> > +
> > + add_test_polyhedron(e0,_e2,_e3,reference_polyhedrons);
> > + reference_volumes.push_back(1.0/2.0);
> > + reference_bary_centers.push_back(Point(0.0,-1.0/3.0,-1.0/3.0));
> > +
> > + add_test_polyhedron(e0,e2,_e3,reference_polyhedrons);
> > + reference_volumes.push_back(1.0/2.0);
> > + reference_bary_centers.push_back(Point(0.0,1.0/3.0,-1.0/3.0));
> > +
> > + //Test sum of polyhedrons
> > + IntList add_indices;
> > + add_indices.push_back(0);
> > +
> > +
> > + add_indices.push_back(1);
> > + add_disjoint_polyhedrons(add_indices,
> > + reference_polyhedrons,
> > + reference_volumes,
> > + reference_bary_centers);
> > +
> > + add_indices.push_back(2);
> > + add_disjoint_polyhedrons(add_indices,
> > + reference_polyhedrons,
> > + reference_volumes,
> > + reference_bary_centers);
> > +
> > + add_indices.push_back(3);
> > + add_disjoint_polyhedrons(add_indices,
> > + reference_polyhedrons,
> > + reference_volumes,
> > + reference_bary_centers);
> > +
> > + add_indices.push_back(4);
> > + add_disjoint_polyhedrons(add_indices,
> > + reference_polyhedrons,
> > + reference_volumes,
> > + reference_bary_centers);
> > +
> > + add_indices.push_back(5);
> > + add_disjoint_polyhedrons(add_indices,
> > + reference_polyhedrons,
> > + reference_volumes,
> > + reference_bary_centers);
> > +
> > + add_indices.push_back(6);
> > + add_disjoint_polyhedrons(add_indices,
> > + reference_polyhedrons,
> > + reference_volumes,
> > + reference_bary_centers);
> > +
> > + add_indices.push_back(7);
> > + add_disjoint_polyhedrons(add_indices,
> > + reference_polyhedrons,
> > + reference_volumes,
> > + reference_bary_centers);
> > +
> > + add_indices.push_back(8);
> > + add_disjoint_polyhedrons(add_indices,
> > + reference_polyhedrons,
> > + reference_volumes,
> > + reference_bary_centers);
> > +
> > + add_indices.push_back(9);
> > + add_disjoint_polyhedrons(add_indices,
> > + reference_polyhedrons,
> > + reference_volumes,
> > + reference_bary_centers);
> > +
> > +
> > + add_indices.push_back(10);
> > + add_disjoint_polyhedrons(add_indices,
> > + reference_polyhedrons,
> > + reference_volumes,
> > + reference_bary_centers);
> > +
> > + add_indices.push_back(11);
> > + add_disjoint_polyhedrons(add_indices,
> > + reference_polyhedrons,
> > + reference_volumes,
> > + reference_bary_centers);
> > +
> > + add_indices.push_back(12);
> > + add_disjoint_polyhedrons(add_indices,
> > + reference_polyhedrons,
> > + reference_volumes,
> > + reference_bary_centers);
> > +
> > + add_indices.push_back(13);
> > + add_disjoint_polyhedrons(add_indices,
> > + reference_polyhedrons,
> > + reference_volumes,
> > + reference_bary_centers);
> > +
> > + add_indices.push_back(14);
> > + add_disjoint_polyhedrons(add_indices,
> > + reference_polyhedrons,
> > + reference_volumes,
> > + reference_bary_centers);
> > +
> > + add_indices.push_back(15);
> > + add_disjoint_polyhedrons(add_indices,
> > + reference_polyhedrons,
> > + reference_volumes,
> > + reference_bary_centers);
> > +
> > + Nef_polyhedron_3 polyhedron = reference_polyhedrons[0];
> > + polyhedron.transform(Aff_transformation_3(CGAL::TRANSLATION,
> > Vector_3(1, 1, 1))); + reference_polyhedrons.push_back(polyhedron);
> > + reference_volumes.push_back(reference_volumes[0]);
> > + reference_bary_centers.push_back(reference_bary_centers[0] +
> > Point(1,1,1)); +
> > + polyhedron = reference_polyhedrons[1];
> > + polyhedron.transform(Aff_transformation_3(CGAL::TRANSLATION,
> > Vector_3(-1, 1, 1))); + reference_polyhedrons.push_back(polyhedron);
> > + reference_volumes.push_back(reference_volumes[1]);
> > + reference_bary_centers.push_back(reference_bary_centers[1] +
> > Point(-1,1,1)); +
> > + polyhedron = reference_polyhedrons[2];
> > + polyhedron.transform(Aff_transformation_3(CGAL::TRANSLATION,
> > Vector_3(1, -1, 1))); + reference_polyhedrons.push_back(polyhedron);
> > + reference_volumes.push_back(reference_volumes[2]);
> > + reference_bary_centers.push_back(reference_bary_centers[2] +
> > Point(1,-1,1)); +
> > + polyhedron = reference_polyhedrons[3];
> > + polyhedron.transform(Aff_transformation_3(CGAL::TRANSLATION,
> > Vector_3(-1, -1, 1))); + reference_polyhedrons.push_back(polyhedron);
> > + reference_volumes.push_back(reference_volumes[3]);
> > + reference_bary_centers.push_back(reference_bary_centers[3] +
> > Point(-1,-1,1)); +
> > + polyhedron = reference_polyhedrons[4];
> > + polyhedron.transform(Aff_transformation_3(CGAL::TRANSLATION,
> > Vector_3(1, 1, -1))); + reference_polyhedrons.push_back(polyhedron);
> > + reference_volumes.push_back(reference_volumes[4]);
> > + reference_bary_centers.push_back(reference_bary_centers[4] +
> > Point(1,1,-1)); +
> > + polyhedron = reference_polyhedrons[5];
> > + polyhedron.transform(Aff_transformation_3(CGAL::TRANSLATION,
> > Vector_3(-1, 1, -1))); + reference_polyhedrons.push_back(polyhedron);
> > + reference_volumes.push_back(reference_volumes[5]);
> > + reference_bary_centers.push_back(reference_bary_centers[5] +
> > Point(-1,1,-1)); +
> > + polyhedron = reference_polyhedrons[6];
> > + polyhedron.transform(Aff_transformation_3(CGAL::TRANSLATION,
> > Vector_3(1, -1, -1))); + reference_polyhedrons.push_back(polyhedron);
> > + reference_volumes.push_back(reference_volumes[6]);
> > + reference_bary_centers.push_back(reference_bary_centers[6] +
> > Point(1,-1,-1)); +
> > + polyhedron = reference_polyhedrons[7];
> > + polyhedron.transform(Aff_transformation_3(CGAL::TRANSLATION,
> > Vector_3(-1, -1, -1))); +
> > reference_polyhedrons.push_back(polyhedron);
> > + reference_volumes.push_back(reference_volumes[7]);
> > + reference_bary_centers.push_back(reference_bary_centers[7] +
> > Point(-1,-1,-1)); +
> > + //Instantiate quadrature rule
> > + BaryCenterQuadrature quadrature_rule;
> > +
> > + //Check volume and barycenter for polyhedrons
> > + for (dolfin::uint i = 0; i < reference_polyhedrons.size(); ++i)
> > + {
> > + quadrature_rule.compute_quadrature_rule(reference_polyhedrons[i]);
> > + CPPUNIT_ASSERT_DOUBLES_EQUAL(reference_volumes[i],
> > + quadrature_rule.weights()[0], 1.0e-5);
> > + almost_equal_points(reference_bary_centers[i],
> > + quadrature_rule.points()[0], 1.0e-5);
> > + }
> > + }
> > +
> > + void testComplexPolyhedrons()
> > + {
> > + }
> > +
> > + void testComplexPolygons()
> > + {
> > + }
> > +
> > +};
> > +
> > +CPPUNIT_TEST_SUITE_REGISTRATION(BaryCenter);
> > +
> > +int main()
> > +{
> > + DOLFIN_TEST;
> > +}
> >
> > === added file
> > 'nitsche_method/integration_on_complex_domains/gauss_projection_green/te
> > tra' ---
> > nitsche_method/integration_on_complex_domains/gauss_projection_green/tet
> > ra 1970-01-01 00:00:00 +0000 +++
> > nitsche_method/integration_on_complex_domains/gauss_projection_green/tet
> > ra 2010-03-18 18:15:26 +0000 @@ -0,0 +1,16 @@
> > +4
> > +
> > +0 0 0
> > +5 0 0
> > +0 4 0
> > +0 0 3
> > +
> > +4
> > +
> > +3 0 3 2
> > +3 3 0 1
> > +3 2 1 0
> > +3 1 2 3
> > +
> > +
> > +
> >
> > === added file
> > 'nitsche_method/integration_on_complex_domains/gauss_projection_green/vo
> > lInt.c' ---
> > nitsche_method/integration_on_complex_domains/gauss_projection_green/vol
> > Int.c 1970-01-01 00:00:00 +0000 +++
> > nitsche_method/integration_on_complex_domains/gauss_projection_green/vol
> > Int.c 2010-03-26 13:05:51 +0000 @@ -0,0 +1,383 @@
> > +
> > +
> > + /*******************************************************
> > + * *
> > + * volInt.c *
> > + * *
> > + * This code computes volume integrals needed for *
> > + * determining mass properties of polyhedral bodies. *
> > + * *
> > + * For more information, see the accompanying README *
> > + * file, and the paper *
> > + * *
> > + * Brian Mirtich, "Fast and Accurate Computation of *
> > + * Polyhedral Mass Properties," journal of graphics *
> > + * tools, volume 1, number 1, 1996. *
> > + * *
> > + * This source code is public domain, and may be used *
> > + * in any way, shape or form, free of charge. *
> > + * *
> > + * Copyright 1995 by Brian Mirtich *
> > + * *
> > + * mirtich@xxxxxxxxxxxxxxx *
> > + * http://www.cs.berkeley.edu/~mirtich *
> > + * *
> > + *******************************************************/
> > +
> > +/*
> > + Revision history
> > +
> > + 26 Jan 1996 Program creation.
> > +
> > + 3 Aug 1996 Corrected bug arising when polyhedron density
> > + is not 1.0. Changes confined to function main().
> > + Thanks to Zoran Popovic for catching this one.
> > +
> > + 27 May 1997 Corrected sign error in translation of inertia
> > + product terms to center of mass frame. Changes
> > + confined to function main(). Thanks to
> > + Chris Hecker.
> > +*/
> > +
> > +
> > +
> > +#include <stdio.h>
> > +#include <string.h>
> > +#include <math.h>
> > +
> > +using namespace std;
> > +
> > +/*
> > +
> > ========================================================================
> > ==== + constants
> > +
> > ========================================================================
> > ==== +*/
> > +
> > +#define MAX_VERTS 100 /* maximum number of polyhedral vertices */
> > +#define MAX_FACES 100 /* maximum number of polyhedral faces */
> > +#define MAX_POLYGON_SZ 10 /* maximum number of verts per polygonal face
> > */ +
> > +#define X 0
> > +#define Y 1
> > +#define Z 2
> > +
> > +/*
> > +
> > ========================================================================
> > ==== + macros
> > +
> > ========================================================================
> > ==== +*/
> > +
> > +#define SQR(x) ((x)*(x))
> > +#define CUBE(x) ((x)*(x)*(x))
> > +
> > +/*
> > +
> > ========================================================================
> > ==== + data structures
> > +
> > ========================================================================
> > ==== +*/
> > +
> > +typedef struct {
> > + int numVerts;
> > + double norm[3];
> > + double w;
> > + int verts[MAX_POLYGON_SZ];
> > + struct polyhedron *poly;
> > +} FACE;
> > +
> > +typedef struct polyhedron {
> > + int numVerts, numFaces;
> > + double verts[MAX_VERTS][3];
> > + FACE faces[MAX_FACES];
> > +} POLYHEDRON;
> > +
> > +
> > +/*
> > +
> > ========================================================================
> > ==== + globals
> > +
> > ========================================================================
> > ==== +*/
> > +
> > +static int A; /* alpha */
> > +static int B; /* beta */
> > +static int C; /* gamma */
> > +
> > +/* projection integrals */
> > +static double P1, Pa, Pb, Paa, Pab, Pbb, Paaa, Paab, Pabb, Pbbb;
> > +
> > +/* face integrals */
> > +static double Fa, Fb, Fc, Faa, Fbb, Fcc, Faaa, Fbbb, Fccc, Faab, Fbbc,
> > Fcca; +
> > +/* volume integrals */
> > +static double T0, T1[3], T2[3], TP[3];
> > +
> > +
> > +/*
> > +
> > ========================================================================
> > ==== + read in a polyhedron
> > +
> > ========================================================================
> > ==== +*/
> > +
> > +void readPolyhedron(char *name, POLYHEDRON *p)
> > +{
> > + FILE *fp;
> > + char line[200], *c;
> > + int i, j, n;
> > + double dx1, dy1, dz1, dx2, dy2, dz2, nx, ny, nz, len;
> > + FACE *f;
> > +
> > +
> > +/* if (!(fp = fopen(name, "r"))) {*/
> > +/* printf("i/o error\n");*/
> > +/* exit(1);*/
> > + }
> > +
> > + fscanf(fp, "%d", &p->numVerts);
> > + printf("Reading in %d vertices\n", p->numVerts);
> > + for (i = 0; i < p->numVerts; i++)
> > + fscanf(fp, "%lf %lf %lf",
> > + &p->verts[i][X], &p->verts[i][Y], &p->verts[i][Z]);
> > +
> > + fscanf(fp, "%d", &p->numFaces);
> > + printf("Reading in %d faces\n", p->numFaces);
> > + for (i = 0; i < p->numFaces; i++) {
> > + f = &p->faces[i];
> > + f->poly = p;
> > + fscanf(fp, "%d", &f->numVerts);
> > + for (j = 0; j < f->numVerts; j++) fscanf(fp, "%d", &f->verts[j]);
> > +
> > + /* compute face normal and offset w from first 3 vertices */
> > + dx1 = p->verts[f->verts[1]][X] - p->verts[f->verts[0]][X];
> > + dy1 = p->verts[f->verts[1]][Y] - p->verts[f->verts[0]][Y];
> > + dz1 = p->verts[f->verts[1]][Z] - p->verts[f->verts[0]][Z];
> > + dx2 = p->verts[f->verts[2]][X] - p->verts[f->verts[1]][X];
> > + dy2 = p->verts[f->verts[2]][Y] - p->verts[f->verts[1]][Y];
> > + dz2 = p->verts[f->verts[2]][Z] - p->verts[f->verts[1]][Z];
> > + nx = dy1 * dz2 - dy2 * dz1;
> > + ny = dz1 * dx2 - dz2 * dx1;
> > + nz = dx1 * dy2 - dx2 * dy1;
> > + len = sqrt(nx * nx + ny * ny + nz * nz);
> > + f->norm[X] = nx / len;
> > + f->norm[Y] = ny / len;
> > + f->norm[Z] = nz / len;
> > + f->w = - f->norm[X] * p->verts[f->verts[0]][X]
> > + - f->norm[Y] * p->verts[f->verts[0]][Y]
> > + - f->norm[Z] * p->verts[f->verts[0]][Z];
> > +
> > + }
> > +
> > + fclose(fp);
> > +
> > +}
> > +
> > +/*
> > +
> > ========================================================================
> > ==== + compute mass properties
> > +
> > ========================================================================
> > ==== +*/
> > +
> > +
> > +/* compute various integrations over projection of face */
> > +void compProjectionIntegrals(FACE *f)
> > +{
> > + double a0, a1, da;
> > + double b0, b1, db;
> > + double a0_2, a0_3, a0_4, b0_2, b0_3, b0_4;
> > + double a1_2, a1_3, b1_2, b1_3;
> > + double C1, Ca, Caa, Caaa, Cb, Cbb, Cbbb;
> > + double Cab, Kab, Caab, Kaab, Cabb, Kabb;
> > + int i;
> > +
> > + P1 = Pa = Pb = Paa = Pab = Pbb = Paaa = Paab = Pabb = Pbbb = 0.0;
> > +
> > + for (i = 0; i < f->numVerts; i++) {
> > + a0 = f->poly->verts[f->verts[i]][A];
> > + b0 = f->poly->verts[f->verts[i]][B];
> > + a1 = f->poly->verts[f->verts[(i+1) % f->numVerts]][A];
> > + b1 = f->poly->verts[f->verts[(i+1) % f->numVerts]][B];
> > + da = a1 - a0;
> > + db = b1 - b0;
> > + a0_2 = a0 * a0; a0_3 = a0_2 * a0; a0_4 = a0_3 * a0;
> > + b0_2 = b0 * b0; b0_3 = b0_2 * b0; b0_4 = b0_3 * b0;
> > + a1_2 = a1 * a1; a1_3 = a1_2 * a1;
> > + b1_2 = b1 * b1; b1_3 = b1_2 * b1;
> > +
> > + C1 = a1 + a0;
> > + Ca = a1*C1 + a0_2; Caa = a1*Ca + a0_3; Caaa = a1*Caa + a0_4;
> > + Cb = b1*(b1 + b0) + b0_2; Cbb = b1*Cb + b0_3; Cbbb = b1*Cbb + b0_4;
> > + Cab = 3*a1_2 + 2*a1*a0 + a0_2; Kab = a1_2 + 2*a1*a0 + 3*a0_2;
> > + Caab = a0*Cab + 4*a1_3; Kaab = a1*Kab + 4*a0_3;
> > + Cabb = 4*b1_3 + 3*b1_2*b0 + 2*b1*b0_2 + b0_3;
> > + Kabb = b1_3 + 2*b1_2*b0 + 3*b1*b0_2 + 4*b0_3;
> > +
> > + P1 += db*C1;
> > + Pa += db*Ca;
> > + Paa += db*Caa;
> > + Paaa += db*Caaa;
> > + Pb += da*Cb;
> > + Pbb += da*Cbb;
> > + Pbbb += da*Cbbb;
> > + Pab += db*(b1*Cab + b0*Kab);
> > + Paab += db*(b1*Caab + b0*Kaab);
> > + Pabb += da*(a1*Cabb + a0*Kabb);
> > + }
> > +
> > + P1 /= 2.0;
> > + Pa /= 6.0;
> > + Paa /= 12.0;
> > + Paaa /= 20.0;
> > + Pb /= -6.0;
> > + Pbb /= -12.0;
> > + Pbbb /= -20.0;
> > + Pab /= 24.0;
> > + Paab /= 60.0;
> > + Pabb /= -60.0;
> > +}
> > +
> > +compFaceIntegrals(FACE *f)
> > +{
> > + double *n, w;
> > + double k1, k2, k3, k4;
> > +
> > + compProjectionIntegrals(f);
> > +
> > + w = f->w;
> > + n = f->norm;
> > + k1 = 1 / n[C]; k2 = k1 * k1; k3 = k2 * k1; k4 = k3 * k1;
> > +
> > + Fa = k1 * Pa;
> > + Fb = k1 * Pb;
> > + Fc = -k2 * (n[A]*Pa + n[B]*Pb + w*P1);
> > +
> > + Faa = k1 * Paa;
> > + Fbb = k1 * Pbb;
> > + Fcc = k3 * (SQR(n[A])*Paa + 2*n[A]*n[B]*Pab + SQR(n[B])*Pbb
> > + + w*(2*(n[A]*Pa + n[B]*Pb) + w*P1));
> > +
> > + Faaa = k1 * Paaa;
> > + Fbbb = k1 * Pbbb;
> > + Fccc = -k4 * (CUBE(n[A])*Paaa + 3*SQR(n[A])*n[B]*Paab
> > + + 3*n[A]*SQR(n[B])*Pabb + CUBE(n[B])*Pbbb
> > + + 3*w*(SQR(n[A])*Paa + 2*n[A]*n[B]*Pab + SQR(n[B])*Pbb)
> > + + w*w*(3*(n[A]*Pa + n[B]*Pb) + w*P1));
> > +
> > + Faab = k1 * Paab;
> > + Fbbc = -k2 * (n[A]*Pabb + n[B]*Pbbb + w*Pbb);
> > + Fcca = k3 * (SQR(n[A])*Paaa + 2*n[A]*n[B]*Paab + SQR(n[B])*Pabb
> > + + w*(2*(n[A]*Paa + n[B]*Pab) + w*Pa));
> > +}
> > +
> > +void compVolumeIntegrals(POLYHEDRON *p)
> > +{
> > + FACE *f;
> > + double nx, ny, nz;
> > + int i;
> > +
> > + T0 = T1[X] = T1[Y] = T1[Z]
> > + = T2[X] = T2[Y] = T2[Z]
> > + = TP[X] = TP[Y] = TP[Z] = 0;
> > +
> > + for (i = 0; i < p->numFaces; i++) {
> > +
> > + f = &p->faces[i];
> > +
> > + nx = fabs(f->norm[X]);
> > + ny = fabs(f->norm[Y]);
> > + nz = fabs(f->norm[Z]);
> > + if (nx > ny && nx > nz) C = X;
> > + else C = (ny > nz) ? Y : Z;
> > + A = (C + 1) % 3;
> > + B = (A + 1) % 3;
> > +
> > + compFaceIntegrals(f);
> > +
> > + T0 += f->norm[X] * ((A == X) ? Fa : ((B == X) ? Fb : Fc));
> > +
> > + T1[A] += f->norm[A] * Faa;
> > + T1[B] += f->norm[B] * Fbb;
> > + T1[C] += f->norm[C] * Fcc;
> > + T2[A] += f->norm[A] * Faaa;
> > + T2[B] += f->norm[B] * Fbbb;
> > + T2[C] += f->norm[C] * Fccc;
> > + TP[A] += f->norm[A] * Faab;
> > + TP[B] += f->norm[B] * Fbbc;
> > + TP[C] += f->norm[C] * Fcca;
> > + }
> > +
> > + T1[X] /= 2; T1[Y] /= 2; T1[Z] /= 2;
> > + T2[X] /= 3; T2[Y] /= 3; T2[Z] /= 3;
> > + TP[X] /= 2; TP[Y] /= 2; TP[Z] /= 2;
> > +}
> > +
> > +
> > +/*
> > +
> > ========================================================================
> > ==== + main
> > +
> > ========================================================================
> > ==== +*/
> > +
> > +
> > +int main(int argc, char *argv[])
> > +{
> > + POLYHEDRON p;
> > + double density, mass;
> > + double r[3]; /* center of mass */
> > + double J[3][3]; /* inertia tensor */
> > +
> > + if (argc != 2) {
> > + printf("usage: %s <polyhedron geometry filename>\n", argv[0]);
> > +/* exit(0);*/
> > + return 0;
> > + }
> > +
> > + readPolyhedron(argv[1], &p);
> > +
> > + compVolumeIntegrals(&p);
> > +
> > +
> > + printf("\nT1 = %+20.6f\n\n", T0);
> > +
> > + printf("Tx = %+20.6f\n", T1[X]);
> > + printf("Ty = %+20.6f\n", T1[Y]);
> > + printf("Tz = %+20.6f\n\n", T1[Z]);
> > +
> > + printf("Txx = %+20.6f\n", T2[X]);
> > + printf("Tyy = %+20.6f\n", T2[Y]);
> > + printf("Tzz = %+20.6f\n\n", T2[Z]);
> > +
> > + printf("Txy = %+20.6f\n", TP[X]);
> > + printf("Tyz = %+20.6f\n", TP[Y]);
> > + printf("Tzx = %+20.6f\n\n", TP[Z]);
> > +
> > + density = 1.0; /* assume unit density */
> > +
> > + mass = density * T0;
> > +
> > + /* compute center of mass */
> > + r[X] = T1[X] / T0;
> > + r[Y] = T1[Y] / T0;
> > + r[Z] = T1[Z] / T0;
> > +
> > + /* compute inertia tensor */
> > + J[X][X] = density * (T2[Y] + T2[Z]);
> > + J[Y][Y] = density * (T2[Z] + T2[X]);
> > + J[Z][Z] = density * (T2[X] + T2[Y]);
> > + J[X][Y] = J[Y][X] = - density * TP[X];
> > + J[Y][Z] = J[Z][Y] = - density * TP[Y];
> > + J[Z][X] = J[X][Z] = - density * TP[Z];
> > +
> > + /* translate inertia tensor to center of mass */
> > + J[X][X] -= mass * (r[Y]*r[Y] + r[Z]*r[Z]);
> > + J[Y][Y] -= mass * (r[Z]*r[Z] + r[X]*r[X]);
> > + J[Z][Z] -= mass * (r[X]*r[X] + r[Y]*r[Y]);
> > + J[X][Y] = J[Y][X] += mass * r[X] * r[Y];
> > + J[Y][Z] = J[Z][Y] += mass * r[Y] * r[Z];
> > + J[Z][X] = J[X][Z] += mass * r[Z] * r[X];
> > +
> > + printf("center of mass: (%+12.6f,%+12.6f,%+12.6f)\n\n", r[X], r[Y],
> > r[Z]); +
> > + printf("inertia tensor with origin at c.o.m. :\n");
> > + printf("%+15.6f %+15.6f %+15.6f\n", J[X][X], J[X][Y], J[X][Z]);
> > + printf("%+15.6f %+15.6f %+15.6f\n", J[Y][X], J[Y][Y], J[Y][Z]);
> > + printf("%+15.6f %+15.6f %+15.6f\n\n", J[Z][X], J[Z][Y], J[Z][Z]);
> > +
> > +}
> >
> > === added directory
> > 'nitsche_method/integration_on_complex_domains/monte_carlo' === added
> > directory 'nitsche_method/integration_on_complex_domains/triangulation'
> > === added directory 'nitsche_method/overlapping_meshes'
> > === added file 'nitsche_method/overlapping_meshes/MeshIntersector.cpp'
> > --- nitsche_method/overlapping_meshes/MeshIntersector.cpp 1970-01-01
> > 00:00:00 +0000 +++
> > nitsche_method/overlapping_meshes/MeshIntersector.cpp 2010-03-16
> > 14:39:09 +0000 @@ -0,0 +1,175 @@
> > +//
> > ========================================================================
> > ============= +//
> > +// Copyright (C) 2010-01-16 André Massing
> > +// Licensed under the GNU LGPL Version 2.1.
> > +//
> > +// Modified by André Massing, 2010
> > +//
> > +// First added: 2010-01-16
> > +// back changed: 2010-01-27
> > +//
> > +//Author: André Massing (am), massing@xxxxxxxxx
> > +//Company: Simula Research Laboratory, Fornebu, Norway
> > +//
> > +//
> > ========================================================================
> > ============= +
> > +#include "OverlappingMeshes.h"
> > +
> > +#include <dolfin/mesh/BoundaryMesh.h>
> > +#include <dolfin/mesh/Vertex.h>
> > +#include <dolfin/mesh/Cell.h>
> > +
> > +#include <dolfin/log/dolfin_log.h>
> > +#include <dolfin/common/NoDeleter.h>
> > +
> > +#include <iostream>
> > +
> > +using namespace dolfin;
> > +using dolfin::uint;
> > +
> > +
> > + MeshIntersection::OverlapData::OverlapData(boost::shared_ptr<const
> > Mesh> mesh) +: mesh(mesh)
> > +{
> > + intersected_domain = MeshFunction<uint>(*mesh,mesh->topology().dim());
> > + intersected_domain = 0;
> > +}
> > +
> > +MeshIntersection::MeshIntersection(const Mesh & mesh_1, const Mesh &
> > mesh_2) + :
> > + _overlapped_domain(new
> > OverlapData(reference_to_no_delete_pointer(mesh_1))) +
> > ,_overlapping_domain(new
> > OverlapData(reference_to_no_delete_pointer(mesh_2))) +
> > ,_overlapped_boundary(new OverlapData(boost::shared_ptr<const Mesh>(new
> > BoundaryMesh(mesh_1)))) + ,_overlapping_boundary(new
> > OverlapData(boost::shared_ptr<const Mesh>(new BoundaryMesh(mesh_2))))
> > +{}
> > +
> > +//MeshIntersection::MeshIntersection(boost::shared_ptr<const Mesh>
> > mesh_1, boost::shared_ptr<const Mesh> mesh_2) +// :
> > +// _overlapped_domain(mesh_1)
> > +// ,_overlapping_domain(mesh_2)
> > +// _overlapped_boundary(boost::shared_ptr<const Mesh>(new
> > BoundaryMesh(mesh_1))) +//
> > ,_overlapping_boundary(boost::shared_ptr<const Mesh>(new
> > BoundaryMesh(mesh_2))) +//{}
> > +
> > +
> > +void MeshIntersection::compute_overlap_map()
> > +{
> > +
> > + const Mesh & mesh_1 = *(_overlapped_domain->mesh);
> > + const Mesh & mesh_2 = *(_overlapping_domain->mesh);
> > +
> > + const Mesh & boundary_1 = *(_overlapped_boundary->mesh);
> > + const Mesh & boundary_2 = *(_overlapping_boundary->mesh);
> > +
> > + EntityEntitiesMap & cell_cell_map =
> > _overlapped_domain->entity_entities_map; + EntityEntitiesMap &
> > facet_1_cell_2_map = _overlapped_boundary->entity_entities_map; +
> > EntityEntitiesMap & facet_2_cell_1_map =
> > _overlapping_boundary->entity_entities_map; +
> > + CellIterator cut_cell(mesh_1);
> > + CellIterator cut_facet(boundary_2);
> > +
> > + //Step 1:
> > + //Intersect boundary of mesh_2 with mesh_1.
> > + //to get the *partially*
> > + //intersected cells of mesh_1.
> > + //This calculates:
> > + // a) *partially* intersected cells of mesh1
> > + // b) the exterior facets of mesh_2 which are (part) of the artificial
> > interface. + // c) *partially* intersected exterior facets of mesh1 and
> > mesh2. +
> > + for (CellIterator cell(boundary_2); !cell.end(); ++cell)
> > + {
> > + mesh_1.all_intersected_entities(*cell,
> > facet_2_cell_1_map[cell->index()]); +
> > + if (facet_2_cell_1_map[cell->index()].empty())
> > + facet_2_cell_1_map.erase(cell->index());
> > + //If not empty add cell index and intersecting cell index to the
> > map. + else
> > + {
> > + //Iterate of intersected cell of mesh1, find the overlapping cells
> > of + //mesh 2 and mark cells in mesh1 as partially overlapped. +
> > for (EntityListIter cell_iter =
> > facet_2_cell_1_map[cell->index()].begin(); cell_iter !=
> > facet_2_cell_1_map[cell->index()].end(); ++cell_iter) + {
> > + mesh_2.all_intersected_entities(cut_cell[*cell_iter],
> > cell_cell_map[*cell_iter]); +
> > _overlapped_domain->intersected_domain[*cell_iter] = 1; + }
> > +
> > + //Compute partially overlapped boundary cells of mesh1 and mesh2.
> > + //
> > + //@remark: Clarify whether it is faster to check first if any and
> > then + //if compute indeces or just try to compute immediately and
> > erase if the cell + //index container is empty. Rational: We want
> > to avoid a copy operator + //(linear). A "any intersection" test
> > should have the same complexity as + //a "compute all intersection"
> > if no intersection occurs. If a + //intersection occurrs, we want
> > to compute all intersection anyway. + //1. Version Compute right
> > away and deleting (delete operation is amortized constant) if empty +
> > //2. Version Check first and compute if intersected.
> > + //3. Compute and assign if not empty
> > + //@remark What is faster? Recompute intersecting cells from mesh2
> > for the + //exterior facets in mesh1 or map facet index to cell
> > index, and assign + //their cell set (which might be bigger as the
> > set, which really only + //intersects the facet).
> > +
> > + EntityList cut_faces;
> > + boundary_1.all_intersected_entities(*cell,cut_faces);
> > +
> > + if (!cut_faces.empty())
> > + {
> > + _overlapping_boundary->intersected_domain[cell->index()] = 1;
> > +
> > + //Compute for each cut exterior facet in mesh1 the cutting cells
> > in + //mesh2, mark facet as partially overlapped.
> > + for (EntityListIter face_iter = cut_faces.begin(); face_iter !=
> > cut_faces.end(); ++face_iter) + {
> > +
> > mesh_2.all_intersected_entities(cut_facet[*face_iter],facet_1_cell_2_map
> > [*face_iter]); +
> > _overlapped_boundary->intersected_domain[*face_iter] = 1; + }
> > + }
> > + else
> > + {
> > + _overlapping_boundary->intersected_domain[cell->index()] = 2;
> > + }
> > + }
> > + }
> > +
> > + //Step 2:
> > + //Determine all cells of Mesh 1, which are fully overlapped. This is
> > done by + //going through the cells, check if they are not partially
> > overlapped and + //therefore must then be fully overlapped if any
> > vertex is intersecting + //mesh2.
> > + for (CellIterator cell(mesh_1); !cell.end(); ++cell)
> > + {
> > + if (_overlapped_domain->intersected_domain[cell->index()] != 1 &&
> > mesh_2.any_intersected_entity(VertexIterator(*cell)->point()) != -1) +
> > _overlapped_domain->intersected_domain[cell->index()] = 2; + }
> > +
> > + //Step 3:
> > + //Determine all cells of the boundary of mesh 1, which are fully
> > overlapped. + //Same method as in Step 2.
> > + for (CellIterator cell(boundary_1); !cell.end(); ++cell)
> > + {
> > + if (_overlapped_boundary->intersected_domain[cell->index()] != 1
> > + && mesh_2.any_intersected_entity(VertexIterator(*cell)->point())
> > != -1) + _overlapped_boundary->intersected_domain[cell->index()] =
> > 2; + }
> > +}
> > +
> > +const MeshFunction<uint> & MeshIntersection::overlapped_domain() const
> > +{
> > + return _overlapped_domain->intersected_domain;
> > +}
> > +
> > +const MeshFunction<uint> & MeshIntersection::overlapping_domain() const
> > +{
> > + return _overlapping_domain->intersected_domain;
> > +}
> > +
> > +const MeshFunction<uint> & MeshIntersection::overlapped_boundary() const
> > +{
> > + return _overlapped_boundary->intersected_domain;
> > +}
> > +
> > +const MeshFunction<uint> & MeshIntersection::overlapping_boundary()
> > const +{
> > + return _overlapping_boundary->intersected_domain;
> > +}
> >
> > === added file 'nitsche_method/overlapping_meshes/MeshIntersector.h'
> > --- nitsche_method/overlapping_meshes/MeshIntersector.h 1970-01-01
> > 00:00:00 +0000 +++
> > nitsche_method/overlapping_meshes/MeshIntersector.h 2010-03-16 14:39:09
> > +0000 @@ -0,0 +1,227 @@
> > +//
> > ========================================================================
> > ============= +//
> > +// Copyright (C) 2010-01-15 André Massing
> > +// Licensed under the GNU LGPL Version 2.1.
> > +//
> > +// Modified by André Massing, 2010
> > +//
> > +// First added: 2010-01-15
> > +// Last changed: 2010-03-08
> > +//
> > +//Author: André Massing (am), massing@xxxxxxxxx
> > +//Company: Simula Research Laboratory, Fornebu, Norway
> > +//
> > +//Description:
> > ========================================================================
> > ============= +
> > +#ifndef __MESHINTERSECTOR_H
> > +#define __MESHINTERSECTOR_H
> > +
> > +#include <vector>
> > +#include <map>
> > +#include <utility>
> > +
> > +#include <boost/shared_ptr.hpp>
> > +#include <boost/shared_array.hpp>
> > +
> > +#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
> > +
> > +#include <CGAL/Nef_polyhedron_3.h>
> > +#include <CGAL/Polyhedron_3.h>
> > +#include <CGAL/Gmpz.h>
> > +#include <CGAL/Homogeneous.h>
> > +
> > +#include <CGAL/IO/Polyhedron_iostream.h>
> > +#include <CGAL/IO/Nef_polyhedron_iostream_3.h>
> > +
> > +#include <dolfin/common/Array.h>
> > +#include <dolfin/common/types.h>
> > +#include <dolfin/mesh/Mesh.h>
> > +#include <dolfin/mesh/MeshFunction.h>
> > +#include <dolfin/mesh/Point.h>
> > +
> > +#include "PrimitiveTraits.h"
> > +
> > +namespace dolfin
> > +{
> > + class Mesh;
> > +
> > + typedef std::vector<uint> EntityList;
> > + typedef std::vector<uint>::const_iterator EntityListIter;
> > + typedef std::map<uint, EntityList> EntityEntitiesMap;
> > + typedef std::map<uint, EntityList>::const_iterator
> > EntityEntitiesMapIter; +// typedef std::map<const Mesh
> > *,EntityEntitiesMap> MeshCutEntitiesMap; +
> > +
> > +// typedef CGAL::Homogeneous<CGAL::Gmpz> Kernel;
> > + typedef CGAL::Exact_predicates_exact_constructions_kernel Kernel;
> > + typedef CGAL::Polyhedron_3<Kernel> Polyhedron_3;
> > + typedef CGAL::Nef_polyhedron_3<Kernel> Nef_polyhedron_3;
> > + typedef Nef_polyhedron_3 Polyhedron;
> > +
> > + ///Defines a quadrature rule by a pair of points and weights.
> > + typedef std::pair<std::vector<Point>,std::vector<double> >
> > QuadratureRule; +
> > + class MeshIntersection;
> > +
> > +
> > + ///@todo:
> > + ///@todo Need a function which indicates the end of the iteration.
> > + ///Think about a better design after the first version is running.
> > + template <int dim>
> > + class MeshIntersectionIterator
> > + {
> > + typedef
> > Primitive_Converter<3,CGAL::Exact_predicates_exact_constructions_kernel>
> > PT; + typedef PT::Polyhedron Polyhedron;
> > +
> > + public:
> > + MeshIntersectionIterator(const MeshIntersection & overlapping_mesh);
> > +
> > + /// Step to the next cut cell and computes the relevant quantities
> > aferwards. + MeshIntersectionIterator<dim> & operator++();
> > +
> > + ///Check if we haved reached the end.
> > + bool end() { return _map_pos == _map_end_pos; }
> > +
> > + ///Return a quadrature rule, meaning a list of points and weights.
> > +// Quadrature_Rule quadrature_rule();
> > +
> > + ///Returns a presentation of the cut cell.
> > + Polyhedron polyhedron() { return _polyhedron ; }
> > +
> > + ///Returns a polyhedron as the presentation of the union of the
> > overlapping cells. + Polyhedron overlapping_polyhedron() { return
> > _overlapping_polyhedron; } +
> > + ///Returns a polyhedron as the presentation of the intersected part.
> > + Polyhedron overlapped_polyhedron();
> > +
> > + private:
> > +
> > + void compute_polyhedrons();
> > +
> > + const MeshIntersection & _overlapping_mesh;
> > +
> > + EntityEntitiesMapIter _map_pos;
> > + EntityEntitiesMapIter _map_end_pos;
> > +
> > + //Intersected MeshEntity
> > + MeshEntityIterator _entity_iter;
> > +
> > + //MeshIterator to iterate over the intersecting cells of the other
> > mesh. + MeshEntityIterator _overlapping_entity_iter;
> > +
> > + //Polydreon, which decodes the intersected part of the cell.
> > + Polyhedron _polyhedron;
> > +
> > + //Polydreon, which decodes the the polyhedron, which is built up by
> > the + //overlapping cells belonging to the other mesh.
> > + Polyhedron _overlapping_polyhedron;
> > +
> > + };
> > +
> > + ///This class present a collection of overlapping meshes and provides
> > + ///functionality to compute cell-cell, cell-facet overlaps.
> > + ///@todo Improve design, it is very unflexible concerning extension to
> > more than 2 meshes. + ///e.g. OverlapData should contain a map, which
> > maps the entity_entities_map to the corresponding + ///mesh, which the
> > entitylist is refering to.
> > + class MeshIntersection {
> > +
> > + ///Helper class to store mesh and corresponding data like
> > intersection maps + ///and meshfunctions.
> > + struct OverlapData {
> > + OverlapData(boost::shared_ptr<const Mesh> mesh);
> > + boost::shared_ptr<const Mesh> mesh;
> > + MeshFunction<uint> intersected_domain;
> > +
> > + EntityEntitiesMap entity_entities_map;
> > +
> > +// MeshCutEntitiesMap entity_entities_map;
> > + };
> > +
> > + public:
> > +
> > + ///Constructor takes a list/vector of meshes. The order of meshes
> > defines + ///also the "overlapp" priority, i.e. if 2 meshes overlap,
> > the one who + //appears later in the list actually covers the later
> > one.
> > + MeshIntersection(const Mesh & mesh_1, const Mesh & mesh_2);
> > +// MeshIntersection(boost::shared_ptr<const Mesh> mesh_1,
> > boost::shared_ptr<const Mesh> mesh_2); +
> > + ///Computes the overlap mapping. Mesh2 overlaps mesh1. Computes
> > (for + ///efficient reasons) in addition the boundary overlaps and
> > the artificial + ///interface.
> > + void compute_overlap_map();
> > +
> > + //Return meshfunctions. Only first test, think about better design,
> > for + //example class like OverlapData or suchlike.
> > + const MeshFunction<uint> & overlapped_domain() const;
> > + const MeshFunction<uint> & overlapping_domain() const;
> > + const MeshFunction<uint> & overlapped_boundary() const;
> > + const MeshFunction<uint> & overlapping_boundary() const;
> > +
> > + private:
> > + template<int dim>
> > + friend class MeshIntersectionIterator;
> > +
> > + const boost::shared_ptr<OverlapData> _overlapped_domain;
> > + const boost::shared_ptr<OverlapData> _overlapping_domain;
> > +
> > + const boost::shared_ptr<OverlapData> _overlapped_boundary;
> > + const boost::shared_ptr<OverlapData> _overlapping_boundary;
> > +
> > + };
> > +
> > +template <int dim>
> > +MeshIntersectionIterator<dim>::MeshIntersectionIterator(const
> > MeshIntersection& overlapping_mesh) + :
> > _overlapping_mesh(overlapping_mesh)
> > +
> > +{
> > + _map_pos =
> > overlapping_mesh._overlapped_domain->entity_entities_map.begin(); +
> > _map_end_pos =
> > overlapping_mesh._overlapped_domain->entity_entities_map.end(); +
> > + ///Oh herregud, please simplify datastructures!!!!
> > + _entity_iter =
> > MeshEntityIterator(*(overlapping_mesh._overlapped_domain->mesh), +
> > overlapping_mesh._overlapped_domain->mesh->topology().dim()); +
> > _entity_iter[_map_pos->first];
> > +
> > + _overlapping_entity_iter =
> > MeshEntityIterator(*(overlapping_mesh._overlapping_domain->mesh),
> > + overlapping_mesh._overlapping_domain->mesh-
>topology().dim()); +
> > _overlapping_entity_iter[_map_pos->second.front()];
> > +
> > +}
> > +
> > +template <int dim>
> > +MeshIntersectionIterator<dim> &
> > MeshIntersectionIterator<dim>::operator++() +{
> > + //Update the entity entities mapping.
> > + ++_map_pos;
> > + //Bit clumsy, abusing operator[] to set
> > + _entity_iter[_map_pos->first];
> > + _overlapping_entity_iter[_map_pos->second.front()];
> > +
> > + ///@todo Change this. Use lazy initialization.
> > + compute_polyhedrons();
> > + return *this;
> > +}
> > +
> > +template <int dim>
> > +void MeshIntersectionIterator<dim>::compute_polyhedrons()
> > +{
> > + Polyhedron cell_polyhedron(PT::datum(_entity_iter[_map_pos->first]));
> > + _overlapping_polyhedron.clear();
> > + for (EntityListIter index = _map_pos->second.begin(); index !=
> > _map_pos->second.end() ; ++index) + {
> > + _overlapping_polyhedron +=
> > PT::datum(_overlapping_entity_iter[*index]); + }
> > + cell_polyhedron -= _overlapping_polyhedron;
> > +}
> > +
> > +template <int dim>
> > +typename MeshIntersectionIterator<dim>::Polyhedron
> > MeshIntersectionIterator<dim>::overlapped_polyhedron() +{
> > + Polyhedron cell_polyhedron(PT::datum(_entity_iter[_map_pos->first]));
> > + return cell_polyhedron * _overlapping_polyhedron;
> > +}
> > +
> > +
> > +} //end namespace dolfin
> > +
> > +#endif // ----- #ifndef __MESHINTERSECTOR_H -----
> >
> > === added file 'nitsche_method/overlapping_meshes/PrimitiveTraits.h'
> > --- nitsche_method/overlapping_meshes/PrimitiveTraits.h 1970-01-01
> > 00:00:00 +0000 +++
> > nitsche_method/overlapping_meshes/PrimitiveTraits.h 2010-02-10 03:14:09
> > +0000 @@ -0,0 +1,69 @@
> > +//
> > ========================================================================
> > ============= +//
> > +// Copyright (C) 2010-02-02 André Massing
> > +// Licensed under the GNU LGPL Version 2.1.
> > +//
> > +// Modified by André Massing, 2010
> > +//
> > +// First added: 2010-02-02
> > +// Last changed: 2010-02-03
> > +//
> > +//Author: André Massing (am), massing@xxxxxxxxx
> > +//Company: Simula Research Laboratory, Fornebu, Norway
> > +//
> > +//
> > ========================================================================
> > ============= +
> > +#include <dolfin/mesh/Vertex.h>
> > +#include <dolfin/mesh/Point.h>
> > +
> > +#include <CGAL/Nef_polyhedron_3.h>
> > +#include <CGAL/Point_3.h>
> > +#include <CGAL/Nef_polyhedron_2.h>
> > +#include <CGAL/Polyhedron_3.h>
> > +
> > +namespace dolfin
> > +{
> > +
> > + template <int dim, typename Kernel > struct Primitive_Converter ;
> > +
> > + template<typename Kernel> struct Primitive_Converter<2,Kernel>
> > + {
> > + typedef CGAL::Polyhedron_3<Kernel> Polyhedron;
> > + typedef CGAL::Nef_polyhedron_2<Kernel> Nef_polyhedron;
> > + typedef Nef_polyhedron Datum;
> > + typedef typename Kernel::Point_3 Point_3;
> > +
> > + static const int dim = 2;
> > +
> > +// static Datum datum(const MeshEntity & entity) {
> > +
> > +// return Datum(point);
> > +// }
> > + };
> > +
> > + template<typename Kernel> struct Primitive_Converter<3,Kernel>
> > + {
> > + typedef CGAL::Polyhedron_3<Kernel> Polyhedron_3;
> > + typedef CGAL::Nef_polyhedron_3<Kernel> Polyhedron;
> > + typedef Polyhedron Datum;
> > + typedef typename Kernel::Point_3 Point_3;
> > +
> > + static const int dim = 3;
> > + static Datum datum(const MeshEntity & entity) {
> > + VertexIterator v(entity);
> > + Point_3 p1(v->point());
> > + ++v;
> > + Point_3 p2(v->point());
> > + ++v;
> > + Point_3 p3(v->point());
> > + ++v;
> > + Point_3 p4(v->point());
> > +
> > + Polyhedron_3 Q;
> > + Q.make_tetrahedron(p1,p2,p3,p4);
> > +
> > + return Datum(Q);
> > + }
> > + };
> > +
> > +} //end namespace dolfin.
> >
> > === added file 'nitsche_method/overlapping_meshes/SConstruct'
> > --- nitsche_method/overlapping_meshes/SConstruct 1970-01-01 00:00:00
> > +0000 +++ nitsche_method/overlapping_meshes/SConstruct 2010-03-16
> > 14:39:09 +0000 @@ -0,0 +1,13 @@
> > +import os, commands
> > +
> > +# Get compiler from pkg-config
> > +compiler = commands.getoutput('pkg-config --variable=compiler dolfin')
> > +
> > +# Create a SCons Environment based on the main os environment
> > +env = Environment(ENV=os.environ, CXX=compiler)
> > +
> > +# Get compiler flags from pkg-config
> > +env.ParseConfig('pkg-config --cflags --libs dolfin')
> > +
> > +#Program
> > +env.Program('overlapping_meshes',['MeshIntersector.cpp','main.cpp'])
> >
> > === added file 'nitsche_method/overlapping_meshes/demo.py'
> > --- nitsche_method/overlapping_meshes/demo.py 1970-01-01 00:00:00 +0000
> > +++ nitsche_method/overlapping_meshes/demo.py 2010-02-10 03:14:09 +0000
> > @@ -0,0 +1,35 @@
> > +
> > +__author__ = "Andre Massing (massing@xxxxxxxxx)"
> > +__date__ = "2010-01-27 "
> > +__copyright__ = "Copyright (C) 2010 Andre Massing"
> > +__license__ = "GNU LGPL Version 2.1"
> > +
> > +from dolfin import *
> > +from numpy import *
> > +
> > +if not has_cgal():
> > + print "DOLFIN must be compiled with CGAL to run this demo."
> > + exit(0)
> > +
> > +# Create meshes (omega0 overlapped by omega1)
> > +#mesh_1 = UnitCircle(20)
> > +mesh_1 = UnitSquare(10, 10)
> > +
> > +mesh_2 = UnitSquare(10, 10)
> > +
> > +# Access mesh geometry
> > +x = mesh_2.coordinates()
> > +
> > +# Move and scale second mesh
> > +#x *= 0.5
> > +x += 0.5
> > +
> > +overlap = OverlappingMeshes(mesh_1,mesh_2)
> > +overlap.compute_overlap_map()
> > +
> > +overlapped_domain = overlap.overlapped_domain();
> > +print overlapped_domain
> > +
> > +p = plot(overlapped_domain, rescale=False)
> > +
> > +interactive()
> >
> > === added file 'nitsche_method/overlapping_meshes/main.cpp'
> > --- nitsche_method/overlapping_meshes/main.cpp 1970-01-01 00:00:00 +0000
> > +++ nitsche_method/overlapping_meshes/main.cpp 2010-03-05 23:36:16 +0000
> > @@ -0,0 +1,108 @@
> > +//
> > ========================================================================
> > ============= +//
> > +// Copyright (C) 2010-01-28 André Massing
> > +// Licensed under the GNU LGPL Version 2.1.
> > +//
> > +// Modified by André Massing, 2010
> > +//
> > +// First added: 2010-01-28
> > +// Last changed: 2010-02-15
> > +//
> > +//Author: André Massing (am), massing@xxxxxxxxx
> > +//Company: Simula Research Laboratory, Fornebu, Norway
> > +//
> > +//
> > ========================================================================
> > ============= +
> > +#include <dolfin/mesh/dolfin_mesh.h>
> > +#include <dolfin/common/types.h>
> > +#include <dolfin/plot/dolfin_plot.h>
> > +
> > +//#include <CGAL/IO/Qt_widget_Nef_3.h>
> > +//#include <qapplication.h>
> > +
> > +//#include <dolfin.h>
> > +
> > +#include "OverlappingMeshes.h"
> > +
> > +using namespace dolfin;
> > +using dolfin::uint;
> > +
> > +int main ()
> > +{
> > +// UnitSquare mesh_1(10,10);
> > +// UnitCube mesh_1(10,10,10);
> > + UnitCube mesh_1(10,10,10);
> > +
> > +// UnitSquare mesh_2(10,10,10);
> > +// UnitCube mesh_2(10,10,10);
> > + UnitSphere mesh_2(10);
> > +
> > + MeshGeometry& geometry = mesh_2.geometry();
> > +// double w = 1;
> > + for (VertexIterator v(mesh_2); !v.end(); ++v)
> > + {
> > + double* x = geometry.x(v->index());
> > +// x[0] = cos(w)*(x[0]-0.5) - sin(w)*(x[1]-0.5);
> > +// x[1] = sin(w)*(x[0]-0.5) + cos(w)*(x[1]-0.5);
> > + x[0] *= 0.5;
> > + x[1] *= 0.5;
> > + x[2] *= 0.5;
> > +
> > + x[0] += 0.4;
> > + x[1] += 0.4;
> > + x[2] += 0.4;
> > + }
> > +
> > + MeshIntersection overlap(mesh_1,mesh_2);
> > + overlap.compute_overlap_map();
> > +
> > + MeshIntersectionIterator<3> cell(overlap);
> > +// Nef_polyhedron_3 cut_polyhedron =
> > + cell.polyhedron();
> > + cell.overlapped_polyhedron();
> > + cell.overlapping_polyhedron();
> > +
> > +// Nef_polyhedron_3 overlapped_polyhedron =
> > cell.overlapped_polyhedron(); +// Nef_polyhedron_3
> > overlapping_polyhedron = cell.overlapping_polyhedron(); +
> > +
> > +// uint_set cells;
> > +// mesh_1.all_intersected_entities(BoundaryMesh(mesh_2),cells);
> > +
> > +// MeshFunction<uint> intersection(mesh_1, mesh_1.topology().dim());
> > +// intersection = 0;
> > +
> > +// for (uint_set::const_iterator i = cells.begin(); i != cells.end();
> > i++) +// intersection[*i] = 1;
> > +// plot(intersection);
> > +
> > +// BoundaryMesh boundary_1(mesh_1);
> > +// BoundaryMesh boundary_2(mesh_2);
> > +
> > +// cells.clear();
> > +// boundary_1.all_intersected_entities(boundary_2,cells);
> > +
> > +// MeshFunction<uint> intersection(boundary_1,
> > boundary_1.topology().dim()); +// intersection = 0;
> > +
> > +// for (uint_set::const_iterator i = cells.begin(); i != cells.end();
> > i++) +// intersection[*i] = 1;
> > +// plot(intersection);
> > +
> > + std::cout <<"overlapped_domain:" << std::endl <<
> > overlap.overlapped_domain().str(true); +
> > plot(overlap.overlapped_domain());
> > +
> > + std::cout <<"overlapped_boundary:" << std::endl <<
> > overlap.overlapped_boundary().str(true); +
> > plot(overlap.overlapped_boundary());
> > +
> > + std::cout <<"overlapping_boundary :" << std::endl <<
> > overlap.overlapping_boundary().str(true); +
> > plot(overlap.overlapping_boundary());
> > +
> > + return 0;
> > +// QApplication a(argc, argv);
> > +// CGAL::Qt_widget_Nef_3<Nef_polyhedron_3>* w = new
> > CGAL::Qt_widget_Nef_3<Nef_polyhedron_3>(cut_polyhedron); +//
> > a.setMainWidget(w);
> > +// w->show();
> > +// return a.exec();
> > +
> > +}
> >
> > === added directory 'nitsche_method/polyhedrons'
> > === added file 'nitsche_method/polyhedrons/SConstruct'
> > --- nitsche_method/polyhedrons/SConstruct 1970-01-01 00:00:00 +0000
> > +++ nitsche_method/polyhedrons/SConstruct 2010-03-25 23:33:08 +0000
> > @@ -0,0 +1,17 @@
> > +import os, commands
> > +
> > +# Get compiler from pkg-config
> > +compiler = commands.getoutput('pkg-config --variable=compiler dolfin')
> > +
> > +# Create a SCons Environment based on the main os environment
> > +env = Environment(ENV=os.environ, CXX=compiler)
> > +env.Append(CPPPATH = '/usr/include/qt4/')
> > +env.Append(CPPPATH = '/usr/include/qt4/Qt')
> > +env.Append(CPPPATH = '/usr/include/qt4/QtGui')
> > +
> > +env.Append(CXXFLAGS = '-ggdb')
> > +
> > +# Get compiler flags from pkg-config
> > +env.ParseConfig('pkg-config --cflags --libs dolfin')
> > +
> > +env.Program(['intersect_polyhedrons.cpp'])
> >
> > === added file 'nitsche_method/polyhedrons/intersect_polyhedrons.cpp'
> > --- nitsche_method/polyhedrons/intersect_polyhedrons.cpp 1970-01-01
> > 00:00:00 +0000 +++
> > nitsche_method/polyhedrons/intersect_polyhedrons.cpp 2010-02-10
03:14:09
> > +0000 @@ -0,0 +1,118 @@
> > +#include <CGAL/Simple_cartesian.h>
> > +#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
> > +#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
> > +
> > +#include <CGAL/Nef_polyhedron_3.h>
> > +#include <CGAL/Nef_polyhedron_2.h>
> > +#include <CGAL/Polyhedron_3.h>
> > +#include <CGAL/Gmpz.h>
> > +#include <CGAL/Homogeneous.h>
> > +
> > +#include <CGAL/IO/Polyhedron_iostream.h>
> > +#include <CGAL/IO/Nef_polyhedron_iostream_3.h>
> > +
> > +//#include <CGAL/IO/Qt_widget_Nef_3.h>
> > +//#include <qapplication.h>
> > +
> > +#include <iostream>
> > +
> > +#include <vector>
> > +#include <list>
> > +
> > +//typedef CGAL::Simple_cartesian<double> K;
> > +//typedef CGAL::Simple_cartesian<double> K;
> > +//typedef
> > CGAL::Exact_predicates_inexact_constructions_kernel<CGAL::Gmpz> K; +
> > +//typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
> > +typedef CGAL::Exact_predicates_exact_constructions_kernel K;
> > +typedef CGAL::Polyhedron_3<K> Polyhedron;
> > +typedef CGAL::Nef_polyhedron_3<K> Nef_polyhedron;
> > +
> > +//typedef CGAL::Homogeneous<CGAL::Gmpz> K;
> > +//typedef CGAL::Nef_polyhedron_3<K> Nef_polyhedron_3;
> > +
> > +typedef K::Tetrahedron_3 Tetrahedron;
> > +typedef K::Triangle_3 Triangle;
> > +typedef K::Segment_3 Segment;
> > +typedef K::Point_3 Point;
> > +
> > +typedef Polyhedron::Vertex_iterator Vertex_iterator;
> > +typedef std::list<Triangle>::iterator Tri_iterator;
> > +
> > +int main()
> > +{
> > +
> > + Point a(1.0, 0.0, 0.0);
> > + Point b(0.0, 1.0, 0.0);
> > + Point c(0.0, 0.0, 1.0);
> > + Point d(0.0, 0.0, 0.0);
> > +
> > + Point A(0.1, 0.0, 0.0);
> > + Point B(0.0, 0.1, 0.0);
> > + Point C(0.0, 0.0, 2.0);
> > + Point D(0.0, 0.0, 0.0);
> > +
> > + //Build a point tetrahedron
> > + Polyhedron P;
> > + P.make_tetrahedron();
> > +
> > + Polyhedron Q;
> > + Q.make_tetrahedron(a, b, c, d);
> > + Nef_polyhedron NQ(Q);
> > +
> > + Polyhedron R;
> > + R.make_tetrahedron(A, B, C, D);
> > + Nef_polyhedron NR(R);
> > +
> > + Nef_polyhedron NQ_NR = NQ * NR;
> > +
> > + Polyhedron F;
> > + F.make_triangle(A,B,C);
> > + Nef_polyhedron NF(F);
> > +
> > + std::cout << "Exact_predicates_exact_constructions_kernel +
> > SNC_indexed_items" + << std::endl
> > + << " allows efficient handling of input "
> > + "using floating point coordinates"
> > + << std::endl;
> > +
> > + Nef_polyhedron N = NF * NQ;
> > +// Nef_polyhedron N = NF;
> > + std ::cout <<"Nef_Polyhedron Tetraeder: " <<std::endl;
> > + std::cout << NQ ;
> > + std ::cout <<"Nef_Polyhedron Triangle: " <<std::endl;
> > + std::cout << NF ;
> > + std ::cout <<"Nef_Polyhedron Intersection: " <<std::endl;
> > + std::cout << N ;
> > +
> > +
> > +// if(N.is_simple()) {
> > +// N.convert_to_polyhedron(P);
> > +// std::cout << P;
> > +// }
> > +// else {
> > +// std::cout << N;
> > +// }
> > +
> > +
> > +// CGAL::set_ascii_mode( std::cout);
> > +// for (Vertex_iterator v = P.vertices_begin(); v != P.vertices_end();
> > ++v) +// std::cout << v->point() << std::endl;
> > +// for (Vertex_iterator v = Q.vertices_begin(); v != Q.vertices_end();
> > ++v) +// std::cout << v->point() << std::endl;
> > +
> > +// if (Q.is_closed())
> > +
> > +// Nef_polyhedron_3 NF(F.vertices_begin(),F.vertices_end());
> > +
> > +// Nef_polyhedron_3 N = NF * NQ;
> > +// std::cout << N;
> > +
> > + return 0;
> > +
> > +// QApplication a(argc, argv);
> > +// CGAL::Qt_widget_Nef_3<Nef_polyhedron_3>* w = new
> > CGAL::Qt_widget_Nef_3<Nef_polyhedron_3>(NQ_NR); +// a.setMainWidget(w);
> > +// w->show();
> > +// return a.exec();
> > +}
> >
> > # Begin bundle
> > IyBCYXphYXIgcmV2aXNpb24gYnVuZGxlIHY0CiMKQlpoOTFBWSZTWUuYf2UAqZL/lH/2YDJ//
> > ///
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> > n3sz
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> > GwVv
> > fTHh36CGScVMEM4hTqajP9RgqhHgtU1Qs5L7F7g8QYKlm2AVncC3oHh3mm5667YnBH7/c93A
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> > XM8t
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> > 9yp2
> > 9KH6LdVVzWytS8/OFiktKgvIPENkwyYdFtHtj48YEIQgQeEL4+DP18LK4jloxsAMXEr2nC9y
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> > aebVnAopUrAD5MUBI5CvGSJzss9FVM0PgVKmWhBTphmMRp2RISExIDEIEVBXQQ2ky8Lcm1bB
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> > qiqDHzetE6hACc4ezlnErw9r+uT19rR51kEy2uFSqd3FN5RWhfxZxorMvTZ42wcZla2vWMq7
> > LbD6
> > +QoRpaNQVnC5nLrDuZbFYcd0ZkZnFwoxs59DxH0ySj4hW1lbfEbEdEn1s/GNnVGbyX9taXPo
> > Z34y
> > 6OVqMuNg/e/K8flXZuYXr89S29ytqROxu1T42PpS1AtLDSxRa4FTr3jYyuDE+3HA1MdYz4Gp
> > YCED
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> > tZ1+YENNnK75lbNqJsrZIBhtyHBFMcd4FVj2T9/t9UQKOCjDw2RCcE8QiB6JmMMbAninuNDS
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> > rRQHqZvpVWuFVDx4wmxrSCIOahA+4PAYNICkHQxpFGV8hvxl2aA5SjwVuyadzsjCM2luMlSG
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> > TiAOrYtAlQdAKkhrxGdo6UhDogFAoYhWXLhvtIzA9JxL8ZEmioTB1V27N6nUsZ1gX4s7uyGR
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> > KPAUjaNjsteMO7CMKqncyPyrAM4MGzeT4m5tNINGUUAqxCMyAZDbhatSnHgbh/wSSLdtmrdt
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> > YTYvZLWOgqrphsvb7vXco9kpkI7HnVyHSnK9KqJ6aa+/a9WRMlbhx21O05LfFjZfs9PDrMwM
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> > fvMJIPCBiZMG7/WAkH0SDuSR3siIGB03L4Y68hRJ6C6+LAyp8fj7T4F2RMo1JA/wSiJNjBCt
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> > za39/pzzVO0wXBeKSIJxMzNZuy7lbu7q7uavWo1cXV/cIxq9JtJWxaVitrk0q52WV2yySDtN
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> > MaWLQ0IEcw0NexHLeCW2/Yr8wpgPnVHtVp4Dd5vSnNDpr7R6ZZnSuvcV8phC80ljGrwkWBKi
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> > iG/jsdAEnmNk2MbInBv4iOzN2gTy1HlshKIinZgs+ecpuqV4SqhFAKFzrNnDSorPbEevIV9V
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> > MFbaU2reBN14OxqWyEs0Ik2aDDsXgnHuHtlRWTmXl1aXkzIQZYwuE1pviCtydIl6EhMmFcdX
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> > JRuO84yS+2Paht5gbyGd9jz2d87mIC5KWOCCZOTYUOMuYOW2bWrGFKzkNCh+VEQN0ODsjflk
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> > aCDCchz7uAaCNiKwYxrsOzfJgHPMvsbjGR5fc8VgYhTSntQHuR+YmaYdrN1Z63yXeG0I8sar
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> > j21xjSDjlXgiHgAxXObeDiD6Dt6zafDQtztxadukSJ0GThlab1zAQl3lkdpWuA9fW961vjHW
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> > NwxB4S08nh03gc7nkSa8+U8d2bnWVgIfGy8WUz2BiGpo0p5oM5jm2pjO/Ani2SamSJyWbwG2
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> > e7W+rmwgi2AyNcH9jdULLorg0oP0dDjQuwZoWJpB559sBcj+jsqsVimzBAYSW/mi8vbLbh2e
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> > EC9jcYZGje/bjza5c+b82va2bqfI9IM2jKbCZ3TjKSRfPDsjaEh4eBTheuUONvXop8GCufsy
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> > Wbz44RwYatVdsSQuTnn9vMrCkgc7e/v0sZ0MUTOMOmcYcx7RgleO5Rju64zjhk4jSU6W3ENT
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> > 8xhciGskN/HI/N+b56ZA/EYwI7WSrHs8yjETY7EdoUjnfRmFg3qmwcGBs14zK2Bg/BgfkArk
> > QYxY
> > REX2+78/nw/yw6g9WpAxAjEhJwqsCsiLEikio6QEN7EUM4gO2UJ0ekAMd7QQDHE5/PQB1dl5
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> > 9QQ4JDJ3D54H9cILggDhtiYFhaH0wQ2wMhTAoo3gFC1o5G+ag2gS+ODRiiLs0sq/ihBD/MoT
> > +oMh
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> > eOIgrkGRSMiaGXHcoyqRkTQy47lGW4O1lbSUalHJhTHMpmpcTBolY4WUsqM1NFNOgVFVGGtU
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> > lUEUBMrx4xloO1lUIxJjGQo6V4xjKUdK8YxlLIllGyGKEGUUIyqEGUoOlYiDhBlG4x4xjIXI
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> > klGyRwwpo1MxSxqYNErrKYxalNS4iDGkMg4iDGkMgOIhHEQg6VlK6UZS5hAiRBMQyGDiIJoY
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> > g4iEMHEQg4iCaGTAcRCGEmQhAlxjKpkGRjjZE0MuDuUZVIyJoYpkGRlyWMtcRBjuMplNAQ/1
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> > MKUjIIWwpGSWIsES2lsspSyWCUthApzgAlJFERFVghGAlhCpFgCJIosBYoKCqKlQRisQkRRk
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> > SKpIpGIMQRVUWCH/XLcwQhaACJsAhg/IP/YP1eebLoyDaLovA8H/Pi9gvOvfEcoOQ1nVWL4W
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> > ohICLl7asQEWq7jMV34pqQqOIimrUk+n35Mg7BcgQgYcWnGiOeWQGHua6nALFN3PQGy4lnDC
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> > 0WN4cKCUE8f5CwVqIqM26g8UePy+QENnIdiqoRcf3vvHmobfwhInw2a3iT1/WB+0P939z/sF
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> > 8M4AXfnf0T3N7gEf+A/3gDk/n4A+irTjAKeTaFxbIh/EfxM7EB3bpoN1/i9grvkIAMUkAGQC
> > H0xq
> > GMBaAN8x5Ho3If7bQB3Y7DeCgicyf2CBRk9l7km9p6Usjk9F1bWFkYbZPrTW2Fe6yXTUxtxD
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> > eVAYN40kFd4hE0Fgn/AghoTUv+yixL37y1rn6s2ziXHo2uFlhyoH7tqZ4a8lrJcaq96G6TEV
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> > kCtnjmEmtSYUxu14UEkk/n9InDA6Bof5IAfhkNgFOeZgShZRZm7AzED1nYDSQqGrikBUHGAj
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> > BuYaUapZ8Ce0AuOvb8dBY5mHcfiHm/zqz4P3Q7giWL/jDvu5Jbng+Ae+yfpdHfGjck1zwHAC
> > rJq3
> > 8+G8zm4XrDpInS2fLOnlKuF6eRiHPpB3KwzHRErpvY8YDhuMaKpfkWKIr7nsTL7ZEpRkQG51
> > HOB7
> > U910wHPOs2OmBhhfAgN2XvQ3Y4YFXwcCyPNgP19tcgIjmTqgdPBBUt47OFgfgOVH+vlNMANy
> > 8CVs
> > 2PIsYseh9HL/jlQt15oeRO0ST2sTroHkleY0NKZSSlgk2AEVCGnh9hr/5c4favNQtEZIDH+z
> > 1+xV
> > gqLCpsoeKW0GB9gHkLngnoPuhMTsQvEG+neeMJjvZ+Y3xxAmn5FyGBhIkA3kE9rPXCcNbPkq
> > 6QL1
> > QvoMUCjqOlGAInKej4XyAHpPjT4HRJ7LJzCGQhPL7JWAsqqr4eE9tL6rYImCjMZmOEckWZd5
> > 4/2c
> > 79k1+5V/H5And8p8XnqZn6lIAvsgvNekoQ+ED0ELwG0Q1Ur5KBKyRPD4PmW/u5hlw4WGd/kO
> > 48Tu
> > RRlh6ygF8Zrs2gajGAiAjAREiIwFWRViJBVRAVYCIkRGAqyKokEE2sPb+VOTOA+z7YTJ8udB
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> > bqk6kDR0ehGgu4u+YWyHkaA/ygbqRh5/5eu2/r1NmeJ6aB9byiKqqqiIooqqIwGagU5b0QWM
> > k17L
> > zFHG41MsDTOSRA5ScgzqBjKyFklTgJ+X2+p9y9LBggTqfJxTq7uBxKNZwWNznQU84XfKfRjS
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> > PoQvLek9od8jAsOClWvhfG3r8duhrWH2w9r0RKZN2bt8tjWpS2UtlLZS2UtlLSWMrLNWZbMj
> > MZRK
> > lLZS2UtlLZDyJ6YTvNtBqe2fZJHMCmAT3AG4FY6btm67zyKkdjCMiaaGlmmcyKkiiSaYGGYG
> > EZoa
> > Vl5zIqRIyMkMn6gdHeGpmqs0KkIUMIyGmhpZpnMipEisRN6HhDwV8Zrm7RRGA/49oYCBOLCw
> > lkqL
> > wqIlsfIN5Ts5LYQ5wNFRRhCIooo4s1qQ30Bv9smHP7fvR3OTD1cyqU6izts/4TACxiCTnIyq
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> > iiiiqqqidm/UBhOUhQ6uodG9pvNg/2LnKJ8hc+gR8QZwjY4IliHmF7XuS5whxB9ycJEHPkmJ
> > 9ou/
> > VpO3sQO9to7vQ8D2zQ4lNqea9yjWMZ5jgnRyGuOra0txPb9GsRchj7GGb3p28Yl9BsBxI2u0
> > BaWL
> > NU9qBLPsqQogdEyTWPN3blotygHYmeBj3+F2rUmHqSYl7g7RwKgYVCDxBlS9spiMeGgZkMy5
> > oljo
> > LIBzq0VGQHtT2JgWQBXpuUm3OGQ2lk7idpNk5UX0DBjMC0rL25hBmkc1BeexVJBohdgGYdEY
> > LcFl
> > yVXfeCyPR9Q3veTds+Q8JkoGm8hfteOTFoMjIuEYkB/0CKAOyMCXCjyOebhLrJEBKxg+gupc
> > BfYg
> > B1DgnJOyn6lwRG9+ShsolQSiwav7js9H8lvw0YJ8/truYf1S/E4F2wzF/2YcbhuMuA0ocC4O
> > BJlk
> > ShrjQwNNqmxXaSTG0mazPARKk/f/g+CH8XuLr/3QDtpIvTp0h4c3iyIMjOnUq9Rbz0Jvz588
> > OZuq
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> > y+y92+ITmq8VMr0r0l7HspEET6bxFzcMGMyqI5gxaoz4WWXOg5RM69rCUsJRPlClB5aKFORh
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> > uKofRQPFseZDu7CQ5KFUamAggO4bqa+S/ChrWwiOthE5VekPbQfghp0CIdXQhLE3c9l4+kEp
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> > jUyQEYJpEu239ybQJ+CIwjGQEiRQP8PwpnCCCzP/V0/j682L4/lNxaP1qfj12/3b5bTR1BdB
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> > QsdhGYVBKqsapcB1sl0Ngo770ZUkBRUbSg6ppkH07myUGyerY/ClN+/9/6dRP0/Vm9FIwRn+
> > T+5e y6pdIzbcfzosvGMPd1aJwwOHl//Ah8wQ//i7kinChIJcw/so
> >
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References
