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#
# torus.m
#
# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
#
global n;
n = 32;
global m;
m = 18;
global R;
R = 3;
global r;
r = 1;
# Knoten, Kanten, Dreiecke
global nvertices;
nvertices = n * m;
global nedges;
nedges = 3 * nvertices;
global ntriangles;
ntriangles = 2 * nvertices;
edges = zeros(nedges, 2);
global edges;
triangles = zeros(ntriangles, 3);
global triangles;
function retval = torus(x, y)
global n;
global m;
global r;
global R;
phi = x * 2 * pi / n;
theta = y * 2 * pi / m;
z = -r * sin(theta);
x = (R + r * cos(theta)) * cos(phi);
y = -(R + r * cos(theta)) * sin(phi);
retval = [x, y, z];
endfunction
coordinates = zeros(nvertices, 3);
for x = (0:n-1)
for y = (0:m-1)
k = x + n * y;
coordinates(k+1,:) = torus(x, y);
endfor
endfor
coordinates
function insert_edges(ll, lr, ul, ur)
global edges;
k = 3 * ll + 1;
edges(k+1,1) = ll;
edges(k+1,2) = lr;
edges(k+0,1) = ll;
edges(k+0,2) = ur;
edges(k+2,1) = ll;
edges(k+2,2) = ul;
endfunction
function insert_triangles(ll, lr, ul, ur)
global triangles;
k = 2 * ll;
printf("ll=%d, k=%d\n", ll, k);
triangles(k+1,1) = ll;
triangles(k+1,2) = lr;
triangles(k+1,3) = ur;
triangles(k+2,1) = ll;
triangles(k+2,2) = ur;
triangles(k+2,3) = ul;
endfunction
# normal squares
for x = (0:n-2)
for y = (0:m-2)
ll = x + n * y;
lr = ll + 1;
ul = ll + n;
ur = ul + 1;
insert_edges(ll, lr, ul, ur);
insert_triangles(ll, lr, ul, ur);
endfor
endfor
# right border
x = n-1;
for y = (0:m-2)
ll = x + n * y;
lr = ll - (n-1);
ul = ll + n;
ur = lr + n;
insert_edges(ll, lr, ul, ur);
insert_triangles(ll, lr, ul, ur);
endfor
# top border
y = m-1;
for x = (0:n-2)
ll = x + n * y;
lr = ll + 1;
ul = x;
ur = ul + 1;
insert_edges(ll, lr, ul, ur);
insert_triangles(ll, lr, ul, ur);
endfor
# upper right corner
x = n-1;
y = m-1;
ll = n * m - 1;
lr = n * (m-1);
ur = 0;
ul = n - 1;
insert_edges(ll, lr, ul, ur);
insert_triangles(ll, lr, ul, ur);
edges;
triangles;
d1 = zeros(nvertices, nedges);
for i = (1:nedges)
d1(edges(i,1) + 1, i) = -1;
d1(edges(i,2) + 1, i) = +1;
endfor
function retval = find_edge(from, to)
global edges;
global nedges;
retval = 0;
for i = (1:nedges)
if ((edges(i,1) == from) && (edges(i,2) == to))
retval = i;
printf(" test (%d,%d) == (%d,%d) -> %d\n", from, to,
edges(i,1), edges(i,2), retval);
elseif ((edges(i,1) == to) && (edges(i,2) == from))
retval = -i;
printf(" test (%d,%d) == (%d,%d) -> %d\n", from, to,
edges(i,1), edges(i,2), retval);
endif
endfor
endfunction
global d2;
d2 = zeros(nedges, ntriangles);
function triangle_edge(i, pointa, pointb)
global d2;
edge = find_edge(pointa, pointb);
if (edge > 0)
d2(edge, i) = +1;
elseif (edge < 0)
d2(-edge, i) = -1;
endif
endfunction
for i = (1:ntriangles)
point1 = triangles(i,1);
point2 = triangles(i,2);
point3 = triangles(i,3);
#printf("triangle %d: %d, %d, %d\n", i-1, point1, point2, point3);
triangle_edge(i, point1, point2);
triangle_edge(i, point2, point3);
triangle_edge(i, point3, point1);
endfor
B = d2';
global zyklentableau
zyklentableau = rref(d1)
i=((zyklentableau != 0) .* (1:nedges));
global determined;
determined = min((i+nedges*(i==0))')';
determined = determined(1:nvertices-1,1);
function retval = is_determined(i)
global nvertices;
global determined;
# printf("test i = %d\n", i);
retval = 0;
for k = (1:nvertices-1)
#printf("check k=%d, i=%d\n", k, i);
if (determined(k,1) == i)
retval = 1;
endif
endfor
endfunction
function retval = zyklus(i)
global zyklentableau
global nedges
global nvertices
global determined
retval = zeros(nedges,1);
retval(i,1) = 1;
for j = (1:nvertices-1)
retval(determined(j,1),1) = -zyklentableau(j,i);
endfor
endfunction
Z = zeros(nedges, nedges - nvertices)
current = 1;
for i = (1:nedges)
if 1 == is_determined(i)
# printf("skipping %d\n", i);
else
Z(:,current) = zyklus(i);
current = current + 1;
endif
endfor
Z;
zh = size(Z)(2);
H = zeros(ntriangles + zh,nedges);
H(1:ntriangles,:) = B;
H((ntriangles+1):(ntriangles+zh),:) = Z';
H;
size(H)
rref(B');
function retval = pivotindex(zeile)
w = size(zeile)(2);
for k = (1:w)
if (zeile(1,k) != 0)
retval = k;
return;
endif
endfor
retval = 0;
endfunction
h = size(H)(1)
w = size(H)(2)
j = 1;
for i = (1:h-1)
j = pivotindex(H(i,:));
printf("reduction for i = %d, j = %d\n", i, j);
if (j != 0)
# find pivot index
pivot = H(i,j);
if (pivot != 0)
H(i,:) = H(i,:) / pivot;
for k = ((i+1):h)
H(k,:) = H(k,:) - H(k,j) * H(i,:);
endfor
endif
endif
endfor
H;
Hbasis = zeros(2,nedges);
current = 1;
for i = ((ntriangles+1):h)
if norm(H(i,:)) > 0
Hbasis(current,:) = H(i,:)
current = current + 1;
endif
endfor
#size(Hbasis)
#nedges
#Hbasis
#Hbasis(1,nedges-2)=0;
#Hbasis(1,nedges-1)=1;
Hbasis
edges(71,:)
coordinates
fn = fopen("torus.inc", "w");
# torusflaeche
fprintf(fn, "#macro torusflaeche()\n");
fprintf(fn, " mesh {\n");
for k = (1:ntriangles)
fprintf(fn, "\ttriangle { ");
punkt1 = coordinates(triangles(k,1)+1,:);
punkt2 = coordinates(triangles(k,2)+1,:);
punkt3 = coordinates(triangles(k,3)+1,:);
fprintf(fn, "<%.4f,%.4f,%.4f>, ", punkt1(1,1), punkt1(1,3), punkt1(1,2));
fprintf(fn, "<%.4f,%.4f,%.4f>, ", punkt2(1,1), punkt2(1,3), punkt2(1,2));
fprintf(fn, "<%.4f,%.4f,%.4f> }\n", punkt3(1,1), punkt3(1,3), punkt3(1,2));
endfor
fprintf(fn, " }\n")
fprintf(fn, "#end\n");
fprintf(fn, "#macro zyklus1()\n");
fprintf(fn, " union {\n");
for i = (1:nedges)
h = Hbasis(1,i);
if h != 0
if h > 0
punkt1 = coordinates(edges(i,1)+1,:);
printf("i=%d\n", i);
punkt2 = coordinates(edges(i,2)+1,:);
else
punkt2 = coordinates(edges(i,1)+1,:);
punkt1 = coordinates(edges(i,2)+1,:);
endif
fprintf(fn, "\tcylinder { ");
fprintf(fn, "<%.4f,%.4f,%.4f>, ", punkt1(1,1), punkt1(1,3), punkt1(1,2));
fprintf(fn, "<%.4f,%.4f,%.4f>, r }\n", punkt2(1,1), punkt2(1,3), punkt2(1,2));
fprintf(fn, "\tsphere { <%.4f,%.4f,%.4f>, r }\n", punkt1(1,1), punkt1(1,3), punkt1(1,2));
endif
endfor
fprintf(fn, " }\n");
fprintf(fn, "#end\n");
fprintf(fn, "#macro zyklus2()\n");
fprintf(fn, " union {\n");
for i = (1:nedges)
h = Hbasis(2,i);
if h != 0
if h > 0
punkt1 = coordinates(edges(i,1)+1,:);
punkt2 = coordinates(edges(i,2)+1,:);
else
punkt2 = coordinates(edges(i,1)+1,:);
punkt1 = coordinates(edges(i,2)+1,:);
endif
fprintf(fn, "\tcylinder { ");
fprintf(fn, "<%.4f,%.4f,%.4f>, ", punkt1(1,1), punkt1(1,3), punkt1(1,2));
fprintf(fn, "<%.4f,%.4f,%.4f>, r }\n", punkt2(1,1), punkt2(1,3), punkt2(1,2));
fprintf(fn, "\tsphere { <%.4f,%.4f,%.4f>, r }\n", punkt1(1,1), punkt1(1,3), punkt1(1,2));
endif
endfor
fprintf(fn, " }\n");
fprintf(fn, "#end\n");
fprintf(fn, "#macro triangulation()\n");
fprintf(fn, " union {\n");
for i = (1:nvertices)
punkt = coordinates(i,:);
fprintf(fn, "\tsphere { <%.4f,%.4f,%.4f>, r/3 }\n", punkt(1,1), punkt(1,3), punkt(1,2));
endfor
for i = (1:nedges)
punkt1 = coordinates(edges(i,1)+1,:);
punkt2 = coordinates(edges(i,2)+1,:);
fprintf(fn, "\tcylinder { <%.4f,%.4f,%.4f>, ", punkt1(1,1), punkt1(1,3), punkt1(1,2));
fprintf(fn, "<%.4f,%.4f,%.4f>, r/3 }\n", punkt2(1,1), punkt2(1,3), punkt2(1,2));
endfor
fprintf(fn, " }\n");
fprintf(fn, "#end\n");
fclose(fn);
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