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#
# spherecurve.m
#
# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
#
global a;
a = 5;
global A;
A = 10;
phisteps = 400;
hphi = 2 * pi / phisteps;
thetasteps = 200;
htheta = pi / thetasteps;
function retval = f(z)
global a;
global A;
retval = A * exp(a * (z^2 - 1));
endfunction
function retval = g(z)
global a;
retval = -f(z) * 2 * a * (2 * a * z^4 + (3 - 2*a) * z^2 - 1);
# 2
# - a 2 4 2 2 a z
#(%o6) - %e (4 a z + (6 a - 4 a ) z - 2 a) %e
endfunction
phi = (1 + sqrt(5)) / 2;
global axes;
axes = [
0, 0, 1, -1, phi, -phi;
1, -1, phi, phi, 0, 0;
phi, phi, 0, 0, 1, 1;
];
axes = axes / (sqrt(phi^2+1));
function retval = kugel(theta, phi)
retval = [
cos(phi) * sin(theta);
sin(phi) * sin(theta);
cos(theta)
];
endfunction
function retval = F(v)
global axes;
s = 0;
for i = (1:6)
z = axes(:,i)' * v;
s = s + f(z);
endfor
retval = s / 6;
endfunction
function retval = F2(theta, phi)
v = kugel(theta, phi);
retval = F(v);
endfunction
function retval = G(v)
global axes;
s = 0;
for i = (1:6)
s = s + g(axes(:,i)' * v);
endfor
retval = s / 6;
endfunction
function retval = G2(theta, phi)
v = kugel(theta, phi);
retval = G(v);
endfunction
function retval = cnormalize(u)
utop = 11;
ubottom = -30;
retval = (u - ubottom) / (utop - ubottom);
if (retval > 1)
retval = 1;
endif
if (retval < 0)
retval = 0;
endif
endfunction
global umin;
umin = 0;
global umax;
umax = 0;
function color = farbe(v)
global umin;
global umax;
u = G(v);
if (u < umin)
umin = u;
endif
if (u > umax)
umax = u;
endif
u = cnormalize(u);
color = [ u, 0.5, 1-u ];
color = color/max(color);
endfunction
function dreieck(fn, v0, v1, v2)
fprintf(fn, " mesh {\n");
c = (v0 + v1 + v2) / 3;
c = c / norm(c);
color = farbe(c);
v0 = v0 * (1 + F(v0));
v1 = v1 * (1 + F(v1));
v2 = v2 * (1 + F(v2));
fprintf(fn, "\ttriangle {\n");
fprintf(fn, "\t <%.6f,%.6f,%.6f>,\n", v0(1,1), v0(3,1), v0(2,1));
fprintf(fn, "\t <%.6f,%.6f,%.6f>,\n", v1(1,1), v1(3,1), v1(2,1));
fprintf(fn, "\t <%.6f,%.6f,%.6f>\n", v2(1,1), v2(3,1), v2(2,1));
fprintf(fn, "\t}\n");
fprintf(fn, "\tpigment { color rgb<%.4f,%.4f,%.4f> }\n",
color(1,1), color(1,2), color(1,3));
fprintf(fn, "\tfinish { metallic specular 0.5 }\n");
fprintf(fn, " }\n");
endfunction
fn = fopen("spherecurve2.inc", "w");
for i = (1:phisteps)
# Polkappe nord
v0 = [ 0; 0; 1 ];
v1 = kugel(htheta, (i-1) * hphi);
v2 = kugel(htheta, i * hphi);
fprintf(fn, " // i = %d\n", i);
dreieck(fn, v0, v1, v2);
# Polkappe sued
v0 = [ 0; 0; -1 ];
v1 = kugel(pi-htheta, (i-1) * hphi);
v2 = kugel(pi-htheta, i * hphi);
dreieck(fn, v0, v1, v2);
endfor
for j = (1:thetasteps-2)
for i = (1:phisteps)
v0 = kugel( j * htheta, (i-1) * hphi);
v1 = kugel((j+1) * htheta, (i-1) * hphi);
v2 = kugel( j * htheta, i * hphi);
v3 = kugel((j+1) * htheta, i * hphi);
fprintf(fn, " // i = %d, j = %d\n", i, j);
dreieck(fn, v0, v1, v2);
dreieck(fn, v1, v2, v3);
endfor
endfor
fclose(fn);
umin
umax
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