diff options
| -rw-r--r-- | buch/papers/kugel/images/Makefile | 12 | ||||
| -rw-r--r-- | buch/papers/kugel/images/spherecurve.m | 160 | ||||
| -rw-r--r-- | buch/papers/kugel/images/spherecurve.maxima | 13 | ||||
| -rw-r--r-- | buch/papers/kugel/images/spherecurve.pov | 73 |
4 files changed, 257 insertions, 1 deletions
diff --git a/buch/papers/kugel/images/Makefile b/buch/papers/kugel/images/Makefile index e8bf919..6187fed 100644 --- a/buch/papers/kugel/images/Makefile +++ b/buch/papers/kugel/images/Makefile @@ -3,7 +3,7 @@ # # (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # -all: curvature.jpg +all: curvature.jpg spherecurve.jpg curvature.inc: curvgraph.m octave curvgraph.m @@ -13,3 +13,13 @@ curvature.png: curvature.pov curvature.inc curvature.jpg: curvature.png convert curvature.png -density 300 -units PixelsPerInch curvature.jpg + +spherecurve.inc: spherecurve.m + octave spherecurve.m + +spherecurve.png: spherecurve.pov spherecurve.inc + povray +A0.1 +W1920 +H1080 +Ospherecurve.png spherecurve.pov + +spherecurve.jpg: spherecurve.png + convert spherecurve.png -density 300 -units PixelsPerInch spherecurve.jpg + diff --git a/buch/papers/kugel/images/spherecurve.m b/buch/papers/kugel/images/spherecurve.m new file mode 100644 index 0000000..ea9c901 --- /dev/null +++ b/buch/papers/kugel/images/spherecurve.m @@ -0,0 +1,160 @@ +# +# spherecurv.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("spherecurve.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 diff --git a/buch/papers/kugel/images/spherecurve.maxima b/buch/papers/kugel/images/spherecurve.maxima new file mode 100644 index 0000000..1e9077c --- /dev/null +++ b/buch/papers/kugel/images/spherecurve.maxima @@ -0,0 +1,13 @@ +/* + * spherecurv.maxima + * + * (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule + */ +f: exp(-a * sin(theta)^2); + +g: ratsimp(diff(sin(theta) * diff(f, theta), theta)/sin(theta)); +g: subst(z, cos(theta), g); +g: subst(sqrt(1-z^2), sin(theta), g); +ratsimp(g); + +f: ratsimp(subst(sqrt(1-z^2), sin(theta), f)); diff --git a/buch/papers/kugel/images/spherecurve.pov b/buch/papers/kugel/images/spherecurve.pov new file mode 100644 index 0000000..86c3745 --- /dev/null +++ b/buch/papers/kugel/images/spherecurve.pov @@ -0,0 +1,73 @@ +// +// curvature.pov +// +// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// + +#version 3.7; +#include "colors.inc" + +global_settings { + assumed_gamma 1 +} + +#declare imagescale = 0.14; + +camera { + location <10, 10, -40> + look_at <0, 0, 0> + right 16/9 * x * imagescale + up y * imagescale +} + +light_source { + <-10, 10, -40> color White + area_light <1,0,0> <0,0,1>, 10, 10 + adaptive 1 + jitter +} + +sky_sphere { + pigment { + color rgb<1,1,1> + } +} + +// +// draw an arrow from <from> to <to> with thickness <arrowthickness> with +// color <c> +// +#macro arrow(from, to, arrowthickness, c) +#declare arrowdirection = vnormalize(to - from); +#declare arrowlength = vlength(to - from); +union { + sphere { + from, 1.1 * arrowthickness + } + cylinder { + from, + from + (arrowlength - 5 * arrowthickness) * arrowdirection, + arrowthickness + } + cone { + from + (arrowlength - 5 * arrowthickness) * arrowdirection, + 2 * arrowthickness, + to, + 0 + } + pigment { + color c + } + finish { + specular 0.9 + metallic + } +} +#end + +arrow(<-2.7,0,0>, <2.7,0,0>, 0.03, White) +arrow(<0,-2.7,0>, <0,2.7,0>, 0.03, White) +arrow(<0,0,-2.7>, <0,0,2.7>, 0.03, White) + +#include "spherecurve.inc" + |