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-rw-r--r--buch/papers/kugel/images/Makefile4
-rw-r--r--buch/papers/kugel/images/curvature.maxima6
-rw-r--r--buch/papers/kugel/images/curvature.pov72
-rw-r--r--buch/papers/kugel/images/curvgraph.m93
4 files changed, 153 insertions, 22 deletions
diff --git a/buch/papers/kugel/images/Makefile b/buch/papers/kugel/images/Makefile
index 8efa228..e8bf919 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.png
+all: curvature.jpg
curvature.inc: curvgraph.m
octave curvgraph.m
@@ -11,3 +11,5 @@ curvature.inc: curvgraph.m
curvature.png: curvature.pov curvature.inc
povray +A0.1 +W1920 +H1080 +Ocurvature.png curvature.pov
+curvature.jpg: curvature.png
+ convert curvature.png -density 300 -units PixelsPerInch curvature.jpg
diff --git a/buch/papers/kugel/images/curvature.maxima b/buch/papers/kugel/images/curvature.maxima
new file mode 100644
index 0000000..6313642
--- /dev/null
+++ b/buch/papers/kugel/images/curvature.maxima
@@ -0,0 +1,6 @@
+
+f: exp(-r^2/sigma^2)/sigma;
+laplacef: ratsimp(diff(r * diff(f,r), r) / r);
+f: exp(-r^2/(2*sigma^2))/(sqrt(2)*sigma);
+laplacef: ratsimp(diff(r * diff(f,r), r) / r);
+
diff --git a/buch/papers/kugel/images/curvature.pov b/buch/papers/kugel/images/curvature.pov
index 3535488..9dbaa86 100644
--- a/buch/papers/kugel/images/curvature.pov
+++ b/buch/papers/kugel/images/curvature.pov
@@ -11,17 +11,17 @@ global_settings {
assumed_gamma 1
}
-#declare imagescale = 0.1;
+#declare imagescale = 0.09;
camera {
- location <40, 10, -20>
+ location <10, 10, -40>
look_at <0, 0, 0>
right 16/9 * x * imagescale
up y * imagescale
}
light_source {
- <10, 10, -40> color White
+ <-10, 10, -40> color White
area_light <1,0,0> <0,0,1>, 10, 10
adaptive 1
jitter
@@ -70,3 +70,69 @@ arrow(<0,-1,0>, <0,1,0>, 0.01, White)
arrow(<0,0,-2.1>, <0,0,2.1>, 0.01, White)
#include "curvature.inc"
+
+#declare sigma = 1;
+#declare N0 = 0.5;
+#declare funktion = function(r) {
+ (exp(-r*r/(sigma*sigma)) / sigma
+ -
+ exp(-r*r/(2*sigma*sigma)) / (sqrt(2)*sigma)) / N0
+};
+#declare hypot = function(xx, yy) { sqrt(xx*xx+yy*yy) };
+
+#declare Funktion = function(x,y) { funktion(hypot(x+1,y)) - funktion(hypot(x-1,y)) };
+#macro punkt(xx,yy)
+ <xx, Funktion(xx, yy), yy>
+#end
+
+#declare griddiameter = 0.006;
+union {
+ #declare xmin = -3;
+ #declare xmax = 3;
+ #declare ymin = -2;
+ #declare ymax = 2;
+
+
+ #declare xstep = 0.2;
+ #declare ystep = 0.02;
+ #declare xx = xmin;
+ #while (xx < xmax + xstep/2)
+ #declare yy = ymin;
+ #declare P = punkt(xx, yy);
+ #while (yy < ymax - ystep/2)
+ #declare yy = yy + ystep;
+ #declare Q = punkt(xx, yy);
+ sphere { P, griddiameter }
+ cylinder { P, Q, griddiameter }
+ #declare P = Q;
+ #end
+ sphere { P, griddiameter }
+ #declare xx = xx + xstep;
+ #end
+
+ #declare xstep = 0.02;
+ #declare ystep = 0.2;
+ #declare yy = ymin;
+ #while (yy < ymax + ystep/2)
+ #declare xx = xmin;
+ #declare P = punkt(xx, yy);
+ #while (xx < xmax - xstep/2)
+ #declare xx = xx + xstep;
+ #declare Q = punkt(xx, yy);
+ sphere { P, griddiameter }
+ cylinder { P, Q, griddiameter }
+ #declare P = Q;
+ #end
+ sphere { P, griddiameter }
+ #declare yy = yy + ystep;
+ #end
+
+ pigment {
+ color rgb<0.8,0.8,0.8>
+ }
+ finish {
+ metallic
+ specular 0.8
+ }
+}
+
diff --git a/buch/papers/kugel/images/curvgraph.m b/buch/papers/kugel/images/curvgraph.m
index 96ca4b1..b83c877 100644
--- a/buch/papers/kugel/images/curvgraph.m
+++ b/buch/papers/kugel/images/curvgraph.m
@@ -13,23 +13,34 @@ sigma2 = 1;
global s;
s = 1;
+global cmax;
+cmax = 0.9;
+global cmin;
+cmin = -0.9;
+
+global Cmax;
+global Cmin;
+Cmax = 0;
+Cmin = 0;
+
xmin = -3;
xmax = 3;
-xsteps = 1000;
+xsteps = 200;
hx = (xmax - xmin) / xsteps;
ymin = -2;
ymax = 2;
-ysteps = 1000;
+ysteps = 200;
hy = (ymax - ymin) / ysteps;
function retval = f0(r)
global sigma2;
- retval = exp(-r^2/sigma2)/sigma2 - exp(-r^2/(2*sigma2))/(sqrt(2)*sigma2);
+ retval = exp(-r^2/sigma2)/sqrt(sigma2) - exp(-r^2/(2*sigma2))/(sqrt(2*sigma2));
end
global N0;
-N0 = f0(0);
+N0 = f0(0)
+N0 = 0.5;
function retval = f1(x,y)
global N0;
@@ -44,10 +55,10 @@ endfunction
function retval = curvature0(r)
global sigma2;
retval = (
- (2*sigma2-r^2)*exp(-r^2/(2*sigma2))
+ -4*(sigma2-r^2)*exp(-r^2/sigma2)
+
- 4*(r^2-sigma2)*exp(-r^2/sigma2)
- ) / (sigma2^2);
+ (2*sigma2-r^2)*exp(-r^2/(2*sigma2))
+ ) / (sigma2^(5/2));
endfunction
function retval = curvature1(x, y)
@@ -56,28 +67,74 @@ endfunction
function retval = curvature(x, y)
global s;
- retval = curvature1(x+s, y) + curvature1(x-s, y);
+ retval = curvature1(x+s, y) - curvature1(x-s, y);
endfunction
function retval = farbe(x, y)
+ global Cmax;
+ global Cmin;
+ global cmax;
+ global cmin;
c = curvature(x, y);
- retval = c * ones(1,3);
+ if (c < Cmin)
+ Cmin = c
+ endif
+ if (c > Cmax)
+ Cmax = c
+ endif
+ u = (c - cmin) / (cmax - cmin);
+ if (u > 1)
+ u = 1;
+ endif
+ if (u < 0)
+ u = 0;
+ endif
+ color = [ u, 0.5, 1-u ];
+ color = color/max(color);
+ color(1,4) = c/2;
+ retval = color;
endfunction
-fn = fopen("curvature.inc", "w");
+function dreieck(fn, A, B, C)
+ fprintf(fn, "\ttriangle {\n");
+ fprintf(fn, "\t <%.4f,%.4f,%.4f>,\n", A(1,1), A(1,3), A(1,2));
+ fprintf(fn, "\t <%.4f,%.4f,%.4f>,\n", B(1,1), B(1,3), B(1,2));
+ fprintf(fn, "\t <%.4f,%.4f,%.4f>\n", C(1,1), C(1,3), C(1,2));
+ fprintf(fn, "\t}\n");
+endfunction
+function viereck(fn, punkte)
+ color = farbe(mean(punkte(:,1)), mean(punkte(:,2)));
+ fprintf(fn, " mesh {\n");
+ dreieck(fn, punkte(1,:), punkte(2,:), punkte(3,:));
+ dreieck(fn, punkte(2,:), punkte(3,:), punkte(4,:));
+ fprintf(fn, "\tpigment { color rgb<%.4f,%.4f,%.4f> } // %.4f\n",
+ color(1,1), color(1,2), color(1,3), color(1,4));
+ fprintf(fn, " }\n");
+endfunction
+
+fn = fopen("curvature.inc", "w");
+punkte = zeros(4,3);
for ix = (0:xsteps)
x = xmin + ix * hx;
+ punkte(1,1) = x;
+ punkte(2,1) = x;
+ punkte(3,1) = x + hx;
+ punkte(4,1) = x + hx;
for iy = (0:ysteps)
y = ymin + iy * hy;
- fprintf(fn, "sphere { <%.4f, %.4f, %.4f>, 0.01\n",
- x, f(x, y), y);
- color = farbe(x, y);
- fprintf(fn, "pigment { color rgb<%.4f,%.4f,%.4f> }\n",
- color(1,1), color(1,2), color(1,3));
- fprintf(fn, "finish { metallic specular 0.5 }\n");
- fprintf(fn, "}\n");
+ punkte(1,2) = y;
+ punkte(2,2) = y + hy;
+ punkte(3,2) = y;
+ punkte(4,2) = y + hy;
+ for i = (1:4)
+ punkte(i,3) = f(punkte(i,1), punkte(i,2));
+ endfor
+ viereck(fn, punkte);
end
end
-
+#fprintf(fn, " finish { metallic specular 0.5 }\n");
fclose(fn);
+
+printf("Cmax = %.4f\n", Cmax);
+printf("Cmin = %.4f\n", Cmin);