Merge branch 'master' of https://github.com/AndreasFMueller/SeminarSpezielleFunktionen

1 files changed, 140 insertions, 0 deletions

diff --git a/buch/papers/kugel/images/curvgraph.m b/buch/papers/kugel/images/curvgraph.m
new file mode 100644
index 0000000..75effd6
--- /dev/null
+++ b/buch/papers/kugel/images/curvgraph.m
@@ -0,0 +1,140 @@
+#
+# curvature.m
+#
+# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+
+global N;
+N = 10;
+
+global sigma2;
+sigma2 = 1;
+
+global s;
+s = 1.4;
+
+global cmax;
+cmax = 0.9;
+global cmin;
+cmin = -0.9;
+
+global Cmax;
+global Cmin;
+Cmax = 0;
+Cmin = 0;
+
+xmin = -3;
+xmax = 3;
+xsteps = 200;
+hx = (xmax - xmin) / xsteps;
+
+ymin = -2;
+ymax = 2;
+ysteps = 200;
+hy = (ymax - ymin) / ysteps;
+
+function retval = f0(r)
+	global sigma2;
+	retval = exp(-r^2/sigma2)/sqrt(sigma2) - exp(-r^2/(2*sigma2))/(sqrt(2*sigma2));
+end
+
+global N0;
+N0 = f0(0)
+N0 = 0.4;
+
+function retval = f1(x,y)
+	global N0;
+	retval = f0(hypot(x, y)) / N0;
+endfunction
+
+function retval = f(x, y)
+	global s;
+	retval = f1(x+s, y) - f1(x-s, y);
+endfunction
+
+function retval = curvature0(r)
+	global sigma2;
+	retval = (
+		-4*(sigma2-r^2)*exp(-r^2/sigma2)
+		+
+		(2*sigma2-r^2)*exp(-r^2/(2*sigma2))
+	) / (sigma2^(5/2));
+endfunction
+
+function retval = curvature1(x, y)
+	retval = curvature0(hypot(x, y));
+endfunction
+
+function retval = curvature(x, y)
+	global s;
+	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);
+	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
+
+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-1)
+	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-1)
+		y = ymin + iy * hy;
+		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);