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-rw-r--r--buch/chapters/050-differential/uebungsaufgaben/airy.cpp4
-rw-r--r--buch/chapters/110-elliptisch/ellintegral.tex2
-rw-r--r--buch/papers/nav/images/Makefile10
-rw-r--r--buch/papers/nav/images/common.inc28
-rw-r--r--buch/papers/nav/images/dreieck3d1.pdfbin0 -> 90451 bytes
-rw-r--r--buch/papers/nav/images/dreieck3d1.pov12
-rw-r--r--buch/papers/nav/images/dreieck3d2.pdfbin0 -> 69523 bytes
-rw-r--r--buch/papers/nav/images/dreieck3d2.pov6
-rw-r--r--buch/papers/nav/images/dreieck3d3.pdfbin0 -> 82512 bytes
-rw-r--r--buch/papers/nav/images/dreieck3d3.pov8
-rw-r--r--buch/papers/nav/images/dreieck3d4.pdfbin0 -> 85037 bytes
-rw-r--r--buch/papers/nav/images/dreieck3d4.pov8
-rw-r--r--buch/papers/nav/images/dreieck3d5.pdfbin0 -> 70054 bytes
-rw-r--r--buch/papers/nav/images/dreieck3d5.pov6
-rw-r--r--buch/papers/nav/images/dreieck3d6.pov2
-rw-r--r--buch/papers/nav/images/dreieck3d7.pov10
-rw-r--r--buch/papers/nav/images/dreieck3d8.jpgbin0 -> 93432 bytes
-rw-r--r--buch/papers/nav/images/dreieck3d8.pdfbin0 -> 107370 bytes
-rw-r--r--buch/papers/nav/images/dreieck3d8.pov96
-rw-r--r--buch/papers/nav/images/dreieck3d8.tex57
20 files changed, 216 insertions, 33 deletions
diff --git a/buch/chapters/050-differential/uebungsaufgaben/airy.cpp b/buch/chapters/050-differential/uebungsaufgaben/airy.cpp
index e4df8e1..eb5c6be 100644
--- a/buch/chapters/050-differential/uebungsaufgaben/airy.cpp
+++ b/buch/chapters/050-differential/uebungsaufgaben/airy.cpp
@@ -44,8 +44,8 @@ double h0f1(double c, double x) {
double f1(double x) {
// unfortunately, gsl_sf_hyperg_0F1 does not work if c<1, because
// it uses a relation to the bessel functions
- //return gsl_sf_hyperg_0F1(2/3, x*x*x/9.);
- return h0f1(2./3., x*x*x/9.);
+ return gsl_sf_hyperg_0F1(2/3, x*x*x/9.);
+ //return h0f1(2./3., x*x*x/9.);
}
double f2(double x) {
diff --git a/buch/chapters/110-elliptisch/ellintegral.tex b/buch/chapters/110-elliptisch/ellintegral.tex
index 4cb2ba3..3acce2f 100644
--- a/buch/chapters/110-elliptisch/ellintegral.tex
+++ b/buch/chapters/110-elliptisch/ellintegral.tex
@@ -651,7 +651,7 @@ werden, dass $1-k'^2=k^2$ ist.
\begin{definition}
Ist $0\le k\le 1$ der Modul eines elliptischen Integrals, dann heisst
-$k' = \sqrt{1-k^2}$ er {\em Komplementärmodul} oder {\em Komplement
+$k' = \sqrt{1-k^2}$ der {\em Komplementärmodul} oder {\em Komplement
des Moduls}. Es ist $k^2+k'^2=1$.
\end{definition}
diff --git a/buch/papers/nav/images/Makefile b/buch/papers/nav/images/Makefile
index c9dcacc..bbdea2f 100644
--- a/buch/papers/nav/images/Makefile
+++ b/buch/papers/nav/images/Makefile
@@ -50,7 +50,8 @@ DREIECKE3D = \
dreieck3d4.pdf \
dreieck3d5.pdf \
dreieck3d6.pdf \
- dreieck3d7.pdf
+ dreieck3d7.pdf \
+ dreieck3d8.pdf
dreiecke3d: $(DREIECKE3D)
@@ -106,3 +107,10 @@ dreieck3d7.jpg: dreieck3d7.png
dreieck3d7.pdf: dreieck3d7.tex dreieck3d7.jpg
pdflatex dreieck3d7.tex
+dreieck3d8.png: dreieck3d8.pov common.inc
+ povray +A0.1 $(POVRAYOPTIONS) -Odreieck3d8.png dreieck3d8.pov
+dreieck3d8.jpg: dreieck3d8.png
+ convert dreieck3d8.png -density 300 -units PixelsPerInch dreieck3d8.jpg
+dreieck3d8.pdf: dreieck3d8.tex dreieck3d8.jpg
+ pdflatex dreieck3d8.tex
+
diff --git a/buch/papers/nav/images/common.inc b/buch/papers/nav/images/common.inc
index 33d9384..e2a1ed0 100644
--- a/buch/papers/nav/images/common.inc
+++ b/buch/papers/nav/images/common.inc
@@ -97,13 +97,13 @@ union {
}
#end
-#macro winkel(w, p, q, staerke)
+#macro winkel(w, p, q, staerke, r)
#declare n = vnormalize(w);
#declare pp = vnormalize(p - vdot(n, p) * n);
#declare qq = vnormalize(q - vdot(n, q) * n);
intersection {
sphere { <0, 0, 0>, 1 + staerke }
- cone { <0, 0, 0>, 0, 1.2 * vnormalize(w), 0.4 }
+ cone { <0, 0, 0>, 0, 1.2 * vnormalize(w), r }
plane { -vcross(n, qq) * vdot(vcross(n, qq), pp), 0 }
plane { -vcross(n, pp) * vdot(vcross(n, pp), qq), 0 }
}
@@ -113,8 +113,30 @@ union {
sphere { p, 1.5 * staerke }
#end
+#macro dreieck(p, q, r, farbe)
+ #declare n1 = vnormalize(vcross(p, q));
+ #declare n2 = vnormalize(vcross(q, r));
+ #declare n3 = vnormalize(vcross(r, p));
+ intersection {
+ plane { n1, 0 }
+ plane { n2, 0 }
+ plane { n3, 0 }
+ sphere { <0, 0, 0>, 1 + 0.001 }
+ pigment {
+ color farbe
+ }
+ finish {
+ metallic
+ specular 0.4
+ }
+ }
+#end
+
#declare fett = 0.015;
-#declare fine = 0.010;
+#declare fein = 0.010;
+
+#declare klein = 0.3;
+#declare gross = 0.4;
#declare dreieckfarbe = rgb<0.6,0.6,0.6>;
#declare rot = rgb<0.8,0.2,0.2>;
diff --git a/buch/papers/nav/images/dreieck3d1.pdf b/buch/papers/nav/images/dreieck3d1.pdf
new file mode 100644
index 0000000..015bce7
--- /dev/null
+++ b/buch/papers/nav/images/dreieck3d1.pdf
Binary files differ
diff --git a/buch/papers/nav/images/dreieck3d1.pov b/buch/papers/nav/images/dreieck3d1.pov
index 8afe60e..e491075 100644
--- a/buch/papers/nav/images/dreieck3d1.pov
+++ b/buch/papers/nav/images/dreieck3d1.pov
@@ -12,9 +12,9 @@ union {
punkt(A, fett)
punkt(B, fett)
punkt(C, fett)
- punkt(P, fine)
- seite(B, P, fine)
- seite(C, P, fine)
+ punkt(P, fein)
+ seite(B, P, fein)
+ seite(C, P, fein)
pigment {
color dreieckfarbe
}
@@ -25,7 +25,7 @@ union {
}
object {
- winkel(A, B, C, fine)
+ winkel(A, B, C, fein, gross)
pigment {
color rot
}
@@ -36,7 +36,7 @@ object {
}
object {
- winkel(B, C, A, fine)
+ winkel(B, C, A, fein, gross)
pigment {
color gruen
}
@@ -47,7 +47,7 @@ object {
}
object {
- winkel(C, A, B, fine)
+ winkel(C, A, B, fein, gross)
pigment {
color blau
}
diff --git a/buch/papers/nav/images/dreieck3d2.pdf b/buch/papers/nav/images/dreieck3d2.pdf
new file mode 100644
index 0000000..6b3f09d
--- /dev/null
+++ b/buch/papers/nav/images/dreieck3d2.pdf
Binary files differ
diff --git a/buch/papers/nav/images/dreieck3d2.pov b/buch/papers/nav/images/dreieck3d2.pov
index c23a54c..c0625ce 100644
--- a/buch/papers/nav/images/dreieck3d2.pov
+++ b/buch/papers/nav/images/dreieck3d2.pov
@@ -12,9 +12,9 @@ union {
punkt(A, fett)
punkt(B, fett)
punkt(C, fett)
- punkt(P, fine)
- seite(B, P, fine)
- seite(C, P, fine)
+ punkt(P, fein)
+ seite(B, P, fein)
+ seite(C, P, fein)
pigment {
color dreieckfarbe
}
diff --git a/buch/papers/nav/images/dreieck3d3.pdf b/buch/papers/nav/images/dreieck3d3.pdf
new file mode 100644
index 0000000..7d79455
--- /dev/null
+++ b/buch/papers/nav/images/dreieck3d3.pdf
Binary files differ
diff --git a/buch/papers/nav/images/dreieck3d3.pov b/buch/papers/nav/images/dreieck3d3.pov
index f2496b5..b6f64d5 100644
--- a/buch/papers/nav/images/dreieck3d3.pov
+++ b/buch/papers/nav/images/dreieck3d3.pov
@@ -12,9 +12,9 @@ union {
punkt(A, fett)
punkt(B, fett)
punkt(C, fett)
- punkt(P, fine)
- seite(B, P, fine)
- seite(C, P, fine)
+ punkt(P, fein)
+ seite(B, P, fein)
+ seite(C, P, fein)
pigment {
color dreieckfarbe
}
@@ -25,7 +25,7 @@ union {
}
object {
- winkel(A, B, C, fine)
+ winkel(A, B, C, fein, gross)
pigment {
color rot
}
diff --git a/buch/papers/nav/images/dreieck3d4.pdf b/buch/papers/nav/images/dreieck3d4.pdf
new file mode 100644
index 0000000..e1ea757
--- /dev/null
+++ b/buch/papers/nav/images/dreieck3d4.pdf
Binary files differ
diff --git a/buch/papers/nav/images/dreieck3d4.pov b/buch/papers/nav/images/dreieck3d4.pov
index bddcf7c..b6f17e3 100644
--- a/buch/papers/nav/images/dreieck3d4.pov
+++ b/buch/papers/nav/images/dreieck3d4.pov
@@ -6,9 +6,9 @@
#include "common.inc"
union {
- seite(A, B, fine)
- seite(A, C, fine)
- punkt(A, fine)
+ seite(A, B, fein)
+ seite(A, C, fein)
+ punkt(A, fein)
punkt(B, fett)
punkt(C, fett)
punkt(P, fett)
@@ -25,7 +25,7 @@ union {
}
object {
- winkel(B, C, P, fine)
+ winkel(B, C, P, fein, gross)
pigment {
color rgb<0.6,0.4,0.2>
}
diff --git a/buch/papers/nav/images/dreieck3d5.pdf b/buch/papers/nav/images/dreieck3d5.pdf
new file mode 100644
index 0000000..6848331
--- /dev/null
+++ b/buch/papers/nav/images/dreieck3d5.pdf
Binary files differ
diff --git a/buch/papers/nav/images/dreieck3d5.pov b/buch/papers/nav/images/dreieck3d5.pov
index 32fc9e6..188f181 100644
--- a/buch/papers/nav/images/dreieck3d5.pov
+++ b/buch/papers/nav/images/dreieck3d5.pov
@@ -6,9 +6,9 @@
#include "common.inc"
union {
- seite(A, B, fine)
- seite(A, C, fine)
- punkt(A, fine)
+ seite(A, B, fein)
+ seite(A, C, fein)
+ punkt(A, fein)
punkt(B, fett)
punkt(C, fett)
punkt(P, fett)
diff --git a/buch/papers/nav/images/dreieck3d6.pov b/buch/papers/nav/images/dreieck3d6.pov
index 7611950..191a1e7 100644
--- a/buch/papers/nav/images/dreieck3d6.pov
+++ b/buch/papers/nav/images/dreieck3d6.pov
@@ -25,7 +25,7 @@ union {
}
object {
- winkel(B, A, P, fine)
+ winkel(B, A, P, fein, gross)
pigment {
color rgb<0.6,0.2,0.6>
}
diff --git a/buch/papers/nav/images/dreieck3d7.pov b/buch/papers/nav/images/dreieck3d7.pov
index fa48f5b..aae5c6c 100644
--- a/buch/papers/nav/images/dreieck3d7.pov
+++ b/buch/papers/nav/images/dreieck3d7.pov
@@ -10,13 +10,13 @@ union {
seite(A, P, fett)
seite(C, P, fett)
- seite(A, B, fine)
- seite(B, C, fine)
- seite(B, P, fine)
+ seite(A, B, fein)
+ seite(B, C, fein)
+ seite(B, P, fein)
punkt(A, fett)
punkt(C, fett)
punkt(P, fett)
- punkt(B, fine)
+ punkt(B, fein)
pigment {
color dreieckfarbe
}
@@ -27,7 +27,7 @@ union {
}
object {
- winkel(A, P, C, fine)
+ winkel(A, P, C, fein, gross)
pigment {
color rgb<0.4,0.4,1>
}
diff --git a/buch/papers/nav/images/dreieck3d8.jpg b/buch/papers/nav/images/dreieck3d8.jpg
new file mode 100644
index 0000000..52bd25e
--- /dev/null
+++ b/buch/papers/nav/images/dreieck3d8.jpg
Binary files differ
diff --git a/buch/papers/nav/images/dreieck3d8.pdf b/buch/papers/nav/images/dreieck3d8.pdf
new file mode 100644
index 0000000..9d630aa
--- /dev/null
+++ b/buch/papers/nav/images/dreieck3d8.pdf
Binary files differ
diff --git a/buch/papers/nav/images/dreieck3d8.pov b/buch/papers/nav/images/dreieck3d8.pov
new file mode 100644
index 0000000..9e9921a
--- /dev/null
+++ b/buch/papers/nav/images/dreieck3d8.pov
@@ -0,0 +1,96 @@
+//
+// dreiecke3d8.pov
+//
+// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+//
+#include "common.inc"
+
+union {
+ seite(A, B, fett)
+ seite(B, C, fett)
+ seite(A, C, fett)
+ seite(A, P, fein)
+ seite(B, P, fett)
+ seite(C, P, fett)
+ punkt(A, fett)
+ punkt(B, fett)
+ punkt(C, fett)
+ punkt(P, fett)
+ pigment {
+ color dreieckfarbe
+ }
+ finish {
+ specular 0.95
+ metallic
+ }
+}
+
+object {
+ winkel(A, B, C, fein, klein)
+ pigment {
+ color rot
+ }
+ finish {
+ specular 0.95
+ metallic
+ }
+}
+
+object {
+ winkel(B, C, A, fein, klein)
+ pigment {
+ color gruen
+ }
+ finish {
+ specular 0.95
+ metallic
+ }
+}
+
+object {
+ winkel(C, A, B, fein, gross)
+ pigment {
+ color blau
+ }
+ finish {
+ specular 0.95
+ metallic
+ }
+}
+
+object {
+ winkel(A, P, C, fein/2, gross)
+ pigment {
+ color rgb<0.8,0,0.8>
+ }
+ finish {
+ specular 0.95
+ metallic
+ }
+}
+
+object {
+ winkel(B, P, C, fein, klein)
+ pigment {
+ color rgb<1,0.8,0>
+ }
+ finish {
+ specular 0.95
+ metallic
+ }
+}
+
+object {
+ winkel(B, P, A, fein/2, gross)
+ pigment {
+ color rgb<0.4,0.6,0.8>
+ }
+ finish {
+ specular 0.95
+ metallic
+ }
+}
+
+dreieck(A, B, C, White)
+
+
diff --git a/buch/papers/nav/images/dreieck3d8.tex b/buch/papers/nav/images/dreieck3d8.tex
new file mode 100644
index 0000000..c59c7b0
--- /dev/null
+++ b/buch/papers/nav/images/dreieck3d8.tex
@@ -0,0 +1,57 @@
+%
+% dreieck3d8.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{times}
+\usepackage{amsmath}
+\usepackage{txfonts}
+\usepackage[utf8]{inputenc}
+\usepackage{graphics}
+\usetikzlibrary{arrows,intersections,math}
+\usepackage{ifthen}
+\begin{document}
+
+\newboolean{showgrid}
+\setboolean{showgrid}{false}
+\def\breite{4}
+\def\hoehe{4}
+
+\begin{tikzpicture}[>=latex,thick]
+
+% Povray Bild
+\node at (0,0) {\includegraphics[width=8cm]{dreieck3d8.jpg}};
+
+% Gitter
+\ifthenelse{\boolean{showgrid}}{
+\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe);
+\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe);
+\draw (-\breite,-\hoehe) grid (\breite, \hoehe);
+\fill (0,0) circle[radius=0.05];
+}{}
+
+\node at (0.7,3.8) {$A$};
+\node at (-3.4,-0.8) {$B$};
+\node at (3.3,-2.1) {$C$};
+\node at (-1.4,-3.5) {$P$};
+
+\node at (-1.9,2.1) {$c$};
+\node at (-0.2,-1.2) {$a$};
+\node at (2.6,1.5) {$b$};
+\node at (-0.8,0) {$l$};
+
+\node at (-2.6,-2.2) {$p_b$};
+\node at (1,-2.9) {$p_c$};
+
+\node at (0.7,3.3) {$\alpha$};
+\node at (0.8,2.85) {$\omega$};
+\node at (-2.6,-0.6) {$\beta$};
+\node at (2.3,-1.2) {$\gamma$};
+\node at (-2.6,-1.3) {$\beta_1$};
+\node at (-2.1,-0.8) {$\kappa$};
+
+\end{tikzpicture}
+
+\end{document}
+