diff options
Diffstat (limited to 'buch')
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 Binary files differnew file mode 100644 index 0000000..015bce7 --- /dev/null +++ b/buch/papers/nav/images/dreieck3d1.pdf 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 Binary files differnew file mode 100644 index 0000000..6b3f09d --- /dev/null +++ b/buch/papers/nav/images/dreieck3d2.pdf 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 Binary files differnew file mode 100644 index 0000000..7d79455 --- /dev/null +++ b/buch/papers/nav/images/dreieck3d3.pdf 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 Binary files differnew file mode 100644 index 0000000..e1ea757 --- /dev/null +++ b/buch/papers/nav/images/dreieck3d4.pdf 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 Binary files differnew file mode 100644 index 0000000..6848331 --- /dev/null +++ b/buch/papers/nav/images/dreieck3d5.pdf 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 Binary files differnew file mode 100644 index 0000000..52bd25e --- /dev/null +++ b/buch/papers/nav/images/dreieck3d8.jpg diff --git a/buch/papers/nav/images/dreieck3d8.pdf b/buch/papers/nav/images/dreieck3d8.pdf Binary files differnew file mode 100644 index 0000000..9d630aa --- /dev/null +++ b/buch/papers/nav/images/dreieck3d8.pdf 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} + |
