From 9fb1f740b7d00b350a008e957d28ecf7daf53797 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 14 Jun 2022 16:24:13 +0200 Subject: new image --- buch/chapters/110-elliptisch/images/Makefile | 11 ++ buch/chapters/110-elliptisch/images/kegelpara.pdf | Bin 0 -> 139626 bytes buch/chapters/110-elliptisch/images/kegelpara.pov | 225 ++++++++++++++++++++++ buch/chapters/110-elliptisch/images/kegelpara.tex | 41 ++++ 4 files changed, 277 insertions(+) create mode 100644 buch/chapters/110-elliptisch/images/kegelpara.pdf create mode 100644 buch/chapters/110-elliptisch/images/kegelpara.pov create mode 100644 buch/chapters/110-elliptisch/images/kegelpara.tex (limited to 'buch/chapters/110-elliptisch/images') diff --git a/buch/chapters/110-elliptisch/images/Makefile b/buch/chapters/110-elliptisch/images/Makefile index a7c9e74..7e4fa0c 100644 --- a/buch/chapters/110-elliptisch/images/Makefile +++ b/buch/chapters/110-elliptisch/images/Makefile @@ -78,3 +78,14 @@ slcldata.tex: slcl ./slcl --outfile=slcldata.tex --a=0 --b=13.4 --steps=200 slcl.pdf: slcl.tex slcldata.tex pdflatex slcl.tex + +POVRAYOPTIONS = -W1920 -H1080 +kegelpara.png: kegelpara.pov + povray +A0.1 -W1080 -H1080 -Okegelpara.png kegelpara.pov + +kegelpara.jpg: kegelpara.png Makefile + convert -extract 1080x1000+0+40 kegelpara.png \ + -density 300 -units PixelsPerInch kegelpara.jpg + +kegelpara.pdf: kegelpara.tex kegelpara.jpg + pdflatex kegelpara.tex diff --git a/buch/chapters/110-elliptisch/images/kegelpara.pdf b/buch/chapters/110-elliptisch/images/kegelpara.pdf new file mode 100644 index 0000000..4b03119 Binary files /dev/null and b/buch/chapters/110-elliptisch/images/kegelpara.pdf differ diff --git a/buch/chapters/110-elliptisch/images/kegelpara.pov b/buch/chapters/110-elliptisch/images/kegelpara.pov new file mode 100644 index 0000000..5d85eed --- /dev/null +++ b/buch/chapters/110-elliptisch/images/kegelpara.pov @@ -0,0 +1,225 @@ +// +// kegelpara.pov +// +// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#version 3.7; +#include "colors.inc" + +#declare O = <0,0,0>; + +global_settings { + assumed_gamma 1 +} + +#declare imagescale = 0.08; + +camera { + location <28, 20, -40> + look_at <0, 0.1, 0> + right x * imagescale + up y * imagescale +} + +light_source { + <30, 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 to with thickness with +// color +// +#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(<-2,0,0>,<2,0,0>,0.02,White) +arrow(<0,-2,0>,<0,2,0>,0.02,White) +arrow(<0,0,-2>,<0,0,2>,0.02,White) + +#declare epsilon = 0.001; +#declare l = 1.5; + +#macro Kegel(farbe) +union { + difference { + cone { O, 0, , l } + cone { O + , 0, , l } + } + difference { + cone { O, 0, <-l, 0, 0>, l } + cone { O + <-epsilon, 0, 0>, 0, <-l-epsilon, 0, 0>, l } + } + pigment { + color farbe + } + finish { + specular 0.9 + metallic + } +} +#end + +#macro F(w, r) + +#end + +#macro Paraboloid(farbe) +mesh { + #declare phi = 0; + #declare phimax = 2 * pi; + #declare phisteps = 100; + #declare phistep = pi / phisteps; + #declare rsteps = 100; + #declare rmax = 1.5; + #declare rstep = rmax / rsteps; + #while (phi < phimax - phistep/2) + #declare r = rstep; + #declare h = r * r / sqrt(2); + triangle { + O, F(phi, r), F(phi + phistep, r) + } + #while (r < rmax - rstep/2) + // ring + triangle { + F(phi, r), + F(phi + phistep, r), + F(phi + phistep, r + rstep) + } + triangle { + F(phi, r), + F(phi + phistep, r + rstep), + F(phi, r + rstep) + } + #declare r = r + rstep; + #end + #declare phi = phi + phistep; + #end + pigment { + color farbe + } + finish { + specular 0.9 + metallic + } +} +#end + +#declare a = sqrt(2); +#macro G(phi,sg) + < a*sg*sqrt(cos(2*phi))*cos(phi), a*cos(2*phi), a*sqrt(cos(2*phi))*sin(phi)> +#end + +#macro Lemniskate3D(s, farbe) +union { + #declare phi = -pi / 4; + #declare phimax = pi / 4; + #declare phisteps = 100; + #declare phistep = phimax / phisteps; + #while (phi < phimax - phistep/2) + sphere { G(phi,1), s } + cylinder { G(phi,1), G(phi+phistep,1), s } + sphere { G(phi,-1), s } + cylinder { G(phi,-1), G(phi+phistep,-1), s } + #declare phi = phi + phistep; + #end + pigment { + color farbe + } + finish { + specular 0.9 + metallic + } +} +#end + +#declare a = sqrt(2); +#macro G2(phi,sg) + a * sqrt(cos(2*phi)) * < sg * cos(phi), 0, sin(phi)> +#end + +#macro Lemniskate(s, farbe) +union { + #declare phi = -pi / 4; + #declare phimax = pi / 4; + #declare phisteps = 100; + #declare phistep = phimax / phisteps; + #while (phi < phimax - phistep/2) + sphere { G2(phi,1), s } + cylinder { G2(phi,1), G2(phi+phistep,1), s } + sphere { G2(phi,-1), s } + cylinder { G2(phi,-1), G2(phi+phistep,-1), s } + #declare phi = phi + phistep; + #end + pigment { + color farbe + } + finish { + specular 0.9 + metallic + } +} +#end + +#macro Projektion(s, farbe) +union { + #declare phistep = pi / 16; + #declare phi = -pi / 4 + phistep; + #declare phimax = pi / 4; + #while (phi < phimax - phistep/2) + cylinder { G(phi, 1), G2(phi, 1), s } + cylinder { G(phi, -1), G2(phi, -1), s } + #declare phi = phi + phistep; + #end + pigment { + color farbe + } + finish { + specular 0.9 + metallic + } +} +#end + +#declare kegelfarbe = rgbt<0.2,0.6,0.2,0.2>; +#declare paraboloidfarbe = rgbt<0.2,0.6,1.0,0.2>; + +Paraboloid(paraboloidfarbe) +Kegel(kegelfarbe) +Lemniskate3D(0.02, Blue) +Lemniskate(0.02, Red) +Projektion(0.01, Yellow) diff --git a/buch/chapters/110-elliptisch/images/kegelpara.tex b/buch/chapters/110-elliptisch/images/kegelpara.tex new file mode 100644 index 0000000..5a724ee --- /dev/null +++ b/buch/chapters/110-elliptisch/images/kegelpara.tex @@ -0,0 +1,41 @@ +% +% kegelpara.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]{kegelpara.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 (3.3,-1.0) {$X$}; +\node at (0.2,3.4) {$Z$}; +\node at (-2.5,-1.4) {$-Y$}; + +\end{tikzpicture} + +\end{document} + -- cgit v1.2.1 From fbcf8833aef79694e448010520f2253e93f2cd4e Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 14 Jun 2022 16:59:48 +0200 Subject: more info about the lemniskate --- buch/chapters/110-elliptisch/images/Makefile | 12 +- .../110-elliptisch/images/torusschnitt.pdf | Bin 0 -> 137159 bytes .../110-elliptisch/images/torusschnitt.pov | 185 +++++++++++++++++++++ .../110-elliptisch/images/torusschnitt.tex | 41 +++++ 4 files changed, 237 insertions(+), 1 deletion(-) create mode 100644 buch/chapters/110-elliptisch/images/torusschnitt.pdf create mode 100644 buch/chapters/110-elliptisch/images/torusschnitt.pov create mode 100644 buch/chapters/110-elliptisch/images/torusschnitt.tex (limited to 'buch/chapters/110-elliptisch/images') diff --git a/buch/chapters/110-elliptisch/images/Makefile b/buch/chapters/110-elliptisch/images/Makefile index 7e4fa0c..2a23d88 100644 --- a/buch/chapters/110-elliptisch/images/Makefile +++ b/buch/chapters/110-elliptisch/images/Makefile @@ -79,7 +79,6 @@ slcldata.tex: slcl slcl.pdf: slcl.tex slcldata.tex pdflatex slcl.tex -POVRAYOPTIONS = -W1920 -H1080 kegelpara.png: kegelpara.pov povray +A0.1 -W1080 -H1080 -Okegelpara.png kegelpara.pov @@ -89,3 +88,14 @@ kegelpara.jpg: kegelpara.png Makefile kegelpara.pdf: kegelpara.tex kegelpara.jpg pdflatex kegelpara.tex + +torusschnitt.png: torusschnitt.pov + povray +A0.1 -W1920 -H1080 -Otorusschnitt.png torusschnitt.pov + +torusschnitt.jpg: torusschnitt.png Makefile + convert -extract 1560x1080+180+0 torusschnitt.png \ + -density 300 -units PixelsPerInch torusschnitt.jpg + +torusschnitt.pdf: torusschnitt.tex torusschnitt.jpg + pdflatex torusschnitt.tex + diff --git a/buch/chapters/110-elliptisch/images/torusschnitt.pdf b/buch/chapters/110-elliptisch/images/torusschnitt.pdf new file mode 100644 index 0000000..430447c Binary files /dev/null and b/buch/chapters/110-elliptisch/images/torusschnitt.pdf differ diff --git a/buch/chapters/110-elliptisch/images/torusschnitt.pov b/buch/chapters/110-elliptisch/images/torusschnitt.pov new file mode 100644 index 0000000..94190be --- /dev/null +++ b/buch/chapters/110-elliptisch/images/torusschnitt.pov @@ -0,0 +1,185 @@ +// +// kegelpara.pov +// +// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#version 3.7; +#include "colors.inc" + +#declare O = <0,0,0>; + +global_settings { + assumed_gamma 1 +} + +#declare imagescale = 0.060; + +camera { + location <28, 20, -40> + look_at <0, 0.55, 0> + right (16/9) * x * imagescale + up y * imagescale +} + +light_source { + <30, 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 to with thickness with +// color +// +#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(<-2,0,0>,<2,0,0>,0.02,White) +arrow(<0,-1.1,0>,<0,2.2,0>,0.02,White) +arrow(<0,0,-1.6>,<0,0,2.4>,0.02,White) + +#declare epsilon = 0.001; +#declare l = 1.5; + + +#declare a = sqrt(2); +#macro G2(phi,sg) + a * sqrt(cos(2*phi)) * < sg * cos(phi), 0, sin(phi)> +#end + +#macro Lemniskate(s, farbe) +union { + #declare phi = -pi / 4; + #declare phimax = pi / 4; + #declare phisteps = 100; + #declare phistep = phimax / phisteps; + #while (phi < phimax - phistep/2) + sphere { G2(phi,1), s } + cylinder { G2(phi,1), G2(phi+phistep,1), s } + sphere { G2(phi,-1), s } + cylinder { G2(phi,-1), G2(phi+phistep,-1), s } + #declare phi = phi + phistep; + #end + pigment { + color farbe + } + finish { + specular 0.9 + metallic + } +} +#end + +#macro Projektion(s, farbe) +union { + #declare phistep = pi / 16; + #declare phi = -pi / 4 + phistep; + #declare phimax = pi / 4; + #while (phi < phimax - phistep/2) + cylinder { G(phi, 1), G2(phi, 1), s } + cylinder { G(phi, -1), G2(phi, -1), s } + #declare phi = phi + phistep; + #end + pigment { + color farbe + } + finish { + specular 0.9 + metallic + } +} +#end + +#macro Ebene(farbe) +box { + <-1.8, 0, -1.4>, <1.8, 0.001, 1.4> + pigment { + color farbe + } + finish { + specular 0.9 + metallic + } +} +#end + +#declare b = 0.5; +#macro T(phi, theta) + b * < (2 + cos(theta)) * cos(phi), (2 + cos(theta)) * sin(phi) + 1, sin(theta) > +#end + +#macro Torus(farbe) +mesh { + #declare phi = 0; + #declare phimax = 2 * pi; + #declare phisteps = 200; + #declare phistep = phimax/phisteps; + #while (phi < phimax - phistep/2) + #declare theta = 0; + #declare thetamax = 2 * pi; + #declare thetasteps = 200; + #declare thetastep = thetamax / thetasteps; + #while (theta < thetamax - thetastep/2) + triangle { + T(phi, theta), + T(phi + phistep, theta), + T(phi + phistep, theta + thetastep) + } + triangle { + T(phi, theta), + T(phi + phistep, theta + thetastep), + T(phi, theta + thetastep) + } + #declare theta = theta + thetastep; + #end + #declare phi = phi + phistep; + #end + pigment { + color farbe + } + finish { + specular 0.9 + metallic + } +} +#end + +#declare torusfarbe = rgbt<0.2,0.6,0.2,0.2>; +#declare ebenenfarbe = rgbt<0.2,0.6,1.0,0.2>; + +Lemniskate(0.02, Red) +Ebene(ebenenfarbe) +Torus(torusfarbe) diff --git a/buch/chapters/110-elliptisch/images/torusschnitt.tex b/buch/chapters/110-elliptisch/images/torusschnitt.tex new file mode 100644 index 0000000..3053ac5 --- /dev/null +++ b/buch/chapters/110-elliptisch/images/torusschnitt.tex @@ -0,0 +1,41 @@ +% +% torusschnitt.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{6} +\def\hoehe{4} + +\begin{tikzpicture}[>=latex,thick] + +% Povray Bild +\node at (0,0) {\includegraphics[width=11.4cm]{torusschnitt.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 (4.4,-2.4) {$X$}; +\node at (3.5,0.6) {$Y$}; +\node at (0.3,3.8) {$Z$}; + +\end{tikzpicture} + +\end{document} + -- cgit v1.2.1 From f62b44e41eb5d9afe46e56c335b96cb48ae3a492 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 14 Jun 2022 17:02:23 +0200 Subject: finalize lemniscate as sections --- buch/chapters/110-elliptisch/images/Makefile | 2 +- .../chapters/110-elliptisch/images/jacobiplots.pdf | Bin 56975 -> 56975 bytes buch/chapters/110-elliptisch/images/kegelpara.pdf | Bin 139626 -> 139626 bytes .../110-elliptisch/images/torusschnitt.pdf | Bin 137159 -> 137159 bytes 4 files changed, 1 insertion(+), 1 deletion(-) (limited to 'buch/chapters/110-elliptisch/images') diff --git a/buch/chapters/110-elliptisch/images/Makefile b/buch/chapters/110-elliptisch/images/Makefile index 2a23d88..30642fe 100644 --- a/buch/chapters/110-elliptisch/images/Makefile +++ b/buch/chapters/110-elliptisch/images/Makefile @@ -5,7 +5,7 @@ # all: lemniskate.pdf ellipsenumfang.pdf unvollstaendig.pdf rechteck.pdf \ ellipse.pdf pendel.pdf jacobiplots.pdf jacobidef.pdf jacobi12.pdf \ - sncnlimit.pdf slcl.pdf + sncnlimit.pdf slcl.pdf torusschnitt.pdf kegelpara.pdf lemniskate.pdf: lemniskate.tex pdflatex lemniskate.tex diff --git a/buch/chapters/110-elliptisch/images/jacobiplots.pdf b/buch/chapters/110-elliptisch/images/jacobiplots.pdf index f0e6e78..4c74a5c 100644 Binary files a/buch/chapters/110-elliptisch/images/jacobiplots.pdf and b/buch/chapters/110-elliptisch/images/jacobiplots.pdf differ diff --git a/buch/chapters/110-elliptisch/images/kegelpara.pdf b/buch/chapters/110-elliptisch/images/kegelpara.pdf index 4b03119..6683709 100644 Binary files a/buch/chapters/110-elliptisch/images/kegelpara.pdf and b/buch/chapters/110-elliptisch/images/kegelpara.pdf differ diff --git a/buch/chapters/110-elliptisch/images/torusschnitt.pdf b/buch/chapters/110-elliptisch/images/torusschnitt.pdf index 430447c..2f8c204 100644 Binary files a/buch/chapters/110-elliptisch/images/torusschnitt.pdf and b/buch/chapters/110-elliptisch/images/torusschnitt.pdf differ -- cgit v1.2.1 From 864b17ee949de5c14ebc3bbf50a90178b4b804f3 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Wed, 15 Jun 2022 20:25:27 +0200 Subject: fix some minor issues --- buch/chapters/110-elliptisch/images/Makefile | 7 +- .../chapters/110-elliptisch/images/jacobiplots.pdf | Bin 56975 -> 56975 bytes buch/chapters/110-elliptisch/images/kegelpara.pdf | Bin 139626 -> 202828 bytes buch/chapters/110-elliptisch/images/kegelpara.pov | 122 +++++++++++++++++++-- buch/chapters/110-elliptisch/images/kegelpara.tex | 6 +- .../110-elliptisch/images/torusschnitt.pdf | Bin 137159 -> 301677 bytes .../110-elliptisch/images/torusschnitt.pov | 88 ++++++++++++++- 7 files changed, 205 insertions(+), 18 deletions(-) (limited to 'buch/chapters/110-elliptisch/images') diff --git a/buch/chapters/110-elliptisch/images/Makefile b/buch/chapters/110-elliptisch/images/Makefile index 30642fe..c8f98cb 100644 --- a/buch/chapters/110-elliptisch/images/Makefile +++ b/buch/chapters/110-elliptisch/images/Makefile @@ -79,11 +79,14 @@ slcldata.tex: slcl slcl.pdf: slcl.tex slcldata.tex pdflatex slcl.tex +KEGELSIZE = -W256 -H256 +KEGELSIZE = -W128 -H128 +KEGELSIZE = -W1080 -H1080 kegelpara.png: kegelpara.pov - povray +A0.1 -W1080 -H1080 -Okegelpara.png kegelpara.pov + povray +A0.1 $(KEGELSIZE) -Okegelpara.png kegelpara.pov kegelpara.jpg: kegelpara.png Makefile - convert -extract 1080x1000+0+40 kegelpara.png \ + convert -extract 1080x1040+0+0 kegelpara.png \ -density 300 -units PixelsPerInch kegelpara.jpg kegelpara.pdf: kegelpara.tex kegelpara.jpg diff --git a/buch/chapters/110-elliptisch/images/jacobiplots.pdf b/buch/chapters/110-elliptisch/images/jacobiplots.pdf index 4c74a5c..c11affc 100644 Binary files a/buch/chapters/110-elliptisch/images/jacobiplots.pdf and b/buch/chapters/110-elliptisch/images/jacobiplots.pdf differ diff --git a/buch/chapters/110-elliptisch/images/kegelpara.pdf b/buch/chapters/110-elliptisch/images/kegelpara.pdf index 6683709..2f76593 100644 Binary files a/buch/chapters/110-elliptisch/images/kegelpara.pdf and b/buch/chapters/110-elliptisch/images/kegelpara.pdf differ diff --git a/buch/chapters/110-elliptisch/images/kegelpara.pov b/buch/chapters/110-elliptisch/images/kegelpara.pov index 5d85eed..13b66cc 100644 --- a/buch/chapters/110-elliptisch/images/kegelpara.pov +++ b/buch/chapters/110-elliptisch/images/kegelpara.pov @@ -67,11 +67,11 @@ union { } #end -arrow(<-2,0,0>,<2,0,0>,0.02,White) -arrow(<0,-2,0>,<0,2,0>,0.02,White) -arrow(<0,0,-2>,<0,0,2>,0.02,White) +arrow(<-2.6,0,0>,<2.5,0,0>,0.02,White) +arrow(<0,-2,0>,<0,2.3,0>,0.02,White) +arrow(<0,0,-3.2>,<0,0,3.7>,0.02,White) -#declare epsilon = 0.001; +#declare epsilon = 0.0001; #declare l = 1.5; #macro Kegel(farbe) @@ -94,6 +94,54 @@ union { } #end +#macro Kegelpunkt(xx, phi) + < xx, xx * sin(phi), xx * cos(phi) > +#end + +#macro Kegelgitter(farbe, r) +union { + #declare s = 0; + #declare smax = 2 * pi; + #declare sstep = pi / 6; + #while (s < smax - sstep/2) + cylinder { Kegelpunkt(l, s), Kegelpunkt(-l, s), r } + #declare s = s + sstep; + #end + #declare phimax = 2 * pi; + #declare phisteps = 100; + #declare phistep = phimax / phisteps; + #declare xxstep = 0.5; + #declare xxmax = 2; + #declare xx = xxstep; + #while (xx < xxmax - xxstep/2) + #declare phi = 0; + #while (phi < phimax - phistep/2) + cylinder { + Kegelpunkt(xx, phi), + Kegelpunkt(xx, phi + phistep), + r + } + sphere { Kegelpunkt(xx, phi), r } + cylinder { + Kegelpunkt(-xx, phi), + Kegelpunkt(-xx, phi + phistep), + r + } + sphere { Kegelpunkt(-xx, phi), r } + #declare phi = phi + phistep; + #end + #declare xx = xx + xxstep; + #end + pigment { + color farbe + } + finish { + specular 0.9 + metallic + } +} +#end + #macro F(w, r) #end @@ -139,6 +187,50 @@ mesh { } #end +#macro Paraboloidgitter(farbe, gr) +union { + #declare phi = 0; + #declare phimax = 2 * pi; + #declare phistep = pi / 6; + + #declare rmax = 1.5; + #declare rsteps = 100; + #declare rstep = rmax / rsteps; + + #while (phi < phimax - phistep/2) + #declare r = rstep; + #while (r < rmax - rstep/2) + cylinder { F(phi, r), F(phi, r + rstep), gr } + sphere { F(phi, r), gr } + #declare r = r + rstep; + #end + #declare phi = phi + phistep; + #end + + #declare rstep = 0.2; + #declare r = rstep; + + #declare phisteps = 100; + #declare phistep = phimax / phisteps; + #while (r < rmax) + #declare phi = 0; + #while (phi < phimax - phistep/2) + cylinder { F(phi, r), F(phi + phistep, r), gr } + sphere { F(phi, r), gr } + #declare phi = phi + phistep; + #end + #declare r = r + rstep; + #end + pigment { + color farbe + } + finish { + specular 0.9 + metallic + } +} +#end + #declare a = sqrt(2); #macro G(phi,sg) < a*sg*sqrt(cos(2*phi))*cos(phi), a*cos(2*phi), a*sqrt(cos(2*phi))*sin(phi)> @@ -215,11 +307,23 @@ union { } #end -#declare kegelfarbe = rgbt<0.2,0.6,0.2,0.2>; -#declare paraboloidfarbe = rgbt<0.2,0.6,1.0,0.2>; +#declare kegelfarbe = rgbf<0.2,0.6,0.2,0.2>; +#declare kegelgitterfarbe = rgb<0.2,0.8,0.2>; +#declare paraboloidfarbe = rgbf<0.2,0.6,1.0,0.2>; +#declare paraboloidgitterfarbe = rgb<0.4,1,1>; + +//intersection { +// union { + Paraboloid(paraboloidfarbe) + Paraboloidgitter(paraboloidgitterfarbe, 0.004) + + Kegel(kegelfarbe) + Kegelgitter(kegelgitterfarbe, 0.004) +// } +// plane { <0, 0, -1>, 0.6 } +//} + -Paraboloid(paraboloidfarbe) -Kegel(kegelfarbe) -Lemniskate3D(0.02, Blue) +Lemniskate3D(0.02, rgb<0.8,0.0,0.8>) Lemniskate(0.02, Red) Projektion(0.01, Yellow) diff --git a/buch/chapters/110-elliptisch/images/kegelpara.tex b/buch/chapters/110-elliptisch/images/kegelpara.tex index 5a724ee..8fcefbf 100644 --- a/buch/chapters/110-elliptisch/images/kegelpara.tex +++ b/buch/chapters/110-elliptisch/images/kegelpara.tex @@ -31,9 +31,9 @@ \fill (0,0) circle[radius=0.05]; }{} -\node at (3.3,-1.0) {$X$}; -\node at (0.2,3.4) {$Z$}; -\node at (-2.5,-1.4) {$-Y$}; +\node at (4.1,-1.4) {$X$}; +\node at (0.2,3.8) {$Z$}; +\node at (4.0,1.8) {$Y$}; \end{tikzpicture} diff --git a/buch/chapters/110-elliptisch/images/torusschnitt.pdf b/buch/chapters/110-elliptisch/images/torusschnitt.pdf index 2f8c204..11bd353 100644 Binary files a/buch/chapters/110-elliptisch/images/torusschnitt.pdf and b/buch/chapters/110-elliptisch/images/torusschnitt.pdf differ diff --git a/buch/chapters/110-elliptisch/images/torusschnitt.pov b/buch/chapters/110-elliptisch/images/torusschnitt.pov index 94190be..43d50c6 100644 --- a/buch/chapters/110-elliptisch/images/torusschnitt.pov +++ b/buch/chapters/110-elliptisch/images/torusschnitt.pov @@ -123,9 +123,34 @@ union { } #end -#macro Ebene(farbe) -box { - <-1.8, 0, -1.4>, <1.8, 0.001, 1.4> +#macro Ebene(l, b, farbe) +mesh { + triangle { <-l, 0, -b>, < l, 0, -b>, < l, 0, b> } + triangle { <-l, 0, -b>, < l, 0, b>, <-l, 0, b> } + pigment { + color farbe + } + finish { + specular 0.9 + metallic + } +} +#end + +#macro Ebenengitter(l, b, s, r, farbe) +union { + #declare lmax = floor(l / s); + #declare ll = -lmax; + #while (ll <= lmax) + cylinder { , , r } + #declare ll = ll + 1; + #end + #declare bmax = floor(b / s); + #declare bb = -bmax; + #while (bb <= bmax) + cylinder { <-l, 0, bb * s>, , r } + #declare bb = bb + 1; + #end pigment { color farbe } @@ -141,6 +166,59 @@ box { b * < (2 + cos(theta)) * cos(phi), (2 + cos(theta)) * sin(phi) + 1, sin(theta) > #end +#macro breitenkreis(theta, r) + #declare phi = 0; + #declare phimax = 2 * pi; + #declare phisteps = 200; + #declare phistep = phimax / phisteps; + #while (phi < phimax - phistep/2) + cylinder { T(phi, theta), T(phi + phistep, theta), r } + sphere { T(phi, theta), r } + #declare phi = phi + phistep; + #end +#end + +#macro laengenkreis(phi, r) + #declare theta = 0; + #declare thetamax = 2 * pi; + #declare thetasteps = 200; + #declare thetastep = thetamax / thetasteps; + #while (theta < thetamax - thetastep/2) + cylinder { T(phi, theta), T(phi, theta + thetastep), r } + sphere { T(phi, theta), r } + #declare theta = theta + thetastep; + #end +#end + +#macro Torusgitter(farbe, r) +union { + #declare phi = 0; + #declare phimax = 2 * pi; + #declare phistep = pi / 6; + #while (phi < phimax - phistep/2) + laengenkreis(phi, r) + #declare phi = phi + phistep; + #end + #declare thetamax = pi; + #declare thetastep = pi / 6; + #declare theta = thetastep; + #while (theta < thetamax - thetastep/2) + breitenkreis(theta, r) + breitenkreis(thetamax + theta, r) + #declare theta = theta + thetastep; + #end + breitenkreis(0, 1.5 * r) + breitenkreis(pi, 1.5 * r) + pigment { + color farbe + } + finish { + specular 0.9 + metallic + } +} +#end + #macro Torus(farbe) mesh { #declare phi = 0; @@ -181,5 +259,7 @@ mesh { #declare ebenenfarbe = rgbt<0.2,0.6,1.0,0.2>; Lemniskate(0.02, Red) -Ebene(ebenenfarbe) +Ebene(1.8, 1.4, ebenenfarbe) +Ebenengitter(1.8, 1.4, 0.5, 0.005, rgb<0.4,1,1>) Torus(torusfarbe) +Torusgitter(Yellow, 0.005) -- cgit v1.2.1