From 100898f1bdf1f00e3f8ba8ddb68703bcbed1e77e Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Wed, 4 Aug 2021 20:24:32 +0200 Subject: add new image stuff --- buch/papers/clifford/3d/Makefile | 13 +++ buch/papers/clifford/3d/common.inc | 206 +++++++++++++++++++++++++++++++++++++ buch/papers/clifford/3d/dq.pov | 25 +++++ 3 files changed, 244 insertions(+) create mode 100644 buch/papers/clifford/3d/Makefile create mode 100644 buch/papers/clifford/3d/common.inc create mode 100644 buch/papers/clifford/3d/dq.pov (limited to 'buch/papers/clifford/3d') diff --git a/buch/papers/clifford/3d/Makefile b/buch/papers/clifford/3d/Makefile new file mode 100644 index 0000000..e6a9be3 --- /dev/null +++ b/buch/papers/clifford/3d/Makefile @@ -0,0 +1,13 @@ +# +# Makefile +# +# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +all: dq.jpg + +dq.png: dq.pov common.inc + povray +A0.1 +W1920 +H1080 -Odq.png dq.pov + +dq.jpg: dq.png + convert dq.png -density 300 -units PixelsPerInch dq.jpg + diff --git a/buch/papers/clifford/3d/common.inc b/buch/papers/clifford/3d/common.inc new file mode 100644 index 0000000..4bc2e7d --- /dev/null +++ b/buch/papers/clifford/3d/common.inc @@ -0,0 +1,206 @@ +// +// common.inc +// +// (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#version 3.7; +#include "colors.inc" + +global_settings { + assumed_gamma 1 +} + +#declare imagescale = 0.14; +#declare r = 0.04; + +camera { + location <40, 10, 15> + look_at <0, 0, 0> + right 16/9 * x * imagescale + up y * imagescale +} + +light_source { + <40, 20, 20> 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(< -3, 0, 0 >, < 3, 0, 0 >, r, White) +arrow(< 0, -3, 0 >, < 0, 3, 0 >, r, White) +arrow(< 0, 0, -3 >, < 0, 0, 3 >, r, White) + +#macro circlearrow0(e1, e2, e3, r1, r2) + +mesh { + #declare N = 100; + #declare phi = 0; + #declare phimax = 1.8 * pi; + #declare phistep = (phimax - phi) / N; + #while (phi < phimax - phistep/2) + triangle { + center + r1 * (cos(phi ) * e1 + sin(phi ) * e2) - h * e3, + center + r2 * (cos(phi ) * e1 + sin(phi ) * e2) - h * e3, + center + r1 * (cos(phi+phistep) * e1 + sin(phi+phistep) * e2) - h * e3 + } + triangle { + center + r1 * (cos(phi+phistep) * e1 + sin(phi+phistep) * e2) - h * e3, + center + r2 * (cos(phi ) * e1 + sin(phi ) * e2) - h * e3, + center + r2 * (cos(phi+phistep) * e1 + sin(phi+phistep) * e2) - h * e3 + } + triangle { + center + r1 * (cos(phi ) * e1 + sin(phi ) * e2) + h * e3, + center + r2 * (cos(phi ) * e1 + sin(phi ) * e2) + h * e3, + center + r1 * (cos(phi+phistep) * e1 + sin(phi+phistep) * e2) + h * e3 + } + triangle { + center + r1 * (cos(phi+phistep) * e1 + sin(phi+phistep) * e2) + h * e3, + center + r2 * (cos(phi ) * e1 + sin(phi ) * e2) + h * e3, + center + r2 * (cos(phi+phistep) * e1 + sin(phi+phistep) * e2) + h * e3 + } + triangle { + center + r1 * (cos(phi ) * e1 + sin(phi ) * e2) - h * e3, + center + r1 * (cos(phi+phistep) * e1 + sin(phi+phistep) * e2) - h * e3, + center + r1 * (cos(phi+phistep) * e1 + sin(phi+phistep) * e2) + h * e3 + } + triangle { + center + r1 * (cos(phi ) * e1 + sin(phi ) * e2) - h * e3, + center + r1 * (cos(phi+phistep) * e1 + sin(phi+phistep) * e2) + h * e3, + center + r1 * (cos(phi ) * e1 + sin(phi ) * e2) + h * e3 + } + triangle { + center + r2 * (cos(phi ) * e1 + sin(phi ) * e2) - h * e3, + center + r2 * (cos(phi+phistep) * e1 + sin(phi+phistep) * e2) - h * e3, + center + r2 * (cos(phi+phistep) * e1 + sin(phi+phistep) * e2) + h * e3 + } + triangle { + center + r2 * (cos(phi ) * e1 + sin(phi ) * e2) - h * e3, + center + r2 * (cos(phi+phistep) * e1 + sin(phi+phistep) * e2) + h * e3, + center + r2 * (cos(phi ) * e1 + sin(phi ) * e2) + h * e3 + } + #declare phi = phi + phistep; + #end + + triangle { + center + r1 * e1 - h * e3, + center + r1 * e1 + h * e3, + center + r2 * e1 + h * e3 + } + triangle { + center + r2 * e1 - h * e3, + center + r2 * e1 + h * e3, + center + r1 * e1 - h * e3 + } + triangle { + center + r1 * cos(phi) * e1 + r1 * sin(phi) * e2 - h * e3, + center + r2 * cos(phi) * e1 + r2 * sin(phi) * e2 - h * e3, + center + 0.5*(r1+r2) * (cos(phi + pi/12) * e1 + sin(phi + pi/12) * e2) - h * e3 + } + triangle { + center + r1 * cos(phi) * e1 + r1 * sin(phi) * e2 + h * e3, + center + r2 * cos(phi) * e1 + r2 * sin(phi) * e2 + h * e3, + center + 0.5*(r1+r2) * (cos(phi + pi/12) * e1 + sin(phi + pi/12) * e2) + h * e3 + } + triangle { + center + r1 * cos(phi) * e1 + r1 * sin(phi) * e2 - h * e3, + center + 0.5*(r1+r2) * (cos(phi + pi/12) * e1 + sin(phi + pi/12) * e2) - h * e3 + center + r1 * cos(phi) * e1 + r1 * sin(phi) * e2 + h * e3 + } + triangle { + center + 0.5*(r1+r2) * (cos(phi + pi/12) * e1 + sin(phi + pi/12) * e2) - h * e3 + center + r1 * cos(phi) * e1 + r1 * sin(phi) * e2 + h * e3, + center + 0.5*(r1+r2) * (cos(phi + pi/12) * e1 + sin(phi + pi/12) * e2) + h * e3 + } + triangle { + center + 0.5*(r1+r2) * (cos(phi + pi/12) * e1 + sin(phi + pi/12) * e2) - h * e3, + center + r2 * cos(phi) * e1 + r2 * sin(phi) * e2 - h * e3, + center + r2 * cos(phi) * e1 + r2 * sin(phi) * e2 + h * e3 + } + triangle { + center + 0.5*(r1+r2) * (cos(phi + pi/12) * e1 + sin(phi + pi/12) * e2) - h * e3, + center + r2 * cos(phi) * e1 + r2 * sin(phi) * e2 + h * e3, + center + 0.5*(r1+r2) * (cos(phi + pi/12) * e1 + sin(phi + pi/12) * e2) + h * e3 + } + + pigment { + color rgb<1, 0.4, 0.4> + } +} + +#end + + +#macro circlearrow(fromdirection, axis, center, r, h) + +#declare e1 = vnormalize(fromdirection); +#declare e2 = -vnormalize(vcross(axis, fromdirection)); +#declare e3 = vnormalize(axis); + +#declare r1 = 0.4 * r; +#declare r2 = r; + +circlearrow0(e1, e2, e3, r1, r2) + +box { + center - r * (e1 + e2) - 0.021 * e3, center + r * (e1 + e2) + 0.021 * e3 + pigment { + color rgb<0.6,0.6,1> + } +} + +cone { + center + 0.02101 * e3, r, center + 2 * r * e3, 0 + pigment { + color rgbt<0.6,0.6,1,0.8> + } +} + +cylinder { + center, center + 2 * r * e3, 0.04*0.2 + pigment { + color rgb<1.0,0.6,0.6> + } +} + +#end + diff --git a/buch/papers/clifford/3d/dq.pov b/buch/papers/clifford/3d/dq.pov new file mode 100644 index 0000000..92b702a --- /dev/null +++ b/buch/papers/clifford/3d/dq.pov @@ -0,0 +1,25 @@ +// +// dq.pov -- Drehung und Quaternion +// +// (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#include "common.inc" + +arrow(<0,0,0>, <1, sqrt(2), 2>, r, Red) + +#declare r = 0.2 * r; + +circlearrow(<1,0,0>, <0,0,1>, <1, sqrt(2), 0>, 1, 0.022) +circlearrow(<1,0,0>, <0,1,0>, <1, 0, 2>, sqrt(2)/2, 0.022) +circlearrow(<0,0,1>, <1,0,0>, <0, sqrt(2), 2>, 0.5, 0.022) + +#declare l = 2.8; +#declare h = 0.0001; +union { + box { <-l,-l,-h>, } + box { <-l,-h,-l>, } + box { <-h,-l,-l>, <-h,l,l> } + pigment { + color rgbt<0.6,0.6,0.6,0.0> + } +} -- cgit v1.2.1 From a8138ae8cf5b0bda133b5c5fb077021ac3d59761 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Thu, 5 Aug 2021 12:59:37 +0200 Subject: add images for clifford article --- buch/papers/clifford/3d/Makefile | 23 ++++++- buch/papers/clifford/3d/common.inc | 59 +++++++++++++++--- buch/papers/clifford/3d/dq.pov | 6 +- buch/papers/clifford/3d/drehung.pov | 120 ++++++++++++++++++++++++++++++++++++ buch/papers/clifford/3d/q23.pov | 12 ++++ buch/papers/clifford/3d/q31.pov | 12 ++++ 6 files changed, 217 insertions(+), 15 deletions(-) create mode 100644 buch/papers/clifford/3d/drehung.pov create mode 100644 buch/papers/clifford/3d/q23.pov create mode 100644 buch/papers/clifford/3d/q31.pov (limited to 'buch/papers/clifford/3d') diff --git a/buch/papers/clifford/3d/Makefile b/buch/papers/clifford/3d/Makefile index e6a9be3..70dffe3 100644 --- a/buch/papers/clifford/3d/Makefile +++ b/buch/papers/clifford/3d/Makefile @@ -3,11 +3,28 @@ # # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # -all: dq.jpg +all: dq.jpg q23.jpg q31.jpg drehung.jpg -dq.png: dq.pov common.inc - povray +A0.1 +W1920 +H1080 -Odq.png dq.pov +size="+W1920 +H1080" +size="+W3840 +H2160" +dq.png: dq.pov common.inc + povray +A0.1 $(size) -Odq.png dq.pov dq.jpg: dq.png convert dq.png -density 300 -units PixelsPerInch dq.jpg +q23.png: q23.pov common.inc + povray +A0.1 $(size) -Oq23.png q23.pov +q23.jpg: q23.png + convert q23.png -density 300 -units PixelsPerInch q23.jpg + +q31.png: q31.pov common.inc + povray +A0.1 $(size) -Oq31.png q31.pov +q31.jpg: q31.png + convert q31.png -density 300 -units PixelsPerInch q31.jpg + +drehung.png: drehung.pov common.inc + povray +A0.1 $(size) -Odrehung.png drehung.pov +drehung.jpg: drehung.png + convert drehung.png -density 300 -units PixelsPerInch drehung.jpg + diff --git a/buch/papers/clifford/3d/common.inc b/buch/papers/clifford/3d/common.inc index 4bc2e7d..54aa7fe 100644 --- a/buch/papers/clifford/3d/common.inc +++ b/buch/papers/clifford/3d/common.inc @@ -11,10 +11,11 @@ global_settings { } #declare imagescale = 0.14; -#declare r = 0.04; +#declare r = 0.02; +#declare thick = 0.040; camera { - location <40, 10, 15> + location <40, 12, 15> look_at <0, 0, 0> right 16/9 * x * imagescale up y * imagescale @@ -70,12 +71,12 @@ arrow(< -3, 0, 0 >, < 3, 0, 0 >, r, White) arrow(< 0, -3, 0 >, < 0, 3, 0 >, r, White) arrow(< 0, 0, -3 >, < 0, 0, 3 >, r, White) -#macro circlearrow0(e1, e2, e3, r1, r2) +#macro circlearrow0(e1, e2, e3, r1, r2, h, winkel) mesh { #declare N = 100; #declare phi = 0; - #declare phimax = 1.8 * pi; + #declare phimax = winkel - pi / 12; #declare phistep = (phimax - phi) / N; #while (phi < phimax - phistep/2) triangle { @@ -170,7 +171,7 @@ mesh { #end -#macro circlearrow(fromdirection, axis, center, r, h) +#macro circlearrow(fromdirection, axis, center, r, h, winkel, anzahl) #declare e1 = vnormalize(fromdirection); #declare e2 = -vnormalize(vcross(axis, fromdirection)); @@ -179,27 +180,67 @@ mesh { #declare r1 = 0.4 * r; #declare r2 = r; -circlearrow0(e1, e2, e3, r1, r2) +#declare w = 0; +#while (w < anzahl) + #declare a = 2 * w * pi / anzahl; + circlearrow0(e1 * cos(a) - e2 * sin(a), e1 * sin(a) + e2 * cos(a), e3, r1, r2, 1.2 * h, winkel) + #declare w = w + 1; +#end + +mesh { + #declare vlu = center - r * e1 - r * e2 - h * e3; + #declare vlo = center - r * e1 - r * e2 + h * e3; + #declare vru = center - r * e1 + r * e2 - h * e3; + #declare vro = center - r * e1 + r * e2 + h * e3; + #declare hlu = center + r * e1 - r * e2 - h * e3; + #declare hlo = center + r * e1 - r * e2 + h * e3; + #declare hru = center + r * e1 + r * e2 - h * e3; + #declare hro = center + r * e1 + r * e2 + h * e3; + triangle { vlu, vru, vro } + triangle { vlu, vro, vlo } + + triangle { vru, hru, hro } + triangle { vru, hro, vro } + + triangle { hru, hlu, hlo } + triangle { hru, hlo, hro } + + triangle { hlu, vlu, vlo } + triangle { hlu, vlo, hlo } + + triangle { vlu, vru, hru } + triangle { vlu, hru, hlu } + + triangle { vlo, vro, hro } + triangle { vlo, hro, hlo } -box { - center - r * (e1 + e2) - 0.021 * e3, center + r * (e1 + e2) + 0.021 * e3 pigment { color rgb<0.6,0.6,1> } + finish { + specular 0.96 + metallic + } } +#if (vlength(axis) > 0.1) cone { - center + 0.02101 * e3, r, center + 2 * r * e3, 0 + center + 1.19 * h * e3, r, center + 2 * r * e3, 0 pigment { color rgbt<0.6,0.6,1,0.8> } } +#end cylinder { center, center + 2 * r * e3, 0.04*0.2 pigment { color rgb<1.0,0.6,0.6> } + finish { + specular 0.96 + metallic + } } #end diff --git a/buch/papers/clifford/3d/dq.pov b/buch/papers/clifford/3d/dq.pov index 92b702a..8002129 100644 --- a/buch/papers/clifford/3d/dq.pov +++ b/buch/papers/clifford/3d/dq.pov @@ -9,9 +9,9 @@ arrow(<0,0,0>, <1, sqrt(2), 2>, r, Red) #declare r = 0.2 * r; -circlearrow(<1,0,0>, <0,0,1>, <1, sqrt(2), 0>, 1, 0.022) -circlearrow(<1,0,0>, <0,1,0>, <1, 0, 2>, sqrt(2)/2, 0.022) -circlearrow(<0,0,1>, <1,0,0>, <0, sqrt(2), 2>, 0.5, 0.022) +circlearrow(<1,0,0>, <0,0,1>, <1, sqrt(2), 0>, 1, thick, 1.8*pi/3, 3) +circlearrow(<1,0,0>, <0,1,0>, <1, 0, 2>, sqrt(2)/2, thick, 1.8*pi/3, 3) +circlearrow(<0,0,1>, <1,0,0>, <0, sqrt(2), 2>, 0.5, thick, 1.8*pi/3, 3) #declare l = 2.8; #declare h = 0.0001; diff --git a/buch/papers/clifford/3d/drehung.pov b/buch/papers/clifford/3d/drehung.pov new file mode 100644 index 0000000..54b5a2e --- /dev/null +++ b/buch/papers/clifford/3d/drehung.pov @@ -0,0 +1,120 @@ +// +// drehung.pov -- Drehung um (1,1,1) +// +// (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#include "common.inc" + +#declare n = vnormalize(<1,1,1>); +#declare V = <0,2.6,0>; +#declare W = <0,0,2.6>; + +#declare Vparallel = vdot(n, V) * n; +#declare Vperp = V - Vparallel; +#declare Wparallel = vdot(n, W) * n; +#declare Wperp = W - Wparallel; + +arrow(<0,0,0>, 2*n, thick, Red) + +arrow(<0,0,0>, V, thick, rgb<0.0,1.0,1.0>) +arrow(<0,0,0>, W, thick, rgb<0.0,1.0,1.0>) + +circlearrow(vnormalize(vcross(<-1,0,1>,n)), -0.01 * <1,1,1>, <0,0,0>, 1, 0.8*thick, 1.98*pi/3, 3) + +arrow(<0,0,0>, Vperp, 0.99*thick, Blue) +arrow(<0,0,0>, Wperp, 0.99*thick, Blue) + +arrow(Vperp, V, thick, Green) +arrow(Wperp, W, thick, Green) + +#declare l = 2.4; +intersection { + box { <-l,-l,-l>, } + //cylinder { -n, n, 3 } + plane { n, 0.01 } + plane { -n, 0.01 } + pigment { + color rgbt<0.6,0.6,1.0,0.8> + } +} + +#declare e1 = vnormalize(Vperp); +#declare e3 = n; +#declare e2 = vnormalize(vcross(e3, e1)); +#declare r = vlength(Vperp); + +mesh { + #declare phi = 0; + #declare phimax = 2*pi/3; + #declare phistep = (phimax - phi) / N; + #while (phi < phimax - phistep/2) + triangle { + <0,0,0>, + r * (cos(phi ) * e1 + sin(phi ) * e2), + r * (cos(phi+phistep) * e1 + sin(phi+phistep) * e2) + } + #declare phi = phi + phistep; + #end + pigment { + color rgbt<0.2,0.2,1.0,0.4> + } +} + +union { + #declare phi = 0; + #declare phimax = 2*pi/3; + #declare phistep = (phimax - phi) / N; + #while (phi < phimax - phistep/2) + cylinder { + r * (cos(phi ) * e1 + sin(phi ) * e2), + r * (cos(phi+phistep) * e1 + sin(phi+phistep) * e2), + 0.01 + } + sphere { r * (cos(phi ) * e1 + sin(phi ) * e2), 0.01 } + #declare phi = phi + phistep; + #end + pigment { + color Blue + } +} + +mesh { + #declare phi = 0; + #declare phimax = 2*pi/3; + #declare phistep = (phimax - phi) / N; + #while (phi < phimax - phistep/2) + triangle { + r * (cos(phi ) * e1 + sin(phi ) * e2), + r * (cos(phi+phistep) * e1 + sin(phi+phistep) * e2), + r * (cos(phi ) * e1 + sin(phi ) * e2) + Vparallel + } + triangle { + r * (cos(phi+phistep) * e1 + sin(phi+phistep) * e2), + r * (cos(phi ) * e1 + sin(phi ) * e2) + Vparallel, + r * (cos(phi+phistep) * e1 + sin(phi+phistep) * e2) + Vparallel + } + #declare phi = phi + phistep; + #end + pigment { + color rgbt<0.2,1,0.2,0.4> + } +} + +union { + #declare phi = 0; + #declare phimax = 2*pi/3; + #declare phistep = (phimax - phi) / N; + #while (phi < phimax - phistep/2) + cylinder { + r * (cos(phi ) * e1 + sin(phi ) * e2) + Vparallel, + r * (cos(phi+phistep) * e1 + sin(phi+phistep) * e2) + Vparallel, + 0.01 + } + sphere { r * (cos(phi ) * e1 + sin(phi ) * e2) + Vparallel, 0.01 } + #declare phi = phi + phistep; + #end + pigment { + color Green + } +} + diff --git a/buch/papers/clifford/3d/q23.pov b/buch/papers/clifford/3d/q23.pov new file mode 100644 index 0000000..e3e5d49 --- /dev/null +++ b/buch/papers/clifford/3d/q23.pov @@ -0,0 +1,12 @@ +// +// q23.pov -- Drehung und Quaternion +// +// (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#include "common.inc" + +circlearrow(<1,0,0>, 0.01*<0,0,-1>, <0, 0, 0>, 1.0, thick, 0.98*pi/2, 4) + +arrow( <0,0,0>, <-2.0,0,0>, 0.99*thick, Blue) +arrow( <0,0,0>, <0,2.0,0>, 0.99*thick, Blue) +arrow( <0,0,0>, <0,0,2.0>, 0.99*thick, Red) diff --git a/buch/papers/clifford/3d/q31.pov b/buch/papers/clifford/3d/q31.pov new file mode 100644 index 0000000..901f838 --- /dev/null +++ b/buch/papers/clifford/3d/q31.pov @@ -0,0 +1,12 @@ +// +// q31.pov -- Drehung und Quaternion +// +// (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#include "common.inc" + +circlearrow(<1,0,0>, 0.01*<0,-1,0>, <0, 0, 0>, 1.0, thick, 0.98*pi/2, 4) + +arrow( <0,0,0>, <-2.0,0,0>, 0.99*thick, Blue) +arrow( <0,0,0>, <0,2.0,0>, 0.99*thick, Red) +arrow( <0,0,0>, <0,0,2.0>, 0.99*thick, Blue) -- cgit v1.2.1 From def3198eb5a2462d296aea81d14b6b982a722b8e Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Thu, 5 Aug 2021 18:48:54 +0200 Subject: bild 1 --- buch/papers/clifford/3d/Makefile | 8 +++--- buch/papers/clifford/3d/dq.pdf | Bin 0 -> 156467 bytes buch/papers/clifford/3d/dq.pov | 11 ++++++--- buch/papers/clifford/3d/dq.tex | 51 +++++++++++++++++++++++++++++++++++++++ 4 files changed, 64 insertions(+), 6 deletions(-) create mode 100644 buch/papers/clifford/3d/dq.pdf create mode 100644 buch/papers/clifford/3d/dq.tex (limited to 'buch/papers/clifford/3d') diff --git a/buch/papers/clifford/3d/Makefile b/buch/papers/clifford/3d/Makefile index 70dffe3..87acb6d 100644 --- a/buch/papers/clifford/3d/Makefile +++ b/buch/papers/clifford/3d/Makefile @@ -3,15 +3,17 @@ # # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # -all: dq.jpg q23.jpg q31.jpg drehung.jpg +all: dq.jpg q23.jpg q31.jpg drehung.jpg dq.pdf size="+W1920 +H1080" size="+W3840 +H2160" dq.png: dq.pov common.inc povray +A0.1 $(size) -Odq.png dq.pov -dq.jpg: dq.png - convert dq.png -density 300 -units PixelsPerInch dq.jpg +dq.jpg: dq.png Makefile + convert -extract 1600x1400+1500+60 dq.png -density 300 -units PixelsPerInch dq.jpg +dq.pdf: dq.jpg dq.tex + pdflatex dq.tex q23.png: q23.pov common.inc povray +A0.1 $(size) -Oq23.png q23.pov diff --git a/buch/papers/clifford/3d/dq.pdf b/buch/papers/clifford/3d/dq.pdf new file mode 100644 index 0000000..1bcaf2c Binary files /dev/null and b/buch/papers/clifford/3d/dq.pdf differ diff --git a/buch/papers/clifford/3d/dq.pov b/buch/papers/clifford/3d/dq.pov index 8002129..762eee2 100644 --- a/buch/papers/clifford/3d/dq.pov +++ b/buch/papers/clifford/3d/dq.pov @@ -9,9 +9,14 @@ arrow(<0,0,0>, <1, sqrt(2), 2>, r, Red) #declare r = 0.2 * r; -circlearrow(<1,0,0>, <0,0,1>, <1, sqrt(2), 0>, 1, thick, 1.8*pi/3, 3) -circlearrow(<1,0,0>, <0,1,0>, <1, 0, 2>, sqrt(2)/2, thick, 1.8*pi/3, 3) -circlearrow(<0,0,1>, <1,0,0>, <0, sqrt(2), 2>, 0.5, thick, 1.8*pi/3, 3) +#declare drehwinkel = 0.95 * 2*pi/3 * 3; +#declare drehwinkel23 = drehwinkel; +#declare drehwinkel12 = drehwinkel / sqrt(2); +#declare drehwinkel13 = drehwinkel / 2; + +circlearrow(<1,0,0>, <0,0,1>, <1, sqrt(2), 0>, 1, thick, drehwinkel23, 1) +circlearrow(<1,0,0>, <0,1,0>, <1, 0, 2>, sqrt(2)/2, thick, drehwinkel12, 1) +circlearrow(<0,0,1>, <1,0,0>, <0, sqrt(2), 2>, 0.5, thick, drehwinkel13, 1) #declare l = 2.8; #declare h = 0.0001; diff --git a/buch/papers/clifford/3d/dq.tex b/buch/papers/clifford/3d/dq.tex new file mode 100644 index 0000000..6b28452 --- /dev/null +++ b/buch/papers/clifford/3d/dq.tex @@ -0,0 +1,51 @@ +% +% dq.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} + +\definecolor{darkred}{rgb}{0.7,0,0} + +\newboolean{showgrid} +\setboolean{showgrid}{false} +\def\breite{6} +\def\hoehe{6} + +\begin{tikzpicture}[>=latex,thick] + +% Povray Bild +\node at (0,0) {\includegraphics[width=12cm]{dq.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 (-2.8,-2.7) {$O$}; +\node at (4.7,-3.4) {$a_1$}; +\node at (-2.6,5.2) {$a_2$}; +\fill[color=white,opacity=0.7] ({-5.7-0.25},{-4.8-0.15}) rectangle ({-5.7+0.25},{-4.8+0.2}); +\node at (-5.7,-4.8) {$a_3$}; + +\node[color=blue] at (-3.6,0.8) {$y\mathbf{e}_{23}$}; +\node[color=blue] at (2.1,0.9) {$x\mathbf{e}_{12}$}; +\node[color=blue] at (1.3,-3.7) {$z\mathbf{e}_{13}$}; + +\node[color=darkred] at (1.3,0.4) {$\vec{q}$}; + +\end{tikzpicture} + +\end{document} + -- cgit v1.2.1 From 001c12e5156f2e3b656bd42608768af5c3db4171 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Thu, 5 Aug 2021 19:14:44 +0200 Subject: Zwei Drehungen --- buch/papers/clifford/3d/Makefile | 16 +++++---- buch/papers/clifford/3d/dq.pdf | Bin 156467 -> 156467 bytes buch/papers/clifford/3d/qq.pdf | Bin 0 -> 170922 bytes buch/papers/clifford/3d/qq.tex | 68 +++++++++++++++++++++++++++++++++++++++ 4 files changed, 78 insertions(+), 6 deletions(-) create mode 100644 buch/papers/clifford/3d/qq.pdf create mode 100644 buch/papers/clifford/3d/qq.tex (limited to 'buch/papers/clifford/3d') diff --git a/buch/papers/clifford/3d/Makefile b/buch/papers/clifford/3d/Makefile index 87acb6d..823ad54 100644 --- a/buch/papers/clifford/3d/Makefile +++ b/buch/papers/clifford/3d/Makefile @@ -3,9 +3,8 @@ # # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # -all: dq.jpg q23.jpg q31.jpg drehung.jpg dq.pdf +all: dq.jpg q23.jpg q31.jpg drehung.jpg dq.pdf qq.pdf -size="+W1920 +H1080" size="+W3840 +H2160" dq.png: dq.pov common.inc @@ -15,15 +14,20 @@ dq.jpg: dq.png Makefile dq.pdf: dq.jpg dq.tex pdflatex dq.tex +extract="1200x1200+1450+350" + q23.png: q23.pov common.inc povray +A0.1 $(size) -Oq23.png q23.pov -q23.jpg: q23.png - convert q23.png -density 300 -units PixelsPerInch q23.jpg +q23.jpg: q23.png Makefile + convert -extract $(extract) q23.png -density 300 -units PixelsPerInch q23.jpg q31.png: q31.pov common.inc povray +A0.1 $(size) -Oq31.png q31.pov -q31.jpg: q31.png - convert q31.png -density 300 -units PixelsPerInch q31.jpg +q31.jpg: q31.png Makefile + convert -extract $(extract) q31.png -density 300 -units PixelsPerInch q31.jpg + +qq.pdf: qq.tex q31.jpg q23.jpg + pdflatex qq.tex drehung.png: drehung.pov common.inc povray +A0.1 $(size) -Odrehung.png drehung.pov diff --git a/buch/papers/clifford/3d/dq.pdf b/buch/papers/clifford/3d/dq.pdf index 1bcaf2c..59a1498 100644 Binary files a/buch/papers/clifford/3d/dq.pdf and b/buch/papers/clifford/3d/dq.pdf differ diff --git a/buch/papers/clifford/3d/qq.pdf b/buch/papers/clifford/3d/qq.pdf new file mode 100644 index 0000000..07a871c Binary files /dev/null and b/buch/papers/clifford/3d/qq.pdf differ diff --git a/buch/papers/clifford/3d/qq.tex b/buch/papers/clifford/3d/qq.tex new file mode 100644 index 0000000..c2ac1bc --- /dev/null +++ b/buch/papers/clifford/3d/qq.tex @@ -0,0 +1,68 @@ +% +% qq.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{times} +\usepackage{amsmath} +\usepackage{txfonts} +\usepackage[utf8]{inputenc} +\usepackage{graphics} +\usetikzlibrary{arrows,intersections,math} +\usepackage{ifthen} +\begin{document} + +\definecolor{darkred}{rgb}{0.7,0,0} + +\newboolean{showgrid} +\setboolean{showgrid}{false} +\def\breite{4} +\def\hoehe{4} + +\begin{tikzpicture}[>=latex,thick] + +% Povray Bild +\begin{scope}[xshift=-3.3cm] +\node at (0,0) {\includegraphics[width=6.3cm]{q23.jpg}}; +% Gitter +\ifthenelse{\boolean{showgrid}}{ +\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw (-\breite,-\hoehe) grid (\breite, \hoehe); +\fill (0,0) circle[radius=0.05]; +}{} +\fill[color=white,opacity=0.5] ({-0.6-0.3},{-0.2-0.2}) rectangle ({-0.6+0.3},{-0.2+0.2}); +\node[color=darkred] at (-0.6,-0.2) {$q_{23}$}; +\node[color=blue] at (-0.4,2.7) {$\mathbf{v}$}; +\node[color=blue] at (0.7,0.4) {$\mathbf{v}''_{23}$}; +\node at (3.1,-1.4) {$a_1$}; +\node at (-2.7,-2.4) {$a_3$}; +\node at (-0.7,3.4) {$a_2$}; +\end{scope} + +\setboolean{showgrid}{false} + +\begin{scope}[xshift=3.3cm] +\node at (0,0) {\includegraphics[width=6.3cm]{q31.jpg}}; +% Gitter +\ifthenelse{\boolean{showgrid}}{ +\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw (-\breite,-\hoehe) grid (\breite, \hoehe); +\fill (0,0) circle[radius=0.05]; +}{} +\fill[color=white,opacity=0.5] ({-0.7-0.3},{-0.9-0.2}) rectangle ({-0.7+0.3},{-0.9+0.2}); +\node[color=darkred] at (-0.7,-0.9) {$q_{13}$}; +\node[color=blue] at (0.7,0.4) {$\mathbf{v}''_{23}$}; +\node[color=blue] at (2.7,-0.7) {$\mathbf{v}''$}; +\node at (3.1,-1.4) {$a_1$}; +\node at (-2.7,-2.4) {$a_3$}; +\node at (-0.7,3.4) {$a_2$}; +\end{scope} + + +\end{tikzpicture} + +\end{document} + -- cgit v1.2.1 From e5df99c1ee45a6897c4fe98b018088ef0289f7e5 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Thu, 5 Aug 2021 19:35:13 +0200 Subject: add images for clifford --- buch/papers/clifford/3d/Makefile | 8 ++++-- buch/papers/clifford/3d/dq.jpg | Bin 0 -> 135038 bytes buch/papers/clifford/3d/dq.pdf | Bin 156467 -> 156467 bytes buch/papers/clifford/3d/drehung.jpg | Bin 0 -> 203814 bytes buch/papers/clifford/3d/drehung.pdf | Bin 0 -> 224521 bytes buch/papers/clifford/3d/drehung.tex | 56 ++++++++++++++++++++++++++++++++++++ buch/papers/clifford/3d/q23.jpg | Bin 0 -> 77888 bytes buch/papers/clifford/3d/q31.jpg | Bin 0 -> 75576 bytes buch/papers/clifford/3d/qq.pdf | Bin 170922 -> 170756 bytes buch/papers/clifford/3d/qq.tex | 12 ++++---- 10 files changed, 67 insertions(+), 9 deletions(-) create mode 100644 buch/papers/clifford/3d/dq.jpg create mode 100644 buch/papers/clifford/3d/drehung.jpg create mode 100644 buch/papers/clifford/3d/drehung.pdf create mode 100644 buch/papers/clifford/3d/drehung.tex create mode 100644 buch/papers/clifford/3d/q23.jpg create mode 100644 buch/papers/clifford/3d/q31.jpg (limited to 'buch/papers/clifford/3d') diff --git a/buch/papers/clifford/3d/Makefile b/buch/papers/clifford/3d/Makefile index 823ad54..147ca81 100644 --- a/buch/papers/clifford/3d/Makefile +++ b/buch/papers/clifford/3d/Makefile @@ -3,7 +3,7 @@ # # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # -all: dq.jpg q23.jpg q31.jpg drehung.jpg dq.pdf qq.pdf +all: dq.jpg q23.jpg q31.jpg drehung.jpg dq.pdf qq.pdf drehung.pdf size="+W3840 +H2160" @@ -31,6 +31,8 @@ qq.pdf: qq.tex q31.jpg q23.jpg drehung.png: drehung.pov common.inc povray +A0.1 $(size) -Odrehung.png drehung.pov -drehung.jpg: drehung.png - convert drehung.png -density 300 -units PixelsPerInch drehung.jpg +drehung.jpg: drehung.png Makefile + convert -extract 1600x1450+1400+50 drehung.png -density 300 -units PixelsPerInch drehung.jpg +drehung.pdf: drehung.tex drehung.jpg + pdflatex drehung.tex diff --git a/buch/papers/clifford/3d/dq.jpg b/buch/papers/clifford/3d/dq.jpg new file mode 100644 index 0000000..bd44a65 Binary files /dev/null and b/buch/papers/clifford/3d/dq.jpg differ diff --git a/buch/papers/clifford/3d/dq.pdf b/buch/papers/clifford/3d/dq.pdf index 59a1498..71727d2 100644 Binary files a/buch/papers/clifford/3d/dq.pdf and b/buch/papers/clifford/3d/dq.pdf differ diff --git a/buch/papers/clifford/3d/drehung.jpg b/buch/papers/clifford/3d/drehung.jpg new file mode 100644 index 0000000..ad7cd47 Binary files /dev/null and b/buch/papers/clifford/3d/drehung.jpg differ diff --git a/buch/papers/clifford/3d/drehung.pdf b/buch/papers/clifford/3d/drehung.pdf new file mode 100644 index 0000000..de29085 Binary files /dev/null and b/buch/papers/clifford/3d/drehung.pdf differ diff --git a/buch/papers/clifford/3d/drehung.tex b/buch/papers/clifford/3d/drehung.tex new file mode 100644 index 0000000..2ed6789 --- /dev/null +++ b/buch/papers/clifford/3d/drehung.tex @@ -0,0 +1,56 @@ +% +% drehung.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} + +\definecolor{darkgreen}{rgb}{0,0.6,0} +\definecolor{darkred}{rgb}{0.6,0,0} + +\newboolean{showgrid} +\setboolean{showgrid}{false} +\def\breite{7} +\def\hoehe{6} + +\begin{tikzpicture}[>=latex,thick] + +% Povray Bild +\node at (0,0) {\includegraphics[width=13cm]{drehung.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 (6.1,-3.3) {$a_1$}; +\node at (-2.0,5.7) {$a_2$}; +\node at (-5.7,-4.9) {$a_3$}; + +\node[color=white] at (-1.9,4.4) {$\boldsymbol{v}$}; +\node[color=white] at (4.5,-2.7) {$\boldsymbol{v}''$}; + +\node[color=darkgreen] at (-3.3,4.4) {$\boldsymbol{v}_{\perp}$}; +\node[color=darkgreen] at (4.2,-4.3) {$\boldsymbol{v}''_{\perp}$}; + +\node[color=blue] at (-3.7,1.5) {$\boldsymbol{v}_{\|}$}; +\node[color=blue] at (1.9,-4.7) {$\boldsymbol{v}''_{\|}$}; + +\node[color=darkred] at (-1.6,-4.2) {$2\alpha=120^\circ$}; +\node[color=darkred] at (-4.9,-0.6) {$\boldsymbol{q}$}; + +\end{tikzpicture} + +\end{document} + diff --git a/buch/papers/clifford/3d/q23.jpg b/buch/papers/clifford/3d/q23.jpg new file mode 100644 index 0000000..50ca028 Binary files /dev/null and b/buch/papers/clifford/3d/q23.jpg differ diff --git a/buch/papers/clifford/3d/q31.jpg b/buch/papers/clifford/3d/q31.jpg new file mode 100644 index 0000000..10313fa Binary files /dev/null and b/buch/papers/clifford/3d/q31.jpg differ diff --git a/buch/papers/clifford/3d/qq.pdf b/buch/papers/clifford/3d/qq.pdf index 07a871c..4c55d57 100644 Binary files a/buch/papers/clifford/3d/qq.pdf and b/buch/papers/clifford/3d/qq.pdf differ diff --git a/buch/papers/clifford/3d/qq.tex b/buch/papers/clifford/3d/qq.tex index c2ac1bc..9baa8bb 100644 --- a/buch/papers/clifford/3d/qq.tex +++ b/buch/papers/clifford/3d/qq.tex @@ -33,9 +33,9 @@ \fill (0,0) circle[radius=0.05]; }{} \fill[color=white,opacity=0.5] ({-0.6-0.3},{-0.2-0.2}) rectangle ({-0.6+0.3},{-0.2+0.2}); -\node[color=darkred] at (-0.6,-0.2) {$q_{23}$}; -\node[color=blue] at (-0.4,2.7) {$\mathbf{v}$}; -\node[color=blue] at (0.7,0.4) {$\mathbf{v}''_{23}$}; +\node[color=darkred] at (-0.6,-0.2) {$\boldsymbol{q}_{23}$}; +\node[color=blue] at (-0.4,2.7) {$\boldsymbol{v}$}; +\node[color=blue] at (0.7,0.4) {$\boldsymbol{v}''_{23}$}; \node at (3.1,-1.4) {$a_1$}; \node at (-2.7,-2.4) {$a_3$}; \node at (-0.7,3.4) {$a_2$}; @@ -53,9 +53,9 @@ \fill (0,0) circle[radius=0.05]; }{} \fill[color=white,opacity=0.5] ({-0.7-0.3},{-0.9-0.2}) rectangle ({-0.7+0.3},{-0.9+0.2}); -\node[color=darkred] at (-0.7,-0.9) {$q_{13}$}; -\node[color=blue] at (0.7,0.4) {$\mathbf{v}''_{23}$}; -\node[color=blue] at (2.7,-0.7) {$\mathbf{v}''$}; +\node[color=darkred] at (-0.7,-0.9) {$\boldsymbol{q}_{13}$}; +\node[color=blue] at (0.7,0.4) {$\boldsymbol{v}''_{23}$}; +\node[color=blue] at (2.7,-0.7) {$\boldsymbol{v}''$}; \node at (3.1,-1.4) {$a_1$}; \node at (-2.7,-2.4) {$a_3$}; \node at (-0.7,3.4) {$a_2$}; -- cgit v1.2.1 From d223220e4fdd827a5c0dd76e3d7b1453876f3e4b Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Sun, 8 Aug 2021 11:47:57 +0200 Subject: add image to reedsolomon --- buch/papers/clifford/3d/common.inc | 24 +++++++++++++++++++++++ buch/papers/clifford/3d/dq.jpg | Bin 135038 -> 135088 bytes buch/papers/clifford/3d/dq.pdf | Bin 156467 -> 156514 bytes buch/papers/clifford/3d/drehung.jpg | Bin 203814 -> 203830 bytes buch/papers/clifford/3d/drehung.pdf | Bin 224521 -> 224538 bytes buch/papers/clifford/3d/drehung.pov | 37 ++---------------------------------- buch/papers/clifford/3d/q23.jpg | Bin 77888 -> 85740 bytes buch/papers/clifford/3d/q23.pov | 2 ++ buch/papers/clifford/3d/q31.jpg | Bin 75576 -> 82876 bytes buch/papers/clifford/3d/q31.pov | 3 +++ buch/papers/clifford/3d/qq.pdf | Bin 170756 -> 185901 bytes 11 files changed, 31 insertions(+), 35 deletions(-) (limited to 'buch/papers/clifford/3d') diff --git a/buch/papers/clifford/3d/common.inc b/buch/papers/clifford/3d/common.inc index 54aa7fe..55bf6e1 100644 --- a/buch/papers/clifford/3d/common.inc +++ b/buch/papers/clifford/3d/common.inc @@ -245,3 +245,27 @@ cylinder { #end +#macro bogen(v1, v2, center, winkelbogen, farbe) + +union { + #declare phi = 0; + #declare phimax = winkelbogen; + #declare phistep = (phimax - phi) / N; + #while (phi < phimax - phistep/2) + cylinder { + cos(phi ) * v1 + sin(phi ) * v2 + center, + cos(phi+phistep) * v1 + sin(phi+phistep) * v2 + center, + 0.01 + } + sphere { + cos(phi ) * v1 + sin(phi ) * v2 + center, + 0.01 + } + #declare phi = phi + phistep; + #end + pigment { + color farbe + } +} + +#end diff --git a/buch/papers/clifford/3d/dq.jpg b/buch/papers/clifford/3d/dq.jpg index bd44a65..690cfdc 100644 Binary files a/buch/papers/clifford/3d/dq.jpg and b/buch/papers/clifford/3d/dq.jpg differ diff --git a/buch/papers/clifford/3d/dq.pdf b/buch/papers/clifford/3d/dq.pdf index 71727d2..797a558 100644 Binary files a/buch/papers/clifford/3d/dq.pdf and b/buch/papers/clifford/3d/dq.pdf differ diff --git a/buch/papers/clifford/3d/drehung.jpg b/buch/papers/clifford/3d/drehung.jpg index ad7cd47..2347296 100644 Binary files a/buch/papers/clifford/3d/drehung.jpg and b/buch/papers/clifford/3d/drehung.jpg differ diff --git a/buch/papers/clifford/3d/drehung.pdf b/buch/papers/clifford/3d/drehung.pdf index de29085..bc8036e 100644 Binary files a/buch/papers/clifford/3d/drehung.pdf and b/buch/papers/clifford/3d/drehung.pdf differ diff --git a/buch/papers/clifford/3d/drehung.pov b/buch/papers/clifford/3d/drehung.pov index 54b5a2e..b86a2c5 100644 --- a/buch/papers/clifford/3d/drehung.pov +++ b/buch/papers/clifford/3d/drehung.pov @@ -60,24 +60,6 @@ mesh { } } -union { - #declare phi = 0; - #declare phimax = 2*pi/3; - #declare phistep = (phimax - phi) / N; - #while (phi < phimax - phistep/2) - cylinder { - r * (cos(phi ) * e1 + sin(phi ) * e2), - r * (cos(phi+phistep) * e1 + sin(phi+phistep) * e2), - 0.01 - } - sphere { r * (cos(phi ) * e1 + sin(phi ) * e2), 0.01 } - #declare phi = phi + phistep; - #end - pigment { - color Blue - } -} - mesh { #declare phi = 0; #declare phimax = 2*pi/3; @@ -100,21 +82,6 @@ mesh { } } -union { - #declare phi = 0; - #declare phimax = 2*pi/3; - #declare phistep = (phimax - phi) / N; - #while (phi < phimax - phistep/2) - cylinder { - r * (cos(phi ) * e1 + sin(phi ) * e2) + Vparallel, - r * (cos(phi+phistep) * e1 + sin(phi+phistep) * e2) + Vparallel, - 0.01 - } - sphere { r * (cos(phi ) * e1 + sin(phi ) * e2) + Vparallel, 0.01 } - #declare phi = phi + phistep; - #end - pigment { - color Green - } -} +bogen(r * e1, r * e2, <0,0,0>, 2*pi/3, Blue) +bogen(r * e1, r * e2, Vparallel, 2*pi/3, Green) diff --git a/buch/papers/clifford/3d/q23.jpg b/buch/papers/clifford/3d/q23.jpg index 50ca028..929ef90 100644 Binary files a/buch/papers/clifford/3d/q23.jpg and b/buch/papers/clifford/3d/q23.jpg differ diff --git a/buch/papers/clifford/3d/q23.pov b/buch/papers/clifford/3d/q23.pov index e3e5d49..2e55c96 100644 --- a/buch/papers/clifford/3d/q23.pov +++ b/buch/papers/clifford/3d/q23.pov @@ -7,6 +7,8 @@ circlearrow(<1,0,0>, 0.01*<0,0,-1>, <0, 0, 0>, 1.0, thick, 0.98*pi/2, 4) +bogen( <0,1.7,0>, <-1.7, 0, 0>, <0,0,0>, pi/2, Blue) + arrow( <0,0,0>, <-2.0,0,0>, 0.99*thick, Blue) arrow( <0,0,0>, <0,2.0,0>, 0.99*thick, Blue) arrow( <0,0,0>, <0,0,2.0>, 0.99*thick, Red) diff --git a/buch/papers/clifford/3d/q31.jpg b/buch/papers/clifford/3d/q31.jpg index 10313fa..c240b4f 100644 Binary files a/buch/papers/clifford/3d/q31.jpg and b/buch/papers/clifford/3d/q31.jpg differ diff --git a/buch/papers/clifford/3d/q31.pov b/buch/papers/clifford/3d/q31.pov index 901f838..4abe1ed 100644 --- a/buch/papers/clifford/3d/q31.pov +++ b/buch/papers/clifford/3d/q31.pov @@ -10,3 +10,6 @@ circlearrow(<1,0,0>, 0.01*<0,-1,0>, <0, 0, 0>, 1.0, thick, 0.98*pi/2, 4) arrow( <0,0,0>, <-2.0,0,0>, 0.99*thick, Blue) arrow( <0,0,0>, <0,2.0,0>, 0.99*thick, Red) arrow( <0,0,0>, <0,0,2.0>, 0.99*thick, Blue) + +bogen( <0,0,1.7>, <-1.7, 0, 0>, <0,0,0>, pi/2, Blue) + diff --git a/buch/papers/clifford/3d/qq.pdf b/buch/papers/clifford/3d/qq.pdf index 4c55d57..fd7dbfa 100644 Binary files a/buch/papers/clifford/3d/qq.pdf and b/buch/papers/clifford/3d/qq.pdf differ -- cgit v1.2.1