Dosiero:Hexahedron.jpg
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Jen dosiero de la Wikimedia-Komunejo. La priskribo en ties priskriba paĝo estas montrata suben.
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Resumo
PriskriboHexahedron.jpg |
English: A Hexahedron (cube). A regular polyhedron. |
Fonto | see below |
Aŭtoro | La originala alŝutanto estis Cyp de angla Vikipedio |
File:Hexahedron.svg estas vektora versio de ĉi tiu bildo. Ĝi estu uzata anstataŭ ĉi tiu rastruma bildo, se ĝi ne estas malpli bonkvalita.
File:Hexahedron.jpg → File:Hexahedron.svg
Pliajn informojn vidu ĉe Help:SVG.
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Permesiloj:
Estas permesite kopii, disdoni kaj/aŭ redakti ĉi tiun dokumenton, sen senŝanĝaj sekcioj, sen antaŭkovrilaj kaj sen dorskovrilaj tekstoj, laŭ la kondiĉoj de la Permesilo GNU por Liberaj Dokumentoj, Versio 1.2 aŭ ajna pli nova versio eldonita de la Free Software Foundation; sen Senŝanĝaj Sekcioj, Antaŭovrilaj Tekstoj aŭ Malantaŭkovrilaj Tekstoj. Kopio de la permesilo estas inkluzivita en la sekcio titolita GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
Ĉi tiu dosiero estas disponebla laŭ la permesilo Krea Komunaĵo Atribuite-Samkondiĉe 3.0 Neadaptita. | ||
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Ĉi tiu permesila etikedo estis aldonita al la dosiero kiel parto de la permesila aktualigo por GFDL.http://creativecommons.org/licenses/by-sa/3.0/CC BY-SA 3.0Creative Commons Attribution-Share Alike 3.0truetrue |
Povray src code
Hexahedron, made by me using POV-Ray, see en:User:Cyp/Poly.pov for source.}}
//Picture *** Use flashiness=1 !!! ***
//
// +w1024 +h1024 +a0.3 +am2
// +w512 +h512 +a0.3 +am2
//
//Movie *** Use flashiness=0.25 !!! ***
//
// +kc +kff120 +w256 +h256 +a0.3 +am2
// +kc +kff60 +w256 +h256 +a0.3 +am2
//"Fast" preview
// +w128 +h128
#declare notwireframe=1;
#declare withreflection=0;
#declare flashiness=0.25; //Still pictures use 1, animated should probably be about 0.25.
#macro This_shape_will_be_drawn()
//PLATONIC SOLIDS ***********
//tetrahedron() #declare rotation=seed(1889/*1894*/);
//hexahedron() #declare rotation=seed(7122);
//octahedron() #declare rotation=seed(4193);
//dodecahedron() #declare rotation=seed(4412);
//icosahedron() #declare rotation=seed(7719);
//weirdahedron() #declare rotation=seed(7412);
//ARCHIMEDIAN SOLIDS ***********
//cuboctahedron() #declare rotation=seed(1941);
//icosidodecahedron() #declare rotation=seed(2241);
//truncatedtetrahedron() #declare rotation=seed(8717);
//truncatedhexahedron() #declare rotation=seed(1345);
//truncatedoctahedron() #declare rotation=seed(7235);
//truncateddodecahedron() #declare rotation=seed(9374);
//truncatedicosahedron() #declare rotation=seed(1666);
//rhombicuboctahedron() #declare rotation=seed(6124);
//truncatedcuboctahedron() #declare rotation=seed(1156);
//rhombicosidodecahedron() #declare rotation=seed(8266);
//truncatedicosidodecahedron() #declare rotation=seed(1422);
//snubhexahedron(-1) #declare rotation=seed(7152);
//snubhexahedron(1) #declare rotation=seed(1477);
//snubdodecahedron(-1) #declare rotation=seed(5111);
//snubdodecahedron(1) #declare rotation=seed(8154);
//CATALAN SOLIDS ***********
//rhombicdodecahedron() #declare rotation=seed(7154);
//rhombictriacontahedron() #declare rotation=seed(1237);
//triakistetrahedron() #declare rotation=seed(7735);
//triakisoctahedron() #declare rotation=seed(5354);
//tetrakishexahedron() #declare rotation=seed(1788);
//triakisicosahedron() #declare rotation=seed(1044);
//pentakisdodecahedron() #declare rotation=seed(6100);
//deltoidalicositetrahedron() #declare rotation=seed(5643);
//disdyakisdodecahedron() #declare rotation=seed(1440);
//deltoidalhexecontahedron() #declare rotation=seed(1026);
//disdyakistriacontahedron() #declare rotation=seed(1556);
//pentagonalicositetrahedron(-1) #declare rotation=seed(7771);
//pentagonalicositetrahedron(1) #declare rotation=seed(3470);
//pentagonalhexecontahedron(-1) #declare rotation=seed(1046);
//pentagonalhexecontahedron(1) #declare rotation=seed(1096);
//PRISMS, ANTIPRISMS, ETC... ***********
//rprism(5) #declare rotation=seed(6620);
antiprism(5) #declare rotation=seed(6620);
//bipyramid(5) #declare rotation=seed(6620);
//trapezohedron(17) #declare rotation=seed(6620);
#end
#declare tau=(1+sqrt(5))/2;
#declare sq2=sqrt(2);
#declare sq297=sqrt(297);
#declare xi=(pow(sq297+17,1/3)-pow(sq297-17,1/3)-1)/3;
#declare sqweird=sqrt(tau-5/27);
#declare ouch=pow((tau+sqweird)/2,1/3)+pow((tau-sqweird)/2,1/3);
#declare alfa=ouch-1/ouch;
#declare veta=(ouch+tau+1/ouch)*tau;
#macro tetrahedron()
addpointsevensgn(<1,1,1>)
autoface()
#end
#macro hexahedron()
addpointssgn(<1,1,1>,<1,1,1>)
autoface()
#end
#macro octahedron()
addevenpermssgn(<1,0,0>,<1,0,0>)
autoface()
#end
#macro dodecahedron()
addpointssgn(<1,1,1>,<1,1,1>)
addevenpermssgn(<0,1/tau,tau>,<0,1,1>)
autoface()
#end
#macro icosahedron()
addevenpermssgn(<0,1,tau>,<0,1,1>)
autoface()
#end
#macro weirdahedron()
addpermssgn(<1,2,3>,<1,1,1>)
autoface()
#end
#macro cuboctahedron()
addevenpermssgn(<0,1,1>,<0,1,1>)
autoface()
#end
#macro icosidodecahedron()
addevenpermssgn(<0,0,2*tau>,<0,0,1>)
addevenpermssgn(<1,tau,1+tau>,<1,1,1>)
autoface()
#end
#macro truncatedtetrahedron()
addevenpermsevensgn(<1,1,3>)
autoface()
#end
#macro truncatedhexahedron()
addevenpermssgn(<sq2-1,1,1>,<1,1,1>)
autoface()
#end
#macro truncatedoctahedron()
addpermssgn(<0,1,2>,<0,1,1>)
autoface()
#end
#macro truncateddodecahedron()
addevenpermssgn(<0,1/tau,2+tau>,<0,1,1>)
addevenpermssgn(<1/tau,tau,2*tau>,<1,1,1>)
addevenpermssgn(<tau,2,1+tau>,<1,1,1>)
autoface()
#end
#macro truncatedicosahedron()
addevenpermssgn(<0,1,3*tau>,<0,1,1>)
addevenpermssgn(<2,1+2*tau,tau>,<1,1,1>)
addevenpermssgn(<1,2+tau,2*tau>,<1,1,1>)
autoface()
#end
#macro rhombicuboctahedron()
addevenpermssgn(<1+sq2,1,1>,<1,1,1>)
autoface()
#end
#macro truncatedcuboctahedron()
addpermssgn(<1,1+sq2,1+sq2*2>,<1,1,1>)
autoface()
#end
#macro rhombicosidodecahedron()
addevenpermssgn(<1,1,1+2*tau>,<1,1,1>)
addevenpermssgn(<tau,2*tau,1+tau>,<1,1,1>)
addevenpermssgn(<2+tau,0,1+tau>,<1,0,1>)
autoface()
#end
#macro truncatedicosidodecahedron()
addevenpermssgn(<1/tau,1/tau,3+tau>,<1,1,1>)
addevenpermssgn(<2/tau,tau,1+2*tau>,<1,1,1>)
addevenpermssgn(<1/tau,1+tau,3*tau-1>,<1,1,1>)
addevenpermssgn(<2*tau-1,2,2+tau>,<1,1,1>)
addevenpermssgn(<tau,3,2*tau>,<1,1,1>)
autoface()
#end
#macro snubhexahedron(s)
addpermsaltsgn(<1,1/xi,xi>*s)
autoface()
#end
#macro snubdodecahedron(s)
addevenpermsevensgn(<2*alfa,2,2*veta>*s)
addevenpermsevensgn(<alfa+veta/tau+tau,-alfa*tau+veta+1/tau,alfa/tau+veta*tau-1>*s)
addevenpermsevensgn(<-alfa/tau+veta*tau+1,-alfa+veta/tau-tau,alfa*tau+veta-1/tau>*s)
addevenpermsevensgn(<-alfa/tau+veta*tau-1,alfa-veta/tau-tau,alfa*tau+veta+1/tau>*s)
addevenpermsevensgn(<alfa+veta/tau-tau,alfa*tau-veta+1/tau,alfa/tau+veta*tau+1>*s)
autoface()
#end
#macro rhombicdodecahedron()
cuboctahedron() dual()
#end
#macro rhombictriacontahedron()
icosidodecahedron() dual()
#end
#macro triakistetrahedron()
truncatedtetrahedron() dual()
#end
#macro triakisoctahedron()
truncatedhexahedron() dual()
#end
#macro tetrakishexahedron()
truncatedoctahedron() dual()
#end
#macro triakisicosahedron()
truncateddodecahedron() dual()
#end
#macro pentakisdodecahedron()
truncatedicosahedron() dual()
#end
#macro deltoidalicositetrahedron()
rhombicuboctahedron() dual()
#end
#macro disdyakisdodecahedron()
truncatedcuboctahedron() dual()
#end
#macro deltoidalhexecontahedron()
rhombicosidodecahedron() dual()
#end
#macro disdyakistriacontahedron()
truncatedicosidodecahedron() dual()
#end
#macro pentagonalicositetrahedron(s)
snubhexahedron(s) dual()
#end
#macro pentagonalhexecontahedron(s)
snubdodecahedron(s) dual()
#end
#macro rprism(n)
#local a=sqrt((1-cos(2*pi/n))/2);
#local b=0; #while(b<n-.5)
addpointssgn(<sin(2*pi*b/n),cos(2*pi*b/n),a>,<0,0,1>)
#local b=b+1; #end
autoface()
#end
#macro antiprism(n)
#local a=sqrt((cos(pi/n)-cos(2*pi/n))/2);
#local b=0; #while(b<2*n-.5)
addpoint(<sin(pi*b/n),cos(pi*b/n),a>)
#local a=-a; #local b=b+1; #end
autoface()
#end
#macro bipyramid(n)
rprism(n) dual()
#end
#macro trapezohedron(n)
antiprism(n) dual()
#end
#declare points=array[1000];
#declare npoints=0;
#declare faces=array[1000];
#declare nfaces=0;
#macro addpoint(a)
#declare points[npoints]=a;
#declare npoints=npoints+1;
#end
#macro addevenperms(a)
addpoint(a)
addpoint(<a.y,a.z,a.x>)
addpoint(<a.z,a.x,a.y>)
#end
#macro addperms(a)
addevenperms(a)
addevenperms(<a.x,a.z,a.y>)
#end
#macro addpointssgn(a,s)
addpoint(a)
#if(s.x) addpointssgn(a*<-1,1,1>,s*<0,1,1>) #end
#if(s.y) addpointssgn(a*<1,-1,1>,s*<0,0,1>) #end
#if(s.z) addpoint(a*<1,1,-1>) #end
#end
#macro addevenpermssgn(a,s)
addpointssgn(a,s)
addpointssgn(<a.y,a.z,a.x>,<s.y,s.z,s.x>)
addpointssgn(<a.z,a.x,a.y>,<s.z,s.x,s.y>)
#end
#macro addpermssgn(a,s)
addevenpermssgn(a,s)
addevenpermssgn(<a.x,a.z,a.y>,<s.x,s.z,s.y>)
#end
#macro addpointsevensgn(a)
addpoint(a)
addpoint(a*<-1,-1,1>)
addpoint(a*<-1,1,-1>)
addpoint(a*<1,-1,-1>)
#end
#macro addevenpermsevensgn(a)
addevenperms(a)
addevenperms(a*<-1,-1,1>)
addevenperms(a*<-1,1,-1>)
addevenperms(a*<1,-1,-1>)
#end
#macro addpermsaltsgn(a)
addevenpermsevensgn(a)
addevenpermsevensgn(<a.x,a.z,-a.y>)
#end
/*#macro addevenpermssgn(a,s) //Calls addevenperms with, for each 1 in s, a.{x,y,z} replaced with {+,-}a.{x,y,z}
addevenperms(a)
#if(s.x) addevenpermssgn(a*<-1,1,1>,s*<0,1,1>) #end
#if(s.y) addevenpermssgn(a*<1,-1,1>,s*<0,0,1>) #end
#if(s.z) addevenperms(a*<1,1,-1>) #end
#end*/
#macro addface(d,l)
#local a=vnormalize(d)/l;
#local f=1;
#local n=0; #while(n<nfaces-.5)
#if(vlength(faces[n]-a)<0.00001) #local f=0; #end
#local n=n+1; #end
#if(f)
#declare faces[nfaces]=a;
#declare nfaces=nfaces+1;
#end
#end
#macro dual()
#declare temp=faces;
#declare faces=points;
#declare points=temp;
#declare temp=nfaces;
#declare nfaces=npoints;
#declare npoints=temp;
#end
#macro autoface() //WARNING: ONLY WORKS IF ALL EDGES HAVE EQUAL LENGTH
//Find edge length
#declare elength=1000;
#local a=0; #while(a<npoints-.5) #local b=0; #while(b<npoints-.5)
#local c=vlength(points[a]-points[b]); #if(c>0.00001 & c<elength) #local elength=c; #end
#local b=b+1; #end #local a=a+1; #end
//Find planes
//#macro planes()
#local a=0; #while(a<npoints-.5)
#local b=a+1; #while(b<npoints-.5)
#if(vlength(points[a]-points[b])<elength+0.00001) #local c=b+1; #while(c<npoints-.5)
#if(vlength(points[a]-points[c])<elength+0.00001)
#local n=vnormalize(vcross(points[b]-points[a],points[c]-points[a]));
#local d=vdot(n,points[a]);
#if(d<0) #local n=-n; #local d=-d; #end
#local f=1;
#local e=0; #while(e<npoints-.5)
#if(vdot(n, points[e])>d+0.00001) #local f=0; #end
#local e=e+1; #end
#if(f)
#declare ld=d;
addface(n,d) //plane { n, d }
#end
#end
#local c=c+1; #end #end
#local b=b+1; #end
#local a=a+1; #end
#end
This_shape_will_be_drawn()
//Random rotations are (hopefully) equally distributed...
#declare rot1=rand(rotation)*pi*2;
#declare rot2=acos(1-2*rand(rotation));
#declare rot3=(rand(rotation)+clock)*pi*2;
#macro dorot()
rotate rot1*180/pi*y
rotate rot2*180/pi*x
rotate rot3*180/pi*y
#end
//Scale shape to fit in unit sphere
#local b=0;
#local a=0; #while(a<npoints-.5)
#local c=vlength(points[a]); #if(c>b) #local b=c; #end
#local a=a+1; #end
#local a=0; #while(a<npoints-.5)
#local points[a]=points[a]/b;
#local a=a+1; #end
#local a=0; #while(a<nfaces-.5)
#local faces[a]=faces[a]*b;
#local a=a+1; #end
//Draw edges
#macro addp(a)
#declare p[np]=a;
#declare np=np+1;
#end
#local a=0; #while(a<nfaces-.5)
#declare p=array[20];
#declare np=0;
#local b=0; #while(b<npoints-.5)
#if(vdot(faces[a],points[b])>1-0.00001) addp(b) #end
#local b=b+1; #end
#local c=0; #while(c<np-.5)
#local d=0; #while(d<np-.5) #if(p[c]<p[d]-.5)
#local f=1;
#local e=0; #while(e<np-.5) #if(e!=c & e!=d & vdot(vcross(points[p[c]],points[p[d]]),points[p[e]])<0)
#local f=0;
#end #local e=e+1; #end
#if(f)
object {
cylinder { points[p[c]], points[p[d]], .01 dorot() }
pigment { colour <.3,.3,.3> }
finish { ambient 0 diffuse 1 phong 1 }
}
#end #end
#local d=d+1; #end
#local c=c+1; #end
#local a=a+1; #end
/*#local a=0; #while(a<npoints-.5)
#local b=a+1; #while(b<npoints-.5)
#if(vlength(points[a]-points[b])<elength+0.00001)
object {
cylinder { points[a], points[b], .01 dorot() }
pigment { colour <.3,.3,.3> }
finish { ambient 0 diffuse 1 phong 1 }
}
#end
#local b=b+1; #end
#local a=a+1; #end*/
//Draw points
#local a=0; #while(a<npoints-.5)
object {
sphere { points[a], .01 dorot() }
pigment { colour <.3,.3,.3> }
finish { ambient 0 diffuse 1 phong 1 }
}
#local a=a+1; #end
#if(notwireframe)
//Draw planes
object {
intersection {
#local a=0; #while(a<nfaces-.5)
plane { faces[a], 1/vlength(faces[a]) }
#local a=a+1; #end
//planes()
//sphere { <0,0,0>, 1 }
//sphere { <0,0,0>, ld+.01 inverse }
dorot()
}
pigment { colour rgbt <.8,.8,.8,.4> }
finish { ambient 0 diffuse 1 phong flashiness #if(withreflection) reflection { .2 } #end }
//interior { ior 1.5 }
photons {
target on
refraction on
reflection on
collect on
}
}
#end
// CCC Y Y PP
// C Y Y P P
// C Y PP
// C Y P
// CCC Y P
#local a=0;
#while(a<11.0001)
light_source { <4*sin(a*pi*2/11), 5*cos(a*pi*6/11), -4*cos(a*pi*2/11)> colour (1+<sin(a*pi*2/11),sin(a*pi*2/11+pi*2/3),sin(a*pi*2/11+pi*4/3)>)*2/11 }
#local a=a+1;
#end
background { color <1,1,1> }
camera {
perspective
location <0,0,0>
direction <0,0,1>
right x/2
up y/2
sky <0,1,0>
location <0,0,-4.8>
look_at <0,0,0>
}
global_settings {
max_trace_level 40
photons {
count 200000
autostop 0
}
}
File:Hexahedron.svg estas vektora versio de ĉi tiu bildo. Ĝi estu uzata anstataŭ la rastruma bildo.
File:Hexahedron.jpg → File:Hexahedron.svg
Pliajn informojn vidu ĉe Help:SVG.
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Dosierhistorio
Alklaku iun daton kaj horon por vidi kiel la dosiero tiam aspektis.
Dato/Horo | Bildeto | Grandecoj | Uzanto | Komento | |
---|---|---|---|---|---|
nun | 20:28, 6 jan. 2005 | 742 × 826 (51 KB) | Kjell André | A Hexahedron (cube). A regular polyhedron. |
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