Vaizdas:Hexahedron.jpg

Didesnės raiškos iliustracija(742 × 826 taškų, rinkmenos dydis: 51 KiB, MIME tipas: image/jpeg)

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English: A Hexahedron (cube). A regular polyhedron.
Šaltinissee below
AutoriusŠią rinkmeną pirmiausia įkėlė Cypanglų kalbos Vikipedija

Licencija

GNU headSuteikiamas leidimas kopijuoti, platinti ir/ar redaguoti šį dokumentą pagal GNU Free Documentation licencijos versijos 1.2 ar bet kurios vėlesnės versijos sąlygas, publikuotas Free Software Foundation; be nekintamų dalių, be priekinių ir galinių tekstinių žymų viršeliuose. Šios licencijos kopija įtraukta dalyje, pavadintoje GNU Free Documentation License.
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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#endThis_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 planesobject {  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;#endbackground { 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  }}

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Data/LaikasMiniatiūraMatmenysNaudotojasPaaiškinimas
dabartinis23:28, 6 sausio 2005Versijos 23:28, 6 sausio 2005 miniatiūra742 × 826 (51 KiB)Kjell AndréA Hexahedron (cube). A regular polyhedron.

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