Datoteka:Hexahedron.jpg

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Sažetak

OpisHexahedron.jpg	English: A Hexahedron (cube). A regular polyhedron.
Izvor	see below
Autor	Izvorno postavio Cyp na Wikipediji na engleskom jeziku

Dostupna je vektorska inačica (SVG) ove slike. Trebala bi se koristiti umjesto ove rasterske slike ako je kvalitetnija.

File:Hexahedron.jpg → File:Hexahedron.svg

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Na drugim jezicima

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Licencija

Dozvoljava se umnožavanje, dijeljenje i/ili mijenjanje ovog dokumenta pod uvjetima GNU-ove licence za slobodnu dokumentaciju, inačica 1.2 ili kasnija ako ju je objavio Free Software Foundation; bez nepromjenjivih ili obveznih dijelova i bez teksta na naslovnoj i/ili posljednjoj stranici. Kopija licencije je uključena u odjeljak naslovljen GNU-ove licence za slobodnu dokumentaciju.

	Ova datoteka je licencirana pod Creative Commons Imenovanje-Dijeli pod istim uvjetima 3.0 nelokaliziranom licencijom.

	Slobodno smijete: dijeliti – umnožavati, distribuirati i javnosti priopćavati djelo remiksirati – prerađivati djelo Pod sljedećim uvjetima: imenovanje autora – Morate pripisati odgovarajuće autorske zasluge, dati poveznicu na licenciju, te naznačiti jesu li načinjene promjene autorskog djela. Prethodno navedeno možete učiniti na svaki razuman način, ali ne na način koji bi sugerirao da Vi ili Vaše korištenje licencorova djela ima izravno licencorovo odobrenje. dijeli pod istim uvjetima – Ako ovo djelo izmijenite, preoblikujete ili stvarate na osnovu tog materijala, svoje doprinose morate distribuirati pod istom ili kompatibilnom licencijom kao što je i licencija originala.
	Ova oznaka za licenciranje dodana je datoteci kao dio GFDL ažuriranja licnciranja.CC BY-SA 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
  }
}

Dostupna je vektorska inačica (SVG) ove slike. Trebala bi se koristiti umjesto ove rasterske slike.

File:Hexahedron.jpg → File:Hexahedron.svg

Za više informacija o vektorskoj grafici, pročitajte o prelasku Zajedničkog poslužitelja na SVG.
Također pročitajte informacije o podršci MediaWiki softvera slikama u SVG formatu.

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	Datum/Vrijeme	Minijatura	Dimenzije	Suradnik	Komentar
sadašnja	22:28, 6. siječnja 2005.		742 × 826 (51 KB)	Kjell André	A Hexahedron (cube). A regular polyhedron.

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