Asymptote using solids.asy – fig0060

Category: Asymptote,Examples 3D,solids.asyPh. Ivaldi @ 7 h 56 min

Figure 0006
(Compiled with Asymptote version 2.14svn-r5318)
    
// Author: John Bowman
import three;
size(6cm,0);
currentprojection=perspective(10,100,50);
real a=2.5;

draw(scale3(a)*unitsphere,lightyellow);
draw(align(unit(currentprojection.vector()))*scale3(a)*unitcircle3,2bp+red);

Étiquettes : , , ,


Asymptote using solids.asy – fig0070

Category: Asymptote,Examples 3D,solids.asyPh. Ivaldi @ 8 h 56 min

Figure 0007
(Compiled with Asymptote version 2.14svn-r5318)
    
import solids;
size(6cm,0);
currentprojection=orthographic(1,2,2);

surface s=surface(sphere(1,n=10));

material[] p={material(0.8*red,yellow,red,blue), invisible, 0.8*(red+blue) , invisible, 0.8*blue};
p.cyclic=true;
draw(s,p);

Étiquettes : , , ,


Asymptote using solids.asy – fig0080

Category: Asymptote,Examples 3D,solids.asyPh. Ivaldi @ 9 h 56 min

Figure 0008
(Compiled with Asymptote version 2.14svn-r5318)
    
import solids;
import palette;
size(14cm,0);
currentlight=light(gray(0.4),specularfactor=3,viewport=false,
                   (-0.5,-0.25,0.45),
                   (0.5,-0.5,0.5),(0.5,0.5,0.75));

nslice=4*nslice;
surface s=surface(sphere(O,1));
draw(s,lightgrey);

path3 pl=plane((1,0,0),(0,1,0),(0,0,-1));
surface pls=shift(3,3,-1e-3)*scale(-6,-6,1)*surface(pl);
draw(pls,0.7*red);

real dist(triple z){return abs(z-Z);}

surface shade;
for (int i=0; i < currentlight.position.length; ++i) {
  shade=planeproject(pl,currentlight.position[i])*s;
  draw(shade,mean(palette((shade.map(dist)),
                          Gradient(black,gray(0.6)))),
       nolight);
}

Étiquettes : , , , , , ,


Asymptote using solids.asy – fig0090

Category: Asymptote,Examples 3D,solids.asyPh. Ivaldi @ 10 h 56 min

Figure 0009
(Compiled with Asymptote version 2.14svn-r5318)
    
size(8cm,0);
import solids;
import graph3;

//Draw 3D right angle (MA,MB)
void drawrightangle(picture pic=currentpicture,
                    triple M, triple A, triple B,
                    real radius=0,
                    pen p=currentpen,
                    pen fillpen=nullpen,
                    projection P=currentprojection)
{
  p=linejoin(0)+linecap(0)+p;
  if (radius==0) radius=arrowfactor*sqrt(2);
  transform3 T=shift(-M);
  triple OA=radius/sqrt(2)*unit(T*A),
    OB=radius/sqrt(2)*unit(T*B),
    OC=OA+OB;
  path3 tp=OA--OC--OB;
  picture tpic;
  draw(tpic, tp, p=p);
  if (fillpen!=nullpen) draw(tpic, surface(O--tp--cycle), fillpen);
  add(pic,tpic,M);
}

currentprojection=orthographic(10,15,3);

real r=10, h=6; // r=sphere radius; h=altitude section
triple Op=(0,0,h);

limits((0,0,0),1.1*(r,r,r));
axes3("x","y","z");

real rs=sqrt(r^2-h^2); // section radius
real ch=180*acos(h/r)/pi;
path3 arcD=Arc(O,r,180,0,ch,0,Y,50);

revolution sphereD=revolution(O,arcD,Z);
draw(surface(sphereD), opacity(0.5)+lightblue);
draw(shift(0,0,h)*scale3(rs)*surface(unitcircle3),opacity(0.5));

path3 arcU=Arc(O,r,ch,0,0,0,Y,10);
revolution sphereU=revolution(O,arcU,Z);
draw(surface(sphereU), opacity(0.33)+lightgrey);

// right triangle OO'A
triple A=rotate(100,Z)*(rs,0,h);
dot("$O$",O,NW);
dot("$O'$",Op,W);
dot("$A$",A,N);
draw(A--O--Op--A);
drawrightangle(Op,O,A);

if(!is3D())
  shipout(format="pdf", bbox(Fill(paleyellow)));

Étiquettes : , , , , ,


Asymptote using solids.asy – fig0100

Category: Asymptote,Examples 3D,solids.asyPh. Ivaldi @ 11 h 56 min

Figure 0010
(Compiled with Asymptote version 2.14svn-r5318)
    
unitsize(1cm);
import solids;

currentprojection=orthographic(0,100,25);

real r=4, h=7;
triple O=(0,0,0);
triple Oprime=(0,0,3);
triple pS=(0,0,h);
triple pA=(r*sqrt(2)/2,r*sqrt(2)/2,0);
revolution rC=cone(O,r,h,axis=Z,n=1);

draw(surface(rC),blue+opacity(0.5));

skeleton s;
real tOprime=abs(Oprime)/h;
rC.transverse(s,reltime(rC.g,tOprime));
triple pAprime=relpoint(pA--pS,tOprime);
draw(s.transverse.back,dashed);
draw(s.transverse.front);

label("$S$",pS,N);
dot(Label("$O$",align=SE),O);
dot(Label("$O'$",align=SE),Oprime);
dot(Label("$A$",align=Z),pA);
dot(Label("$A'$",align=Z),pAprime);

draw(pS--O^^O--pA^^Oprime--pAprime,dashed);

Étiquettes : , , ,


Asymptote using solids.asy – fig0110

Category: Asymptote,Examples 3D,solids.asyPh. Ivaldi @ 12 h 56 min

Figure 0011
(Compiled with Asymptote version 2.14svn-r5318)
    
import solids;
unitsize(4cm);

currentprojection=orthographic(2,2,1);

draw(cylinder(c=(0,0,-1.5),r=1,h=3), m=3);
draw(sphere(r=1), m=2, frontpen=defaultbackpen);

Étiquettes : , , ,


Asymptote using solids.asy – fig0120

Category: Asymptote,Examples 3D,solids.asyPh. Ivaldi @ 13 h 56 min

Figure 0012
(Compiled with Asymptote version 2.14svn-r5318)
    
import solids;

size(10cm,0);
currentprojection=orthographic(-50,100,40);

//Draw right angle (MA,MB) in 3D
void drawrightangle(picture pic=currentpicture,
                    triple M, triple A, triple B,
                    real radius=0,
                    pen p=currentpen,
                    pen fillpen=nullpen,
                    projection P=currentprojection)
{
  p=linejoin(0)+linecap(0)+p;
  if (radius==0) radius=arrowfactor*sqrt(2);
  transform3 T=shift(-M);
  triple OA=radius/sqrt(2)*unit(T*A),
    OB=radius/sqrt(2)*unit(T*B),
    OC=OA+OB;
  path3 _p=OA--OC--OB;
  picture pic_;
    draw(pic_, _p, p=p);
    if (fillpen!=nullpen) draw(pic_, surface(O--_p--cycle), fillpen);
  add(pic,pic_,M);
}

// *...............Construction starts here................*

real r=1, h=.75;
real gle=60;
real gleA=20;
transform3 tR=rotate(gle,Z);
transform3 tT=shift((0,0,-h));

triple H=(0,0,h),//the label is O in the picture.
  A=rotate(gleA,Z)*(0,r,h),
  F=tR*A,
  B=tR*F,
  D=tT*A,
  C=tT*B,
  Ei=intersectionpoint(H--F,A--B);

revolution r=cylinder(O,r,h,Z);
// draw(surface(r));
draw(r);

draw(O--H, dashed);
draw(O--D--C--cycle^^O--H^^B--C, dashed);

drawrightangle(Ei,H,B,fillpen=black);

dot(Label("$O'$",align=invert(NE+E,O)), O);
// layer();
draw(surface(A--B--C--D--cycle),lightgrey+opacity(.5));

dot(Label("$A$",align=NW), A);
dot(Label("$B$",align=N),B);
dot(Label("$C$",align=S), C);
dot(Label("$D$",align=NW), D);
dot(Label("$E$",align=S), Ei);
dot(Label("$F$",align=S), F);
dot(Label("$O$",align=N), H);

draw(H--B--F--A--cycle^^H--F^^A--B^^A--D);

Étiquettes : , , , ,


Asymptote using solids.asy – fig0130

Category: Asymptote,Examples 3D,solids.asyPh. Ivaldi @ 14 h 56 min

Figure 0013
(Compiled with Asymptote version 2.14svn-r5318)
    
import solids;
size(8cm,0);
currentprojection=orthographic((2, 1, 2));

revolution r=cylinder((0, 0, 0), 1, -10, X);

draw(r);
draw("$x$",O--X,Arrow3);
draw("$y$",O--Y,Arrow3);
draw("$z$",O--Z,Arrow3);

label(XY()*(scale(2.5)*"This is not a cylinder"), (-5,0,1), align=Z);

Étiquettes : , , , ,


Asymptote using solids.asy – fig0140

Category: Asymptote,Examples 3D,solids.asyPh. Ivaldi @ 15 h 56 min

Figure 0014
(Compiled with Asymptote version 2.14svn-r5318)
    
/*
Author: Jens Schwaiger	
With its pleasant authorization.
*/

size(10cm,0);
import bsp;

currentprojection=perspective(10,3,-2);
guide achteck=polygon(8);
real lge=length(point(achteck,1)-point(achteck,0));
int n=8;
face[] faces;
guide3[] sq;
guide3[] tr;
triple a,b,c,d;

a=(point(achteck,0).x,point(achteck,0).y,-lge/2);
b=(point(achteck,1).x,point(achteck,1).y,-lge/2);
c=(point(achteck,1).x,point(achteck,1).y,lge/2);
d=(point(achteck,0).x,point(achteck,0).y,lge/2);

sq[0]=a--b--c--d--cycle;
for(int i=1;i<n;i=i+1) sq[i]=rotate(45*i,Z)*sq[0];
for(int i=0;i<3;i=i+1) sq[n+i]=rotate(90,Y)*sq[i];
for(int i=4;i<7;i=i+1) sq[n-1+i]=rotate(90,Y)*sq[i];
for(int i=2;i<3;i=i+1) sq[12+i]=rotate(90,X)*sq[i];
sq[14]=rotate(90,X)*sq[2];
sq[15]=rotate(90,X)*sq[4];
sq[16]=rotate(90,X)*sq[6];
sq[17]=rotate(90,X)*sq[0];

tr[0]=point(sq[2],3)--point(sq[2],2)--point(sq[14],1)--cycle;
for(int i=1;i<4;i=i+1) tr[i]=rotate(90*i,Z)*tr[0];
tr[4]=reverse(point(sq[2],0)--point(sq[2],1)--point(sq[9],2)--cycle);
for(int i=5;i<8;i=i+1) tr[i]=rotate(90*(i-4),Z)*tr[4];

real hgtsq=3;
triple[][][] pyrsq=new triple[18][4][3];
path3[] pyrsqfc=new path3[4*18];
int nofface=0;
for(int i=0;i<18;i=i+1){
  triple cog=0.5(point(sq[i],0)+point(sq[i],2));
  triple sp=cog+
    hgtsq*unit(cross(point(sq[i],1)-point(sq[i],0),point(sq[i],3)-point(sq[i],0))); 
  for(int j=0;j<3;j=j+1){
    pyrsq[i][j][0]=point(sq[i],j);
    pyrsq[i][j][1]=point(sq[i],j+1);
    pyrsq[i][j][2]=sp;
    pyrsqfc[nofface]=pyrsq[i][j][0]--pyrsq[i][j][1]--pyrsq[i][j][2]--cycle;
    nofface=nofface+1;
  }
  pyrsq[i][3][0]=point(sq[i],3);
  pyrsq[i][3][1]=point(sq[i],0);
  pyrsq[i][3][2]=sp;    
  pyrsqfc[nofface]=pyrsq[i][3][0]--pyrsq[i][3][1]--pyrsq[i][3][2]--cycle;
  nofface=nofface+1;
 }

for(int i=0;i<18*4;i=i+1) faces.push(pyrsqfc[i]);
for(int i=0;i<18*4;i=i+1) filldraw(faces[i],project(pyrsqfc[i]),yellow,black+2.5bp);

path3[] pyrtrfc=new path3[3*8];
real hgttr=2;
int nuoftr=0;

for(int i=0;i<8;i=i+1){
  triple cog=(1/3)*(point(tr[i],0)+point(tr[i],1)+point(tr[i],2));
  triple sp=cog+hgttr*unit(cross(point(tr[i],1)-point(tr[i],0),point(tr[i],2)-point(tr[i],0)));
  pyrtrfc[nuoftr]=point(tr[i],0)--point(tr[i],1)--sp--cycle;
  pyrtrfc[nuoftr+1]=point(tr[i],1)--point(tr[i],2)--sp--cycle;
  pyrtrfc[nuoftr+2]=point(tr[i],2)--point(tr[i],0)--sp--cycle;
  nuoftr=nuoftr+3;
 }

for(int j=0;j<24;j=j+1) faces.push(pyrtrfc[j]);
for(int j=0;j<24;j=j+1) filldraw(faces[4*18+j],project(pyrtrfc[j]),orange+yellow,black+2bp);

add(faces);
shipout(defaultfilename,bbox(0.2cm,black,RadialShade(paleblue,darkblue)));

Étiquettes : , ,


Asymptote using solids.asy – fig0150

Category: Asymptote,Examples 3D,solids.asyPh. Ivaldi @ 16 h 56 min

Figure 0015
(Compiled with Asymptote version 2.14svn-r5318)
    
/*
Author: Jens Schwaiger
With its pleasant authorization.
*/
// PRC/OpenGL version

size(10cm,0);
import graph3;

currentprojection=orthographic(10,3,-2);
// currentlight=nolight;

guide achteck=polygon(8);
real lge=length(point(achteck,1)-point(achteck,0));
int n=8;
guide3[] sq;
guide3[] tr;
triple a,b,c,d;

a=(point(achteck,0).x,point(achteck,0).y,-lge/2);
b=(point(achteck,1).x,point(achteck,1).y,-lge/2);
c=(point(achteck,1).x,point(achteck,1).y,lge/2);
d=(point(achteck,0).x,point(achteck,0).y,lge/2);

sq[0]=a--b--c--d--cycle;
for(int i=1;i<n;i=i+1) sq[i]=rotate(45*i,Z)*sq[0];
for(int i=0;i<3;i=i+1) sq[n+i]=rotate(90,Y)*sq[i];
for(int i=4;i<7;i=i+1) sq[n-1+i]=rotate(90,Y)*sq[i];
for(int i=2;i<3;i=i+1) sq[12+i]=rotate(90,X)*sq[i];
sq[14]=rotate(90,X)*sq[2];
sq[15]=rotate(90,X)*sq[4];
sq[16]=rotate(90,X)*sq[6];
sq[17]=rotate(90,X)*sq[0];

tr[0]=point(sq[2],3)--point(sq[2],2)--point(sq[14],1)--cycle;
for(int i=1;i<4;i=i+1) tr[i]=rotate(90*i,Z)*tr[0];
tr[4]=reverse(point(sq[2],0)--point(sq[2],1)--point(sq[9],2)--cycle);
for(int i=5;i<8;i=i+1) tr[i]=rotate(90*(i-4),Z)*tr[4];

real hgtsq=3;
triple[][][] pyrsq=new triple[18][4][3];
path3[] pyrsqfc=new path3[4*18];
int nofface=0;
for(int i=0;i<18;i=i+1){
  triple cog=0.5(point(sq[i],0)+point(sq[i],2));
  triple sp=cog+
    hgtsq*unit(cross(point(sq[i],1)-point(sq[i],0),point(sq[i],3)-point(sq[i],0)));
  for(int j=0;j<3;j=j+1){
    pyrsq[i][j][0]=point(sq[i],j);
    pyrsq[i][j][1]=point(sq[i],j+1);
    pyrsq[i][j][2]=sp;
    pyrsqfc[nofface]=pyrsq[i][j][0]--pyrsq[i][j][1]--pyrsq[i][j][2]--cycle;
    nofface=nofface+1;
  }
  pyrsq[i][3][0]=point(sq[i],3);
  pyrsq[i][3][1]=point(sq[i],0);
  pyrsq[i][3][2]=sp;
  pyrsqfc[nofface]=pyrsq[i][3][0]--pyrsq[i][3][1]--pyrsq[i][3][2]--cycle;
  nofface=nofface+1;
 }

for(int i=0;i<18*4;i=i+1)
  draw(surface(pyrsqfc[i]),yellow,black+2.5bp);

path3[] pyrtrfc=new path3[3*8];
real hgttr=2;
int nuoftr=0;

for(int i=0;i<8;i=i+1){
  triple cog=(1/3)*(point(tr[i],0)+point(tr[i],1)+point(tr[i],2));
  triple sp=cog+hgttr*unit(cross(point(tr[i],1)-point(tr[i],0),point(tr[i],2)-point(tr[i],0)));
  pyrtrfc[nuoftr]=point(tr[i],0)--point(tr[i],1)--sp--cycle;
  pyrtrfc[nuoftr+1]=point(tr[i],1)--point(tr[i],2)--sp--cycle;
  pyrtrfc[nuoftr+2]=point(tr[i],2)--point(tr[i],0)--sp--cycle;
  nuoftr=nuoftr+3;
 }

for(int j=0;j<24;j=j+1)
  draw(surface(pyrtrfc[j]),orange+yellow,black+2bp);

Étiquettes : , ,