Tag Function creation -- Asymptote Gallery

🔗Asymptote Gallery Tagged by “Function creation” #99

🔗fractales-fig001

$Figure fractales 001 Generated with Asymptote$

// From documentation of Asymptote
size(250);

real a=3;
real b=4;
real c=hypot(a,b);

transform ta=shift(c,c)*rotate(-aCos(a/c))*scale(a/c)*shift(-c);
transform tb=shift(0,c)*rotate(aCos(b/c))*scale(b/c);

picture Pythagorean(int n) {
  picture pic;
  fill(pic,scale(c)*unitsquare,1/(n+1)*green+n/(n+1)*brown);
  if(n == 0) return pic;
  picture branch=Pythagorean(--n);
  add(pic,ta*branch);
  add(pic,tb*branch);
  return pic;
}

add(Pythagorean(12));

🔗fractales-fig002

$Figure fractales 002 Generated with Asymptote$

Show fractales/fig0020.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Surveys | Fractals
Tags : #Fractals | #Recursion | #Transform | #Function (creating)

size(10cm,0);

transform scale(pair center, real k) {
  return shift(center)*scale(k)*shift(-center);
}

path trk=(0,0)--(0,1);

void tree(path p, int n, real a=30, real b=40, real r=.75) {
  if (n!=0) {
    pair h=point(p,length(p));
    transform tb=rotate(180-b,h)*scale(h,r);
    transform ta=rotate(-180+a,h)*scale(h,r);
    draw(p,n/3+1/(n+1)*green+n/(n+1)*brown);
    tree(tb*reverse(p),n-1,a,b,r);
    tree(ta*reverse(p),n-1,a,b,r);
  }
}

tree(trk,12,a=25,b=40,r=.75);

🔗fractales-fig003

$Figure fractales 003 Generated with Asymptote$

// Barnsley's fern
// Fougère de Barnsley

size(5cm,0);

real ab=85, ac=-5;
real rc=.85, rb=-.31;
path trk=(0,0)--(0,1);

transform ta=shift(0,1)*rotate(ab)*scale(rb);
transform tb=shift(0,1)*rotate(-ab)*scale(rb);
transform tc=shift(0,1)*rotate(ac)*scale(rc);

picture fern(int n) {
  picture opic;
  draw(opic,trk^^ta*trk^^tb*trk^^tc*trk);
  if (n==0) return opic;
  picture branch=fern(n-1);
  add(opic,branch);
  add(opic,ta*branch);
  add(opic,tb*branch);
  add(opic,tc*branch);
  return opic;
}

add(fern(6));

🔗fractales-fig006

$Figure fractales 006 Generated with Asymptote$

Show fractales/fig0060.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Surveys | Fractals
Tags : #Fractals | #Recursion | #Random | #Function (creating)

//From documentation of Asymptote
size(10cm);

// Draw Sierpinski triangle with top vertex A, side s, and depth q.
void Sierpinski(pair A, real s, int q,
                bool top=true, bool randcolor=false) {
  pair B=A-(1,sqrt(2))*s/2;
  pair C=B+s;
  if(top) draw(A--B--C--cycle);
  if (randcolor) {
    filldraw((A+B)/2--(B+C)/2--(A+C)/2--cycle,
             (.33*rand()/randMax*red+.33*rand()/randMax*green+.33*rand()/randMax*blue));
  } else draw((A+B)/2--(B+C)/2--(A+C)/2--cycle);
  if(q > 0) {
    Sierpinski(A,s/2,q-1,false,randcolor);
    Sierpinski((A+B)/2,s/2,q-1,false,randcolor);
    Sierpinski((A+C)/2,s/2,q-1,false,randcolor);
  }
}

Sierpinski((0,1), 1, 5, randcolor=true);

🔗generalities-fig099

Figure generalities 099 Generated with Asymptote

size(6cm,0);

//Return Circle AB diameter
path circle(pair A, pair B)
{
  return shift(midpoint(A--B))*scale(abs(A-B)/2)*unitcircle;
}

pair A=(0,0), B=(1,0), C=(2,0);
path cleAB=circle(A,B);
path cleAC=circle(A,C);

for(real t=0; t<length(cleAB); t+=0.01)
  fill(circle(point(cleAB,t),point(cleAC,t)));

🔗generalities-fig152

Figure generalities 152 Generated with Asymptote

size(0,0);

pair inversion(pair O, real k, pair M)
{
  return (O + k*unit(M-O)/abs(M-O));
}

guide inversion(pair O, real k, path M)
{
  guide opath=inversion(O,k,point(M,0));
  for (real i=0; i<=length(M); i+=length(M)/100)
    opath = opath .. inversion(O,k,point(M,i));
  return opath .. cycle;
}

real u=10cm;
path [] p;
path A = scale(u)*unitcircle;
path B = scale(3)*A;
pair z = rotate(10)*(5u,0);


draw(inversion( z, 2*u^2, A ),linewidth(1pt));
draw(inversion( z, 2*u^2, B ),linewidth(1pt));

p[0] = shift(2u,0)*scale(u)*unitcircle;

for (int i=0; i<=5; ++i)
  {
    if (i!=0) p[i] = rotate(360/6)*p[i-1];
    draw(inversion( z, 2 (u^2), p[i] ));
  }

🔗generalities-fig153

Figure generalities 153 Generated with Asymptote

Show generalities/fig1540.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Function creation | #Loop/for/while

size(10cm,0);

path unitpolygon(int n)
{
  guide opath;
  for (int i=1; i<=n; ++i)
    opath=opath--rotate((i-1)*360/n)*E;
  return opath--cycle;
}

for (int i=3; i<9; ++i)
  draw(shift(2.5*(i%3),-2.5*quotient(i,3))*unitpolygon(i));

🔗generalities-fig161

Figure generalities 161 Generated with Asymptote

Show generalities/fig1620.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Circle | #Loop/for/while | #Function creation

size(6cm,0);

pair A=2expi(pi/2);

pair homography(pair z)
{
  return (z^2+A)/(z+2);
}

guide image;
pair tpt;

draw(unitcircle);
for(real t=0; t<length(unitcircle);t+=.05)
  {
    tpt=homography(point(unitcircle,t));
    image=image..tpt;
    draw(point(unitcircle,t)--tpt,dotted);
  }
draw(image..cycle,red);

🔗generalities-fig176

Figure generalities 176 Generated with Asymptote

Show generalities/fig1770.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Circle | #Intersection | #Function creation

size(6cm,0);

import math;

pair A=(0,0), B=(1,.5);
path cle=shift(1.75,2.5)*unitcircle;
pair pt, ptp;

pair project(pair pt, pair A, pair B)
  {
    return extension(pt,pt-dir(90+degrees(A-B,false)),A,B);
  }

draw(A--B);
draw(cle);

for (real t=0; t<=4; t+=.01)
  {
    pt=point(cle,t);
    ptp=project(pt,A,B);
    dot(ptp, red);
    draw(pt--ptp,dotted);

  }

🔗generalities-fig180

Figure generalities 180 Generated with Asymptote

size(6cm,0);
import math;

pair project(pair pt, pair A, pair B)
  {
    return extension(pt,pt-dir(90+degrees(A-B,false)),A,B);
  }


pair ecenter(pair A, pair B, pair C)
  {
    return extension(A, A+rotate(90)*dir(A--B,A--C), B, B+rotate(90)*dir(B--A,B--C));
  }

path ecircle(pair A, pair B, pair C)
  {
    return shift(ecenter(A,B,C))*scale(abs(ecenter(A,B,C)-project(ecenter(A,B,C),B,C)))*unitcircle;
  }

pair A=(0,0), B=(3,0), C=(3,4);
path tr=A--B--C--cycle;

draw(ecircle(A,B,C));
draw(ecircle(B,C,A));

pen p=linewidth(1pt);
drawline(A,B, p);
drawline(A,C, p);
drawline(B,C, p);

🔗randomwalk-fig001

Figure randomwalk 001 Generated with Asymptote

Show randomwalk/fig0010.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Surveys | Random Walk (3D)
Tags : #Random | #Function (creating) | #Array | #Loop/for/while

import three;
settings.render=0;

// The available directions of steps
triple[] dirs={X,-X,Y,-Y,Z,-Z};
dirs.cyclic=true;

// Return the nodes of the path
triple[] randWalk(real Srnd(), int n)
{
  triple[] randPath;
  triple camera=1e10*currentprojection.camera;
  triple pos=O, tpos;
  int R;
  for (int i=0; i < n; ++i) {
    R=round(Srnd());
    tpos=pos+dirs[R];
    randPath.push(tpos);
    pos=tpos;
  }
  return randPath;
}
triple[] randWalk(int Srnd(), int n)
{
  real R(){ return Srnd();}
  return randWalk(R,n);
}

void drawWalk(triple[] nodes, pen p=white)
{
  triple camera=currentprojection.camera;
  if(currentprojection.infinity)
    camera *= max(abs(minbound(nodes)),abs(maxbound(nodes)));
  real[][] depth;
  for(int i=0; i < nodes.length-1; ++i) {
    real d=abs(camera-0.5*(nodes[i]+nodes[i+1]));
    depth.push(new real[] {d,i});
  }
  depth=sort(depth);
  triple M=nodes[round(depth[0][1])];
  triple m=nodes[round(depth[depth.length-1][1]+1)];
  // Draw from farthest to nearest
  while(depth.length > 0) {
    real[] a=depth.pop();
    int i=round(a[1]);
    draw(nodes[i]--nodes[i+1],abs(nodes[i]-m)/abs(M-m)*p);
  }
}


size(18cm);
currentprojection=orthographic((1,1,1));

drawWalk(randWalk(rand,50000),cyan);
shipout(bbox(3mm,Fill));

🔗tiling-fig001

Figure tiling 001 Generated with Asymptote

Show tiling/fig0010.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Surveys | Tiling
Tags : #Tiling | #Function (creating) | #Picture

size(10cm,0);

picture pavehexagonal(int depth=1)
{
  picture opic;
  path hexa=polygon(6);
  pair center;
  real a,ap,r,rp,r_d=180/pi;

  for(int j=0; j<depth; ++j)
    {
      for (int i=1; i<=6; ++i)
	{
	  a=i*60-30;
	  r=j*sqrt(3);
	  center=r*(rotate(a)*(1,0));
	  filldraw(opic, shift(center)*hexa, j/depth*.8red+(1-j/depth)*.8*blue);
	  //Uncomment to see centers of hexagons
	  dot(opic, shift(center)*midpoint(point(hexa,0)--point(hexa,3)));
	  //Uncomment to see circles passing by centers
	  //draw(opic, scale(r)*unitcircle, j/depth*red+(1-j/depth)*blue);
	  rp=r;
	  ap=0;
	  for (real k=0; k<j-1; ++k)
	    {
	      r=sqrt((1.5*(j-1 - k))^2 + 3/4*(j+1 + k)^2);
	      ap+=r_d*acos((rp^2 + r^2 - 3)/(2*r*rp));
	      center=r*(rotate(a + ap)*(1,0));
	      filldraw(opic, shift(center)*hexa, j/depth*.8*red+(1-j/depth)*.8*blue);
	      //Uncomment to see the centers of hexagons
	      //dot(opic, shift(center)*midpoint(point(hexa,0)--point(hexa,3)));
	      rp=r;
	      //Uncomment to see circles passing by centers
	      //draw(opic, scale(r)*unitcircle, j/depth*red+(1-j/depth)*blue);
            }
        }
    }
  return opic;
}


add(pavehexagonal(7));

🔗various-fig002

Figure various 002 Generated with Asymptote

Show various/fig0200.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Miscellaneous
Tags : #Loop/for/while | #Fill/Unfill | #Basis | #Function (creating)

size(10cm);
path g=box((-1,-1),(1,1));
pen [] col= new pen[]{gray,yellow};

path pairToSquare(pair pt){ return pt -- I*pt -- -pt -- -I*pt --cycle; }

int nb=10;
for (int i=0; i<nb; ++i)
  {
    filldraw(g,col[i%2]);
    g=pairToSquare(relpoint(g,1/16));
  }