Tag Path -- Asymptote Gallery

🔗Asymptote Gallery Tagged by “Path” #68

🔗generalities-fig014

Show generalities/fig0140.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Size

size(6cm,6cm);

pair A=(0,0), B=(1,0), C=(0,1);
draw (A--B--C);

🔗generalities-fig015

Show generalities/fig0150.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Size

size(6cm, 6cm);
pair A=(0,0), B=(1,0), C=(0,1);
draw (A--B--C--cycle);

🔗generalities-fig016

Show generalities/fig0160.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Array | #Path

size(6cm, 6cm);

pair [] A;
A[0]=(-1, -1);
A[1]=( 1, -1);
A[2]=( 1,  1);
A[3]=(-1,  1);
draw (A[0]--A[1]--A[2]--A[3]--cycle);
draw (A[0]--A[2]);
draw (A[1]--A[3]);

🔗generalities-fig017

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Categories : Examples 2D | Generalities
Tags : #Basis | #Point/Dot | #Path | #Size

size(6cm,6cm);

draw(unitsquare);
dot((0,0)--(1,1)--(0,1)--(1,0));
draw((0,0)--(1,1));
draw((1,0)--(0,1));

🔗generalities-fig018

Show generalities/fig0180.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Point/Dot | #Path | #Size

size(6cm,3cm,false);

draw(unitsquare);
dot((0,0)--(1,1)--(0,1)--(1,0));
draw((0,0)--(1,1));
draw((1,0)--(0,1));

🔗generalities-fig020

Show generalities/fig0200.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Point/Dot | #Line type | #Transform/scale/shift/rotate | #Unitsize | #Path

unitsize(3cm);

pair A=(0,0), B=(1,0), C=(0,1);
path trig;
trig=A--B--C--cycle;
draw(trig);
dot(trig,linewidth(4bp));
dot(shift(3,0)*trig,red+4bp);

🔗generalities-fig021

Show generalities/fig0210.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Position

size(6cm,6cm);

pair A, B, C;
A=(0,0); B=(1,0); C=(0,1);
draw(A--B--C--cycle);
draw (midpoint(A--B) -- C);
draw (B+0.5*(C-B) -- A);
draw (interp(A,C,0.5) -- B);

🔗generalities-fig022

Show generalities/fig0220.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Position

size(6cm,6cm);

pair A, B, C;
A=(0,0); B=(1,0); C=(0,1);
draw(A--B--C--cycle);
draw (midpoint(A--B) -- C);
draw (B+0.5*(C-B) -- A);
draw (interp(A,C,0.5) -- B);
dot(A/3 + B/3 + C/3);

🔗generalities-fig023

Show generalities/fig0230.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Line type | #Path

size(6cm,0);

pair A=(0,0), B=(1,0), C=(0,1);
draw(A--B--C--cycle);
draw(A--B,linewidth(4bp));

🔗generalities-fig024

Show generalities/fig0240.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Line type | #Path

size(6cm,0);

pair A=(0,0), B=(1,0), C=(0,1);
draw(A--B--C--cycle);
draw(A--B,(red+green));

🔗generalities-fig025

Show generalities/fig0250.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Line type | #Path

size(6cm,0);

pair A=(0,0), B=(1,0), C=(0,1);

draw(A--B,.8white+6bp);
draw(A--C,.6white+6bp);
draw(B--C,.4white+6bp);

draw(A--B--C--cycle,yellow);

🔗generalities-fig026

Show generalities/fig0260.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Line type | #Path

size(8cm,0);

path p1=(0,0)--(1,1);
path p2=(2,0)--(3,1);

draw(p1,linewidth(5mm));
draw(p2,linewidth(5mm));
draw(p1--p2, 3mm+.8blue);
draw(reverse(p1)--p2, 1mm+.8red);

🔗generalities-fig052

Show generalities/fig0520.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Fill/Unfill | #Shading | #Array | #Path

pen[][] p={{rgb(black)}, {rgb(.8red)}};

latticeshade((0,0)--(0,6cm)--(6cm,0)--cycle, p);

🔗generalities-fig060

Show generalities/fig0600.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Fill/Unfill | #Path

size(8cm,0);

pair A, B, C, D;
A=(0,0); B=(1,0);
C=(1,1); D=(0,1);
fill(A--C--B--D--cycle,grey);

🔗generalities-fig061

Show generalities/fig0610.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Fill/Unfill | #Path

size(8cm,0);

pair A, B, C, D;
A=(0,0); B=(1,0);
C=(1,1); D=(0,1);
filldraw(A--C--B--D--cycle,grey);

🔗generalities-fig085

Show generalities/fig0850.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Label | #Path

size(6cm,0);
pair A=0, B=(1,0), C=(1,1);

draw("$1$",A--B);
draw("$1$",B--C);
draw("$\sqrt{2}$",C--A);

🔗generalities-fig086

Show generalities/fig0860.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Label | #Path | #Tex/latex features | #Align | #Rotate

size(6cm,0);
pair A=0, B=(1,0), C=(1,1);

draw("$1$",A--B);
draw("$1$",B--C);

// draw(rotate(dir(C--A))*"$\sqrt{2}$",C--A);
draw(Label("$\sqrt{2}$",Rotate(-dir(C--A))),C--A);

🔗generalities-fig087

Show generalities/fig0870.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Label | #Path | #Align | #Rotate

size(6cm,0);
path g=(1,1)--(3,2);
draw(Label("a text",Rotate(dir(g))), g);
draw(Label("a text",red,Rotate(-dir(g)),align=I*dir(g)), g);

🔗generalities-fig092

Show generalities/fig0920.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Circle

size(6cm,0);

draw(E--N--W--S--cycle,.5red+1mm);

draw(E..N..W..S..cycle);
dot(E..N..W..S..cycle,red);

🔗generalities-fig093

Show generalities/fig0930.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Size | #Path | #Circle

size(0,0);
pair O=0;

draw(circle(O,4cm));
dot(circle(O,4cm), red+4bp);

🔗generalities-fig094

Show generalities/fig0940.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Size | #Path | #Circle

size(6cm);

draw(unitcircle, dot);
dotfactor*=3;
draw(shift(-0.5,-0.5)*unitsquare, dot(blue,Fill(red)));

🔗generalities-fig095

Show generalities/fig0950.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Size | #Path | #Transform/scale/shift/rotate

size(0,0);

real R=4cm;

draw(scale(R)*unitcircle);
dot((0,0),linewidth(4bp));
dot((R*cos(pi/6),R*sin(pi/6)),red+8bp);

🔗generalities-fig096

Show generalities/fig0960.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Size | #Path

size(6cm,0);

import graph;

path PerfectCircle=Circle((0,0),1);

draw(PerfectCircle,linewidth(2mm));
dot(PerfectCircle,.8red);

🔗generalities-fig097

Show generalities/fig0970.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Size | #Path | #Circle

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);

draw(circle(A,B));
dot(A--B);

🔗generalities-fig098

Show generalities/fig0980.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Size | #Path | #Circle

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=(3,0), C=(2,1);

draw(A--B,.8blue);
draw(A--C,.8red);
draw(B--C,.8green);
draw(circle(A,B),.8blue);
draw(circle(A,C),.8red);
draw(circle(B,C),.8green);

🔗generalities-fig099

Show generalities/fig0990.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Size | #Path | #Circle | #Function creation

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-fig111

Show generalities/fig1120.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Point/Dot | #Path

size(6cm,0);
import roundedpath;

pair A=(0,0), B=(0,1), C=(1,0), D=(1,1);

draw(roundedpath(A--B--C--D,.5));
dot(A--B--C--D);

🔗generalities-fig122

Show generalities/fig1230.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Fill/Unfill

//From documentation of Asymptote
size(0,6cm);
guide center = (0,1){W}..tension 0.8..(0,0){(1,-.5)}..tension 0.8..{W}(0,-1); 

draw((0,1)..(-1,0)..(0,-1));
filldraw(center{E}..{N}(1,0)..{W}cycle);
unfill(circle((0,0.5),0.125));
fill(circle((0,-0.5),0.125));

🔗generalities-fig123

Show generalities/fig1240.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Circle

size(8cm);
draw(unitcircle, linewidth(bp));
pen p;
for (int t=-88; t <= 88; t += 2) {
  if(t%5 == 0) {
    p=linewidth(bp);
    draw((0,1){dir (t-90)}..{dir (270-t)}(0,-1), linewidth(bp));
  } else p=currentpen;
  draw((Cos(t),Sin(t)){dir(180+t)}..{dir(180-t)}(-Cos(t),Sin(t)), p);
}

🔗generalities-fig131

Show generalities/fig1320.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Path

size(0,0);

pair A=0, B=(3cm,5cm), C=(6cm,0);

pair ctrl_rgt_A, ctrl_lft_B, ctrl_rgt_B, ctrl_lft_C;
ctrl_rgt_A=A+2cm*E;
ctrl_lft_B=B+3cm*W;
ctrl_rgt_B=B+3cm*E;
ctrl_lft_C=C+2cm*W;

draw(A..B..C);
draw(A.. controls ctrl_rgt_A and ctrl_lft_B ..B.. controls ctrl_rgt_B and ctrl_lft_C ..C,1mm+grey);
dot(A--B--C,linewidth(6bp));
draw((A--ctrl_rgt_A),Arrow, p=grey);
draw((B--ctrl_rgt_B),Arrow, p=grey);
draw((B--ctrl_lft_B),Arrow, p=grey);
draw((C--ctrl_lft_C),Arrow, p=grey);

🔗generalities-fig132

Show generalities/fig1330.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Path

size(0,0);

pair A=0, B=(3cm,5cm), C=(6cm,0);

pair ctrl_rgt_A, ctrl_lft_B, ctrl_rgt_B, ctrl_lft_C;
ctrl_rgt_A=A+2cm*NE;
ctrl_lft_B=B+5cm*SW;
ctrl_rgt_B=B+2cm*SE;
ctrl_lft_C=C+5cm*NW;

draw(A..B..C);
draw(A.. controls ctrl_rgt_A and ctrl_lft_B ..B.. controls ctrl_rgt_B and ctrl_lft_C ..C,1mm+grey);
dot(A--B--C,linewidth(6bp));
draw((A--ctrl_rgt_A),Arrow, p=grey);
draw((B--ctrl_rgt_B),Arrow, p=grey);
draw((B--ctrl_lft_B),Arrow, p=grey);
draw((C--ctrl_lft_C),Arrow, p=grey);

🔗generalities-fig133

Show generalities/fig1340.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Path

size(8cm);
path p1 = (0,0){up}..(5,4)..(10,0){down};

pair post0=postcontrol(p1,0);
pair pre1=precontrol(p1,1);
pair post1=postcontrol(p1,1);
pair pre2=precontrol(p1,2);

dot(post0^^pre1^^post1^^pre2);
path p2 = (0,0)..controls post0 and pre1..(5,4)..controls post1 and pre2..(10,0); 

draw(p1,2mm+red);
draw(p2,linewidth(1mm));

🔗generalities-fig134

Show generalities/fig1350.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Circle

size(0,0);

path pt1=scale(4cm)*unitcircle;
path pt2=scale(2cm)*unitcircle;

draw(pt1^^pt2);
dot(pt1^^pt2);

🔗generalities-fig135

Show generalities/fig1360.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Circle | #Point/Dot | #Transform/scale/shift/rotate

size(0,0);

path cle=scale(4cm)*unitcircle;

draw(cle);

for(real i=0; i<=length(cle); i+=.2)
  {
    dot(point(cle,i));
    draw((0,0)--point(cle,i),dotted);
  }

🔗generalities-fig136

Show generalities/fig1370.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Circle | #Loop/for/while

size(0,0);

path cle=scale(4cm)*unitcircle;

draw(cle);

for(real i=0; i<=length(cle); i+=.2)
  draw(point(cle,i)--2cm*dir(cle,i)+point(cle,i),Arrow,p=i/length(cle)*red);

🔗generalities-fig137

Show generalities/fig1380.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Circle | #Loop/for/while

size(0,0);

path cle=scale(4cm)*reverse(unitcircle);

draw(cle);

for(real i=0; i<=length(cle); i+=.2)
  draw(point(cle,i)--2cm*dir(cle,i)+point(cle,i),Arrow,p=i/length(cle)*red);

🔗generalities-fig138

Show generalities/fig1390.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Path

size(8cm,0);
pair O=(0,0);
path p=(0,0){dir(0)}..{dir(45)}(2,2){dir(-45)}..{dir(0)}(4,0);

pair En1=dir(p, 1, -1);
pair En2=dir(p, 2, -1);
draw(p);
draw(Label("dir(p,1,-1)", EndPoint), point(p,1)--point(p,1)+En1, red, Arrow);
draw(Label("dir(p,2,-1)", EndPoint), point(p,2)--point(p,2)+En2, red, Arrow);

pair Ep0=dir(p, 0, 1);
pair Ep1=dir(p, 1, 1);
draw(Label("dir(p,0,1)", EndPoint), point(p,0)--point(p,0)+Ep0, blue, Arrow);
draw(Label("dir(p,1,1)", EndPoint, E), point(p,1)--point(p,1)+Ep1, blue, Arrow);

draw(p, dot);

🔗generalities-fig139

Show generalities/fig1400.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Circle | #Loop/for/while

size(0,0);

path cle=scale(4cm)*reverse(unitcircle);

draw(cle);

for(real i=0; i<=length(cle); i+=.2)
  draw(point(cle,i)--(1cm*I*dir(cle,i))+point(cle,i),Arrow,p=i/length(cle)*red);

🔗generalities-fig141

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Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Loop/for/while

size(6cm,0);

path curv=reverse((0,2){dir(-60)}..(1,0)..{dir(60)}(2,2));

draw(curv);

for(real i=0; i<=length(curv); i+=.1)
  draw(point(curv,i)--dir(curv,i)+point(curv,i),grey);

🔗generalities-fig142

Show generalities/fig1430.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Loop/for/while

size(10cm,0);

path curv=reverse((0,2){dir(10)}..(1,0)..{dir(-50)}(3,2));
guide dirc;

draw(curv,linewidth(1mm)+grey);

for(real i=0; i<=length(curv); i+=.005)
  {
    draw(point(curv,i)--dir(curv,i)+point(curv,i),grey+yellow);
    dirc=dirc..dir(curv,i)+point(curv,i);
  }

draw(dirc,grey);

🔗generalities-fig143

Show generalities/fig1440.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Path

// Author: John Bowman
pair[] z=new pair[10]; 
z[0]=(0,100); z[1]=(50,0); z[2]=(180,0); 
for(int n=3; n <= 9; ++n) 
  z[n]=z[n-3]+(200,0); 
path p=z[0]..z[1]---z[2]---z[3] 
&z[3]..z[4]--z[5]::{up}z[6] 
&z[6]::z[7]---z[8]..{up}z[9]; 
defaultpen(linewidth(1));
draw(p, grey); 
dot(p); 

real len=50;
for(int i = 0; i < z.length; ++i) {
  pair z=point(p,i);
  draw(z--z+len*dir(p,i,-1),red);
  draw(z--z+len*dir(p,i,1),blue+dashed);
  draw(z-len*dir(p,i)--z+len*dir(p,i),green+Dotted(defaultpen()));
}

🔗generalities-fig144

Show generalities/fig1450.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Full line

size(10cm,0);
import math;

path cle=unitcircle;
path curv=reverse((1.5,2){dir(-60)}..(2.5,0)..{dir(60)}(3.5,2));

draw(cle);
draw(curv);

pair pt_cle=point(cle, 1.35);
pair pt_dir_cle=dir(cle, 1.35);

drawline((pt_cle - pt_dir_cle), (pt_cle + pt_dir_cle), red);

pair pt_curv=point(curv, dirtime(curv, pt_dir_cle));

drawline((pt_curv - pt_dir_cle), (pt_curv + pt_dir_cle), blue);

🔗generalities-fig147

Show generalities/fig1480.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Transform/scale/shift/rotate

size(0,0);

path p= (5mm,-5mm){right} .. (4cm,0);

for(int i=10; i<360; i+=10)
  draw(rotate(i)*p);

draw(p,red+1mm);

🔗generalities-fig148

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Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Transform/scale/shift/rotate

size(6cm,0);

path p= (1,-1){right} .. (4,0);
pair O=(3,.25);

for(int i=10; i<360; i+=10)
  draw(rotate(i,O)*p);

dot(O,blue);
draw(p,red+1mm);

🔗generalities-fig149

Show generalities/fig1500.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Path

size(8cm,0);

path curv=(0,0)..(1,1)..(1.5,-1)..(3,0);
pair A=(0,-1), B=(3,.75);

defaultpen(1mm);
draw(curv);
draw(reflect(A,B)*curv,.8red);
draw(A--B,grey);

🔗generalities-fig150

Show generalities/fig1510.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Transform/scale/shift/rotate

size(6cm,0);

path cle=unitcircle;

draw(cle,red);
draw(xscale(2)*cle);
draw(yscale(2)*cle);
draw(scale(2)*cle,blue);

🔗generalities-fig151

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Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Transform/scale/shift/rotate | #Circle

size(8cm,0);

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

path cle=unitcircle;
pair A=(4,0);
draw(cle);

draw(scale(A,.5)*cle,red);
draw(scale(A,-.75)*cle,blue);

for (real t; t<length(cle); t+=1)
  draw(point(cle,t)--point(scale(A,-.75)*cle,t),dotted);

dot("$A$",A,N);

🔗generalities-fig152

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Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Transform/scale/shift/rotate | #Circle | #Function creation

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

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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-fig154

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Categories : Examples 2D | Generalities
Tags : #Basis | #Array | #Path | #Loop/for/while | #Direction | #Label

size(0,0);

pair [] P, Q, R, S;
real u=1cm;

for (int i=0; i<=4; ++i)
  P[i] = rotate(i*360/5)*(0,-u);

P[5] = P[0];
for (int i=0; i<=4; ++i)
  Q[i] = 3*midpoint(P[i]--P[i+1]);

Q[5] = Q[0];
for (int i=0; i<=4; ++i)
  R[i] = 1/3*( Q[i] + Q[i+1] + P[i+1] );

R[5] = R[0];
for (int i=0; i<=5; ++i)
  S[i] = 1.5*Q[i];

for (int i=0; i<=4; ++i)
  {
    draw(P[i]   -- P[i+1]);
    draw(P[i+1] -- R[i]);
    draw(Q[i]   -- R[i]);
    draw(R[i]   -- Q[i+1]);
    draw(Q[i]   -- S[i]);
    draw(S[i]   -- S[i+1]);
    label(format("\small$P_%i$",i),P[i],-unit(P[i]));
    label(format("\small$Q_%i$",i),Q[i],rotate(60)*unit(Q[i]));
    label(format("\small$R_%i$",i),R[i],unit(R[i]));
    label(format("\small$S_%i$",i),S[i],unit(S[i]));
  }

🔗generalities-fig155

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Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Array | #Path

size(0,0);

pair [] P, Q, R, S;
real u=2cm;

for (int i=0; i<=4; ++i)
  P[i] = rotate(i*360/5)*(0,-u);

P[5] = P[0];
for (int i=0; i<=4; ++i)
  Q[i] = 3*midpoint(P[i]--P[i+1]);

Q[5] = Q[0];
for (int i=0; i<=4; ++i)
  R[i] = 1/3*( Q[i] + Q[i+1] + P[i+1] );

R[5] = R[0];
for (int i=0; i<=5; ++i)
  S[i] = 1.5*Q[i];

for (int i=0; i<=4; ++i)
  {
    draw(P[i]   -- P[i+1]);
    draw(P[i+1] -- R[i]);
    draw(Q[i]   -- R[i]);
    draw(R[i]   -- Q[i+1]);
    draw(Q[i]   -- S[i]);
    draw(S[i]   -- S[i+1]);
  }

draw(P[2] -- P[3] -- P[4] -- P[0] -- P[1] --
     R[0] -- Q[0] -- R[4] -- Q[4] -- R[3]
     -- Q[3] -- R[2] -- Q[2] --
     S[2] -- S[3] -- S[4] -- S[0] -- S[1] --
     Q[1] -- R[1] -- cycle,
     linewidth(2bp));

🔗generalities-fig163

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Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Path

size(8cm,0);

path apath=(0,0)..(1,1)..(2,.5){dir(0)};

draw(subpath(apath,0,length(apath)/2),1pt+.8red,EndPenMargin);
draw(subpath(apath,length(apath)/2,length(apath)),1pt+.8blue,BeginPenMargin);

🔗generalities-fig164

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Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Path

size(10cm,0);
texpreamble("\usepackage{amsmath}");

path p = (0,0)..(1,1)..(2,.5){dir(0)};
real al    = arclength(p);
real l     = length(p);
pair pt    = point(p,l/2);
pair apt   = arcpoint(p,al/2);

draw(p);
draw(subpath(p,0,arctime(p,al/2)),blue);
dot(pt,red);
dot(apt,blue);

arrow("$\frac{\text{lenght(p)}}{2}$",pt,SSE,1cm);
arrow("$\frac{\text{arclenght(p)}}{2}$",apt,SSW,1cm);
label("\small The sizes of the blue path and the black path are equal",(1,.25));

🔗generalities-fig165

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Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Length

size(10cm,0);

path apath=(0,0)..(1,1)..(2,.5){dir(0)};
real l=length(apath);
real step=l/15;

for(real i=0; i<l-step; i+=step)
  draw(subpath(apath,i,i+step),4bp+(i/l*red+(l-i)/l*blue),PenMargins);
draw(apath);

🔗generalities-fig166

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Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Length | #Margin

size(10cm,0);

path apath=(0,0)..(1,1)..(2,.5){dir(0)};
real l=arclength(apath);
real step=l/15;

path arcpath(path apath, real t1, real t2)
{
  return subpath(apath, arctime(apath,t1), arctime(apath,t2));
}

for(real i=0; i<l-step; i+=step)
  draw(arcpath(apath,i,i+step),4bp+(i/l*red+(l-i)/l*blue),PenMargins);
draw(apath);

🔗generalities-fig167

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Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Label | #Length

unitsize(5cm);

string text="A text along a curve";
path p=(0,0)..(1,1)..(2,0.5){dir(0)};
int n=length(text);
real at=0;
real step=arclength(p)/n;

for (int i=0; i<n; ++i){
  real t=arctime(p,at);
  label(rotate(degrees(angle(dir(p,t),false)))*scale(3)*baseline(substr(text,i,1)),point(p,t));
  at += step;
 }

draw(p,lightgrey);

🔗generalities-fig168

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Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Length | #Label

import labelpath;

unitsize(5cm);
string text="\Huge A text along a curve";
path p=(0,0)..(1,1)..(2,0.5){dir(0)};

labelpath(text,p);
draw(p, lightgrey);

🔗generalities-fig169

Show generalities/fig1700.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Path

size(6cm,0);

path pth1=(0,-0.5)--(2,1);
path pth2=(0,0.5)--(2,-1);

draw(pth1^^pth2);

dot(intersectionpoint(pth1,pth2),red);

🔗generalities-fig170

Show generalities/fig1710.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Path

size(6cm,0);

path p = (0,0){up} .. (2cm,0){up};
path q = (0,1cm){dir(-60)}..(1cm,-1cm)..{dir(60)}(2cm,1cm);

draw(p^^q);
dot(intersectionpoint(p,q) , red);
dot(intersectionpoint(p,reverse(q)) , blue);

🔗generalities-fig171

Show generalities/fig1720.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Path

size(6cm,0);
import math;

pair A=(0,-.5), B=A+dir(45);
pair C=(0,1), D=C+5dir(20);

pair I=extension(A,B,C,D);

path AB=A--B;
path CD=C--D;

draw(AB^^CD);
dot("$I$",I,N,red);
draw(B--I,1pt+dotted);
dot("$A$",A,SE);
dot("$B$",B,SE);
dot("$C$",C,N);
dot("$D$",D,N);

🔗generalities-fig172

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Categories : Examples 2D | Generalities
Tags : #Basis | #Path

size(6cm,0);
import math;

pair A=(0,-.5), B=A+dir(45);
pair C=(0,1)+2dir(20);
path cle=shift(C)*scale(1)*unitcircle;

pair I1=intersectionpoint(A--interp(A,B,2),cle);
pair I2=intersectionpoint(A--interp(A,B,10),cle);

path AB=A--B;

draw(AB^^cle);
dot(I1^^I2,red);
draw(B--I2,1pt+dotted);

🔗generalities-fig173

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Categories : Examples 2D | Generalities
Tags : #Basis | #Path

size(6cm,0);

path Line(pair A, pair B)
{
  return interp(A,B,-100000/arclength(A--B))--interp(A,B,100000/arclength(A--B));
}

path Parallel(pair A, pair dir)
{
  return Line(A,A+dir);
}

pair A=0, B=(1,0), C=(.7,.7);
draw(A--B, .8red);
draw(A--C, .8green);
draw(B--C, .8blue);

label("$A$",A,SW);
label("$B$",B,SE);
label("$C$",C,N);

pair Ap=intersectionpoint(Parallel(B, A-C), Parallel(C, A-B));
pair Bp=intersectionpoint(Parallel(A, B-C), Parallel(C, A-B));
pair Cp=intersectionpoint(Parallel(A, B-C), Parallel(B, A-C));

draw(Ap--Bp, .8red);
draw(Ap--Cp, .8green);
draw(Bp--Cp, .8blue);

label("$A'$",Ap,NE);
label("$B'$",Bp,NW);
label("$C'$",Cp,S);

🔗generalities-fig174

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Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Intersection

size(6cm,0);

path p = (0,0){up} .. (2cm,0){up};
path q = (0,1cm){dir(-60)}..(1cm,-1cm)..{dir(60)}(2cm,1cm);

draw(p, red);
draw(q, blue);
dot(intersectionpoint(p,q));
draw(point(p, intersect(p,q)[0])--postcontrol(p, intersect(p,q)[0]), .8red,Arrow);
draw(point(q, intersect(p,q)[1])--postcontrol(q, intersect(p,q)[1]), .8blue,Arrow);

🔗generalities-fig175

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Categories : Examples 2D | Generalities
Tags : #Basis | #Graph | #Direction | #Path | #Fill/Unfill | #Shipout

import graph;
size(8cm,0);

path a = polargraph(new real(real t){return t;}, 0, 3pi, operator ..);
path b = polargraph(new real(real t){return 2t;}, 0, 3.75pi, operator ..);

real sharp=40;
path c=relpoint(a,1){relpoint(a,1)-postcontrol(a,length(a)-1)}..{dir(sharp)}relpoint(b,1);

fill(a..c..reverse(b)&cycle,0.8*red);
shipout(bbox(2mm, Fill(0.15*blue)));

🔗generalities-fig181

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Categories : Examples 2D | Generalities
Tags : #Basis | #Path

size(6cm,0);
defaultpen(2mm+linecap(0));

path p = (0,0){up} .. (2cm,0){up};
path q = (0,1cm){dir(-60)}..(1cm,-1cm)..{dir(60)}(2cm,1cm);


draw(firstcut(p,q).before, .8red);
draw(firstcut(p,q).after, .8blue);

draw(lastcut(q,p).before, .8green);
draw(lastcut(q,p).after, .8yellow);

🔗generalities-fig182

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Categories : Examples 2D | Generalities
Tags : #Basis | #Path

size(6cm,0);

defaultpen(2mm+linecap(0));

path p = (0,0){up} .. (2cm,0){up};
path q = (0,1cm){dir(-60)}..(1cm,-1cm)..{dir(60)}(2cm,1cm);

real[] ipq=intersect(p,q);
real[] iprq=intersect(p,reverse(q));

draw(subpath(p, 0, ipq[0]), .8red);
draw(subpath(p, ipq[0], iprq[0]), .5red);
draw(subpath(p, iprq[0], length(p)), .3red);

draw(subpath(reverse(q), 0, iprq[1]), .8green);
draw(subpath(reverse(q), iprq[1], length(q)-ipq[1]), .5green);
draw(subpath(reverse(q), length(q)-ipq[1], length(q)), .3green);

🔗generalities-fig183

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Categories : Examples 2D | Generalities
Tags : #Basis | #Path

size(0,0);

defaultpen(linewidth(1bp));
real u=4cm;
pair A, B, C, D, E;
path p, q, r;

A = u*up;
p = interp(A, rotate(72)*A, -.2) -- interp(A, rotate(72)*A,1.2);
for(int i=0; i<=5; ++i)
  draw(rotate(72i)*p);

B = midpoint(A--rotate(72)*A );
C = .8*B;

p = B --- C .. (rotate(2*72)*C){right};
// On allonge le chemin p
p = (point(p,0) - 4mm*dir(p,0.001))
  --
  point(p,0)
  & p &
  point(p,2)
  --
  (point(p,2) + 4mm*dir(p,2));

E = intersectionpoint(p, rotate(72)*p);
q = firstcut(p,shift(E)*scale(2mm)*unitcircle).before;
r = lastcut(p,shift(E)*scale(2mm)*unitcircle).after;

for(int i=0; i<=4; ++i)
  {
    draw(rotate(72i)*q);
    draw( rotate(72i)*r);
    draw(rotate(72i)*A,linewidth(4bp));
    draw(rotate(72i)*B,linewidth(4bp));
    draw(rotate(72i)*C,linewidth(4bp));
  }

🔗generalities-fig184

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Categories : Examples 2D | Generalities
Tags : #Basis | #Venn diagram | #Path | #Array

// Venn diagram // Diagramme de Venn
// Edwards' construction // Construction d'Edwards
import roundedpath;
size(14cm,0);

path [] EdVenn(int n)
{
  path [] opath;
  if (n>=1)
    opath.push(shift(-1.4,-.9)*roundedpath(xscale(2.8)*yscale(.9)*unitsquare,.1));
  if (n>=2)
    opath.push(shift(0,-.9)*roundedpath(xscale(1.4)*yscale(1.8)*unitsquare,.1));
  if (n>=3)
    opath.push(scale(.5)*unitcircle);
  for (int i=1; i<=n-3; ++i)
    {
      pair pcle=point(opath[2],1/(2^i)),
        ccle=intersectionpoint(pcle--(pcle-dir(opath[2],1/(2^i))), (0,0)--(1,0));
      path cle=shift(ccle)*scale(abs(pcle-ccle))*unitcircle;
      real[] p1=intersect(cle, opath[2]);
      path ocle=subpath(cle,-p1[0],p1[0]);
      guide tpath;
      real step=360/(2^i), a=0;
      for (int j=0; j<2^i; ++j)
        {
          tpath=tpath..rotate(a)*ocle;
          a+=step;
        }
      opath.push(tpath..cycle);
    }
    return opath;
}

draw(EdVenn(6));

🔗generalities-fig185

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Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Intersection

size(15cm,0);

srand(rand());
path p1 = randompath(9);
path p2 = randompath(8);
real Minx=min(min(p1).x,min(p2).x);
real Maxx=max(max(p1).x,max(p2).x);
real Miny=min(min(p1).y,min(p2).y);

pair[] inter=intersectionpoints(p1,p2);
int nb=inter.length;
for (int i=0 ; i<nb; ++i)
  {
    dot(inter[i]);
    label("$" + (string) i +"$", inter[i],N);
  }

draw(p1,.8red);
draw(p2,.8green);
label("I found " + (string) nb + " points of intersection.",((Maxx+Minx)/2,Miny),2S);

🔗generalities-fig186

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Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Intersection

size(10cm,0);

pair[] self_intersection(path p, int n=100)
{
  pair[] rpair=new pair[];
  path tpath;
  real [] tpoint;
  real l=length(p);
  int i=1;
  for (real t1=0; t1<l ; t1+=l/n)
    {
      for (real t2=t1+2*l/n; t2<l; t2+=l/n)
        {
          tpoint=intersect(subpath(p,t1,t1+l/n),
                           subpath(p,t2,t2+l/n));
          if (tpoint.length == 2)
            {
              rpair[i]=point(subpath(p,t1,t1+l/n),tpoint[0]);
              ++i;
            }
        }
    }
  return rpair;
}

void dott(pair[] pt, pen p)
{
  for (int i=1 ; i<pt.length; ++i)
    {
      dot(pt[i], p);
    }
}

srand(rand());
path p = randompath(15);

pair[] inter=self_intersection(p);
dott(inter, .8red);
draw(p);

🔗generalities-fig187

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Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Intersection | #Buildcycle | #Transform/scale/shift/rotate | #Circle

size(6cm,0);
path [] c;

c[1] = xscale(2)*unitcircle;
c[2] = shift((0,1))*c[1];
draw(c[1]^^c[2]);
draw(buildcycle(c[1],c[2]), .8red+4bp);

🔗generalities-fig188

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Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Intersection | #Buildcycle | #Transform/scale/shift/rotate | #Array

size(8cm,0);

path a,b,c,d;
a = (-1,-.2){up} .. tension 1.2 .. (1,-.2){down};
transform r90=rotate(90);
b = r90*a;
c = r90*b;
d = r90*c;
path bound=buildcycle(a,b,c,d);
fill(bound, lightgrey);
draw(a^^b^^c^^d,grey);
draw(bound);

🔗generalities-fig189

Show generalities/fig1910.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Intersection | #Buildcycle | #Transform/scale/shift/rotate | #Circle | #Fill/Unfill

size(8cm,0);

path a,b,c;
a = shift(1,0)*scale(2)*unitcircle;
b = rotate(120)*a;
c = rotate(120)*b;

fill(a, red);
fill(b, green);
fill(c, blue);
fill(buildcycle(a,b), red + green);
fill(buildcycle(b,c), green + blue);
fill(buildcycle(c,a), blue + red);
fill(buildcycle(a,b,c), white);

draw(a^^b^^c);

🔗generalities-fig190

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Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Circle | #Fill/Unfill

size(0,0);

path pt1=scale(2cm)*unitcircle;
path pt2=scale(1cm)*unitcircle;

filldraw(pt1^^pt2,yellow+.9white);

🔗generalities-fig191

Show generalities/fig1930.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Intersection | #Transform/scale/shift/rotate | #Circle

size(0,0);

path pt1=scale(2cm)*unitcircle;
path pt2=scale(1cm)*unitcircle;

filldraw(pt1^^pt2,evenodd+yellow+.9white);

🔗generalities-fig192

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Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Intersection | #Transform/scale/shift/rotate | #Circle

size(0,0);

path pt1=scale(2cm)*unitcircle;
path pt2=scale(1cm)*unitcircle;
path pt3=shift(0,.5cm)*pt2;

filldraw(pt1^^pt2^^pt3,evenodd+yellow+.9white);

🔗generalities-fig193

Show generalities/fig1950.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Intersection | #Transform/scale/shift/rotate | #Circle

size(0,0);

path pt1=scale(2cm)*unitcircle;
path pt2=scale(1cm)*unitcircle;
path pt3=shift(0,1.5cm)*pt2;

filldraw(pt1^^pt2^^pt3,evenodd+yellow+.9white);

🔗geometry-fig015

Show geometry/fig0150.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Line | #Intersection | #Path

size(12cm,0);
import geometry;
import base_pi;
dotfactor*=2;

currentcoordsys=cartesiansystem((0,0),i=(1,0.5),j=(-1,1));
coordsys Rp=currentcoordsys;
show("$O'$","$\vec{u}$","$\vec{v}$", Rp, xpen=invisible);

path cle=randompath(20);
draw(cle);

point A=(0,1.5), B=(1,-0.5);

line l=line(A,B);
draw(l);

/*<asyxml><view file="modules/geometry.asy" type="pair[]" signature="intersectionpoints(line,path)"/></asyxml>*/
dot(intersectionpoints(l,cle));

🔗geometry-fig026

Show geometry/fig0260.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Path | #Point | #Pair

import geometry;

size(5cm,0);

point M=(1,1);
point N=(0.25,0.28);
point P=(0.75,0.66);

path g=origin--M;
line l=line(origin,M);
pen p=linewidth(5mm);
draw(l,p);

dot(N,p+red);
dot(N,blue);

dot(P,p+red);
dot(P,blue);

draw(box(origin,(1,1)),invisible);

/*<asyxml><view file="modules/geometry.asy" type="bool" signature="@(point,line)"/></asyxml>*/
write(N@l);// Return 'false'

/*<asyxml><view file="modules/geometry.asy" type="bool" signature="onpath(picture,path,point,pen)"/></asyxml>*/
write(onpath(g,N,p));// Return 'true'
write(onpath(g,P,p));// Return 'false'

🔗geometry-fig027

Show geometry/fig0270.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Coords system | #Circle | #Ellipse | #Path

import geometry;
size(8cm,0);

currentcoordsys=cartesiansystem((0,0),i=(1,1),j=(-0.5,.75));
show("","$\vec{u}$", "$\vec{v}$", currentcoordsys, ipen=blue);
show(defaultcoordsys);

point A=(0,0);

real R=2;
/*<asyxml><view file="modules/geometry.asy" type="" signature="struct circle"/></asyxml>*/
circle C=circle(A,R);
draw(C,1.5mm+red);

circle Cp=circle(point(defaultcoordsys,A),R);
draw(Cp,0.75mm+blue);

// One can draw in the 'currentcoordsys' a circle definided in
// the 'defaultcoordsys'
/*<asyxml><view file="modules/geometry.asy" type="path" signature="*(coordsys,path)"/></asyxml>*/
draw(currentcoordsys*Cp, red+blue);

🔗tiling-fig003

Show tiling/fig0030.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Surveys | Tiling
Tags : #Path | #Picture | #Tiling

size(10cm,0);

transform r60=rotate(60);

pair A=(sqrt(3)/2,-.5);
pair B=r60*A, C=r60*B, D=r60*C, E=r60*D, F=r60*E;

path AB=A{dir(90)}..(.6,.5)..B{dir(0)};
path DE=shift(E-A)*reverse(AB);
path BC=B{dir(45)}..(.75,.7){dir(150)}..{dir(135)}(.65,.75){dir(70)}..(.5,1.25)..C{dir(255)};
path EF=shift(F-B)*reverse(BC);
path CD=C{dir(255)}..(-.4,.5){dir(200)}..D{dir(160)};
path FA=shift(A-C)*reverse(CD);

draw(A--B--C--D--E--F--cycle,linewidth(2pt));
draw(AB,2pt+.8red);
draw(DE,2pt+.8red);
draw(BC,2pt+.8blue);
draw(EF,2pt+.8blue);
draw(CD,2pt+.8green);
draw(FA,2pt+.8green);

picture hexa;
picture eye;

filldraw(hexa,AB--BC--CD--DE--EF--FA--cycle,black,white);
filldraw(eye,rotate(5)*xscale(.4)*unitcircle,white);
filldraw(hexa,subpath(AB,1,2)--subpath(BC,0,2){dir(225)}..{dir(245)}cycle,.1red+yellow,white);
draw(hexa,point(BC,0.1){dir(115)}.. (.8,.55) ..(.6,.65){dir(180)},yellow+grey);
filldraw(eye,rotate(5)*xscale(.4)*unitcircle,white);
fill(eye,rotate(5)*shift(0,-.1)*xscale(.25)*scale(.5)*unitcircle);
add(hexa,shift(.6,.9)*scale(.1)*eye);

add(shift(3,0)*hexa);

🔗tube-fig013

Show tube/fig0130.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Tube.asy
Tags : #Tube | #Path | #Graph

import tube;
import graph;
size(12cm,0);
currentprojection=perspective(4,3,6);

real f(real t) {return cos(2*t);}
path g=polargraph(f,0,2pi,10,operator ..)&cycle;
path3 p=path3(scale(20)*g);

draw(tube(p,rotate(60)*polygon(3)), 0.8*red);
draw(tube(shift(Z)*p,scale(0.25)*unitcircle), orange);
draw(shift(1.25*Z)*p);

🔗tube-fig014

Show tube/fig0140.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Tube.asy
Tags : #Tube | #Path | #Graph

import tube;
import graph;
size(12cm,0);
currentprojection=perspective(0,3,6);

real f(real t) {return cos(2*t);}
path g=polargraph(f,0,2pi,10,operator --)&cycle;
path3 p=path3(scale(20)*g);

draw(tube(p,2W--2E), red, bp+black);
draw(tube(p,unitcircle), orange, bp+black);

This page was generated by the Asymptote Exemples Builder
Last modified the 2025-04-20 12:26:19
©2011 Philippe Ivaldi