Tag Coords system -- Asymptote Gallery

🔗Asymptote Gallery Tagged by “Coords system” #119

🔗geometry-fig001

Figure geometry 001 Generated with Asymptote

Show geometry/fig0010.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Coords system | #Point | #Pair

size(8cm,0);
import geometry;

/*<asyxml><view file="modules/geometry.asy" type="" signature="struct coordsys"/></asyxml>*/
show(currentcoordsys);

pair a=(0,0.5), b=(1,0.5);
/*<asyxml><view file="modules/geometry.asy" type="" signature="struct point"/></asyxml>*/
point A=a, B=b;

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

🔗geometry-fig002

Figure geometry 002 Generated with Asymptote

Show geometry/fig0020.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Coords system | #Point | #Pair

size(8cm,0);
import geometry;

show(currentcoordsys);

pair a=(0,0.5), b=(1,0.5);
point A=a, B=b;

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

/*<asyxml><view file="modules/geometry.asy" type="coordsys" signature="cartesiansystem(pair,pair,pair)"/></asyxml>*/
currentcoordsys=cartesiansystem((0.5,0.5), i=(0.7,0.7), j=(-0.7,0.7));
show("$O'$", "$\vec{u'}$", "$\vec{v'}$", currentcoordsys, xpen=invisible);

point Ap=a;
/*<asyxml><view file="modules/geometry.asy" type="point" signature="point(coordsys,explicit point)"/></asyxml>*/
point Bp=point(currentcoordsys,B); // same as 'point Bp=b;'

dot("$A'$",Ap);
dot("$B'$",Bp);
dot("$M$",(Ap+Bp)/2);

🔗geometry-fig003

Figure geometry 003 Generated with Asymptote

Show geometry/fig0030.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Coords system | #Point | #Pair

size(8cm,0);
import geometry;

show(currentcoordsys);

pair a=(0,0.5), b=(1,0.5);
point A=a, B=b;

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

/*<asyxml><view file="modules/geometry.asy" type="coordsys" signature="cartesiansystem(pair,pair,pair)"/></asyxml>*/
currentcoordsys=cartesiansystem((0.5,0.5), i=(0.7,0.7), j=(-0.7,0.7));
show("$O'$", "$\vec{u'}$", "$\vec{v'}$", currentcoordsys, xpen=invisible);

point Ap=a;
/*<asyxml><view file="modules/geometry.asy" type="point" signature="point(coordsys,explicit point,real)"/></asyxml>*/
point Bp=point(currentcoordsys,B); // same as 'point Bp=b;'

dot("$A'$",Ap);
dot("$B'$",Bp);
dot("$M$",(Ap+Bp)/2);

draw(Ap--Bp);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="locate(pair)"/></asyxml>*/
draw(locate((0,0))--Bp,blue);

/*<asyxml><view file="modules/geometry.asy" type="pair" signature="locate(point)"/></asyxml>*/
draw((0,0)--locate(Bp),0.8*green);

🔗geometry-fig004

Figure geometry 004 Generated with Asymptote

size(8cm,0);
import geometry;

coordsys R=defaultcoordsys;
show(R);

coordsys Rp=cartesiansystem((0.5,0.5), i=(0.35,0.35), j=(-0.35,0.35));
show("$O'$", "$\vec{\imath'}$", "$\vec{\jmath'}$", Rp, ipen=blue, xpen=invisible);

coordsys Rpp=cartesiansystem((-1,-0.5),
                                      i=rotate(-90)*(0.35,0.35),
                                      j=rotate(-90)*(-0.35,0.35));
show("$O''$", "$\vec{\imath''}$", "$\vec{\jmath''}$", Rpp, ipen=green, xpen=invisible);


pair m=(1,1);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="point(coordsys,pair,real)"/></asyxml>*/
dot("",point(R,m),red); // Same as 'dot("",m,red);'
dot("",point(Rp,m),blue);

point M=m;
/*<asyxml><view file="modules/geometry.asy" type="point" signature="point(coordsys,explicit point,real)"/></asyxml>*/
dot("",point(Rpp,M),green); // Works also with 'point'

pair p=(-0.75,0.75);
point P=point(R,(-0.75,0.75));

dot("$P$",P,2E,4mm+red);

// There are two methods for changing
// the coordinate system of a point (or a pair)

/*<asyxml><view file="modules/geometry.asy" type="pair" signature="/(pair,coordsys)"/></asyxml>*/
dot("$P'$",point(Rp,p/Rp),2S,3mm+blue); // Necessary for 'pair'
dot("$P'$",point(Rp,P/Rp),2N,3mm+blue); // but works with 'point' by casting.

/*<asyxml><view file="modules/geometry.asy" type="point" signature="changecoordsys(coordsys,point)"/></asyxml>*/
dot("$P''$",changecoordsys(Rpp,P),2W,1.5mm+green); // Useful for 'point'.

🔗geometry-fig005

Figure geometry 005 Generated with Asymptote

Show geometry/fig0050.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Coords system | #Point | #Pair

import geometry;
size(8cm,0);

currentcoordsys=cartesiansystem((1.25,0.75),i=(1,1),j=(-1,1));
coordsys Rp=currentcoordsys;
coordsys R=defaultcoordsys;

show("$O$", "$\vec{\imath}$", "$\vec{\jmath}$", R);
show("$O'$","$\vec{u}$","$\vec{u}$", Rp, xpen=invisible);

vector w=(0.125,0.5);
point P=(1,0.5);

dot("$P$",P);
draw(Label("$\overrightarrow{w}$",EndPoint), origin()--origin()+w, Arrow);
draw("$\overrightarrow{O'P}+\overrightarrow{w}$",
     origin()--P+w, Arrow);

dot("$M$",P+w,red);

/*<asyxml><view file="modules/geometry.asy" type="pair" signature="locate(explicit vector)"/></asyxml>*/
draw("$\overrightarrow{w}$", (0,0)--locate(w), W,Arrow);

🔗geometry-fig006

Figure geometry 006 Generated with Asymptote

Show geometry/fig0060.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Coords system | #Point | #Transform/scale/shift/rotate

import geometry;
size(12cm,0);

currentcoordsys=cartesiansystem((1.25,0.75),i=(1,0.5),j=(-1,1));
coordsys Rp=currentcoordsys;
coordsys R=defaultcoordsys;

show(Label("$O$",align=SE), "$\vec{\imath}$", Label("$\vec{\jmath}$",align=E), R);
show("$O'$", "$\vec{u}$", "$\vec{v}$", Rp, xpen=invisible);

vector w=(0.25,0.5);
point P=(1,0.5);

dot("$P$",P,W);
show("$\overrightarrow{w}$", w);

/*<asyxml><view file="modules/geometry.asy" type="transform" signature="rotateO(real)"/></asyxml>*/
point Pp=rotateO(90)*P;

dot("Pp=rotateO(90)*P", Pp, W);

dot("rotate(90,Pp)*P", rotate(90,Pp)*P, W);
/*<asyxml><view file="modules/geometry.asy" type="transform" signature="scale(real,point)"/></asyxml>*/
dot("scale(-2,Pp)*P", scale(-2,Pp)*P, NE);

/*<asyxml><view file="modules/geometry.asy" type="transform" signature="scaleO(real)"/></asyxml>*/
dot("scaleO(2)*P", scaleO(2)*P,red);
/*<asyxml><view file="modules/geometry.asy" type="transform" signature="xscaleO(real)"/></asyxml>*/
dot("xscaleO(2)*P", xscaleO(2)*P);
/*<asyxml><view file="modules/geometry.asy" type="transform" signature="yscaleO(real)"/></asyxml>*/
dot("yscaleO(2)*P", yscaleO(2)*P,W);

vector wp=rotateO(90)*w;

show("$\overrightarrow{w'}$", wp);

draw("$\overrightarrow{w}$", (0,0)--locate(w), W, Arrow);
draw("$\overrightarrow{w'}$", (0,0)--locate(wp), S, Arrow);

🔗geometry-fig007

Figure geometry 007 Generated with Asymptote

import geometry;
size(15cm);

currentcoordsys=cartesiansystem((0,0),i=(1,0.5),j=(-1,0.5));
coordsys R=currentcoordsys;
show(R, xpen=invisible);

point A=(2,2);
dot("A",A,SE);

point B=(3,1.5);
dot("B",B,SE);

point C=A+(4,2);
dot("C",C);

drawline(A,B,red);
drawline(A,C,blue);

/*<asyxml><view file="modules/geometry.asy" type="transform" signature="scale(real,point,point,point,point,bool)"/></asyxml>*/
transform t=scale(2,A,B,A,C);
/*<asyxml><view file="modules/geometry.asy" type="transform" signature="projection(point,point,point,point,bool)"/></asyxml>*/
transform proj=projection(A,B,A,C);

point M=(2,4);
point Mh=proj*M;
dot("$H_M$",Mh,SE);
dot("$M$",M);
point Mp=t*M;
dot("\small$scale(2,A,B,A,C)*M=M'$",Mp,W);
drawline(M,Mh);

point P=(1,-1);
point Ph=proj*P;
dot("$H_P$",Ph,NW);
drawline(P,Ph);
dot("$P$",P);

transform t=scale(-1,A,B,A,C);
point Pp=t*P;
dot("\small$P'=scale(-1,A,B,A,C)*P$",Pp);
draw(P--Pp);

🔗geometry-fig008

Figure geometry 008 Generated with Asymptote

import geometry;
size(10cm,0);

currentcoordsys=cartesiansystem((1.5,1.5),i=(1,0.5),j=(-1,1));
coordsys Rp=currentcoordsys;
coordsys Rs=cartesiansystem((-1.5,1.5),i=(-1,0.5),j=(-1,-1));
coordsys R=defaultcoordsys;

show("$O$","$\vec{\imath}$", "$\vec{\jmath}$", R);
show("$O'$","$\vec{u}$","$\vec{v}$", Rp, xpen=invisible);
show("$O''$","$\vec{u'}$","$\vec{v'}$", Rs, xpen=invisible);

pair w=(0.75,1.5);
draw("$\overrightarrow{w}$",(0,0)--w,Arrow);

pair P=(1,1);
dot("$P$",P);
dot("$P$",point(Rp,P/Rp),N);
dot("$P$",point(Rs,P/Rs),S);

show("$\overrightarrow{w'}$", vector(w));
show("$\overrightarrow{w''}$", vector(Rs,w));

dot("$P'$",point(Rp,P));
dot("$P''$",point(Rs,P));

🔗geometry-fig009

Figure geometry 009 Generated with Asymptote

import geometry;
size(10cm,0);

currentcoordsys=cartesiansystem((1.5,1.5),i=(1,0.5),j=(-1,1));
coordsys Rp=currentcoordsys;
coordsys Rs=cartesiansystem((-1.5,1.5),i=(-1,0.5),j=(-1,-1));
coordsys R=defaultcoordsys;

show("$O$","$\vec{\imath}$", "$\vec{\jmath}$", R);
show("$O'$","$\vec{u}$","$\vec{v}$", Rp, xpen=invisible);
show("$O''$","$\vec{u'}$","$\vec{v'}$", Rs, xpen=invisible);

pair P=(1,1);
dot("$P$",P);

draw(format("$\vert OP\vert\simeq %.2f$",abs(P)),(0,0)--P,Arrows);

point Pp=P;
dot("$P'$",Pp);
vector wp=Pp;
show(format("$\vert O'P'\vert= %.2f$",abs(Pp)), wp, Arrows);

point Ps=point(Rs,P);
dot("$P''$",Ps,S);
vector ws=Ps;
show(format("$\vert O''P''\vert\simeq %.2f$",abs(Ps)), ws, Arrows);

🔗geometry-fig010

Figure geometry 010 Generated with Asymptote

import geometry;
size(10cm,0);

currentcoordsys=cartesiansystem((1.5,1.5),i=(1,0.5),j=(-1,1));
coordsys Rp=currentcoordsys;
coordsys R=defaultcoordsys;

show("$O$","$\vec{\imath}$", "$\vec{\jmath}$", R);
show("$O'$", "$\vec{u}$", Label("$\vec{v}$",align=NE), Rp, xpen=invisible);

pair w=(1.5,0.75);
draw("$\overrightarrow{w}$",(0,0)--w,Arrow);

pair P=(1,-1);
dot("$P$",P);

show("$\overrightarrow{w'}$", vector(w));

dot("$P'$",point(Rp,P),N);

point Ip=I;
dot("$I'$",Ip,N);
dot("$I'*P'$",Ip*point(Rp,P),S);
dot("$I*P'$",I*point(Rp,P),N);

vector wp=Ip*vector(w);
show(Label("$I'*\overrightarrow{w'}$",EndPoint), wp);

vector foo=I*vector(w);
show("$I*\overrightarrow{w'}$", foo);

🔗geometry-fig011

Figure geometry 011 Generated with Asymptote

Show geometry/fig0110.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Coords system | #Point

import geometry;
size(10cm,0);

currentcoordsys=cartesiansystem((1.5,1.5),i=(1,0.5),j=(-1,1));
coordsys Rp=currentcoordsys;
coordsys Rs=cartesiansystem((-1.5,1.5),i=(-1,0.5),j=(-1,-1));
coordsys R=defaultcoordsys;

show("$O$","$\vec{\imath}$", "$\vec{\jmath}$", R);
show("$O'$","$\vec{u}$","$\vec{v}$", Rp, xpen=invisible);
show("$O''$","$\vec{u'}$","$\vec{v'}$", Rs, xpen=invisible);

int n=64;
real step=2pi/n;

for (int i=0; i<n; ++i) {
  pen p=(i/n)*red;
  dot(point(R,R.polar(1,step*i)),p);
  dot(point(Rp,Rp.polar(1,step*i)),p);
  dot(point(Rs,Rs.polar(1,step*i)),p);
}

🔗geometry-fig012

Figure geometry 012 Generated with Asymptote

import geometry;
size(10cm,0);

currentcoordsys=cartesiansystem((2,1),i=(1,0.5),j=(-1,1));
coordsys Rp=currentcoordsys;
coordsys R=defaultcoordsys;

show("$O$","$\vec{\imath}$", "$\vec{\jmath}$", R);
show("$O'$", "$\vec{u}$", "$\vec{v}$", Rp, xpen=invisible);

pair a=(0.5,0.5);
pair b=(-0.5,-1);

point A=point(R,a), B=point(R,b);
dot("$A$",A,NW); dot("$B$",B,S);
line l=line(A,B);

point Ap=a, Bp=b;
dot("$A'$",Ap,W); dot("$B'$",Bp,SE);
line lp=line(Ap,Bp);

draw(l^^lp);

draw(l.A--l.A+l.u,blue,Arrow);
draw(l.A--l.A+l.v,blue,Arrow);
draw(lp.A--lp.A+lp.u,blue,Arrow);
draw(lp.A--lp.A+lp.v,blue,Arrow);

🔗geometry-fig013

Figure geometry 013 Generated with Asymptote

import geometry;
size(10cm,0);

currentcoordsys=cartesiansystem((2,1),i=(1,0.5),j=(-1,1));
coordsys Rp=currentcoordsys;
coordsys Rs=cartesiansystem((-1,2),i=(-1,0.5),j=(-1,-1));
coordsys R=defaultcoordsys;

show("$O$","$\vec{\imath}$", "$\vec{\jmath}$", R);
show("$O'$","$\vec{u}$","$\vec{v}$", Rp, xpen=invisible);
show("$O''$", "$\vec{u'}$", "$\vec{v'}$", Rs, xpen=invisible);

pair a=(0.5,0.5);
pair b=(-0.5,-1);

point A=point(R,a), B=point(R,b);
dot("$A$",A,S); dot("$B$",B,S);
line l=line(A,B);

point Ap=a, Bp=b;
dot("$A'$",Ap); dot("$B'$",Bp,SE);
line lp=line(Ap,Bp);

point As=point(Rs,a), Bs=point(Rs,b);
dot("$A''$",As,S); dot("$B''$",Bs,SE);
line ls=line(As,Bs);

draw(l^^lp^^ls);

dot(intersectionpoint(l,lp),2mm+red);
dot(intersectionpoint(l,ls),2mm+red);
dot(intersectionpoint(lp,ls),2mm+red);

🔗geometry-fig014

Figure geometry 014 Generated with Asymptote

include fig0130;

point w=l.A+1.5*l.v;
draw(Label("$w$",EndPoint),l.A--w,Arrow);

point wp=lp.A+1.5*lp.v;
draw(Label("$w'$",EndPoint),lp.A--wp,Arrow);

point ws=ls.A+1.5*ls.v;
draw(Label("$w''$",EndPoint),ls.A--ws,Arrow);

int n=64;
real step=2pi/n;

for (int i=0; i<n; ++i) {
  point p=B+point(R,R.polar(1,step*i));
  dot(p,sameside(p,w,l) ? black : blue);
  
  point p=Ap+point(Rp,Rp.polar(1,step*i));
  dot(p,sameside(p,wp,lp) ? black : blue);

  point p=As+point(Rs,Rs.polar(1,step*i));
  dot(p,sameside(p,ws,ls) ? black : blue);
}

🔗geometry-fig016

Figure geometry 016 Generated with Asymptote

size(10cm);
import geometry;
dotfactor*=1.5;
linemargin = 5mm;

currentcoordsys=cartesiansystem((2,1),i=(1,1),j=(-4,1));
show(currentcoordsys);

point A=(1,1), B=(2,1);
/*<asyxml><view file="modules/geometry.asy" type="" signature="struct line"/></asyxml>*/
line l1=line(A,B);/*<asyxml><view file="modules/geometry.asy" type="line" signature="line(point,bool,point,bool)"/></asyxml>*/

/*<asyxml><view file="modules/geometry.asy" type="void" signature="draw(picture,Label,line,bool,bool,align,pen,arrowbar,Label,marker)"/></asyxml>*/
draw(l1,red);
dot("$A$",A);
dot("$B$",B);

for (int i=0; i<10; ++i){
  pair bad=(i,l1.slope*i+l1.origin);
  point good=bad;
  draw(Label("bad",align=S),bad,linewidth(2bp));
  draw(Label(good @ l1 ? "good":"bad",align=W),good,linewidth(2bp));
}

🔗geometry-fig017

Figure geometry 017 Generated with Asymptote

unitsize(1cm);
import geometry;
dotfactor*=1.5;
linemargin=5mm;

// currentcoordsys=cartesiansystem((2,1),i=(1,0.5),j=(-1,1));
show(currentcoordsys);

point A=(-3,-1), B=(3,4);
line l1=line(A,B);

draw(l1,red);
dot("$A$",A,SE);
dot("$B$",B,NW);

point M=(2,-2);
dot("$M$",M);

/*<asyxml><view file="modules/geometry.asy" type="line" signature="parallel(point,line)"/></asyxml>*/
draw(parallel(M,l1),red);

/*<asyxml><view file="modules/geometry.asy" type="line" signature="perpendicular(point,line)"/></asyxml>*/
line perp=perpendicular(M,l1);
draw(perp);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="intersectionpoint(line,line)"/></asyxml>*/
point interp=intersectionpoint(l1,perp);
dot(interp,green);

/*<asyxml><view file="modules/geometry.asy" type="void" signature="markrightangle(picture,point,point,point,real,pen,margin,filltype)"/></asyxml>*/
markrightangle(l1.A,interp,rotate(180,interp)*M,size=5mm);

draw(box((-5,-5),(5,5)),invisible);

🔗geometry-fig018

Figure geometry 018 Generated with Asymptote

unitsize(1cm);
import geometry;
dotfactor*=1.5;

currentcoordsys=cartesiansystem((0,0),i=expi(pi/8)*(1.5,0),j=expi(pi/8)*(0,1));
show(currentcoordsys);

point A=(-1,-3), B=(5,2);
line l1=line(A,B);

draw(l1,red);
dot("$A$",A,SE);
dot("$B$",B,NW);

point M=(3,-3);
dot("$M$",M);

/*<asyxml><view file="modules/geometry.asy" type="transform" signature="projection(line)"/></asyxml>*/
point P=projection(l1)*M;
dot("$P$",P,2W);
draw(M--P);
markrightangle(l1.A,P,M);


/*<asyxml><view file="modules/geometry.asy" type="transform" signature="vprojection(line,bool)"/></asyxml>*/
point Q=vprojection(l1)*M;
dot("$Q$",Q,2W);
draw(M--Q);

/*<asyxml><view file="modules/geometry.asy" type="transform" signature="hprojection(line,bool)"/></asyxml>*/
point R=hprojection(l1)*M;
dot("$R$",R,2W);
draw(M--R);

/*<asyxml><view file="modules/geometry.asy" type="transform" signature="projection(line,line,bool)"/></asyxml>*/
point S=projection(l1,line((0,0),(0,1)))*M;
dot("$S$",S,2W);
draw(M--S,red);

draw(box((-1,-4),(7,5)),invisible);

🔗geometry-fig020

Figure geometry 020 Generated with Asymptote

size(12cm);
import geometry;
dotfactor*=1.5;

currentcoordsys=cartesiansystem((2,1),i=(1,1),j=(-4,1));
show(currentcoordsys);

point A=(1,1), B=(2,1);
line l1=line(A,B);

draw(l1);
dot("$A$",A);
dot("$B$",B);

point C=(-1,0), D=(-2,-2);
line l2=line(C,D);

draw(l2);
dot("$C$",C,S);
dot("$D$",D,N);

point M=(2,-0.5);
dot("$M$",M,0.8*red);

/*<asyxml><view file="modules/geometry.asy" type="point[]" signature="sameside(point,line,line)"/></asyxml>*/
point[] Ms=sameside(M,l1,l2);
draw(M--Ms[0]^^M--Ms[1],0.8red);
dot(Ms[0]^^Ms[1],0.8red);

point P=(-3,-1);
dot("$P$",P,S,blue);

point[] Ps=sameside(P,l1,l2);
draw(P--Ps[0]^^P--Ps[1],blue);
dot(Ps[0]^^Ps[1],blue);

point Q=(2,1.5);
dot("$Q$",Q,N,green);

point[] Qs=sameside(Q,l1,l2);
draw(Q--Qs[0]^^Q--Qs[1],green);
dot(Qs[0]^^Qs[1],green);

🔗geometry-fig021

Figure geometry 021 Generated with Asymptote

Show geometry/fig0210.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Coords system | #Line | #Markers

size(12cm);
import geometry;

currentcoordsys=cartesiansystem((2,1),i=(1,0.5),j=(-0.25,1));
show(currentcoordsys);

point A=(1,1);
line l1=line(45,A);
draw("$(l_1)$",l1);
dot("$A$",A);

point B=(3,1);
line l2=line(-60,B);
draw("$(l_2)$",l2);
dot("$B$",B);

markangleradiusfactor*=5;
/*<asyxml><view file="modules/geometry.asy" type="void" signature="markangle(picture,Label,int,real,real,line,line,arrowbar,pen,filltype,margin,marker)"/></asyxml>*/
markangle(2,l2,l1,0.8*green,StickIntervalMarker(i=1,n=2));

markangle(2,radius=-0.5*markangleradius(),
          l2,l1,0.8*blue);

markangle(reverse(l2),reverse(l1),Arrow,StickIntervalMarker(i=1,n=2));

/*<asyxml><view file="modules/geometry.asy" type="real" signature="sharpdegrees(line,line)"/></asyxml>*/
markangle((string) sharpdegrees(l2,l1),
          radius=-1.5*markangleradius(),
          reverse(l2),l1,Arrow,red);

🔗geometry-fig022

Figure geometry 022 Generated with Asymptote

unitsize(2cm);
import geometry;

currentcoordsys=cartesiansystem((2,1),i=(1,0.25),j=(-0.25,.75));
show(lo=Label("$O$",align=SE+0.5E), currentcoordsys);

pair A=(1,1), B=(2,2);
line l1=line(A,B);
draw("$(l_1)$",l1);

line l2=rotate(100,(3,3))*l1;
draw("$(l_2)$",l2);
write(locate(intersectionpoint(l1,l2)));
/*<asyxml><view file="modules/geometry.asy" type="line" signature="bisector(line,line,real,bool)"/></asyxml>*/
line bis=bisector(l1,l2);
draw(bis);

line Bis=bisector(l1,l2,90);
draw(Bis,0.8*red);
markangleradiusfactor*=5;

/*<asyxml><view file="modules/geometry.asy" type="void" signature="markangle(picture,Label,int,real,real,line,line,arrowbar,pen,filltype,margin,marker)"/></asyxml>*/
markangle(2, l1, l2, StickIntervalMarker(2,2,true));
markangle(2, reverse(l2), l1, radius=1.25*markangleradius(), StickIntervalMarker(2,1,true));

/*<asyxml><view file="modules/geometry.asy" type="bool" signature="concurrent(...line[])"/></asyxml>*/
if (concurrent(bis,l1,l2,Bis)) label("Concurrent",(3,3), dir(135));

draw(box(locate((-1,0)),locate((5,5))),invisible);

🔗geometry-fig023

Figure geometry 023 Generated with Asymptote

Show geometry/fig0230.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Coords system | #Line | #Intersection

import geometry;
size(12cm,0);

currentcoordsys=cartesiansystem((2,1),i=expi(pi/18)*(1,0),j=expi(pi/18)*(0,1));
show(currentcoordsys,xpen=invisible);

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

dot("$A$", A, 2W);
dot("$B$", B, 2E);

line l1=hline()+C;
draw("$(l_1)$", l1, blue);
dot("$C$", C, NE);

line l2=line(A, B, false);
draw(Label("$(AB]$",Relative(.25),SE), l2, green);

/*<asyxml><view file="modules/geometry.asy" type="line" signature="complementary(explicit line)"/></asyxml>*/
draw("Complementary of $(AB]$", complementary(l2), dotted+roundcap);

point p=intersectionpoint(l1,l2);

/*<asyxml><view file="modules/geometry.asy" type="bool" signature="defined(pair)"/></asyxml>*/
string s="$(l_1)$" + (defined(p) ? " intersects " : " does not intersect ") + "$(AB]$";
label(s, A+1.75*l2.u,W);

draw(box(locate((-2,-2)),locate((2,2))), invisible);

🔗geometry-fig024

Figure geometry 024 Generated with Asymptote

import geometry;
size(15cm,0);

// currentcoordsys=cartesiansystem((2,1),i=(1,0.25),j=(-0.25,.75));
// show(lj=Label("$\vec{\jmath}$",EndPoint), currentcoordsys);

point A=(-1,-0.5);
point B=(1,-0.5);
point C=(-1,0.5);

line l1=line(A,B);
draw("$(l_1)$",l1,red);

/*<asyxml><view file="modules/geometry.asy" type="" signature="struct segment"/></asyxml>*/
segment s=segment(A,B);
draw(s, linewidth(2bp));
dot("$A$", A, SW);
dot("$B$", B, SE);
dot("$C$", C, S);

segment s1=parallel(C,s);
draw(Label("$s_1$",Relative(0.75)),s1);

Label lt=Label("Complementary of $s_1$",Relative(0.5),align=N,grey);
Label[] L={lt, lt};

/*<asyxml><view file="modules/geometry.asy" type="line[]" signature="complementary(explicit segment)"/></asyxml>*/
line[] cs1=complementary(s1);

/*<asyxml><view file="modules/geometry.asy" type="void" signature="draw(picture,Label[],line[],align,pen,arrowbar,Label,marker)"/></asyxml>*/
draw(L, cs1, 2mm+lightgrey);

draw(box(locate((-2.5,-1)),locate((2.5,1))), invisible);

🔗geometry-fig027

Figure geometry 027 Generated with Asymptote

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);

🔗geometry-fig029

Figure geometry 029 Generated with Asymptote

import geometry;
size(8cm,0);

currentcoordsys=cartesiansystem((2,1),i=(1,0.5),j=(-0.25,.75));
show(currentcoordsys);

point A=(1,1);
dot("$A$",A,S,red);

real R=2;
circle C=circle(A,R);
draw(C,Arrow);

/*<asyxml><view file="modules/geometry.asy" type="ellipse" signature="*(transform,circle)"/></asyxml>*/
ellipse el=xscale(2)*C;
draw(el,blue,Arrow);

// /*<asyxml><view file="modules/geometry.asy" type="transform" signature="xscale(real,point)"/></asyxml>*/
ellipse el=xscale(2,A)*C;
draw(el,red,Arrow);

🔗geometry-fig030

Figure geometry 030 Generated with Asymptote

import geometry;
size(8cm,0);

currentcoordsys=cartesiansystem((2,1),i=(1,0.5),j=(-0.25,.75));
show(currentcoordsys);

point A=(1,1);
dot("$A$",A,S,red);

real R=2;
circle C=circle(A,R);
draw(C,Arrow);

/*<asyxml><view file="modules/geometry.asy" type="ellipse" signature="*(transform,circle)"/></asyxml>*/
draw(scale(0.5)*C,red,Arrow);

draw(scale(0.5,A)*C,2mm+0.8*blue);

/*<asyxml><view file="modules/geometry.asy" type="circle" signature="/(explicit circle,real)"/></asyxml>*/
draw(C/2,0.75mm+green,Arrow(4mm));

// Note that the point 'point(C,0)' is always at the same place relatively to 'C'.
draw(rotateO(180)*C/2,0.8*yellow,Arrow);

🔗geometry-fig031

Figure geometry 031 Generated with Asymptote

import geometry;
size(10cm,0);

currentcoordsys=cartesiansystem((2,1),i=(1,0.5),j=(-0.25,.75));
show(currentcoordsys);

point A=(1,1);
dot("$A$",A,S,red);

real a=3, b=2;
ellipse el=ellipse(A,a,b,0);
draw(el,Arrow);

/*<asyxml><view file="modules/geometry.asy" type="ellipse" signature="*(transform,ellipse)"/></asyxml>*/
draw(scale(0.5)*el,red,Arrow);

draw(scale(0.5,A)*el,2mm+0.8*blue);

/*<asyxml><view file="modules/geometry.asy" type="ellipse" signature="/(ellipse,real)"/></asyxml>*/
draw(el/2,0.75mm+green,Arrow(4mm));

// Note that the point 'point(el,0)' is always at the same place relatively to 'el'.
draw(rotateO(135)*el/2,0.8*yellow,Arrow);

🔗geometry-fig032

Figure geometry 032 Generated with Asymptote

Show geometry/fig0320.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Coords system | #Parabola

import geometry;
size(10cm,0);

currentcoordsys=cartesiansystem((2,1),i=(1,0.5),j=(-0.25,.75));
show(currentcoordsys);

point F=(0.25,0.5);

dot("$F$",F,SW,red);

// Enlarge the bounding box of the current picture
draw(box(locate((-1.5,0)),locate((1,1))), invisible);

line l=rotateO(10)*line((0,-0.4),(1,-0.4));
draw(l);

/*<asyxml><view file="modules/geometry.asy" type="parabola" signature="parabola(point,line)"/></asyxml>*/
parabola p=parabola(F,l);
draw(p,linewidth(3mm));

/*<asyxml><view file="modules/geometry.asy" type="parabola" signature="parabola(point,point)"/></asyxml>*/
draw(parabola(p.F,p.V),2mm+red);

/*<asyxml><view file="modules/geometry.asy" type="parabola" signature="parabola(point,real,real)"/></asyxml>*/
draw(parabola(p.F,p.a,p.angle),1mm+green);

🔗geometry-fig053

Figure geometry 053 Generated with Asymptote

Show geometry/fig0530.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Coords system | #Circle | #Point

import geometry;
size(8cm,0);

currentcoordsys=cartesiansystem((0,0),i=(1,0.5),j=(-0.5,.75));
show(currentcoordsys, xpen=invisible);

point A=(-0.5,-0.5);
point B=(1,0.5);
point C=(0.5,1);
dot("$A$",A,SW);
dot("$B$",B,2N+0.5W);
dot("$C$",C,2N+0.5W);

/*<asyxml><view file="modules/geometry.asy" type="circle" signature="circle(point,point,point)"/></asyxml>*/
circle c1=circle(A,B,C);
dot("$\Omega$",c1.C,N);
draw(c1);

🔗geometry-fig054

Figure geometry 054 Generated with Asymptote

Show geometry/fig0540.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Coords system | #Ellipse | #Point

import geometry;
size(8cm,0);

currentcoordsys=cartesiansystem((2,1),i=(1,1),j=(-0.5,1));
show(currentcoordsys, xpen=invisible);

point A=(3.5,1),
B=(1.75,3),
C=(-1,2),
D=(-1.5,-0.5),
F=(1.5,-1);

dot("$A$",A);
dot("$B$",B,N);
dot("$C$",C,NW);
dot("$D$",D,SW);
dot("$F$",F,SE);

/*<asyxml><view file="modules/geometry.asy" type="ellipse" signature="ellipse(point,point,point,point,point)"/></asyxml>*/
ellipse el=ellipse(A,B,C,D,F);
draw(el);

dot("$F_1$",el.F1,NW);
dot("$F_2$",el.F2,NW);

/*<asyxml><view file="modules/geometry.asy" type="coordsys" signature="canonicalcartesiansystem(ellipse)"/></asyxml>*/
coordsys R=canonicalcartesiansystem(el);
show("$C$", "$\vec{u}$", "$\vec{v}$", R, xpen=blue);

🔗geometry-fig055

Figure geometry 055 Generated with Asymptote

Show geometry/fig0550.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Coords system | #Parabola | #Point

import geometry;
size(8cm,0);

currentcoordsys=cartesiansystem((2,1),i=(1,0.5),j=(-0.25,.75));
show(currentcoordsys);

// Enlarge the bounding box of the current picture
draw(box(locate((-1,-1.5)),locate((2,1))),invisible);

point A=(0,-1);
point B=(1.25,1);
point C=(-1,0.5);

dot("$A$",A,SW,red);
dot("$B$",B,E,red);
dot("$C$",C,N,red);


line l=rotateO(20)*line((0,0),(1,0));
/*<asyxml><view file="modules/geometry.asy" type="parabola" signature="parabola(point,point,point,line)"/></asyxml>*/
parabola p=parabola(A,B,C,l);
draw(p,blue);
draw(p.D,blue);

🔗geometry-fig100

Figure geometry 100 Generated with Asymptote

import geometry;
size(6cm,0);

currentcoordsys=cartesiansystem((1,2),i=(1,0.5),j=(-0.5,.75));
show(currentcoordsys, xpen=invisible);

point A=(-1,1);
point B=(2,2);
point M=(1,3);

/*<asyxml><view file="modules/geometry.asy" type="arc" signature="arccircle(point,point,point)"/></asyxml>*/
arc AMB=arccircle(A,M,B);
draw(AMB,linewidth(3mm),Arrow(5mm),TrueMargin(0,0.5mm));
dot("$C$",AMB.el.C);
draw(arccircle(A,B,M),1mm+red,Arrow(3mm));

dot("$A$",A,2SW,blue);
dot("$B$",B,2E,blue);
dot("$M$",M,2N,blue);

🔗geometry-fig101

Figure geometry 101 Generated with Asymptote

import geometry;
size(8cm,0);

currentcoordsys=cartesiansystem((1,2),i=(1,0.5),j=(-0.5,.75));
show(currentcoordsys, xpen=invisible);

real R=2;

point A=(1,1);
dot("$A$", A, S, red);
point B=A+(2,1);
dot("$B$", B, N, blue);

arc a=arc(circle(A,R), -40, 180);
arc b=arc(circle(B,R), -45, 220);
line l=line(A,B);

draw(a,red);
draw(b,blue);
draw(l);

/*<asyxml><view file="modules/geometry.asy" type="point[]" signature="intersectionpoints(arc,arc)"/></asyxml>*/
point[] inter=intersectionpoints(a,b);
dot(inter);

/*<asyxml><view file="modules/geometry.asy" type="point[]" signature="intersectionpoints(line,arc)"/></asyxml>*/
point[] inter=intersectionpoints(l,a);
dot(inter);

point[] inter=intersectionpoints(l,b);
dot(inter);

🔗geometry-fig102

Figure geometry 102 Generated with Asymptote

import geometry;
size(8cm,0);

// currentcoordsys=cartesiansystem((1,2),i=(1,0.5),j=(-0.5,.75));
// show(currentcoordsys, xpen=invisible);

real R=2;

point A=(1,1);
dot("$A$", A, S, red);
point B=A+(2,1);
dot("$B$", B, N, blue);

arc a=arc(ellipse(A,R,R/2), -40, 180);
arc b=arc(ellipse(B,R,R/2), -45, 220);

line l=line(A,B);

draw(a,red);
draw(b,blue);
draw(l);

/*<asyxml><view file="modules/geometry.asy" type="point[]" signature="intersectionpoints(arc,arc)"/></asyxml>*/
point[] inter=intersectionpoints(a,b);
dot(inter);

/*<asyxml><view file="modules/geometry.asy" type="point[]" signature="intersectionpoints(line,arc)"/></asyxml>*/
point[] inter=intersectionpoints(l,a);
dot(inter);

point[] inter=intersectionpoints(l,b);
dot(inter);

🔗geometry-fig103

Figure geometry 103 Generated with Asymptote

import geometry;
size(8cm,0);

currentcoordsys=cartesiansystem((1,2),i=(1,0.5),j=(-0.5,.75));
show(currentcoordsys, xpen=invisible);

real R=2;

point A=(1,1.5);
dot("$A$",A,S,red);
point B=A+(2,1);
dot("$B$",B,S,blue);

arc a=arc(circle(A,R),-40,180);
arc b=arc(circle(B,R),-45,220);

draw(a,red);
draw(b,blue);

point M=intersectionpoints(a,b)[0];
dot(M);

/*<asyxml><view file="modules/geometry.asy" type="line" signature="tangent(explicit arc,point)"/></asyxml>*/
draw(tangent(a,M), grey);
draw(tangent(b,M), grey);

/*<asyxml><view file="modules/geometry.asy" type="line" signature="tangent(explicit arc,abscissa)"/></asyxml>*/
draw(tangent(a,angabscissa(45)), grey);

🔗geometry-fig104

Figure geometry 104 Generated with Asymptote

import geometry;
size(10cm,0);

// currentcoordsys=cartesiansystem((1,2),i=(1,0.5),j=(-0.5,.75));
// show(currentcoordsys, xpen=invisible);

real R=2;

point A=(1,1.5);
dot("$A$",A,S,red);
point B=A+(2.5,1);
dot("$B$",B,E,blue);

arc a=arc(ellipse(A,R,R/2,30),-40,180);
// ellispenodesnumberfactor=400;
arc b=arc(ellipse(B,2R,R/2,-10),-30,180);

draw(a,red);
draw(b,blue);

point M=intersectionpoints(a,b)[0];
dot(M);

/*<asyxml><view file="modules/geometry.asy" type="line" signature="tangent(explicit arc,point)"/></asyxml>*/
draw(tangent(a,M), grey);
draw(tangent(b,M), grey);

/*<asyxml><view file="modules/geometry.asy" type="line" signature="tangent(explicit arc,abscissa)"/></asyxml>*/
draw(tangent(a,angabscissa(45)), grey);