Tag Abscissa -- Asymptote Gallery

🔗Asymptote Gallery Tagged by “Abscissa” #128

🔗geometry-fig046

Show geometry/fig0460.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Line | #Intersection | #Ellipse | #Abscissa | #Point | #Tangent

import geometry;
size(10cm,0);

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

point A=(-1,-1);
point B=(0.75,0.5);
dot("$A$",A,NW,red);
dot("$B$",B,N,red);

ellipse el1=ellipse(A,2,1.5);
ellipse el2=ellipse(B,3,2);
draw(el1);
draw(el2,Arrow);

point[] inter=intersectionpoints(el1,el2);
dot("$M$", inter[0], 2NW, red);

/*<asyxml><view file="modules/geometry.asy" type="line[]" signature="tangents(ellipse,point)"/></asyxml>*/
draw(tangents(el1,inter[0]), grey);
draw(tangents(el2,inter[0]), grey);

/*<asyxml><view file="modules/geometry.asy" type="line" signature="tangent(ellipse,abscissa)"/></asyxml>*/
draw(tangent(el2,angabscissa(90)), grey);

🔗geometry-fig047

Show geometry/fig0470.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Line | #Intersection | #Parabola | #Abscissa | #Point | #Tangent

import geometry;
size(12cm);

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

point F1=(0,0);
dot("$F1$",F1,NW);
point F2=(-0.25,0.5);
dot("$F2$",F2,SE);

parabola p=parabola(F1, 0.1, 120);
draw(p, bp+red);

parabola pp=parabola(F2, 0.06, 280);
draw(pp, bp+blue);

abscissa x=angabscissa(180);
dot(point(p,x));
/*<asyxml><view file="modules/geometry.asy" type="line" signature="tangent(parabola,abscissa)"/></asyxml>*/
draw(tangent(p,x), 0.8*red);

point[] P=intersectionpoints(p,pp);
dot(P);

/*<asyxml><view file="modules/geometry.asy" type="line[]" signature="tangents(parabola,point)"/></asyxml>*/
draw(tangents(p,P[0]), 0.8*red);
draw(tangents(pp,P[0]), 0.8*blue);

// Enlarge the bounding box
draw(box((-1,-0.4), (0.5,0.6)),invisible);

🔗geometry-fig048

Show geometry/fig0480.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Line | #Intersection | #Hyperbola | #Abscissa | #Point | #Tangent

import geometry;
size(10cm);

point C=(4,2);
dot("$C$",C,E+NE,red);

hyperbola h=hyperbola(C,1.5,1,-20);
draw(h, linewidth(bp));

/*<asyxml><view file="modules/geometry.asy" type="line" signature="tangent(hyperbola,abscissa)"/></asyxml>*/
line l=tangent(h,angabscissa(85));
draw(l, grey);
dot(intersectionpoints(h,l));

l=tangent(h,angabscissa(0,fromCenter));
draw(l, grey);
dot(intersectionpoints(h,l));

// Enlarge the bounding box of the current picture.
draw(box((-1,-0.5), (9,4)), invisible);

🔗geometry-fig056

Show geometry/fig0560.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Line | #Abscissa | #Point

import geometry;
size(10cm,0);

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

point A=(0,0), B=(2,1);

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

/*<asyxml><view file="modules/geometry.asy" type="point" signature="relpoint(line,real)"/></asyxml>*/
point P=relpoint(l, 1);
dot("relpoint(l, 1)", P, 2E,linewidth(2mm));
/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="relabscissa(line,point)"/></asyxml>*/
dot(point(l,relabscissa(l,P)), red);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="curpoint(line,real)"/></asyxml>*/
point P=curpoint(l, 1);
dot("curpoint(l, 1)", P, SE, blue+2mm);
/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="curabscissa(line,point)"/></asyxml>*/
dot(point(l,curabscissa(l,P)), yellow);


point P=relpoint(l, 2);
dot("relpoint(l, 2)", P, NW,linewidth(2mm));
dot(point(l,relabscissa(l,P)), red);

point P=curpoint(l, 2);
dot("curpoint(l, 2)", P, NW, blue+2mm);
dot(point(l,curabscissa(l,P)), yellow);

🔗geometry-fig057

Show geometry/fig0570.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Distance | #Circle | #Abscissa | #Point

import geometry;
size(10cm,0);

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

point A=(2,-2);
dot("$A$",A,S,red);

circle C=circle(A,2);
draw(C);
/*<asyxml><view file="modules/geometry.asy" type="void" signature="distance(picture pic,Label,point,point,bool,real,pen,pen,arrow)"/></asyxml>*/
distance("$R=2$",A,point(C,0),0);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="relpoint(explicit circle,real)"/></asyxml>*/
dot("relpoint(C, 0)",relpoint(C,0),E);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="point(circle,abscissa)"/></asyxml>*/
dot("relpoint(C, 0.25)",point(C,Relative(0.25)),NW);
// point(C,Relative(0.25)) can be replaced by relpoint(C,0.25) OR point(C,relabscissa(0.25))

dot("relpoint(C, 0.5)",relpoint(C,0.5),W);
dot("relpoint(C, 0.75)",relpoint(C,0.75),SE);
dot("relpoint(C, 1.125)",relpoint(C,1.125),NE);

🔗geometry-fig058

Show geometry/fig0580.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Ellipse | #Abscissa | #Point

import geometry;
size(12cm,0);

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

point A=(2,-1.5);
dot("$A$",A,S,red);

ellipse el=ellipse(A,3,1,20);
draw(el);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="relpoint(explicit ellipse,real)"/></asyxml>*/
dot("relpoint(el, 0)",relpoint(el,0),E);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="point(ellipse,abscissa)"/></asyxml>*/
dot("relpoint(el, 0.25)",point(el,Relative(0.25)),NW);
// point(el,Relative(0.25)) can be replaced by relpoint(el,0.25) OR point(el,relabscissa(0.25))

dot("relpoint(el, 0.5)",relpoint(el,0.5),W);
dot("relpoint(el, 0.75)",relpoint(el,0.75),SE);
dot("relpoint(el, 1.125)",relpoint(el,1.125),NW);

🔗geometry-fig059

Show geometry/fig0590.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Parabola | #Abscissa | #Point

import geometry;
size(12cm,0);

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

point F=(2,-1.5);
dot("$F$",F,N,red);

// Enlarge the bounding box of the current picture.
draw(box((-0.5,-0.4),(4,1.5)),invisible);

parabola p=parabola(F,0.2,90);

// Define the bounding box to draw the parabola.
// Try finalbounds(); to determine the final bounding box.
p.bmin=(-0.5,-0.4);
p.bmax=(3.7,0.75);

draw(p,dashed); /* Defered drawing to adjust the path to the final
                   bounding box.*/

draw((path)p); /* The path of 'p' is restricted to the box whose
                  the corners are p.bmin, p.bmax.*/

/*<asyxml><view file="modules/geometry.asy" type="point" signature="relpoint(explicit parabola,real)"/></asyxml>*/
dot("relpoint(p, 0)",relpoint(p,0),SE);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="point(parabola,abscissa)"/></asyxml>*/
dot("relpoint(p, 0.25)",point(p,Relative(0.25)),NE);
// point(p,Relative(0.25)) can be replaced by relpoint(p,0.25) OR point(p,relabscissa(0.25))

dot("relpoint(p, -0.5)",relpoint(p,-0.5),W);
dot("relpoint(p, -1)",relpoint(p,-1),W);
dot("relpoint(p, 1)",relpoint(p,1),E);

🔗geometry-fig060

Show geometry/fig0600.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Circle | #Abscissa | #Point

import geometry;
size(11cm,0);

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

point A=(2,-2);
dot("$A$",A,S,red);

circle C=circle(A,2);
draw(C);
distance("$R=2$",A,point(C,0),0);

/*<asyxml><view file="modules/geometry.asy" type="pair" signature="curpoint(explicit circle,real)"/></asyxml>*/
dot("curpoint(C, pi/2)", curpoint(C,pi/2),NE);

dot("curpoint(C, -pi/2)", curpoint(C,-pi/2));

/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="curabscissa(real)"/></asyxml>*/
dot("curpoint(C, pi)", point(C,curabscissa(pi)),NW);
// point(C,curabscissa(pi)) can be replaced by curpoint(C,pi)

dot("curpoint(C, 2*pi)", curpoint(C,2*pi),W);
dot("curpoint(C, 3*pi)", curpoint(C,3*pi),SE);
dot("curpoint(C, 4.25*pi)", curpoint(C,4.25*pi),E);

🔗geometry-fig061

Show geometry/fig0610.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Ellipse | #Abscissa | #Point

import geometry;
size(12cm,0);

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

point A=(4,2);

ellipse el=ellipse(A,3,2,30);
draw(el);
dot("$C$",el.C,S,red);


/*<asyxml><view file="modules/geometry.asy" type="pair" signature="curpoint(explicit ellipse,real)"/></asyxml>*/
dot("curpoint(el, 0)", curpoint(el,0), E);

real L=arclength(el);


dot("curpoint(el, L/8)", curpoint(el,L/8),NW);

dot("curpoint(el, -L/8)", curpoint(el,-L/8));

/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="curabscissa(real)"/></asyxml>*/
dot("point(el,curabscissa(L/4))", point(el,curabscissa(L/4)),NW);
// point(el,curabscissa(pi)) can be replaced by curpoint(el,pi)

dot("curpoint(el, L/2)", curpoint(el,L/2),W);
dot("curpoint(el, 3*L/4)", curpoint(el,3*L/4),SE);
dot("curpoint(el, 9*L/8)", curpoint(el,9*L/8),4N+4W);

🔗geometry-fig062

Show geometry/fig0620.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Parabola | #Abscissa | #Point

import geometry;
size(10cm);

point F=(1,-1.5);
dot("$F$",F,N,red);

parabola p=parabola(F,0.2,110);

draw(p);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="curpoint(explicit parabola,real)"/></asyxml>*/
dot("curpoint(p, 0)",curpoint(p,0),SE);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="point(parabola,abscissa)"/></asyxml>*/
dot("curpoint(p, 0.5)",point(p,curabscissa(0.5)),NE);
// point(p,curabscissa(0.5)) can be replaced by curpoint(p,0.5)

dot("curpoint(p, -0.5)",curpoint(p,-0.5),W);
dot("curpoint(p, -2)",curpoint(p,-2),W);
dot("curpoint(p, 2)",curpoint(p,2),E);

🔗geometry-fig063

Show geometry/fig0630.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Circle | #Abscissa | #Point

import geometry;
size(11cm,0);

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

point A=(2,-2);
dot("$A$",A,S,red);

circle C=circle(A,2);
draw(C);
distance("$R=2$",A,point(C,0),0);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="angpoint(explicit circle,real)"/></asyxml>*/
dot("angpoint(C, 90)", angpoint(C,90),NW);

/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="angabscissa(real,polarconicroutine)"/></asyxml>*/
dot("angpoint(C, 180)", point(C,angabscissa(180)), W);
// point(C,angabscissa(180)) can be replaced by angpoint(C,180)

dot("angpoint(C, 270)", angpoint(C,270),SE);
dot("angpoint(C, 405)", angpoint(C,405),NE);
dot("angpoint(C, -45)", angpoint(C,-45),SE);

🔗geometry-fig064

Show geometry/fig0640.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Ellipse | #Abscissa | #Point

import geometry;
size(12cm,0);

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

point A=(4,2);

ellipse el=ellipse(A,3,2,20);
draw(el);
dot("$C$",el.C,2W,red);

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


/*<asyxml><view file="modules/geometry.asy" type="point" signature="angpoint(explicit ellipse,real,polarconicroutine)"/></asyxml>*/
point P=angpoint(el, 0);
dot("angpoint(el, 0)", P,E);
draw(el.F1--P);

point P=angpoint(el, 90);
dot("angpoint(el, 90)", P,NW);
draw(el.F1--P);

point P=angpoint(el, 90, fromCenter);
dot("angpoint(el,90,fromCenter)", P,NW);
draw(el.C--P);


/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="angabscissa(real,polarconicroutine)"/></asyxml>*/
dot("angpoint(el, 180)", point(el,angabscissa(180)), W);
// point(el,angabscissa(180)) can be replaced by angpoint(el,180)

dot("angpoint(el, 270)", angpoint(el,270),SE);
dot("angpoint(el, 370)", angpoint(el,370),NE);
dot("angpoint(el, -45)", angpoint(el,-45),SE);

point P=angpoint(el, -45, fromCenter);
dot("angpoint(el,-45,fromCenter)", P,S);
draw(el.C--P);

🔗geometry-fig065

Show geometry/fig0650.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Ellipse | #Abscissa | #Point

import geometry;
size(15cm,0);

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

point A=(4,2);

ellipse el=ellipse(A,3,2,20);
draw(el);
dot("$C$",el.C,S,red);

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


///////////////////////////////////////
currentpolarconicroutine=fromCenter;//
/////////////////////////////////////

/*<asyxml><view file="modules/geometry.asy" type="point" signature="angpoint(explicit ellipse,real,polarconicroutine)"/></asyxml>*/
point P=angpoint(el, 0);
dot("angpoint(el, 0)", P,E);
draw(el.C--P);

point P=angpoint(el, 90);
dot("angpoint(el, 90)", P,NW);
draw(el.C--P);

point P=angpoint(el, 90, fromFocus);
dot("angpoint(el,90,fromFocus)", P,NW);
draw(el.F1--P);


/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="angabscissa(real,polarconicroutine)"/></asyxml>*/
dot("angpoint(el, 180)", point(el,angabscissa(180)), W);

dot("angpoint(el, 370)", angpoint(el,370),NE);
dot("angpoint(el, -45)", angpoint(el,-45),SE);

point P=angpoint(el, -45, fromFocus);
dot("angpoint(el,-45,fromFocus)", P,S);
draw(el.F1--P);

🔗geometry-fig066

Show geometry/fig0660.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Abscissa | #Parabola | #Point

import geometry;
size(10cm);

point F=(1,0.5);
dot("$F$",F,E,red);

parabola p=parabola(F,0.2,110);

draw(p);

coordsys R=currentcoordsys;
show(R);

coordsys Rp=canonicalcartesiansystem(p);
show(Label("$O'$",align=NW+W,blue), Label("$\vec{u}$",blue), Label("$\vec{v}$",blue), Rp, ipen=blue);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="angpoint(explicit parabola,real)"/></asyxml>*/
dot("angpoint(p, 180)",angpoint(p,180),SE+E);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="point(parabola,abscissa)"/></asyxml>*/
point P=point(p,angabscissa(55));
// point(p,angbscissa(0.5)) can be replaced by angpoint(p,0.5)
dot("angpoint(p, 55)",P,NE);

segment s=segment(F,P);
draw(s);
line l=line(F,F+Rp.i);
markangle("$"+(string)degrees(l,s)+"^\circ$",l,(line)s,Arrow);

dot("angpoint(p, -45)",angpoint(p,-45),W);
dot("angpoint(p, -55)",angpoint(p,-55),W);

🔗geometry-fig067

Show geometry/fig0670.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Abscissa | #Parabola | #Point | #Arc

import geometry;
size(10cm);

point C=(4,2);
dot("$C$",C,E+NE,red);

hyperbola h=hyperbola(C,1.5,1,-20);
draw(h, linewidth(bp));

coordsys R=currentcoordsys;
show(R);

coordsys Rp=canonicalcartesiansystem(h);
show(Label("$O'$",align=SW,blue), Label("$\vec{u}$",blue), Label("$\vec{v}$",blue), Rp, ipen=blue);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="angpoint(explicit hyperbola,real,polarconicroutine)"/></asyxml>*/
dot(rotate(70)*"angpoint(h, 180)",angpoint(h,180),E);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="point(hyperbola,abscissa)"/></asyxml>*/
point P=point(h,angabscissa(55));
// point(h,angbscissa(0.5)) can be replaced by angpoint(h,0.5)
dot("angpoint(h, 55)",P,SE);

/*<asyxml><view file="modules/geometry.asy" type="path" signature="arcfromfocus(conic,real,real,int,bool)"/></asyxml>*/
draw(arcfromfocus(h,55,180), bp+red);

segment s=segment(h.F1,P);
draw(s);
dot("$F_1$",h.F1,N+NW);
line l=line(h.F1,h.F1-Rp.i);
markangle("$55^\circ$",l,(line)s,Arrow);

dot("angpoint(p, -50)",angpoint(h,-50),W);
dot("angpoint(p, -55)",angpoint(h,-55),NE);

🔗geometry-fig068

Show geometry/fig0680.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Abscissa | #Hyperbola | #Point | #Arc

import geometry;
size(12cm);

// currentcoordsys=cartesiansystem((0,0),i=(1,0.5),j=(-0.5,.75));
coordsys R=currentcoordsys;
show(R);

point C=(4,2);
dot("$C$", C, NW, red);

hyperbola h=hyperbola(C, 2, 1.5, -10);
draw(h);

///////////////////////////////////////
currentpolarconicroutine=fromCenter;//
/////////////////////////////////////

coordsys Rp=canonicalcartesiansystem(h);
show(Label("$O'$", align=SW,blue),
     Label("$\vec{u}$",blue),
     Label("$\vec{v}$",blue),
     Rp, ipen=blue);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="angpoint(explicit hyperbola,real,polarconicroutine)"/></asyxml>*/
dot("angpoint(h, 0)", angpoint(h,0), E+NE);
dot(rotate(80)*"angpoint(h, 180)", angpoint(h,180),E);

draw(arcfromcenter(h,0,30), bp+red);

// point(p,angbscissa(150)) can be replaced by angpoint(p,150)
dot("angpoint(h, 150)", point(h, angabscissa(150)), E);

point P=point(h, angabscissa(210));
dot("angpoint(h, 210)", P, E);

point P=angpoint(h, 30);
dot("angpoint(h, 30)", P, E);

segment s=segment(C, P);
draw(s);
markangle("$30^\circ$", Ox(Rp),(line) s, radius=1.5cm, Arrow);

🔗geometry-fig069

Show geometry/fig0690.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Abscissa | #Circle | #Point

import geometry;
size(10cm,0);

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

point A=(4,2);
dot("$A$",A,S,red);

real R=2;
circle C=circle(A,R);
draw(C,linewidth(1mm));
draw("$R="+(string)R+"$", A--point(C,0), N, Arrows);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="point(explicit circle,explicit real)"/></asyxml>*/
dot("point(C, 15)", point(C,15),2E,3mm+blue);

/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="nodabscissa(real)"/></asyxml>*/
dot("point(C, 40)",
    point(C,nodabscissa(40)),
    2W,3mm+blue);
// point(C,nodabscissa(40)) can be replaced by point(C,40)

/*<asyxml><view file="modules/geometry.asy" type="int" signature="circlenodesnumber(real)"/></asyxml>*/
dot("point(C, 3*circlenodesnumber(R)/4)",
    point(C, 3*circlenodesnumber(R)/4), S, 3mm+blue);

dot((path)C, yellow);

write(length((path)C));

🔗geometry-fig070

Show geometry/fig0700.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Abscissa | #Ellipse | #Point

import geometry;
size(10cm,0);

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

point A=(4,2);

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

dot("$C$",el.C,N,red);
draw(el,linewidth(1mm));

/*<asyxml><view file="modules/geometry.asy" type="point" signature="point(explicit ellipse,explicit real)"/></asyxml>*/
dot("point(el, 0)", point(el,0),N,3mm+blue);

dot("point(el, 15)", point(el,15),2W,3mm+blue);

/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="nodabscissa(real)"/></asyxml>*/
dot("point(el, 40)",
    point(el,nodabscissa(40)),
    2W,3mm+blue);
// point(el,nodabscissa(40)) can be replaced by point(el,40)

/*<asyxml><view file="modules/geometry.asy" type="int" signature="circlenodesnumber(real)"/></asyxml>*/
dot("point(el, 3*circlenodesnumber(max(a,b))/4)",
    point(el, 3*circlenodesnumber(max(a,b))/4), S, 3mm+blue);

dot((path)el, yellow);

🔗geometry-fig071

Show geometry/fig0710.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Abscissa | #Parabola | #Point

import geometry;
size(12cm);

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

point F=(2,-1.5);
dot("$F$",F,N,red);

// Enlarge the bounding box of the current picture.
draw(box((-0.5,-0.4),(4,1.5)),invisible);

parabola p=parabola(F,0.2,90);

draw(p,bp+dashed); /* Defered drawing to adjust the path to the final
                   bounding box.*/

// Define the bounding box to draw the parabola.
// Try finalbounds(); to determine the final bounding box.
p.bmin=(-0.5,-0.4);
p.bmax=(3.7,0.75);
draw((path)p, linewidth(bp)); /* The path of 'p' is restricted to the box whose
                  the corners are p.bmin, p.bmax.*/

/*<asyxml><view file="modules/geometry.asy" type="point" signature="point(explicit parabola,explicit real)"/></asyxml>*/
dot("point(p, 0)", point(p,0),2E,3mm+blue);

dot("point(p, 15)", point(p,15),2W,3mm+blue);

/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="nodabscissa(real)"/></asyxml>*/
dot("point(p, 40)", point(p,nodabscissa(40)), 2W,3mm+blue);
// point(p,nodabscissa(40)) can be replaced by point(p,40)

/*<asyxml><view file="modules/geometry.asy" type="real[]" signature="bangles(picture,parabola)"/></asyxml>*/
real[] bg=bangles(p);

/*<asyxml><view file="modules/geometry.asy" type="int" signature="parabolanodesnumber(parabola,real,real)"/></asyxml>*/
dot("point(p, parabolanodesnumber(p,bg[0],bg[1])/2)",
    point(p, parabolanodesnumber(p,bg[0],bg[1])/2), S, 3mm+blue);

dot((path)p, yellow);

🔗geometry-fig072

Show geometry/fig0720.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Abscissa | #Hyperbola | #Point

import geometry;
size(12cm);

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

point C=(3,2);
dot("$C$", C, N, red);

// Enlarge the bounding box of the current picture.
draw(box((0,0),(5,4.5)), invisible);

hyperbola h=hyperbola(C, 1, 2);

draw(h, bp+dashed); /* Defered drawing to adjust the path to the final
                       bounding box.*/

// Define the bounding box to draw the hyperbola.
// Try finalbounds(); to determine the final bounding box.
h.bmin=(0,0.5); h.bmax=(5,4);
draw((path)h, linewidth(bp)); /* The path of 'p' is restricted to the box whose
                                 the corners are p.bmin, p.bmax.*/

/*<asyxml><view file="modules/geometry.asy" type="point" signature="point(explicit hyperbola,explicit real)"/></asyxml>*/
dot("point(h, 0)", point(h,0), 2W, 3mm+blue);

dot("point(h, 15)", point(h,15), 2W, 3mm+blue);

/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="nodabscissa(real)"/></asyxml>*/
dot("point(h, 40)", point(h,nodabscissa(40)), 2W,3mm+blue);
// point(h,nodabscissa(40)) can be replaced by point(h,40)

/*<asyxml><view file="modules/geometry.asy" type="real[]" signature="bangles(picture,hyperbola)"/></asyxml>*/
real[][] bg=bangles(h);

dot((path)h, yellow);

🔗geometry-fig073

Show geometry/fig0730.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Abscissa | #Circle | #Point

import geometry;
unitsize(2cm);

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

point A=(-2,2);
dot("$A$",A,S);
point B=A+(cos(0.5),cos(1));
dot("$B$",B,S);


circle c=circle(A,2);
draw(c);

line l=line(A,B);
draw(l);
point M=intersectionpoints(l,c)[0];
point P=intersectionpoints(l,c)[1];

/*<asyxml><view file="modules/geometry.asy" type="void" signature="dot(picture,Label,explicit point,align,string,pen)"/></asyxml>*/
dot("",M,2E,linewidth(2mm));
dot("$M$",M,2W);
dot("",P,2E,linewidth(2mm));
dot("$P$",P,2W);

pair p=A-(4,2.5);
transform t=shift((0,-0.3));
transform T=shift((4,0));
real x;

/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="angabscissa(circle,point)"/></asyxml>*/
x=angabscissa(c,M).x;
label("angabscissa(c,M).x=$"+(string)x+"^\circ$",p,E);
dot(angpoint(c,x),1mm+red);
x=angabscissa(c,P).x;
label("angabscissa(c,P).x=$"+(string)x+"^\circ$",T*p,E);
dot(angpoint(c,x),1mm+red);

p=t*p;
/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="curabscissa(circle,point)"/></asyxml>*/
x=curabscissa(c,M).x;
dot(curpoint(c,x),1mm+red);
label("curabscissa(c,M).x="+(string)x,p,E);
x=curabscissa(c,P).x;
label("curabscissa(c,P).x="+(string)x,T*p,E);
dot(curpoint(c,x),1mm+red);

p=t*p;
/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="nodabscissa(circle,point)"/></asyxml>*/
x=nodabscissa(c,M).x;
label("nodabscissa(c,M).x="+(string)x,p,E);
dot(point(c,x),1mm+red);
x=nodabscissa(c,P).x;
label("nodabscissa(c,P).x="+(string)x,T*p,E);
dot(point(c,x),1mm+red);

p=t*p;
/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="relabscissa(circle,point)"/></asyxml>*/
x=relabscissa(c,M).x;
label("relabscissa(c,M).x="+(string)x,p,E);
dot(relpoint(c,x),1mm+red);
x=relabscissa(c,P).x;
label("relabscissa(c,P).x="+(string)x,T*p,E);
dot(relpoint(c,x),1mm+red);

🔗geometry-fig074

Show geometry/fig0740.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Abscissa | #Ellipse | #Point

import geometry;
unitsize(2cm);

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

point A=(-2,2);
dot("$A$",A,S);
point B=A+(cos(0.5),cos(1));
dot("$B$",B,S);


ellipse el=ellipse(A,3,2,0);
draw(el);
line l=line(A,B);
draw(l);
point M=intersectionpoints(l,el)[0];
point P=intersectionpoints(l,el)[1];

/*<asyxml><view file="modules/geometry.asy" type="void" signature="dot(picture,Label,explicit point,align,string,pen)"/></asyxml>*/
dot("",M,2E,linewidth(2mm));
dot("$M$",M,2W);
dot("",P,2E);
dot("$P$",P,2W,linewidth(2mm));

pair p=A-(4,2.5);
transform t=shift((0,-0.3));
transform T=shift((4,0));
real x;

/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="angabscissa(ellipse,point,polarconicroutine)"/></asyxml>*/
x=angabscissa(el,M).x;
label("angabscissa(el,M).x=$"+(string)x+"^\circ$",p,E);
dot(angpoint(el,x),1mm+red);
x=angabscissa(el,P).x;
label("angabscissa(el,P).x=$"+(string)x+"^\circ$",T*p,E);
dot(angpoint(el,x),1mm+red);

p=t*p;
/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="curabscissa(ellipse,point)"/></asyxml>*/
x=curabscissa(el,M).x;
dot(curpoint(el,x),1mm+red);
label("curabscissa(el,M).x="+(string)x,p,E);
x=curabscissa(el,P).x;
label("curabscissa(el,P).x="+(string)x,T*p,E);
dot(curpoint(el,x),1mm+red);

p=t*p;
/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="nodabscissa(ellipse,point)"/></asyxml>*/
x=nodabscissa(el,M).x;
label("nodabscissa(el,M).x="+(string)x,p,E);
dot(point(el,x),1mm+red);
x=nodabscissa(el,P).x;
label("nodabscissa(el,P).x="+(string)x,T*p,E);
dot(point(el,x),1mm+red);

p=t*p;
/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="relabscissa(ellipse,point)"/></asyxml>*/
x=relabscissa(el,M).x;
label("relabscissa(el,M).x="+(string)x,p,E);
dot(relpoint(el,x),1mm+red);
x=relabscissa(el,P).x;
label("relabscissa(el,P).x="+(string)x,T*p,E);
dot(relpoint(el,x),1mm+red);

🔗geometry-fig075

Show geometry/fig0750.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Abscissa | #Parabola | #Point/Dot | #Point

import geometry;
unitsize(2cm);

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

point A=(-2.5,2);
dot("$A$",A,S);
point B=A+(cos(0.5),cos(1));
dot("$B$",B,S);

point F=(-1,0.5);
dot("$F$",F,NW);

parabola pb=parabola(F,0.2,130);
draw(pb);
line l=line(A,B);
draw(l);
point M=intersectionpoints(l,pb)[0];
point P=intersectionpoints(l,pb)[1];

/*<asyxml><view file="modules/geometry.asy" type="void" signature="dot(picture,Label,explicit point,align,string,pen)"/></asyxml>*/
dot("",M,2E,linewidth(2mm));
dot("$M$",M,2W);
dot("",P,2E,linewidth(2mm));
dot("$P$",P,2W);

pair p=A-(4,2.5);
transform t=shift((0,-0.3));
transform T=shift((4,0));
real x;

/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="angabscissa(parabola,point)"/></asyxml>*/
x=angabscissa(pb,M).x;
label("angabscissa(pb,M).x=$"+(string)x+"^\circ$",p,E);
dot(angpoint(pb,x),1mm+red);
x=angabscissa(pb,P).x;
label("angabscissa(pb,P).x=$"+(string)x+"^\circ$",T*p,E);
dot(angpoint(pb,x),1mm+red);

// p=t*p;
// /*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="curabscissa(parabola,point)"/></asyxml>*/
// x=curabscissa(pb,M).x;
// dot(curpoint(pb,x),1mm+red);
// label("curabscissa(pb,M).x="+(string)x,p,E);
// x=curabscissa(pb,P).x;
// label("curabscissa(pb,P).x="+(string)x,T*p,E);
// dot(curpoint(pb,x),1mm+red);

// p=t*p;
// /*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="nodabscissa(parabola,point)"/></asyxml>*/
// x=nodabscissa(pb,M).x;
// label("nodabscissa(pb,M).x="+(string)x,p,E);
// dot(point(pb,x),1mm+red);
// x=nodabscissa(pb,P).x;
// label("nodabscissa(pb,P).x="+(string)x,T*p,E);
// dot(point(pb,x),1mm+red);

🔗geometry-fig086

Show geometry/fig0860.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Arc | #Circle | #Abscissa | #Point

import geometry;
size(10cm,0);

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

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

arc C=arc(circle(A,2), 45, 270);
draw(C, Arrow);

/*<asyxml><view file="modules/geometry.asy" type="real" signature="degrees(arc)"/></asyxml>*/
write(degrees(C)); // Output is 225

draw(complementary(C), grey+dashed);
distance("$R=2$",A,point(C,0),0);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="relpoint(arc,real)"/></asyxml>*/
dot("relpoint(C, 0)", relpoint(C,0),E);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="point(arc,abscissa)"/></asyxml>*/
dot("relpoint(C, 0.25)", point(C,Relative(0.25)),N);// point(C,Relative(0.25)) is similar to relpoint(C,0.25)
dot("relpoint(C, -0.5)", relpoint(C,-0.5),E);
dot("relpoint(C, 0.5)",  relpoint(C,0.5),W);
dot("relpoint(C, 0.75)", relpoint(C,0.75),W);
dot("relpoint(C, 1.25)", relpoint(C,1.25),E);

🔗geometry-fig087

Show geometry/fig0870.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Arc | #Ellipse | #Abscissa | #Point

import geometry;
size(12cm,0);

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

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

arc C=arc(ellipse(A,2,1,45), 45, 270, fromCenter);
// arc C=arc(ellipse(A,2,1), 45, -45);

draw(C, Arrow);
draw(complementary(C), grey+dashed);
distance("$R=2$",A,point(C.el,0),0);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="relpoint(arc,real)"/></asyxml>*/
dot("relpoint(C, 0)", relpoint(C,0),W);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="point(arc,abscissa)"/></asyxml>*/
dot("relpoint(C, 0.25)", point(C,Relative(0.25)),W);// point(C,Relative(0.25)) is similar to relpoint(C,0.25)
dot("relpoint(C, -0.5)", relpoint(C,-0.5),E);
dot("relpoint(C, 0.5)",  relpoint(C,0.5),W);
dot("relpoint(C, 0.75)", relpoint(C,0.75),SE);
dot("relpoint(C, 1.25)", relpoint(C,1.25),E);

🔗geometry-fig088

Show geometry/fig0880.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Arc | #Circle | #Abscissa | #Point

import geometry;
size(10cm,0);

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

point A=(3.5,0.5);
dot("$A$",A,S,red);

arc C=arc(circle(A,2),45,270,CCW);
draw(C,Arrow);
draw(complementary(C),grey+dashed);
/*<asyxml><view file="modules/geometry.asy" type="void" signature="distance(picture pic,Label,point,point,bool,real,pen,pen,arrow)"/></asyxml>*/
distance("$R=2$",A,point(C.el,0),0);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="curpoint(arc,real)"/></asyxml>*/
dot("curpoint(C, 0)", curpoint(C,0),E);
dot("curpoint(C, pi/2)", curpoint(C,pi/2),N);
dot("curpoint(C, -pi/2)", curpoint(C,-pi/2));

// dot("curpoint(C, pi)", point(C,curabscissa(pi)),W); // OR curpoint(C,pi)
dot("curpoint(C, pi)", curpoint(C,pi),W);

dot("curpoint(C, 2*pi)", curpoint(C,2*pi),SW);
dot("curpoint(C, 3*pi)", curpoint(C,3*pi),E);

🔗geometry-fig089

Show geometry/fig0890.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Arc | #Ellipse | #Abscissa | #Point

import geometry;
size(12cm,0);

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

point A=(3.5,0.5);
dot("$A$",A,SW,red);

arc C=arc(ellipse(A,2,1,-30),90,270,fromCenter,CCW);
real l=arclength(C);

draw(C,Arrow);
draw(complementary(C),grey+dashed);
distance("$R=2$",A,point(C.el,0),0);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="curpoint(arc,real)"/></asyxml>*/
dot("curpoint(C, 0)", curpoint(C,0),E);
dot("curpoint(C, l/4)", curpoint(C,l/4),0.5N+E);
dot("curpoint(C, -l/4)", curpoint(C,-l/4));

dot("curpoint(C, l/2)", point(C,curabscissa(l/2)),W); // point(C,curabscissa(l/2)) is similar to curpoint(C,pi)
dot("curpoint(C, l)", curpoint(C,l), SW);
dot("curpoint(C, 3*l/2)", curpoint(C,3*l/2),E);

🔗geometry-fig090

Show geometry/fig0900.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Arc | #Circle | #Abscissa | #Point

import geometry;
size(10cm,0);

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

point A=(3.5,0.5);
dot("$A$", A, S, red);

arc C=arc(circle(A,2), 60, 270, CCW);
draw(C,Arrow);
draw(complementary(C), grey+dashed);
distance("$R=2$",A,point(C.el,0),0);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="angpoint(arc,real)"/></asyxml>*/
dot("angpoint(C, 90)",  angpoint(C,90), W);

dot("angpoint(C, 180)", point(C,angabscissa(180)), SW); // point(C,angabscissa(180)) is similar to angpoint(C,180)

dot("angpoint(C, 270)", angpoint(C,270), E);
dot("angpoint(C, -45)", angpoint(C,-45), E);

🔗geometry-fig091

Show geometry/fig0910.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Arc | #Ellipse | #Point | #Abscissa

import geometry;
size(12cm,0);

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

point A=(3.5,0.5);
dot("$A$", A, S, red);

/*<asyxml><view file="modules/geometry.asy" type="arc" signature="reverse(arc)"/></asyxml>*/
arc C=reverse(arc(ellipse(A,2,1,20), 45, 270, fromCenter));
draw(C,Arrow);
draw(complementary(C), grey+dashed);
distance("$R=2$",A,point(C.el,0),0);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="angpoint(arc,real)"/></asyxml>*/
dot("angpoint(C, 90)",  angpoint(C,90), SW);

dot("angpoint(C, 180)", point(C,angabscissa(180)), NW); // point(C,angabscissa(180)) is similar to angpoint(C,180)

dot("angpoint(C, 270)", angpoint(C,270), E);
dot("angpoint(C, -45)", angpoint(C,-45), E);

🔗geometry-fig092

Show geometry/fig0920.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Arc | #Circle | #Abscissa | #Point

import geometry;
unitsize(1.5cm);

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

real R=2;
point A=(3.5,1.5);

dot("$A$",A,S,red);

arc C=arc(circle(A,2), 45, 270);
draw(C,Arrow);
draw(complementary(C),grey+dashed);
distance("$R=2$",A,point(C,0),0);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="point(arc,real)"/></asyxml>*/
dot("point(C, 15)", point(C,15), 2N, 3mm+blue);

dot("point(C, 30)",
    point(C,nodabscissa(30)), // OR point(C,40)
    2W,3mm+blue);

/*<asyxml><view file="modules/geometry.asy" type="int" signature="arcnodesnumber(explicit arc)"/></asyxml>*/
dot(Label("point(C, 3*arcnodesnumber(R)/4)",UnFill),
    point(C, 3*arcnodesnumber(C)/4), 2E, 3mm+blue);

dot((path)C, yellow);

🔗geometry-fig093

Show geometry/fig0930.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Arc | #Ellipse | #Abscissa | #Point

import geometry;
unitsize(1.5cm);

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

real R=2;
point A=(3.5,1.5);

dot("$A$",A,S,red);

arc C=arc(ellipse(A,2,1,45), 45, 270, fromCenter);
draw(C,Arrow);
draw(complementary(C),grey+dashed);
distance("$R=2$",A,point(C.el,0),0);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="point(arc,real)"/></asyxml>*/
dot("point(C, 15)", point(C,15), W, 3mm+blue);

dot("point(C, 30)",
    point(C,nodabscissa(30)), // OR point(C,40)
    S,3mm+blue);

/*<asyxml><view file="modules/geometry.asy" type="int" signature="arcnodesnumber(explicit arc)"/></asyxml>*/
dot(Label("point(C, 3*arcnodesnumber(R)/4)",UnFill),
    point(C, 3*arcnodesnumber(C)/4), 2E, 3mm+blue);

dot((path)C, yellow);

🔗geometry-fig094

Show geometry/fig0940.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Arc | #Circle | #Abscissa | #Point

import geometry;
unitsize(2cm);
linemargin=0.5cm;

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

point A=(3.5,0.75);
dot("$A$",A,S);
point B=A+(cos(0.5),cos(1));
dot("$B$",B,S);


arc c=arc(circle(A,2), 45, 270, CCW);
arc cc=complementary(c);
draw(c,Arrow);
draw(cc,dashed+grey);

line l=line(A,B);
draw(l);
point M=intersectionpoints(l,c)[0];
point P=intersectionpoints(l,cc)[0];

dot("", M, 2E);
dot("$M$", M, 2W, linewidth(2mm));
dot("", P, 2E);
dot("$P$", P, 2W, linewidth(2mm));
dot("$O$", point(c,0), SE);

point p=A-(4,2.5);
transform t=shift((0,-0.3));
transform T=shift((4,0));
real x;

/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="angabscissa(arc,point)"/></asyxml>*/
x=angabscissa(c,M).x;
label("angabscissa(c,M).x=$"+(string)x+"^\circ$",p,E);
dot(angpoint(c,x),1mm+red);
x=angabscissa(c,P).x;
label("angabscissa(c,P).x=$"+(string)x+"^\circ$",T*p,E);
dot(angpoint(c,x),1mm+red);

p=t*p;
/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="curabscissa(arc,point)"/></asyxml>*/
x=curabscissa(c,M).x;
dot(curpoint(c,x),1mm+red);
label("curabscissa(c,M).x="+(string)x,p,E);
x=curabscissa(c,P).x;
label("curabscissa(c,P).x="+(string)x,T*p,E);
dot(curpoint(c,x),1mm+red);

p=t*p;
/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="nodabscissa(arc,point)"/></asyxml>*/
x=nodabscissa(c,M).x;
label("nodabscissa(c,M).x="+(string)x,p,E);
dot(point(c,x),1mm+red);
label("nodabscissa(c,P).x= \scriptsize{ERROR (point is not on the arc!)}",T*p,E);

p=t*p;
/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="relabscissa(arc,point)"/></asyxml>*/
x=relabscissa(c,M).x;
label("relabscissa(c,M).x="+(string)x,p,E);
dot(relpoint(c,x),1mm+red);
x=relabscissa(c,P).x;
label("relabscissa(c,P).x="+(string)x,T*p,E);
dot(relpoint(c,x),1mm+red);

🔗geometry-fig095

Show geometry/fig0950.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Arc | #Ellipse | #Abscissa | #Point

import geometry;
unitsize(2cm);
linemargin=0.5cm;

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

point A=(3.5,0.75);
dot("$A$",A,S);
point B=A+(cos(0.5),cos(1));
dot("$B$",B,S);


arc c=rotate(45,B)*xscale(2,A)*arc(circle(A,2), 45, 270, CCW);
arc cc=complementary(c);
draw(c,Arrow);
draw(cc,dashed+grey);

line l=line(A,B);
draw(l);
point M=intersectionpoints(l,c)[0];
point P=intersectionpoints(l,cc)[0];

dot("", M, 2E);
dot("$M$", M, 2W, linewidth(2mm));
dot("", P, 2E);
dot("$P$", P, 2W, linewidth(2mm));
dot("$O$", point(c,0), SE);

point p=A-(4,2.5);
transform t=shift((0,-0.3));
transform T=shift((4,0));
real x;

/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="angabscissa(arc,point)"/></asyxml>*/
x=angabscissa(c,M).x;
label("angabscissa(c,M).x=$"+(string)x+"^\circ$",p,E);
dot(angpoint(c,x),1mm+red);
x=angabscissa(c,P).x;
label("angabscissa(c,P).x=$"+(string)x+"^\circ$",T*p,E);
dot(angpoint(c,x),1mm+red);

p=t*p;
/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="curabscissa(arc,point)"/></asyxml>*/
x=curabscissa(c,M).x;
dot(curpoint(c,x),1mm+red);
label("curabscissa(c,M).x="+(string)x,p,E);
x=curabscissa(c,P).x;
label("curabscissa(c,P).x="+(string)x,T*p,E);
dot(curpoint(c,x),1mm+red);

p=t*p;
/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="nodabscissa(arc,point)"/></asyxml>*/
x=nodabscissa(c,M).x;
label("nodabscissa(c,M).x="+(string)x,p,E);
dot(point(c,x),1mm+red);
label("nodabscissa(c,P).x= \scriptsize{ERROR (point is not on the arc!)}",T*p,E);

p=t*p;
/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="relabscissa(arc,point)"/></asyxml>*/
x=relabscissa(c,M).x;
label("relabscissa(c,M).x="+(string)x,p,E);
dot(relpoint(c,x),1mm+red);
x=relabscissa(c,P).x;
label("relabscissa(c,P).x="+(string)x,T*p,E);
dot(relpoint(c,x),1mm+red);

🔗geometry-fig096

Show geometry/fig0960.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Arc | #Circle | #Line | #Abscissa | #Intersection | #Point

import geometry;
size(8cm);

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

point A=(-1,0) ; dot("$A$",A,S);
point B=(1,1)  ; dot("$B$",B,S);
point C=(0,0)  ;
point D=(1,-1) ; dot("$D$",D,SW);

arc c=arc(circle(C,2), 0, 270);
draw(complementary(c),dashed+grey);

line l1=line(A,B); draw(l1);
line l2=line(C,D); draw(l2);

point[] J=intersectionpoints(l1,c);
point[] K=intersectionpoints(l2,c);

/*<asyxml><view file="modules/geometry.asy" type="arc" signature="arc(explicit arc,point,point)"/></asyxml>*/
draw(arc(c,K[0],J[0]),2mm+0.8yellow);
draw(arc(c,J[1],K[0]),2mm+0.8red);
/*<asyxml><view file="modules/geometry.asy" type="arc" signature="arc(explicit arc,abscissa,abscissa)"/></asyxml>*/
draw(arc(c,relabscissa(c,J[0]),relabscissa(1)),2mm+0.8green);
draw(arc(c,relabscissa(0),relabscissa(c,J[1])),2mm+0.8blue);

dot("$J_0$",J[0],2NW);
dot("$J_1$",J[1],2N);
dot("$K_0$",K[0],2W);

draw(c, 1mm+white);

🔗geometry-fig097

Show geometry/fig0970.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Arc | #Ellipse | #Line | #Abscissa | #Intersection | #Point

import geometry;
size(8cm);

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

point A=(-1,0) ; dot("$A$",A,S);
point B=(1,1)  ; dot("$B$",B,S);
point C=(0,0)  ;
point D=(1,-1) ; dot("$D$",D,SW);

arc c=arc(ellipse(C,2,1,20), 0, 270);
draw(complementary(c),dashed+grey);

line l1=line(A,B); draw(l1);
line l2=line(C,D); draw(l2);

point[] J=intersectionpoints(l1,c);
point[] K=intersectionpoints(l2,c);

/*<asyxml><view file="modules/geometry.asy" type="arc" signature="arc(explicit arc,point,point)"/></asyxml>*/
draw(arc(c,J[0],K[0]),2mm+0.8yellow);
draw(arc(c,K[0],J[1]),2mm+0.8red);
/*<asyxml><view file="modules/geometry.asy" type="arc" signature="arc(explicit arc,abscissa,abscissa)"/></asyxml>*/
draw(arc(c,relabscissa(c,J[1]),relabscissa(1)),2mm+0.8green);
draw(arc(c,relabscissa(0),relabscissa(c,J[0])),2mm+0.8blue);

dot("$J_0$",J[0],2N);
dot("$J_1$",J[1],N+2W);
dot("$K_0$",K[0],2N);

draw(c, 1mm+white);

🔗geometry-fig098

Show geometry/fig0980.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Arc | #Arrows/Bars | #Circle | #Abscissa

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

arc a=arc(circle(A,2), 45, 270);
draw(a,linewidth(3mm),ArcArrow(5mm));

/*<asyxml><view file="modules/geometry.asy" type="arc" signature="arc(explicit arc,abscissa,abscissa)"/></asyxml>*/
draw(arc(a,angabscissa(135),angabscissa(225)),1mm+red,ArcArrow(3mm),TrueMargin(0,0.5mm));

🔗geometry-fig099

Show geometry/fig0990.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Arc | #Arrows/Bars | #Ellipse | #Abscissa

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

arc a=arc(ellipse(A,2,1,45), 45, 270, fromCenter);
draw(a,linewidth(3mm),ArcArrow(5mm));

/*<asyxml><view file="modules/geometry.asy" type="arc" signature="arc(explicit arc,abscissa,abscissa)"/></asyxml>*/
draw(arc(a,angabscissa(135),angabscissa(225)),1mm+red,ArcArrow(3mm),TrueMargin(0,0.5mm));

🔗geometry-fig100

Show geometry/fig1000.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Arc | #Arrows/Bars | #Circle | #Abscissa | #Coords system

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);

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