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Asymptote: 3d graph over a disc

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5

Is there a straightforward way to draw a 3D graph over a disc domain? Say
z=x^2-y^2 for x^2+y^2<1.

[I just started to use asymptote; this page explained me how to do it for a rectangular domain. I hope it is an easy question.]

graphs asymptote

share|improve this question

asked yesterday

Anton PetruninAnton Petrunin

542313

add a comment | 

5

Is there a straightforward way to draw a 3D graph over a disc domain? Say
z=x^2-y^2 for x^2+y^2<1.

[I just started to use asymptote; this page explained me how to do it for a rectangular domain. I hope it is an easy question.]

graphs asymptote

share|improve this question

asked yesterday

Anton PetruninAnton Petrunin

542313

add a comment | 

Is there a straightforward way to draw a 3D graph over a disc domain? Say
z=x^2-y^2 for x^2+y^2<1.

[I just started to use asymptote; this page explained me how to do it for a rectangular domain. I hope it is an easy question.]

graphs asymptote

share|improve this question

asked yesterday

Anton PetruninAnton Petrunin

542313

share|improve this question

asked yesterday

Anton PetruninAnton Petrunin

542313

share|improve this question

asked yesterday

Anton PetruninAnton Petrunin

542313

asked yesterday

Anton PetruninAnton Petrunin

542313

asked yesterday

Anton PetruninAnton Petrunin

542313

1 Answer
1

active

oldest

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5

One way to make sure that x^2+y^2<1 is to use polar coordinates. Then x=r cos(phi) and y=r sin(phi).

documentclass[variwidth,border=3.14mm]standalone
usepackageasypictureB
begindocument
beginasypicturename=discgraph
 usepackage("mathrsfs");
 import graph3;
 import solids;
 import interpolate;

 settings.outformat="pdf";


 size(500); 

 defaultpen(0.5mm);
 pen darkgreen=rgb(0,138/255,122/255);

 draw(Label("$x$",1),(0,0,0)--(1.2,0,0),darkgreen,Arrow3);
 draw(Label("$y$",1),(0,0,0)--(0,1.2,0),darkgreen,Arrow3);
 draw(Label("$f(x,y)$",1),(0,0,0)--(0,0,0.6),darkgreen,Arrow3);



 //function: call the radial coordinate r=t.x and the angle phi=t.y
 triple f(pair t) 
 return ((t.x)*cos(t.y), (t.x)*sin(t.y),
 ((t.x)*cos(t.y))^2-((t.x)*sin(t.y))^2);
 

 surface s=surface(f,(0,1),(0.49,2.5*pi),32,16,
 usplinetype=new splinetype[] notaknot,notaknot,monotonic,
 vsplinetype=Spline);
 pen p=rgb(0,0,.7); 
 draw(s,lightolive+white);
endasypicture 
enddocument

share|improve this answer

answered yesterday

marmotmarmot

114k5145276

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Thank you, but is there a direct way to make a condition x^2+y^2<1 for the arguments?
  
  – Anton Petrunin
  yesterday
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  @marmot: The x-axis near origin should be hidden from the given point of view. Is there any way to improve this issue? E.g., by setting some samples-option?
  
  – Marian G.
  yesterday
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  
  A line has a thickness, a surface not. It is why you see the x-axis near origin. You can observe the same behavior with a simple square surface and the x-axis. Perhaps it is possible to avoid its by creating two z translated surfaces, but you have to manage the boundary...
  
  – O.G.
  yesterday
  

  
  
  
  

add a comment | 

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5

One way to make sure that x^2+y^2<1 is to use polar coordinates. Then x=r cos(phi) and y=r sin(phi).

documentclass[variwidth,border=3.14mm]standalone
usepackageasypictureB
begindocument
beginasypicturename=discgraph
 usepackage("mathrsfs");
 import graph3;
 import solids;
 import interpolate;

 settings.outformat="pdf";


 size(500); 

 defaultpen(0.5mm);
 pen darkgreen=rgb(0,138/255,122/255);

 draw(Label("$x$",1),(0,0,0)--(1.2,0,0),darkgreen,Arrow3);
 draw(Label("$y$",1),(0,0,0)--(0,1.2,0),darkgreen,Arrow3);
 draw(Label("$f(x,y)$",1),(0,0,0)--(0,0,0.6),darkgreen,Arrow3);



 //function: call the radial coordinate r=t.x and the angle phi=t.y
 triple f(pair t) 
 return ((t.x)*cos(t.y), (t.x)*sin(t.y),
 ((t.x)*cos(t.y))^2-((t.x)*sin(t.y))^2);
 

 surface s=surface(f,(0,1),(0.49,2.5*pi),32,16,
 usplinetype=new splinetype[] notaknot,notaknot,monotonic,
 vsplinetype=Spline);
 pen p=rgb(0,0,.7); 
 draw(s,lightolive+white);
endasypicture 
enddocument

share|improve this answer

answered yesterday

marmotmarmot

114k5145276

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Thank you, but is there a direct way to make a condition x^2+y^2<1 for the arguments?
  
  – Anton Petrunin
  yesterday
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  @marmot: The x-axis near origin should be hidden from the given point of view. Is there any way to improve this issue? E.g., by setting some samples-option?
  
  – Marian G.
  yesterday
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  
  A line has a thickness, a surface not. It is why you see the x-axis near origin. You can observe the same behavior with a simple square surface and the x-axis. Perhaps it is possible to avoid its by creating two z translated surfaces, but you have to manage the boundary...
  
  – O.G.
  yesterday
  

  
  
  
  

add a comment | 

5

One way to make sure that x^2+y^2<1 is to use polar coordinates. Then x=r cos(phi) and y=r sin(phi).

documentclass[variwidth,border=3.14mm]standalone
usepackageasypictureB
begindocument
beginasypicturename=discgraph
 usepackage("mathrsfs");
 import graph3;
 import solids;
 import interpolate;

 settings.outformat="pdf";


 size(500); 

 defaultpen(0.5mm);
 pen darkgreen=rgb(0,138/255,122/255);

 draw(Label("$x$",1),(0,0,0)--(1.2,0,0),darkgreen,Arrow3);
 draw(Label("$y$",1),(0,0,0)--(0,1.2,0),darkgreen,Arrow3);
 draw(Label("$f(x,y)$",1),(0,0,0)--(0,0,0.6),darkgreen,Arrow3);



 //function: call the radial coordinate r=t.x and the angle phi=t.y
 triple f(pair t) 
 return ((t.x)*cos(t.y), (t.x)*sin(t.y),
 ((t.x)*cos(t.y))^2-((t.x)*sin(t.y))^2);
 

 surface s=surface(f,(0,1),(0.49,2.5*pi),32,16,
 usplinetype=new splinetype[] notaknot,notaknot,monotonic,
 vsplinetype=Spline);
 pen p=rgb(0,0,.7); 
 draw(s,lightolive+white);
endasypicture 
enddocument

share|improve this answer

answered yesterday

marmotmarmot

114k5145276

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Thank you, but is there a direct way to make a condition x^2+y^2<1 for the arguments?
  
  – Anton Petrunin
  yesterday
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  @marmot: The x-axis near origin should be hidden from the given point of view. Is there any way to improve this issue? E.g., by setting some samples-option?
  
  – Marian G.
  yesterday
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  
  A line has a thickness, a surface not. It is why you see the x-axis near origin. You can observe the same behavior with a simple square surface and the x-axis. Perhaps it is possible to avoid its by creating two z translated surfaces, but you have to manage the boundary...
  
  – O.G.
  yesterday
  

  
  
  
  

add a comment | 

One way to make sure that x^2+y^2<1 is to use polar coordinates. Then x=r cos(phi) and y=r sin(phi).

documentclass[variwidth,border=3.14mm]standalone
usepackageasypictureB
begindocument
beginasypicturename=discgraph
 usepackage("mathrsfs");
 import graph3;
 import solids;
 import interpolate;

 settings.outformat="pdf";


 size(500); 

 defaultpen(0.5mm);
 pen darkgreen=rgb(0,138/255,122/255);

 draw(Label("$x$",1),(0,0,0)--(1.2,0,0),darkgreen,Arrow3);
 draw(Label("$y$",1),(0,0,0)--(0,1.2,0),darkgreen,Arrow3);
 draw(Label("$f(x,y)$",1),(0,0,0)--(0,0,0.6),darkgreen,Arrow3);



 //function: call the radial coordinate r=t.x and the angle phi=t.y
 triple f(pair t) 
 return ((t.x)*cos(t.y), (t.x)*sin(t.y),
 ((t.x)*cos(t.y))^2-((t.x)*sin(t.y))^2);
 

 surface s=surface(f,(0,1),(0.49,2.5*pi),32,16,
 usplinetype=new splinetype[] notaknot,notaknot,monotonic,
 vsplinetype=Spline);
 pen p=rgb(0,0,.7); 
 draw(s,lightolive+white);
endasypicture 
enddocument

share|improve this answer

answered yesterday

marmotmarmot

114k5145276

documentclass[variwidth,border=3.14mm]standalone
usepackageasypictureB
begindocument
beginasypicturename=discgraph
 usepackage("mathrsfs");
 import graph3;
 import solids;
 import interpolate;

 settings.outformat="pdf";


 size(500); 

 defaultpen(0.5mm);
 pen darkgreen=rgb(0,138/255,122/255);

 draw(Label("$x$",1),(0,0,0)--(1.2,0,0),darkgreen,Arrow3);
 draw(Label("$y$",1),(0,0,0)--(0,1.2,0),darkgreen,Arrow3);
 draw(Label("$f(x,y)$",1),(0,0,0)--(0,0,0.6),darkgreen,Arrow3);



 //function: call the radial coordinate r=t.x and the angle phi=t.y
 triple f(pair t) 
 return ((t.x)*cos(t.y), (t.x)*sin(t.y),
 ((t.x)*cos(t.y))^2-((t.x)*sin(t.y))^2);
 

 surface s=surface(f,(0,1),(0.49,2.5*pi),32,16,
 usplinetype=new splinetype[] notaknot,notaknot,monotonic,
 vsplinetype=Spline);
 pen p=rgb(0,0,.7); 
 draw(s,lightolive+white);
endasypicture 
enddocument

share|improve this answer

answered yesterday

marmotmarmot

114k5145276

answered yesterday

marmotmarmot

114k5145276

answered yesterday

marmotmarmot

114k5145276