Difference between revisions of "Asymptote: 3D graphics"

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{{Asymptote}}
 
{{Asymptote}}
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 +
==Three==
 +
Three is a module in Asymptote that allows the user to create three dimensional graphics. Usually all you must do is add <code>import three;</code> to your code, then change from using doubles eg. (x,y) to using triples eg. (x,y,z) as coordinates. Some functions do not work when three is active. For example: To fill a surface, one must define a surface and draw that, instead of using <tt>[[asymptote: Filling|filldraw]]</tt>. This is also described at http://www.artofproblemsolving.com/Forum/viewtopic.php?f=519&t=399845.
  
==Three==
+
===Data types===
Three is a module in Asymptote that allows the user to create three dimensional graphics. Usually all you must do is import three,
+
three defines the data types:
<code>
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* path3, (3D version of path)
 +
* guide3, (3D version of guide)
 +
* and surface (a surface bounded by a path(3))
 +
and other, less important ones.
 +
 
 +
===Definitions===
 +
three defines the surfaces:
 +
* unitcube
 +
* unitsphere
 +
* unitdisk
 +
* unitplane
 +
* unitcylinder
 +
* unitcone
 +
* unitsolidcone
 +
* and unithemisphere.
 +
These can be drawn like you would normally draw an object in 2D.
 +
<pre><nowiki>
 +
draw(unitcylinder,heavymagenta);
 +
</nowiki></pre>
 +
<asy>
 +
import three;
 +
draw(unitcylinder,heavymagenta);</asy>
 +
Transforms also work:
 +
<pre><nowiki>
 +
draw(shift(2,3,4)*scale(5,20,7)*unitcone,paleblue);
 +
</nowiki></pre>
 +
<asy>
 +
import three;
 +
draw(shift(2,3,4)*scale(5,20,7)*unitcone,paleblue);</asy>
 +
You can even add an outline:
 +
<pre><nowiki>
 +
draw(unitcube,orange,blue);
 +
</nowiki></pre>
 +
<asy>
 +
import three;
 +
draw(unitcube,orange,blue);</asy>
 +
(Just beware - if you give something with a circle as a base an outline then it gets really wonky, like a unitsphere with an outline:
 +
<pre><nowiki>
 +
draw(unitsphere,red,black);
 +
</nowiki></pre>
 +
<asy>
 
import three;
 
import three;
</code>
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draw(unitsphere,red,black);</asy>
 +
So try not to do that unless you want your stuff to look wonky.)
  
then change from using doubles to using triples as coordinates. Though some functions do not work when three is active. In order to fill a surface, for example, one must define a surface and draw that. instead of using [[asymptote: Filling|filldraw]]. This is also described <url>http://www.artofproblemsolving.com/Forum/viewtopic.php?f=519&t=399845 here</url>.
 
 
==Projection==
 
==Projection==
 
You can use
 
You can use
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currentprojection=orthographic(x,y,z);
 
currentprojection=orthographic(x,y,z);
 
</code>
 
</code>
To change current the view.
+
to change the current view.
 
<code>
 
<code>
 
currentprojection=perspective(x,y,z);
 
currentprojection=perspective(x,y,z);
 
</code>
 
</code>
Does the same thing, but is distorts the picture to copy actual viewing.
+
does the same thing, but it distorts the picture to imitate actual perspective.
  
 
'''Example:'''
 
'''Example:'''
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<pre><nowiki>
 
<pre><nowiki>
 
import three;
 
import three;
/* perspective line /*
+
/* perspective line */
 
draw(unitcube,palegrey);
 
draw(unitcube,palegrey);
 
</nowiki></pre>
 
</nowiki></pre>
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  draw(unitcube,palegrey);
 
  draw(unitcube,palegrey);
 
</asy>
 
</asy>
==Example==
+
 
 +
'''Note:''' When current projection is not given, <tt>three</tt> tries to find the "best" view.
 +
 
 +
==Interactive Projection==
 +
When using Asymptote on your computer (but not on AoPS), you can add some code that lets you rotate/pan/zoom with the mouse.
 +
<pre><nowiki>
 +
import settings;
 +
leftbutton=new string[] {"rotate","zoom","shift","pan"};
 +
middlebutton=new string[] {"menu"};
 +
rightbutton=new string[] {"zoom/menu","rotateX","rotateY","rotateZ"};
 +
wheelup=new string[] {"zoomin"};
 +
wheeldown=new string[] {"zoomout"};
 +
</nowiki></pre>
 +
When compiling to PDF, it will allow you to rotate/pan/zoom with the mouse.
 +
 
 +
==Arrows and bars==
 +
Arrows and bars in 3D are the same as in 2D except you add a 3 to the end of the name.
 +
Example.
 +
<pre><nowiki>
 +
import three;
 +
draw((0,0,0)--(1,1,1),green,Arrows3);
 +
draw((0,1,0)--(1,0,1),blue,Bars3);
 +
</nowiki></pre>
 +
<asy>
 +
import three;
 +
draw((0,0,0)--(1,1,1),green,Arrows3);
 +
draw((0,1,0)--(1,0,1),blue,Bars3);
 +
</asy>
 +
==Examples==
 
<pre><nowiki>
 
<pre><nowiki>
 
import three;
 
import three;
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label("$y=1$",(1,1,0.5),E);
 
label("$y=1$",(1,1,0.5),E);
 
label("$z=1$",(1,0.5,0),SE);
 
label("$z=1$",(1,0.5,0),SE);
label("$c$",(0.5,0.5,0.5),N);[/asy]
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label("$c$",(0.5,0.5,0.5),N);
 
</nowiki></pre>
 
</nowiki></pre>
 
Which renders to
 
Which renders to
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label("$z=1$",(1,0.5,0),SE);
 
label("$z=1$",(1,0.5,0),SE);
 
label("$c$",(0.5,0.5,0.5),N);</asy>
 
label("$c$",(0.5,0.5,0.5),N);</asy>
 +
 +
For other examples, see [[Platonic solids]] and [[2000 AMC 12 Problems/Problem 25]].
 +
 
==Other 3D Modules==
 
==Other 3D Modules==
 
Other modules in Asymptote that are for 3D are:
 
Other modules in Asymptote that are for 3D are:
graph3, grid3, contour3
+
* graph3
 +
* grid3
 +
* contour3
 +
* and solids.

Latest revision as of 08:53, 4 August 2024

Asymptote (Vector Graphics Language)
Getting Started - Basics - Drawing - Labeling - Filling - Useful functions - Examples - Macros and Packages

Help - Reference - Advanced Asymptote - 3D Graphics - CSE5 Package - How to


Three

Three is a module in Asymptote that allows the user to create three dimensional graphics. Usually all you must do is add import three; to your code, then change from using doubles eg. (x,y) to using triples eg. (x,y,z) as coordinates. Some functions do not work when three is active. For example: To fill a surface, one must define a surface and draw that, instead of using filldraw. This is also described at http://www.artofproblemsolving.com/Forum/viewtopic.php?f=519&t=399845.

Data types

three defines the data types:

  • path3, (3D version of path)
  • guide3, (3D version of guide)
  • and surface (a surface bounded by a path(3))

and other, less important ones.

Definitions

three defines the surfaces:

  • unitcube
  • unitsphere
  • unitdisk
  • unitplane
  • unitcylinder
  • unitcone
  • unitsolidcone
  • and unithemisphere.

These can be drawn like you would normally draw an object in 2D.

draw(unitcylinder,heavymagenta);

[asy] import three; draw(unitcylinder,heavymagenta);[/asy] Transforms also work:

draw(shift(2,3,4)*scale(5,20,7)*unitcone,paleblue);

[asy] import three; draw(shift(2,3,4)*scale(5,20,7)*unitcone,paleblue);[/asy] You can even add an outline:

draw(unitcube,orange,blue);

[asy] import three; draw(unitcube,orange,blue);[/asy] (Just beware - if you give something with a circle as a base an outline then it gets really wonky, like a unitsphere with an outline:

draw(unitsphere,red,black);

[asy] import three; draw(unitsphere,red,black);[/asy] So try not to do that unless you want your stuff to look wonky.)

Projection

You can use currentprojection=orthographic(x,y,z); to change the current view. currentprojection=perspective(x,y,z); does the same thing, but it distorts the picture to imitate actual perspective.

Example:

base code:

import three;
/* perspective line */
draw(unitcube,palegrey);

Using currentprojection=orthographic(1,1/2,1/2); We get a unit cube as: [asy] import three; currentprojection=orthographic(1,1/2,1/2);  draw(unitcube,palegrey); [/asy] Using currentprojection=perspective(1,1/2,1/2); We get a unit cube as: [asy] import three; currentprojection=perspective(1,1/2,1/2);  draw(unitcube,palegrey); [/asy]

Note: When current projection is not given, three tries to find the "best" view.

Interactive Projection

When using Asymptote on your computer (but not on AoPS), you can add some code that lets you rotate/pan/zoom with the mouse.

import settings;
leftbutton=new string[] {"rotate","zoom","shift","pan"};
middlebutton=new string[] {"menu"};
rightbutton=new string[] {"zoom/menu","rotateX","rotateY","rotateZ"};
wheelup=new string[] {"zoomin"};
wheeldown=new string[] {"zoomout"};

When compiling to PDF, it will allow you to rotate/pan/zoom with the mouse.

Arrows and bars

Arrows and bars in 3D are the same as in 2D except you add a 3 to the end of the name. Example.

import three;
draw((0,0,0)--(1,1,1),green,Arrows3);
draw((0,1,0)--(1,0,1),blue,Bars3);

[asy] import three; draw((0,0,0)--(1,1,1),green,Arrows3); draw((0,1,0)--(1,0,1),blue,Bars3); [/asy]

Examples

import three;
unitsize(1cm);
size(200);
currentprojection=perspective(1/3,-1,1/2);
draw((0,0,0)--(1,0,0)--(1,1,0)--(0,1,0)--cycle,red);
draw((0,0,0)--(0,0,1),red);
draw((0,1,0)--(0,1,1),red);
draw((1,1,0)--(1,1,1),red);
draw((1,0,0)--(1,0,1),red);
draw((0,0,1)--(1,0,1)--(1,1,1)--(0,1,1)--cycle,red);
draw((0,0,0)--(1,0,0)--(1,1,0)--cycle,red);
draw((0,0,0)--(1,1,0)--(1,1,1)--cycle,blue);
label("$o$",(0,0,0),NW);
label("$x=1$",(0.5,0,0),S);
label("$y=1$",(1,1,0.5),E);
label("$z=1$",(1,0.5,0),SE);
label("$c$",(0.5,0.5,0.5),N);

Which renders to [asy] import three; unitsize(1cm); size(200); currentprojection=orthographic(1/3,-1,1/2); draw((0,0,0)--(1,0,0)--(1,1,0)--(0,1,0)--cycle,red); draw((0,0,0)--(0,0,1),red); draw((0,1,0)--(0,1,1),red); draw((1,1,0)--(1,1,1),red); draw((1,0,0)--(1,0,1),red); draw((0,0,1)--(1,0,1)--(1,1,1)--(0,1,1)--cycle,red); draw((0,0,0)--(1,0,0)--(1,1,0)--cycle,red); draw((0,0,0)--(1,1,0)--(1,1,1)--cycle,blue); label("$o$",(0,0,0),NW); label("$x=1$",(0.5,0,0),S); label("$y=1$",(1,1,0.5),E); label("$z=1$",(1,0.5,0),SE); label("$c$",(0.5,0.5,0.5),N);[/asy]

For other examples, see Platonic solids and 2000 AMC 12 Problems/Problem 25.

Other 3D Modules

Other modules in Asymptote that are for 3D are:

  • graph3
  • grid3
  • contour3
  • and solids.