Difference between revisions of "Asymptote: 3D graphics"
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{{Asymptote}} | {{Asymptote}} | ||
+ | |||
+ | ==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. | ||
+ | |||
+ | ===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 | ||
+ | <pre><nowiki> | ||
+ | draw(unitcube,green); | ||
+ | </nowiki></pre> | ||
+ | <asy> | ||
+ | import three; | ||
+ | draw(unitcube,green);</asy> | ||
+ | Transforms also work | ||
+ | <pre><nowiki> | ||
+ | draw(shift(2,3,4)*scale(5,20,7)*unitcone,paleblue); | ||
+ | </nowiki></pre> | ||
+ | <asy> | ||
import three; | import three; | ||
− | </ | + | draw(shift(2,3,4)*scale(5,20,7)*unitcone,paleblue);</asy> |
− | |||
==Projection== | ==Projection== | ||
You can use | You can use | ||
Line 14: | Line 42: | ||
currentprojection=orthographic(x,y,z); | currentprojection=orthographic(x,y,z); | ||
</code> | </code> | ||
− | + | to change the current view. | |
<code> | <code> | ||
currentprojection=perspective(x,y,z); | currentprojection=perspective(x,y,z); | ||
</code> | </code> | ||
− | + | does the same thing, but it distorts the picture to imitate actual perspective. | |
'''Example:''' | '''Example:''' | ||
Line 25: | Line 53: | ||
<pre><nowiki> | <pre><nowiki> | ||
import three; | import three; | ||
− | /* perspective line / | + | /* perspective line */ |
draw(unitcube,palegrey); | draw(unitcube,palegrey); | ||
</nowiki></pre> | </nowiki></pre> | ||
Line 48: | Line 76: | ||
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; | ||
Line 66: | Line 122: | ||
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); | + | label("$c$",(0.5,0.5,0.5),N); |
</nowiki></pre> | </nowiki></pre> | ||
Which renders to | Which renders to | ||
Line 87: | Line 143: | ||
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 | + | * graph3 |
+ | * grid3 | ||
+ | * contour3 | ||
+ | * and solids. |
Revision as of 09:08, 23 May 2024
Contents
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(unitcube,green);
Transforms also work
draw(shift(2,3,4)*scale(5,20,7)*unitcone,paleblue);
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:
Using
currentprojection=perspective(1,1/2,1/2);
We get a unit cube as:
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);
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
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.