Asymptote: 3D graphics

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Asymptote (Vector Graphics Language)
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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 import three, import three;

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: In order 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);

[asy] import three; draw(shift(2,3,4)*scale(5,20,7)*unitcone,paleblue);[/asy]

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 (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.
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