Difference between revisions of "AoPSWiki:Sandbox"

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<h1>Asymptote tutorial for AoPS</h1>
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<span style="font-size: 200%; color: #27445C">'''Essential Reference for Using Asymptote in AoPS'''</span>
<dd>
+
A focused asymptote reference with examples and short code.<p style="margin-left: 40px"><small><br><i>Original source from eagle702 bulletin board post. Adapted and edited by <b>aquadragon.</b></i></small></p>
<div class="mw-collapsible mw-collapsed" style="width:100%">
+
----
'''The Name Asymptote'''
+
==Introduction==
<div class="mw-collapsible-content">
+
<br><dd>
<blockquote>Why Asymptote is called Asymptote?
+
=== Why Asymptote is called Asymptote? ===
<blockquote> http://asymptote.sourceforge.net/FAQ/section1.html#whyasy
+
 
Question 1.4. Why was the name Asymptote chosen?
+
<blockquote>http://asymptote.sourceforge.net/FAQ/section1.html#whyasy
Well, it isn't the perfect graphics package, but we do think it is getting there asymptotically...
+
<dd><b>Question 1.4. Why was the name Asymptote chosen?</b>
 +
 
 +
<i>Well, it isn't the perfect graphics package, but we do think it is getting there asymptotically...</i></dd>
 
</blockquote>
 
</blockquote>
</blockquote></div></div>
 
  
<div class="mw-collapsible mw-collapsed" style="width:100%">
+
=== Tips ===
'''Tips'''
+
 
<div class="mw-collapsible-content">
 
<blockquote>
 
 
* To see the asymptote code of any diagram made with asymptote, click on the diagram and it will come up.
 
* To see the asymptote code of any diagram made with asymptote, click on the diagram and it will come up.
 
* If your code is not working check to make sure you have a semicolon after each line, no extra parentheses or brackets, and no open parentheses or brackets.
 
* If your code is not working check to make sure you have a semicolon after each line, no extra parentheses or brackets, and no open parentheses or brackets.
 
* Another thing to check if your code is not working, is to make sure every variable you've used in your code is in the pair.
 
* Another thing to check if your code is not working, is to make sure every variable you've used in your code is in the pair.
</blockquote></div></div>
+
</dd><br>
  
<div class="mw-collapsible mw-collapsed" style="width:100%">
+
== Beginning your code ==
'''#1 Beginning your code'''
+
<dd>
<div class="mw-collapsible-content">
 
<blockquote>
 
 
To start your asymptote diagram you have to include [asy] at the beginning, and [/asy] at the ending.
 
To start your asymptote diagram you have to include [asy] at the beginning, and [/asy] at the ending.
</blockquote></div></div>
+
</dd><br>
  
<div class="mw-collapsible mw-collapsed" style="width:100%">
+
== Setting points ==
'''#2 Setting points'''
+
<dd>
<div class="mw-collapsible-content">
 
 
To create points in your diagram you can use
 
To create points in your diagram you can use
 
   <code>A = (0,0);</code>
 
   <code>A = (0,0);</code>
Line 37: Line 33:
  
 
Note: You should not use E, S, N, or W as variables, instead you should use EE, SS, NN, and WW, but label them as E, S, N, W. This is because E, S, N, and W are used to indicate directions in asymptote.
 
Note: You should not use E, S, N, or W as variables, instead you should use EE, SS, NN, and WW, but label them as E, S, N, W. This is because E, S, N, and W are used to indicate directions in asymptote.
</div></div>
+
</dd><br>
  
<div class="mw-collapsible mw-collapsed" style="width:100%">
+
== Pair part 1 ==
'''#3 Pair part 1'''
+
<dd>
<div class="mw-collapsible-content">
 
 
If you include variables in your diagram you have to have <math>\verb#pair#</math> somewhere in your code.
 
If you include variables in your diagram you have to have <math>\verb#pair#</math> somewhere in your code.
  
 
Example: You have two points <math>A</math> and <math>B</math>, and you're drawing a line connecting them, you need to include
 
Example: You have two points <math>A</math> and <math>B</math>, and you're drawing a line connecting them, you need to include
 
+
  <code> pair A,B; </code>
[asymptote]pair A,B;[/asymptote]
 
 
 
 
in your diagram to make it work.
 
in your diagram to make it work.
</div></div>
+
</dd><br>
  
<div class="mw-collapsible mw-collapsed" style="width:100%">
+
==Connecting two points, coloring the line'==
'''#4 Connecting two points, coloring the line'''
+
<dd>
<div class="mw-collapsible-content">
 
 
Once you have set variables <math>A</math> and <math>B</math>, you can connect them by writing
 
Once you have set variables <math>A</math> and <math>B</math>, you can connect them by writing
  
<code>draw(A--B);</code>
+
  <code>draw(A--B);</code>
  
 
Example:
 
Example:
Line 103: Line 95:
 
draw(A--B--cycle, dashed+red);
 
draw(A--B--cycle, dashed+red);
 
</asy>
 
</asy>
</div></div>
+
</dd><br>
<div class="mw-collapsible mw-collapsed" style="width:100%">
+
 
'''#5 Labeling, Midpoint'''
+
== Labeling, Midpoint ==
<div class="mw-collapsible-content">
+
<dd>
 
To label a point you can use
 
To label a point you can use
  
Line 145: Line 137:
 
label("$x$", midpoint(A--B), NE);
 
label("$x$", midpoint(A--B), NE);
 
</asy>
 
</asy>
</div></div>
+
</dd><br>
<div class="mw-collapsible mw-collapsed" style="width:100%">
+
 
'''#6 Angle Measures'''
+
== Angle Measures ==
<div class="mw-collapsible-content">
+
<dd>
 
If you want to draw an angle measure on an angle use
 
If you want to draw an angle measure on an angle use
  
Line 195: Line 187:
 
label(scale(.75)*"$90^\circ$", B, 2.5*dir(50));
 
label(scale(.75)*"$90^\circ$", B, 2.5*dir(50));
 
</asy>
 
</asy>
</div></div>
+
</dd><br>
<div class="mw-collapsible mw-collapsed" style="width:100%">
+
 
''' #7 Distance Function'''
+
== Distance Function ==
<div class="mw-collapsible-content">
+
<dd>
(Source: fath2012)
 
 
''' My distance function'''
 
''' My distance function'''
 
<code>
 
<code>
Line 209: Line 200:
 
''' A note '''
 
''' A note '''
 
Apparently a pair has an x property and a y property. I kind of discovered this it by testing. I think it might be documented somewhere.
 
Apparently a pair has an x property and a y property. I kind of discovered this it by testing. I think it might be documented somewhere.
</div></div>
+
</dd><br>
<div class="mw-collapsible mw-collapsed" style="width:100%">
+
 
'''#8 Casting'''
+
== Casting ==
<div class="mw-collapsible-content">
+
<dd>
 
(Source: fath2012)
 
(Source: fath2012)
 
''' Casting '''
 
''' Casting '''
Line 230: Line 221:
 
label((string) b,a,S);
 
label((string) b,a,S);
 
</code>
 
</code>
</div></div>
+
</dd><br>
<div class="mw-collapsible mw-collapsed" style="width:100%">
+
 
'''#9 Right Angle Mark'''
+
== Right Angle Mark ==
<div class="mw-collapsible-content">
+
<dd>
 
If you want to draw a right angle mark use this:
 
If you want to draw a right angle mark use this:
  
Line 254: Line 245:
 
draw(rightanglemark(A,B,C,1.5));
 
draw(rightanglemark(A,B,C,1.5));
 
</asy>
 
</asy>
</div></div>
+
</dd><br>
<div class="mw-collapsible mw-collapsed" style="width:100%">
+
 
'''#10 Intersection'''
+
 
<div class="mw-collapsible-content">
+
== Intersection ==
 +
<dd>
 
If you want to draw a point on an intersection of two lines you can use:
 
If you want to draw a point on an intersection of two lines you can use:
  
Line 281: Line 273:
 
F = intersectionpoint(A -- B, C -- D);
 
F = intersectionpoint(A -- B, C -- D);
 
</asy>
 
</asy>
</div></div>
+
</dd><br>
<div class="mw-collapsible mw-collapsed" style="width:100%">
+
 
'''#11 Filling'''
+
 
<div class="mw-collapsible-content">
+
== Filling ==
 +
<dd>
 
To show you how to fill in a part of a diagram with a color I'll use an example from Week 3 Problem 5 in AoPS's Introduction to Geometry course.
 
To show you how to fill in a part of a diagram with a color I'll use an example from Week 3 Problem 5 in AoPS's Introduction to Geometry course.
  
Line 373: Line 366:
 
Try out different colors to see which ones you prefer for your asymptote diagrams.
 
Try out different colors to see which ones you prefer for your asymptote diagrams.
 
Have fun!
 
Have fun!
</div></div>
+
</dd><br>
<div class="mw-collapsible mw-collapsed" style="width:100%">
+
 
'''#12 Dot'''
+
== Dot ==
<div class="mw-collapsible-content">
+
<dd>
 
If you want to draw a dot on a point on your diagram use
 
If you want to draw a dot on a point on your diagram use
  
Line 395: Line 388:
  
 
<code>dot(A);</code>
 
<code>dot(A);</code>
</div></div>
+
<br></div></div>
 +
 
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
'''#13 Size'''
 
'''#13 Size'''
Line 434: Line 428:
 
draw(rightanglemark(A,B,C,1.5));
 
draw(rightanglemark(A,B,C,1.5));
 
</asy>
 
</asy>
</div></div>
+
</dd><br>
 +
 
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
'''#14 Tick Marks'''
 
'''#14 Tick Marks'''
 
<div class="mw-collapsible-content">
 
<div class="mw-collapsible-content">
 +
<br>
 
If you want to add tick marks to a line use
 
If you want to add tick marks to a line use
  
Line 476: Line 472:
 
add(pathticks(A--B, 2, spacing=1, s=2));
 
add(pathticks(A--B, 2, spacing=1, s=2));
 
</asy>
 
</asy>
</div></div>
+
<br></div></div>
 +
 
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
'''#15 Arrows'''
 
'''#15 Arrows'''
 
<div class="mw-collapsible-content">
 
<div class="mw-collapsible-content">
 +
<br>
 
If you want to draw arrow marks to show that two lines are parallel you can use
 
If you want to draw arrow marks to show that two lines are parallel you can use
  
Line 495: Line 493:
 
draw(A--C, MidArrow(size=0.2cm));
 
draw(A--C, MidArrow(size=0.2cm));
 
</asy>
 
</asy>
</div></div>
+
<br></div></div>
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 +
 
'''#16 Shifting Coordinates'''
 
'''#16 Shifting Coordinates'''
 
<div class="mw-collapsible-content">
 
<div class="mw-collapsible-content">
 +
<br>
 
(Source: fath2012)
 
(Source: fath2012)
 
You can use these to shift coordinates if you're shifting lots of coordinates
 
You can use these to shift coordinates if you're shifting lots of coordinates
Line 508: Line 508:
 
return  (p.x,p.y + amount);
 
return  (p.x,p.y + amount);
 
}</code>
 
}</code>
</div></div>
+
<br></div></div>
 +
 
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
'''#17 Rotating'''
 
'''#17 Rotating'''
 
<div class="mw-collapsible-content">
 
<div class="mw-collapsible-content">
 +
<br>
 
(Source: nosaj and Zhaom)
 
(Source: nosaj and Zhaom)
 
Maybe if you really wanted to: rotate
 
Maybe if you really wanted to: rotate
Line 518: Line 520:
 
</code>
 
</code>
 
rotate B <math>x</math> degrees around center A is where C is.
 
rotate B <math>x</math> degrees around center A is where C is.
</div></div>
+
<br></div></div>
 +
 
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
'''#18 Circles'''
 
'''#18 Circles'''
 +
<br>
 
<div class="mw-collapsible-content">
 
<div class="mw-collapsible-content">
 
If you want to draw a circle use
 
If you want to draw a circle use
Line 540: Line 544:
 
draw(Circle((0,0),0.4),p=green+1.5bp);
 
draw(Circle((0,0),0.4),p=green+1.5bp);
 
</asy>
 
</asy>
</div></div>
+
/<br></div></div>
 +
 
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
'''#19 Dashed Lines'''
 
'''#19 Dashed Lines'''
 
<div class="mw-collapsible-content">
 
<div class="mw-collapsible-content">
 +
<br>
 
(Source: independentstudyproject)
 
(Source: independentstudyproject)
 
If you want to draw a dashed line you can use
 
If you want to draw a dashed line you can use
Line 563: Line 569:
 
dot(B);
 
dot(B);
 
</asy>
 
</asy>
</div></div>
+
<br></div></div>
 +
 
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
'''#20 Angle Mark'''
 
'''#20 Angle Mark'''
 
<div class="mw-collapsible-content">
 
<div class="mw-collapsible-content">
 +
<br>
 
(Source: Zhaom & mag1c)
 
(Source: Zhaom & mag1c)
 
To make an actual angle mark:
 
To make an actual angle mark:
 
at the top do
 
at the top do
<code><asy>
+
<code>
 
import markers;</code>
 
import markers;</code>
 
and then do for the angle:
 
and then do for the angle:
Line 590: Line 598:
 
dot("A",A,SW*0.5);
 
dot("A",A,SW*0.5);
 
</asy>
 
</asy>
</div></div>
+
<br></div></div>
 +
 
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
'''#21 "for" Command'''
 
'''#21 "for" Command'''
 
<div class="mw-collapsible-content">
 
<div class="mw-collapsible-content">
 +
<br>
 
(Source: Zhaom & heatherfinotti)
 
(Source: Zhaom & heatherfinotti)
 
If you want to do the for thing you do
 
If you want to do the for thing you do
Line 615: Line 625:
 
</asy></code>
 
</asy></code>
 
[/hide]
 
[/hide]
</div></div>
+
<br></div></div>
 +
 
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
'''#22 Extension'''
 
'''#22 Extension'''
 
<div class="mw-collapsible-content">
 
<div class="mw-collapsible-content">
 +
<br>
 
If you want to extend a line you can use this
 
If you want to extend a line you can use this
  
Line 666: Line 678:
  
 
You have the extension <math>A, B,C,</math> and <math>I</math>, because you want it to go down from point <math>C</math>, through <math>I</math>, and end on <math>\overline{AB}</math>.
 
You have the extension <math>A, B,C,</math> and <math>I</math>, because you want it to go down from point <math>C</math>, through <math>I</math>, and end on <math>\overline{AB}</math>.
</div></div>
+
<br></div></div>
 +
 
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
'''#23 How to draw an equilateral triangle'''
 
'''#23 How to draw an equilateral triangle'''
 
<div class="mw-collapsible-content">
 
<div class="mw-collapsible-content">
 +
<br>
 
In #23 we'll walkthrough how to make an equilateral triangle.
 
In #23 we'll walkthrough how to make an equilateral triangle.
  
Line 734: Line 748:
 
</asy>
 
</asy>
 
</code>
 
</code>
</div></div>
+
<br></div></div>
 +
 
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
'''#24 How to draw an isosceles triangle'''
 
'''#24 How to draw an isosceles triangle'''
 
<div class="mw-collapsible-content">
 
<div class="mw-collapsible-content">
 +
<br>
 
In #24 we'll walkthrough how to make an isosceles triangle.
 
In #24 we'll walkthrough how to make an isosceles triangle.
 
Let's start by placing <math>A</math> at <math>(0,0)</math>.
 
Let's start by placing <math>A</math> at <math>(0,0)</math>.
Line 795: Line 811:
 
</asy>
 
</asy>
 
</code>
 
</code>
</div></div>
+
<br></div></div>
 +
 
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
'''#25 How to draw a scalene triangle'''
 
'''#25 How to draw a scalene triangle'''
 
<div class="mw-collapsible-content">
 
<div class="mw-collapsible-content">
 +
<br>
 
In #25 we'll walkthrough how to make a scalene triangle.
 
In #25 we'll walkthrough how to make a scalene triangle.
  
Line 834: Line 852:
 
</asy>
 
</asy>
 
</code>
 
</code>
</div></div>
+
<br></div></div>
 +
 
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
'''#26 Labeling Angles'''
 
'''#26 Labeling Angles'''
 
<div class="mw-collapsible-content">
 
<div class="mw-collapsible-content">
 +
<br>
 
(Source: independentstudyproject)
 
(Source: independentstudyproject)
 
This is similar to #6 but it labels the angle with the arc.
 
This is similar to #6 but it labels the angle with the arc.
Line 853: Line 873:
 
label("$60^\circ$",(0.1,0.1),E);
 
label("$60^\circ$",(0.1,0.1),E);
 
</asy>
 
</asy>
</div></div>
+
<br></div></div>
 +
 
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
'''#27 Drawing triangles using SSS, SAS, AAS, and ASA'''
 
'''#27 Drawing triangles using SSS, SAS, AAS, and ASA'''
 
<div class="mw-collapsible-content">
 
<div class="mw-collapsible-content">
 +
<br>
 
(Source: Zhaom)
 
(Source: Zhaom)
 
drawing triangles:
 
drawing triangles:
Line 922: Line 944:
 
label("$C$",C,SE);
 
label("$C$",C,SE);
 
</asy>[/hide],then <math>A</math>=[hide][c](0,0);[/c][/hide],<math>B</math>=[hide][c]dir(c)*b;[/c][/hide],and <math>C</math>=[hide][c](a,0);[/c][/hide].
 
</asy>[/hide],then <math>A</math>=[hide][c](0,0);[/c][/hide],<math>B</math>=[hide][c]dir(c)*b;[/c][/hide],and <math>C</math>=[hide][c](a,0);[/c][/hide].
</div></div>
+
<br></div></div>
 +
 
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
'''#28 Arcs'''
 
'''#28 Arcs'''
 
<div class="mw-collapsible-content">
 
<div class="mw-collapsible-content">
 +
<br>
 
(Source: Zhaom and heatherfinotti)
 
(Source: Zhaom and heatherfinotti)
 
If you want to draw an arc you can use
 
If you want to draw an arc you can use
Line 949: Line 973:
 
</asy>
 
</asy>
 
</code>
 
</code>
</div></div>
+
<br></div></div>
 +
 
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
'''#29 The Nine Point Circle'''
 
'''#29 The Nine Point Circle'''
 
<div class="mw-collapsible-content">
 
<div class="mw-collapsible-content">
 +
<br>
 
(Source: Zhaom)
 
(Source: Zhaom)
 
The nine point circle:
 
The nine point circle:
Line 1,004: Line 1,030:
 
</asy>[/hide]
 
</asy>[/hide]
 
The center is N and the radius is r/2.
 
The center is N and the radius is r/2.
</div></div>
+
<br></div></div>
 +
 
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
'''#30 Pair Part 2'''
 
'''#30 Pair Part 2'''
 
<div class="mw-collapsible-content">
 
<div class="mw-collapsible-content">
 +
<br>
 
(Source: Zhaom, eagle702)
 
(Source: Zhaom, eagle702)
 
Another way to use the variables in the pair at the start of your code, is by using
 
Another way to use the variables in the pair at the start of your code, is by using
Line 1,034: Line 1,062:
 
label("$B$", A[2], S);
 
label("$B$", A[2], S);
 
</code>
 
</code>
</div></div>
+
<br></div></div>
 +
 
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
'''#31 Finding the midpoint'''
 
'''#31 Finding the midpoint'''
 
<div class="mw-collapsible-content">
 
<div class="mw-collapsible-content">
 +
<br>
 
(Source: fath2012)
 
(Source: fath2012)
 
This is really just a tool from the documetation but here it is anyway.
 
This is really just a tool from the documetation but here it is anyway.
Line 1,053: Line 1,083:
 
dot(midpoint(A--B));
 
dot(midpoint(A--B));
 
</asy>
 
</asy>
</div></div>
+
<br></div></div>
 +
 
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
'''#32 Foot Command'''
 
'''#32 Foot Command'''
 
<div class="mw-collapsible-content">
 
<div class="mw-collapsible-content">
 +
<br>
 
If you want to draw a perpendicular line from a point to another line, you can use the foot command:
 
If you want to draw a perpendicular line from a point to another line, you can use the foot command:
 
<code>draw(A--foot(A,B,C));</code>
 
<code>draw(A--foot(A,B,C));</code>
Line 1,094: Line 1,126:
 
</asy>
 
</asy>
 
</code>
 
</code>
</div></div>
+
<br></div></div>
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 
<div class="mw-collapsible mw-collapsed" style="width:100%">
 +
 
'''#33 Introduction to 3D Geometry'''
 
'''#33 Introduction to 3D Geometry'''
 
<div class="mw-collapsible-content">
 
<div class="mw-collapsible-content">
 +
<br>
 
Making 3D figures in asymptote is a bit different from making 2D figures in asymptote. I'll state some of the differences here.
 
Making 3D figures in asymptote is a bit different from making 2D figures in asymptote. I'll state some of the differences here.
  
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<code>A = (x,y,z);</code>
 
<code>A = (x,y,z);</code>
 
<math>x</math> and <math>y</math> are the coordinates of the base of the 3D figure, and <math>z</math> is the height of the coordinate on the 3D figure.[/quote]
 
<math>x</math> and <math>y</math> are the coordinates of the base of the 3D figure, and <math>z</math> is the height of the coordinate on the 3D figure.[/quote]
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<br></div></div>
 
</dd>
 
</dd>

Latest revision as of 11:42, 17 September 2024

Essential Reference for Using Asymptote in AoPS

A focused asymptote reference with examples and short code.


Original source from eagle702 bulletin board post. Adapted and edited by aquadragon.


Introduction


Why Asymptote is called Asymptote?

http://asymptote.sourceforge.net/FAQ/section1.html#whyasy

Question 1.4. Why was the name Asymptote chosen?

Well, it isn't the perfect graphics package, but we do think it is getting there asymptotically...

Tips

  • To see the asymptote code of any diagram made with asymptote, click on the diagram and it will come up.
  • If your code is not working check to make sure you have a semicolon after each line, no extra parentheses or brackets, and no open parentheses or brackets.
  • Another thing to check if your code is not working, is to make sure every variable you've used in your code is in the pair.


Beginning your code

To start your asymptote diagram you have to include [asy] at the beginning, and [/asy] at the ending.


Setting points

To create points in your diagram you can use

 A = (0,0);

Say you want to have point $B$ $4$ units to the right of point $A$, then you can use

 B = (4,0);

Setting points on your diagram is like setting points on a graph. The first number is the $x$-coordinate of the point and the second number is the $y$-coordinate of the point.

Note: You should not use E, S, N, or W as variables, instead you should use EE, SS, NN, and WW, but label them as E, S, N, W. This is because E, S, N, and W are used to indicate directions in asymptote.


Pair part 1

If you include variables in your diagram you have to have $\verb#pair#$ somewhere in your code.

Example: You have two points $A$ and $B$, and you're drawing a line connecting them, you need to include

  pair A,B; 

in your diagram to make it work.


Connecting two points, coloring the line'

Once you have set variables $A$ and $B$, you can connect them by writing

 draw(A--B);

Example:

[asy] pair A,B; A=(0,0); B=(1,0); draw(A--B); [/asy]

If you want to make the line you're using to connect them red, you can use

draw(A--B--cycle, red);

This will make the line red.

Example:

[asy] pair A,B; A=(0,0); B=(1,0); draw(A--B--cycle, red); [/asy]

You can also make a line dashed by writing draw(A--B--cycle, dashed)

Example:

[asy] pair A,B; A=(0,0); B=(1,0); draw(A--B--cycle, dashed); [/asy]

If you wanted to give the line multiple characteristics, such as a red dashed line, you write + in between the characteristics. draw(A--B--cycle, dashed+red)

Example:

[asy] pair A,B; A=(0,0); B=(1,0); draw(A--B--cycle, dashed+red); [/asy]


Labeling, Midpoint

To label a point you can use

label("$A$",A,dir(135));

The $A$ means you will label the point $A$. The A (no dollar signs) means you will be labeling the point A. The dir(135) determines where on the point the variable will be. Or you can use label("$A$",A,N);. The N means that the label will be above (North) of the point.

Example:

[asy] pair A,B; A=(0,0); B=(1,0); draw(A--B); label("$A$",A,N); label("$B$",B,N); [/asy]

If you want to draw a variable (x) or number at the center of a line you can use

label("$x$", midpoint(A--B), NE);

The NE at the end means North-East, this will decide where on the line the variable will be (above it to the right for NE).

Example:

[asy] pair A,B; A=(0,0); B=(1,0); draw(A--B); label("$A$",A,N); label("$B$",B,N); label("$x$", midpoint(A--B), NE); [/asy]


Angle Measures

If you want to draw an angle measure on an angle use

label(scale(.75)*"$x$", Z, 2.5*dir(150));

In this line of code, there is a very important command. The "dir" command.

The angle for the dir command always starts facing east. So dir(0) would label the part exactly east of what you are labeling. Similarly dir(90) would label it exactly north, dir(180) would label it exactly west, and dir(270) would label it exactly south.

This is called the unit circle; the unit circle is a large concept that will be discussed in AoPS's Precalculus course. Basically, because a circle has $360^\circ$, the starting point is to the right of the circle and the degrees move counterclockwise around the circle. This also means that dir(0) is the same as dir(360). :)

Here's a diagram that will make this tricky concept more understandable.

The starting point, which we will call $w$ is at dir(0). dir(90) is the starting point rotated $90^\circ$ counter clockwise from the starting position; we will call this point $x$. Similarly, dir(180) is the starting point rotated $180^\circ$ counterclockwise from the starting position; we will call this point $y$. Finally, dir(270) is the starting point rotated $270^\circ$ counterclockwise from the starting position; we will call this point $z$.

Here are the variables on the unit circle:

[asy] size(150); import TrigMacros; rr_cartesian_axes(-5,5,-5,5, usegrid = false); draw(Circle((0,0),4),p=black+1bp); label("$w$", (4, 0), NE); label("$x$", (0, 4), NE); label("$y$", (-4, 0), NW); label("$z$", (0, -4), SE); [/asy]

The dir(150), at the end you have to play around with, it will move around the angle to see where the degree mark is. The $Z$ in it means that it is on point $Z$. The $x$ means that the angle is $x$ degrees. The scale(.75) defines the size of the angle mark. The 2.5* defines how far from the point the angle sign is.

Example:

[asy] pair A,B,C; A=(0,1); B=(0,0); C=(1,0); draw(A--B--C--A); label("$A$",A,N); label("$B$",B,W); label("$C$",C,E); label(scale(.75)*"$90^\circ$", B, 2.5*dir(50)); [/asy]


Distance Function

My distance function real dist(pair a,pair b){ return sqrt(abs(a.x-b.x)^2+abs(a.y-b.y)^2); } Took me some much time just to write a distance function. Hopefully, everybody else doesn't have to go through lots of research to make this. A note Apparently a pair has an x property and a y property. I kind of discovered this it by testing. I think it might be documented somewhere.


Casting

(Source: fath2012) Casting This is not really a command but helps you convert a data type to another data type if you can. [asy] pair a = (5,5); int b = 2; dot(a); label((string) a,a,N); label((string) b,a,S); [/asy] pair a = (5,5); int b = 2; dot(a); label((string) a,a,N); label((string) b,a,S);


Right Angle Mark

If you want to draw a right angle mark use this:

draw(rightanglemark(A,B,C,1.5));

The A,B,C means that it will draw the right angle mark on $\angle ABC$. The $1.5$ defines the size of the right angle mark.

Example:

[asy] pair A,B,C; A=(0,1); B=(0,0); C=(1,0); draw(A--B--C--A); label("$A$",A,N); label("$B$",B,W); label("$C$",C,E); draw(rightanglemark(A,B,C,1.5)); [/asy]



Intersection

If you want to draw a point on an intersection of two lines you can use:

F = intersectionpoint(A -- C, B -- D);

In this code $F$ is the intersection point of lines $AC$ and $BD$.

Example:

[asy] pair A, B, C, D, F; A = (1,0); B = -A; C = (0.7,0.7); D = -C; draw(A--B); draw(C--D); label("$A$",A,E); label("$B$",B,N); label("$C$",C,N); label("$D$",D,S); label("$F$",F,SE); F = intersectionpoint(A -- B, C -- D); [/asy]



Filling

To show you how to fill in a part of a diagram with a color I'll use an example from Week 3 Problem 5 in AoPS's Introduction to Geometry course.

[asy] fill((0,0)--(0,5)--(1,5)--(5,0)--cycle,red); fill((7,0)--(1,5)--(7,5)--cycle,red); for (int i=0;i<=7;i+=1) { draw((i,0)--(i,5)); }; for (int j=0;j<=5;j+=1) { draw((0,j)--(7,j)); }; draw((7,0)--(1,5)--(5,0)); [/asy]

Let's walkthrough how the left side of the rectangle is red.

Whoever made the asymptote code for this used the line

fill((0,0)--(0,5)--(1,5)--(5,0)--cycle,red);

The coordinates mean that it will fill in the quadrilateral at points (0,0); (0,5); (1,5); and (5,0). The red at the end means that the color will be red, here's what it would look like if I put blue instead of red (on the left and right side).

[asy] fill((0,0)--(0,5)--(1,5)--(5,0)--cycle,blue); fill((7,0)--(1,5)--(7,5)--cycle,blue); for (int i=0;i<=7;i+=1) { draw((i,0)--(i,5)); }; for (int j=0;j<=5;j+=1) { draw((0,j)--(7,j)); }; draw((7,0)--(1,5)--(5,0)); [/asy]

If you want to make it a color like light blue, light brown, dark blue, etc. do not put a space between the two words.

If you wanted to make both sides dark blue you would put

fill((0,0)--(0,5)--(1,5)--(5,0)--cycle,darkblue); fill((7,0)--(1,5)--(7,5)--cycle,darkblue);

Here's what it would look like:

[asy] fill((0,0)--(0,5)--(1,5)--(5,0)--cycle,darkblue); fill((7,0)--(1,5)--(7,5)--cycle,darkblue); for (int i=0;i<=7;i+=1) { draw((i,0)--(i,5)); }; for (int j=0;j<=5;j+=1) { draw((0,j)--(7,j)); }; draw((7,0)--(1,5)--(5,0)); [/asy]

(It looks more like navy to me. But inserting "navy" does not work so I guess that's why.)

You don't have to have both sides the same color though, you could have the left side blue and the right side pink.

[asy] fill((0,0)--(0,5)--(1,5)--(5,0)--cycle,blue); fill((7,0)--(1,5)--(7,5)--cycle,pink); for (int i=0;i<=7;i+=1) { draw((i,0)--(i,5)); }; for (int j=0;j<=5;j+=1) { draw((0,j)--(7,j)); }; draw((7,0)--(1,5)--(5,0)); [/asy]

Or vice versa.

[asy] fill((0,0)--(0,5)--(1,5)--(5,0)--cycle,pink); fill((7,0)--(1,5)--(7,5)--cycle,blue); for (int i=0;i<=7;i+=1) { draw((i,0)--(i,5)); }; for (int j=0;j<=5;j+=1) { draw((0,j)--(7,j)); }; draw((7,0)--(1,5)--(5,0)); [/asy]

Try out different colors to see which ones you prefer for your asymptote diagrams. Have fun!


Dot

If you want to draw a dot on a point on your diagram use

dot(A, p=black+3bp);

This will draw a black dot on point $A$.

Example:

[asy] pair A; A=(0,0); dot(A, p=black+3bp); label("$A$",A,N); [/asy]

You can also use

dot(A);


Expand

#13 Size


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#14 Tick Marks

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#15 Arrows

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#16 Shifting Coordinates

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#17 Rotating

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#18 Circles

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#19 Dashed Lines

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#20 Angle Mark

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#21 "for" Command

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#22 Extension

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#23 How to draw an equilateral triangle

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#24 How to draw an isosceles triangle

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#25 How to draw a scalene triangle

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#26 Labeling Angles

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#27 Drawing triangles using SSS, SAS, AAS, and ASA

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#28 Arcs

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#29 The Nine Point Circle

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#30 Pair Part 2

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#31 Finding the midpoint

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#32 Foot Command

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#33 Introduction to 3D Geometry