Difference between revisions of "Asymptote: Useful functions"
(→Marking Angles) |
(fixed display of second example of intersectionpoints()) |
||
| (6 intermediate revisions by 2 users not shown) | |||
| Line 3: | Line 3: | ||
__TOC__ | __TOC__ | ||
| − | == Labeling | + | == Labeling angles == |
The bundled <code>markers</code> package provides a useful function for marking angles. The exact same function exists in the <code>geometry</code> package. | The bundled <code>markers</code> package provides a useful function for marking angles. The exact same function exists in the <code>geometry</code> package. | ||
<blockquote> | <blockquote> | ||
| Line 12: | Line 12: | ||
margin ''margin''=NoMargin, marker ''marker''=nomarker) | margin ''margin''=NoMargin, marker ''marker''=nomarker) | ||
</blockquote> | </blockquote> | ||
| − | As with other angle functions, you can replace <code>line l1, line l2</code> with <code>pair A, pair O, pair B</code>, which would mark the angle <math>\angle AOB</math>. The function will draw an arc from line AO or l1 to line BO or l2, counterclockwise, with radius <math> | + | As with other angle functions, you can replace <code>line l1, line l2</code> with <code>pair A, pair O, pair B</code>, which would mark the angle <math>\angle AOB</math>. The function will draw an arc from line AO or l1 to line BO or l2, counterclockwise, with radius <math>|\textrm{radius}|</math> and label it with the provided <code>Label L</code>. |
If the function draws the angle in the wrong direction, try swapping the first pair with the third pair, or, if you put in lines, swapping l1 and l2. | If the function draws the angle in the wrong direction, try swapping the first pair with the third pair, or, if you put in lines, swapping l1 and l2. | ||
| Line 43: | Line 43: | ||
<blockquote> | <blockquote> | ||
path '''anglemark'''(pair ''A'', pair ''B'', pair ''C'',<br/> | path '''anglemark'''(pair ''A'', pair ''B'', pair ''C'',<br/> | ||
| − | real ''t''=8, real | + | real ''t''=8, ... real[] ''s''=8) |
</blockquote> | </blockquote> | ||
| + | ''t'' is the radius of the first line, and s[] stores the radius of subsequent lines. | ||
To label it, simply use the label() function per usual. | To label it, simply use the label() function per usual. | ||
<syntaxhighlight lang="asy"> | <syntaxhighlight lang="asy"> | ||
| Line 55: | Line 56: | ||
import olympiad; | import olympiad; | ||
draw(anglemark(B, O, A), p=orange); | draw(anglemark(B, O, A), p=orange); | ||
| − | label("$45^\circ$", anglemark(B, O, A), | + | label("$45^\circ$", anglemark(B, O, A), NE); |
</syntaxhighlight> | </syntaxhighlight> | ||
<asy> | <asy> | ||
| Line 63: | Line 64: | ||
draw(O--A); | draw(O--A); | ||
draw(O--B); | draw(O--B); | ||
| − | |||
import olympiad; | import olympiad; | ||
draw(anglemark(B, O, A), p=orange); | draw(anglemark(B, O, A), p=orange); | ||
| − | label("$45^\circ$", anglemark(B, O, A), | + | label("$45^\circ$", anglemark(B, O, A), NE); |
</asy> | </asy> | ||
| − | As you can see, the labeling is | + | As you can see, this is an inferior method as the path also covers part of the angle and the origin of labeling is the point instead of the angle mark. However, anglemark() makes a bit more abstract sense and is more flexible. |
== Intersection points == | == Intersection points == | ||
| Line 74: | Line 74: | ||
Examples: | Examples: | ||
| − | < | + | <syntaxhighlight lang="asy"> |
| + | size(8cm,0); | ||
import math; | import math; | ||
import graph; | import graph; | ||
| Line 90: | Line 91: | ||
dot(x[0],3bp+blue); | dot(x[0],3bp+blue); | ||
dot(x[1],3bp+blue); | dot(x[1],3bp+blue); | ||
| − | draw(x[0] -- x[1],1bp+red);</ | + | draw(x[0] -- x[1],1bp+red); |
| + | </syntaxhighlight> | ||
<asy>size(200,200); | <asy>size(200,200); | ||
| Line 110: | Line 112: | ||
draw(x[0] -- x[1],1bp+red);</asy> | draw(x[0] -- x[1],1bp+red);</asy> | ||
| − | < | + | <syntaxhighlight lang="asy"> |
path g=(-3,-sqrt(3))--(3,-sqrt(3))--(0,2*sqrt(3))--cycle; | path g=(-3,-sqrt(3))--(3,-sqrt(3))--(0,2*sqrt(3))--cycle; | ||
draw(g,black); | draw(g,black); | ||
| Line 118: | Line 120: | ||
fill(x[0]--x[1]--x[2]--x[3]--x[4]--x[5]--cycle,black); | fill(x[0]--x[1]--x[2]--x[3]--x[4]--x[5]--cycle,black); | ||
dot((0,0),white); | dot((0,0),white); | ||
| − | </ | + | </syntaxhighlight> |
<asy> | <asy> | ||
path g=(-3,-sqrt(3))--(3,-sqrt(3))--(0,2*sqrt(3))--cycle; | path g=(-3,-sqrt(3))--(3,-sqrt(3))--(0,2*sqrt(3))--cycle; | ||
| Line 128: | Line 130: | ||
dot((0,0),white); | dot((0,0),white); | ||
</asy> | </asy> | ||
| + | |||
Note that this function will cause an error if the paths involved do not intersect. | Note that this function will cause an error if the paths involved do not intersect. | ||
Latest revision as of 04:21, 13 August 2024
Labeling angles
The bundled markers package provides a useful function for marking angles. The exact same function exists in the geometry package.
void markangle(picture pic=currentpicture,
Label L="", int n=1, real radius=0, real space=0,
line l1, line l2,
arrowbar arrow=None, pen p=currentpen,
margin margin=NoMargin, marker marker=nomarker)
As with other angle functions, you can replace line l1, line l2 with pair A, pair O, pair B, which would mark the angle 
. The function will draw an arc from line AO or l1 to line BO or l2, counterclockwise, with radius 
and label it with the provided Label L.
If the function draws the angle in the wrong direction, try swapping the first pair with the third pair, or, if you put in lines, swapping l1 and l2.
Here's an example to do that with an orange pen:
pair A = (1,1);
pair O = (0,0);
pair B = (2,0);
draw(O--A);
draw(O--B);
import geometry;
markangle("$45^o$", B, O, A, p=orange);
![[asy] pair A = (1,1); pair O = (0,0); pair B = (2,0); draw(O--A); draw(O--B); import geometry; markangle("$45^\circ$", B, O, A, p=orange); [/asy]](http://latex.artofproblemsolving.com/6/3/b/63b342a8db26894549d771a5147b0955f0009493.png)
Olympiad
The olympiad package provides a function that generates a path that can then be drawn using the draw() function.
path anglemark(pair A, pair B, pair C,
real t=8, ... real[] s=8)
t is the radius of the first line, and s[] stores the radius of subsequent lines. To label it, simply use the label() function per usual.
pair A = (1,1);
pair O = (0,0);
pair B = (2,0);
draw(O--A);
draw(O--B);
import olympiad;
draw(anglemark(B, O, A), p=orange);
label("$45^\circ$", anglemark(B, O, A), NE);
![[asy] pair A = (1,1); pair O = (0,0); pair B = (2,0); draw(O--A); draw(O--B); import olympiad; draw(anglemark(B, O, A), p=orange); label("$45^\circ$", anglemark(B, O, A), NE); [/asy]](http://latex.artofproblemsolving.com/0/c/a/0ca8b3fed16e2462c82791066d899c4c377d3d90.png)
As you can see, this is an inferior method as the path also covers part of the angle and the origin of labeling is the point instead of the angle mark. However, anglemark() makes a bit more abstract sense and is more flexible.
Intersection points
pair[] intersectionpoints(path, path);
Examples:
size(8cm,0);
import math;
import graph;
real r,s;
pair a,b, common;
path circ1, circ2;
r=1; s=1;
a=(0,0);
b=(1,0);
circ1=circle(a,r);
circ2=circle(b,s);
draw(circ1,linewidth(1bp));
draw(circ2,1bp+green);
pair [] x=intersectionpoints(circ1, circ2);
dot(x[0],3bp+blue);
dot(x[1],3bp+blue);
draw(x[0] -- x[1],1bp+red);
![[asy]size(200,200); import math; import graph; real r,s; pair a,b, common; path circ1, circ2; r=1; s=1; a=(0,0); b=(1,0); circ1=circle(a,r); circ2=circle(b,s); draw(circ1,linewidth(1bp)); draw(circ2,1bp+green); pair [] x=intersectionpoints(circ1, circ2); dot(x[0],3bp+blue); dot(x[1],3bp+blue); draw(x[0] -- x[1],1bp+red);[/asy]](http://latex.artofproblemsolving.com/6/7/8/67824240657a60c0f3421ebf4ddb53f7e753deeb.png)
path g=(-3,-sqrt(3))--(3,-sqrt(3))--(0,2*sqrt(3))--cycle;
draw(g,black);
path p=-2/3*(-3,-sqrt(3))--(-2/3)*(3,-sqrt(3))--(-2/3)*(0,2*sqrt(3))--cycle;
draw(p,black);
pair [] x=intersectionpoints(g, p);
fill(x[0]--x[1]--x[2]--x[3]--x[4]--x[5]--cycle,black);
dot((0,0),white);
![[asy] path g=(-3,-sqrt(3))--(3,-sqrt(3))--(0,2*sqrt(3))--cycle; draw(g,black); path p=-2/3*(-3,-sqrt(3))--(-2/3)*(3,-sqrt(3))--(-2/3)*(0,2*sqrt(3))--cycle; draw(p,black); pair [] x=intersectionpoints(g, p); fill(x[0]--x[1]--x[2]--x[3]--x[4]--x[5]--cycle,black); dot((0,0),white); [/asy]](http://latex.artofproblemsolving.com/6/3/c/63c0ef9f2f3270e07ae7b2f7c8377f977d6bbb1f.png)
Note that this function will cause an error if the paths involved do not intersect.
