View source for Autograph

{| class="wikitable" style="border:1px solid black; background:#CEE0F2;text-align:center;"
|-
|style="background:#B0C4DE;"|'''[[Asymptote (Vector Graphics Language)]]'''
|-
|[[Asymptote: Getting Started|Getting&nbsp;Started]] - [[Asymptote: Basics|Basics]] - [[Asymptote: Reference|Reference]] - [[Asymptote: Useful commands and their Output|Examples]] - [[Asymptote: Macros and Packages|Macros&nbsp;and&nbsp;Packages]] - [[Asymptote: Advanced | Advanced&nbsp;Asymptote]] - [[3D graphics for Asymptote|3D Graphics]] - [[Asymptote: Help|Help]]
[[Asymptote: Useful functions|Useful functions]] - [[Asymptote: CSE5|CSE5 Package]] - [[Asymptote: How to|How to]]
[[Category:Asymptote]]
|}<noinclude>
==Autograph==
<asy>
import contour;
import graph;
real f(real x)
{
return x^2-1.333;
}
draw(graph(f,-1.5,1.5),blue+linewidth(0.5),Arrows);
size(75);
real f(real x, real y) {return abs(x^3) + abs(y^3);}
draw(contour(f,(-6,-6),(6,6), new real[] {5}),red+linewidth(1));
label("$Auto\;Graph$",(0,0.3),red);
label("$V-4\beta$",(0,-0.3),red);
dot((1.5,0),red);
dot((0,1.5),red);
dot((0,-1.5),red);
dot((-1.5,0),red);</asy>
Autograph is a piece of code written in [[Asymptote]] that lets the user graph a function with ease. The user must only set the function, and optionally 
* the x and y maximums and minimums
* the color of the graph line
* the density of the ticks
* whether to show the grid or not
* wether to mark lattice points or not
* the ratio of x to y
* the width of the line
It is targeted to beginners in asymptote who don't want to learn all of it, but still want to make nice graphs.
Anyone is allowed to use it if they do not remove the labels at the beginning and end of the code. 
==Examples==
Some pretty graphs:
<asy>
/* AUTO-GRAPH V-4 beta by PythonNut*/

/* Customizations: feel free to edit */
import math;
import graph;
/* x maximum and minimum */
int X_max = 10;
int X_min =-10;
/* y maximum and minimum */
int Y_max = 10;
int Y_min = -10;
/* linewidth */
real line_width = 0.75;
/* graph color */
pen graph_color = heavygreen;
/* special */
bool mark_lattice = true;
bool show_grid = true;
real X_tick_density = 1;
real Y_tick_density = 1;
real ratio = 1;
real resolution = 0.0001;
int size = 300;
/* graph function */
real f(real x)
   {
   return 2x^3-6x^2+3x-1; /* type function to be graphed here */
}

/* The Code. Do not disturb unless you know what you are doing */

size(size);unitsize(size*ratio,size);Label l;l.p=fontsize(6);
xaxis("$x$",X_min,X_max,Ticks(l,X_tick_density,(X_tick_density/2),NoZero),Arrows);
yaxis("$y$",Y_min,Y_max,Ticks(l,Y_tick_density,(Y_tick_density/2),NoZero),Arrows);//
if (show_grid){add(shift(X_min,Y_min)*grid(X_max-X_min,Y_max-Y_min));}
real temp = X_min;
while (! (f(temp) <= Y_max && f(temp) >= Y_min && temp < X_max))
{temp += resolution;}
real Temp1 = temp;
while (f(Temp1) <= Y_max && f(Temp1) >= Y_min && Temp1 < X_max)
{Temp1 += resolution;}
real Temp2 = temp;
while (f(Temp2) <= Y_max && f(Temp2) >= Y_min && Temp2 > X_min)
{Temp2 -= resolution;}
draw(graph(f,Temp2,Temp1,n=2400),graph_color+linewidth(line_width),Arrows);
temp = Temp1+resolution;
while (temp <= X_max)
{while (! (f(temp) <= Y_max && f(temp) >= Y_min) && temp < X_max)
{temp += resolution;}
real Temp1 = temp;
while (f(Temp1) <= Y_max && f(Temp1) >= Y_min && Temp1 < X_max)
{Temp1 += resolution;}
real Temp2 = temp;
while (f(Temp2) <= Y_max && f(Temp2) >= Y_min && Temp2 > X_min)
{Temp2 -= resolution;}
if (Temp1 <= X_max)
{draw(graph(f,Temp2,Temp1,n=2400),graph_color+linewidth(line_width),Arrows);}
temp = Temp1+resolution;
continue;}
temp = X_max;
while (f(temp) <= Y_max && f(temp) >= Y_min && temp >= X_min)
{temp -= resolution;}
if (f(X_max) <= Y_max && f(X_max) >= Y_min)
{draw(graph(f,temp,X_max,n=2400),graph_color+linewidth(line_width),Arrows);}
if (mark_lattice)
{for (real temp = X_min; temp <= X_max; ++temp)
{if (f(temp)%1==0 && f(temp)<=Y_max && f(temp)>=Y_min)
{dot((temp,f(temp)),graph_color+linewidth(line_width*4));}}}
dot((0,0));
/* Property of "PythonNut" 2011*/
</asy>
<asy>
/* AUTO-GRAPH V-4 beta by PythonNut*/

/* Customizations: feel free to edit */
import math;
import graph;
/* x maximum and minimum */
int X_max = 10;
int X_min =-10;
/* y maximum and minimum */
int Y_max = 1;
int Y_min = -1;
/* linewidth */
real line_width = 0.75;
/* graph color */
pen graph_color = blue;
/* special */
bool mark_lattice = false;
bool show_grid = true;
real X_tick_density = 1;
real Y_tick_density = 1;
real ratio = 1;
real resolution = 0.0001;
int size = 300;
/* graph function */
real f(real x)
   {
   return sin(x); /* type function to be graphed here */
}

/* The Code. Do not disturb unless you know what you are doing */

size(size);unitsize(size*ratio,size);Label l;l.p=fontsize(6);
xaxis("$x$",X_min,X_max,Ticks(l,X_tick_density,(X_tick_density/2),NoZero),Arrows);
yaxis("$y$",Y_min,Y_max,Ticks(l,Y_tick_density,(Y_tick_density/2),NoZero),Arrows);//
if (show_grid){add(shift(X_min,Y_min)*grid(X_max-X_min,Y_max-Y_min));}
real temp = X_min;
while (! (f(temp) <= Y_max && f(temp) >= Y_min && temp < X_max))
{temp += resolution;}
real Temp1 = temp;
while (f(Temp1) <= Y_max && f(Temp1) >= Y_min && Temp1 < X_max)
{Temp1 += resolution;}
real Temp2 = temp;
while (f(Temp2) <= Y_max && f(Temp2) >= Y_min && Temp2 > X_min)
{Temp2 -= resolution;}
draw(graph(f,Temp2,Temp1,n=2400),graph_color+linewidth(line_width),Arrows);
temp = Temp1+resolution;
while (temp <= X_max)
{while (! (f(temp) <= Y_max && f(temp) >= Y_min) && temp < X_max)
{temp += resolution;}
real Temp1 = temp;
while (f(Temp1) <= Y_max && f(Temp1) >= Y_min && Temp1 < X_max)
{Temp1 += resolution;}
real Temp2 = temp;
while (f(Temp2) <= Y_max && f(Temp2) >= Y_min && Temp2 > X_min)
{Temp2 -= resolution;}
if (Temp1 <= X_max)
{draw(graph(f,Temp2,Temp1,n=2400),graph_color+linewidth(line_width),Arrows);}
temp = Temp1+resolution;
continue;}
temp = X_max;
while (f(temp) <= Y_max && f(temp) >= Y_min && temp >= X_min)
{temp -= resolution;}
if (f(X_max) <= Y_max && f(X_max) >= Y_min)
{draw(graph(f,temp,X_max,n=2400),graph_color+linewidth(line_width),Arrows);}
if (mark_lattice)
{for (real temp = X_min; temp <= X_max; ++temp)
{if (f(temp)%1==0 && f(temp)<=Y_max && f(temp)>=Y_min)
{dot((temp,f(temp)),graph_color+linewidth(line_width*4));}}}
dot((0,0));
/* Property of "PythonNut" 2011*/
</asy>
<asy>
/* AUTO-GRAPH V-4 beta by PythonNut*/

/* Customizations: feel free to edit */
import math;
import graph;
/* x maximum and minimum */
int X_max = 8;
int X_min =-8;
/* y maximum and minimum */
int Y_max = 16;
int Y_min = 0;
/* linewidth */
real line_width = 0.75;
/* graph color */
pen graph_color = heavygreen;
/* special */
bool mark_lattice = true;
bool show_grid = true;
real X_tick_density = 2;
real Y_tick_density = 1;
real ratio = 1;
real resolution = 0.0001;
int size = 300;
/* graph function */
real f(real x)
   {
   return x^2; /* type function to be graphed here */
}

/* The Code. Do not disturb unless you know what you are doing */

size(size);unitsize(size*ratio,size);Label l;l.p=fontsize(6);
xaxis("$x$",X_min,X_max,Ticks(l,X_tick_density,(X_tick_density/2),NoZero),Arrows);
yaxis("$y$",Y_min,Y_max,Ticks(l,Y_tick_density,(Y_tick_density/2),NoZero),Arrows);//
if (show_grid){add(shift(X_min,Y_min)*grid(X_max-X_min,Y_max-Y_min));}
real temp = X_min;
while (! (f(temp) <= Y_max && f(temp) >= Y_min && temp < X_max))
{temp += resolution;}
real Temp1 = temp;
while (f(Temp1) <= Y_max && f(Temp1) >= Y_min && Temp1 < X_max)
{Temp1 += resolution;}
real Temp2 = temp;
while (f(Temp2) <= Y_max && f(Temp2) >= Y_min && Temp2 > X_min)
{Temp2 -= resolution;}
draw(graph(f,Temp2,Temp1,n=2400),graph_color+linewidth(line_width),Arrows);
temp = Temp1+resolution;
while (temp <= X_max)
{while (! (f(temp) <= Y_max && f(temp) >= Y_min) && temp < X_max)
{temp += resolution;}
real Temp1 = temp;
while (f(Temp1) <= Y_max && f(Temp1) >= Y_min && Temp1 < X_max)
{Temp1 += resolution;}
real Temp2 = temp;
while (f(Temp2) <= Y_max && f(Temp2) >= Y_min && Temp2 > X_min)
{Temp2 -= resolution;}
if (Temp1 <= X_max)
{draw(graph(f,Temp2,Temp1,n=2400),graph_color+linewidth(line_width),Arrows);}
temp = Temp1+resolution;
continue;}
temp = X_max;
while (f(temp) <= Y_max && f(temp) >= Y_min && temp >= X_min)
{temp -= resolution;}
if (f(X_max) <= Y_max && f(X_max) >= Y_min)
{draw(graph(f,temp,X_max,n=2400),graph_color+linewidth(line_width),Arrows);}
if (mark_lattice)
{for (real temp = X_min; temp <= X_max; ++temp)
{if (f(temp)%1==0 && f(temp)<=Y_max && f(temp)>=Y_min)
{dot((temp,f(temp)),graph_color+linewidth(line_width*4));}}}
dot((0,0));
/* Property of "PythonNut" 2011*/
</asy>
== The code==
The code is:
<pre><nowiki>
/* AUTO-GRAPH V-4 beta by PythonNut*/

/* Customizations: feel free to edit */
import math;
import graph;
/* x maximum and minimum */
int X_max = 10;
int X_min =-10;
/* y maximum and minimum */
int Y_max = 10;
int Y_min = -10;
/* linewidth */
real line_width = 0.75;
/* graph color */
pen graph_color = heavygreen;
/* special */
bool mark_lattice = false;
bool show_grid = true;
real X_tick_density = 1;
real Y_tick_density = 1;
real ratio = 1;
real resolution = 0.0001;
int size = 300;
/* graph function */
real f(real x)
   {
   return 2x^3-6x^2+3x-1; /* type function to be graphed here */
}

/* The Code. Do not disturb unless you know what you are doing */
bool ib(real t){ return (Y_min <= f(t) && f(t) <= Y_max); }

size(size);unitsize(size*ratio,size);Label l;l.p=fontsize(6);
xaxis("$x$",X_min,X_max,Ticks(l,X_tick_density,(X_tick_density/2),NoZero),Arrows);
yaxis("$y$",Y_min,Y_max,Ticks(l,Y_tick_density,(Y_tick_density/2),NoZero),Arrows);//
if (show_grid){add(shift(X_min,Y_min)*grid(X_max-X_min,Y_max-Y_min));}

real t, T1, T2;

for (T1 = X_min ; T1 <= X_max ; T1 += resolution){
    while (! ib(T1) && T1 <= X_max){T1 += resolution;}
    if(T1 > X_max){break;}
    T2 = T1; 
    while (  ib(T1) && T1 <= X_max){T1 += resolution;}
    T1 -= resolution;
    draw(graph(f,T2,T1,n=2400),graph_color+linewidth(line_width),Arrows);
}

if (mark_lattice){
    for (t = X_min; t <= X_max; ++t){
        if (f(t)%1==0 && ib(t)){
            dot((t,f(t)),graph_color+linewidth(line_width*4));
        }
    }
}
dot((0,0));
/* Property of "PythonNut" 2011*/
</nowiki></pre>

== Autograph Micro==
<asy>
import contour;
import graph;
real f(real x)
{
return x^2-1.333;
}
draw(graph(f,-1.5,1.5),blue+linewidth(0.5),Arrows);
size(75);
real f(real x, real y) {return abs(x^3) + abs(y^3);}
draw(contour(f,(-6,-6),(6,6), new real[] {5}),red+linewidth(1));
label("$Auto\;Graph$",(0,0.3),red);
label("$micro$",(0,-0.3),red);
dot((1.5,0),red);
dot((0,1.5),red);
dot((0,-1.5),red);
dot((-1.5,0),red);</asy>
Autograph micro is a version of autograph made to fit in the AoPS classroom character limit.
<pre><nowiki>
[asy]int X=10,x=-10,Y=10,y=-10;
real f(real x){return 11*sin(x);}
size(300); Label l;l.p=fontsize(6);dot((0,0));
xaxis(x,X,Ticks(l,1.0,0.5));yaxis(y,Y,Ticks(l,1.0,0.5));
add(shift(x,y)*grid(X-x,Y-y));
draw(graph(f,x,X,n=2400),heavygreen+linewidth(1),Arrows);
clip((x,y)--(x,Y)--(X,Y)--(X,y)--cycle);[/asy]
</nowiki></pre>
==Autograph implicit==
<asy>
import contour;
import graph;
real f(real x)
{
return x^2-1.333;
}
draw(graph(f,-1.5,1.5),blue+linewidth(0.5),Arrows);
size(75);
real f(real x, real y) {return abs(x^3) + abs(y^3);}
draw(contour(f,(-6,-6),(6,6), new real[] {5}),red+linewidth(1));
label("$Auto\;Graph$",(0,0.3),red);
label("$implict$",(0,-0.3),red);
dot((1.5,0),red);
dot((0,1.5),red);
dot((0,-1.5),red);
dot((-1.5,0),red);</asy>
Autograph implicit Is a version of Autograph used to graph implicit functions such as 
<math>x^{13}+5\cdot x^5\cdot y^3+x\cdot y^5+y^5=2.5</math>
<asy>
/* AUTO-GRAPH implict by PythonNut*/
/* Customizations: feel free to edit */
import math;
import graph;
import contour;
/* x maximum and minimum */
int X_max = 10;
int X_min =-10;
/* y maximum and minimum */
int Y_max = 10;
int Y_min = -10;
/* graph color */
pen graph_line = heavygreen+linewidth(0.75);
/* special */
bool show_grid = true;
real X_tick_density = 1;
real Y_tick_density = 1;
real ratio = 1;
int size = 300;
real value = 2.5; /* value to set to */
/* graph function */
real f(real x, real y)
{
return x^13+5*x^5*y^3+x*y^5+y^5; /* type function to be graphed here */
}
/* The Code. Do not disturb unless you know what you are doing */
size(size);unitsize(size*ratio,size);Label l;l.p=fontsize(6);
xaxis("$x$",X_min,X_max,Ticks(l,X_tick_density,(X_tick_density/2),NoZero),Arrows);
yaxis("$y$",Y_min,Y_max,Ticks(l,Y_tick_density,(Y_tick_density/2),NoZero),Arrows);//
if (show_grid){add(shift(X_min,Y_min)*grid(X_max-X_min,Y_max-Y_min));}
draw(contour(f,(X_min,Y_min),(X_max,Y_max), new real[] {value}),graph_line);</asy>
The code is
<pre><nowiki>
[asy]
/* AUTO-GRAPH implict by PythonNut*/
/* Customizations: feel free to edit */
import math;
import graph;
import contour;
/* x maximum and minimum */
int X_max = 10;
int X_min =-10;
/* y maximum and minimum */
int Y_max = 10;
int Y_min = -10;
/* graph color */
pen graph_line = heavygreen+linewidth(0.75);
/* special */
bool show_grid = true;
real X_tick_density = 1;
real Y_tick_density = 1;
real ratio = 1;
int size = 300;
real value = 2.5; /* value to set to */
/* graph function */
real f(real x, real y)
{
return x^13+5*x^5*y^3+x*y^5+y^5; /* type function to be graphed here */
}
/* The Code. Do not disturb unless you know what you are doing */
size(size);unitsize(size*ratio,size);Label l;l.p=fontsize(6);
xaxis("$x$",X_min,X_max,Ticks(l,X_tick_density,(X_tick_density/2),NoZero),Arrows);
yaxis("$y$",Y_min,Y_max,Ticks(l,Y_tick_density,(Y_tick_density/2),NoZero),Arrows);//
if (show_grid){add(shift(X_min,Y_min)*grid(X_max-X_min,Y_max-Y_min));}
draw(contour(f,(X_min,Y_min),(X_max,Y_max), new real[] {value}),graph_line);[/asy]
</nowiki></pre>