complex-plotter

Hosted on https://tobylam.xyz/plotter

Plot graphs of functions from $\mathbb{R}^2$ to $\mathbb{R}^2$ and $\mathbb{C}$ to $\mathbb{C}$
- Sketch any curve and see the image of that curve under the function in real time
Supports one time parameter for animations
Works on Desktop / Mobile browsers

A fork of mabokin's complex mapping visualizer. Raise an issue for any bugs / suggestions!

Documentation

The visualizer webpage should work on all desktop / mobile browsers.

Basic Usage

Click the Randomize button on the center bottom to have a feel of what the plotter can do
- Draw on the left plane by holding your mouse button and see the output on the right
- Click the Clear Canvas button on the left to clear the canvas
Decide if you're plotting a function from ℝ² to ℝ² or a function from ℂ → ℂ

ℝ² to ℝ² functions

Input the functions u(x,y,t) and v(x,y,t) in the textboxes
- t is a time parameter that can be set constant or be used as a parameter for animation
- e.g. u(x,y,t)=2*x, v(x,y,t)=y+1
If you intend t to be a constant parameter, set a value to it
- Example: t=0
Click the Set Phi Map button
- Click this button everytime after you change the t parameter or the functions u and v
Draw on the left plane using the Pen tool and see the output on the right

ℂ to ℂ functions

Input the functions f(z,t) in the textboxes
- t is a time parameter that can be set constant or be used as a parameter for animation
- e.g. f(z,t)=1/z
If you intend t to be a constant parameter, set a value to it
- Example: t=0
Click the Set f Map button
- Click this button everytime after you change the t parameter or the function f
Draw on the left plane using the Pen tool and see the output on the right

Advanced usage

Function input

Type a*b for $a\times b$ and a^b for $a^b$. You're allowed to use the following functions. You could find their definitions here.

sqrt(), cbrt(), exp(), e^(), log(), Log(), ln(), gamma(), fact(), factorial(), sin(), cos(), tan(), sec(), csc(), cot(), arcsin(), arccos(), arctan(), arcsec(), arccsc(), arccot(), arsin(), arcos(), artan(), arsec(), arcsc(), arcot(), asin(), acos(), atan(), asec(), acsc(), acot(), sinh(), cosh(), tanh(), sech(), csch(), coth(), arcsinh(), arccosh(), arctanh(), arcsech(), arccsch(), arccoth(), arsinh(), arcosh(), artanh(), arsech(), arcsch(), arcoth(), asinh(), acosh(), atanh(), asech(), acsch(), acoth(), re(), real(), im(), imag(), abs(), mag(), arg(), conj(), norm(), normal(), floor(), ceil(), ceiling(), round(), fpart(), frac(), ipart(), int()

(Currently conj() is not supported)

You could also use pi for $\pi$.

Animation

Select the function you'd like to animate
- Φ for ℝ² to ℝ² functions, f for ℂ → ℂ functions
Set the initial and end values of t
Set the total duration of the animation
- The plotter will try to finish the whole animation within the timeframe
Click Play
Click Stop and reset which will redraw the plot with the t parameter set as the initial value.

Settings

Autolink Max Distance
- Whenever you draw quickly on the Canvas, the canvas only registers a small number of points. Autolink interpolates these points with straight lines. The fewer the points, the better the quality of interpolation, but at the cost of performance
- Choose a higher Max Distance for a better performance at the cost of quality
Branch cut threshold
- The branch cut threshold ensures that discontinuities in the function are visually represented as breaks in the lines drawn on the right plane. A higher branch cut threshold means that the code will tolerate larger differences in function values before visually breaking the line

Errata

Not all aspects of the plotter is covered here. If you are confused about anything, please raise an issue!