Implicit Function Family f(x,y,a[i])=0 Plotter(Line-Scan Method) (version 2.0)

Click "Run/Re-Run Plotter" button to plot the pre-defined example function family.
Input your own function formula or change the example function.
Input your own parameters a[i]=a0,a1,a2,a3,,, or change the default parameters.
Change or set the x/y plot range, [xmin, xmax] and [ymin, ymax], for your new/re-defined function, if needed.
Click "Run/Re-Run Plotter" button to plot the new/re-defined function family.
If the existence range of f(x,y)=0 graph is not known beforehand, you can set a larger x/y plot range to catch the graph.
If the displayed graph is too small, you can use the mouse(left key, down-move-up) to select part of the graph and the plotter will zoom-in and magnify the selected graph part automatically. Use "Zoom-out/Back" button to reverse the zoom-in.
A more detailed usage of this function plotter is at the end of this page.

Restart/Reload This Web Page

Keep Graph Shape or Not:

Set Width of Graph Line:

Click "Run/Re-Run Plotter" Button to Start

Input Your Own Function f(x,y,a) or Change the Pre-defined Example:

Input Parameter a[i]=(a0,a1,a2,a3,,,,). Graph Color Spectrum from Blue to Red:

Input X Plot Range---xmin and xmax:

Input Y Plot Range---ymin and ymax:

Saved Projects:

How to save your projects for later use:
Click "Save Project" to save the current project to your device. All necessary function(s) and parameters will be saved.
Click "Load Project" to load a saved project and run it.
Click "Delete Project" to remove the selected project from your device.
Note: Your projects will remain saved to your device unless you delete them or you clear the site data of your browser.

Sharing your projects:
To create a URL link for the current project, click the "Share Function" button below the graph(s).
This will copy a link containing the current project to your clipboard that you can share with others.
You can also save a PNG image of the current graph by clicking the "Save Graph as Image" button.

Disclaimer: No data saved with these tools are kept by or sent to mathonthecloud.com. Everything is saved locally to your device only.

More Usage Information for the Function Plotter:

The plotter provides a set of example functions to demo the function formula syntax, use the "Select Menu,,," to see and plot the examples.
For each input parameter a[i], one graph is added and plotted. The graphs are colored with a spectrum from blue to red.
The function formula follows JavaScript syntax and support all the JavaScript Math functions, such as cos(), sin(), abs(), sqrt(), etc.. See"Supported Operators and Functions".
For function formula input, supported operators are limited to:
+ (Addition), - (Subtraction), * (Multiplication), / (Division), and ^ (or **)(Exponentiation).
Other operators, such as &, &&, |, ||, >>, >, <<, <, %, !, etc., are not supported for function formula and they will be treated as errors, although they are legal JavaScript operators.
When move the mouse cursor on the graph, the mouse position on the math space (x,y) will be displayed.
The plotter will catch most of user-input errors and function singularity errors, and will display a notice for possible error correction.
After correct the error, click "Run/Re-Run Plotter" button to re-run the plotter.
This "line-scan" graph plot method is based on detecting sign (+/-) change of f(x,y,a). If f(x,y,a) always >=0 or always <=0, the f(x,y,a)=0 graph can not be plotted. For example, f(x,y)=(x^2+y^2-a)^2=0 graph can not be plotted, but f(x,y)=x^2+y^2-a=0 or f(x,y)=(x^2+y^2-a)^3=0 graph will be plotted correctly.
The plotted graph is auto-scaled and auto-centered on the canvas plot area. If the checkbox "Keep Graph Shape or Not" is checked, the plotter uses the same scale factor in both x and y directions and the graph will keep its original shape. If the checkbox is unchecked, the graph will be stretched in one direction to make full use of the canvas plot area.