ImplicitPlotter

ImplicitPlotter is a powerful command-line tool designed for generating plots of binary implicit function equations and inequalities. It supports both Cartesian and polar coordinates, providing flexibility for users in visualizing complex mathematical relationships.

The plotting capabilities are built upon a robust algorithm utilizing interval arithmetic, ensuring high accuracy in the rendered graphs.

Key Features

• Flexible Function Support: Plot any binary implicit function or inequality.
• Customizable Output: Set dimensions and colors for output images to suit individual preferences.
• Adjustable Coordinates: Easily switch between Cartesian and polar coordinate systems.

Usage Example

Users can utilize the ImplicitPlotter tool via command line with various options, as shown in the following examples:

Plotting a Curve

ImplicitPlotter --relation "sin(x^2-y^2)=sin(x+y)+cos(x*y)" --output "./output.png" --width 1000 --height 1000 --xmin -10 --xmax 10 --ymin -10 --ymax 10 --drawColor "#0078D7"

Plotting a Heart Shape

ImplicitPlotter --relation "17*x^2-16*abs(x)*y+17*y^2+150/abs(5*x+sin(5*y))<225" --output "./output.png" --width 1000 --height 1000 --xmin -6 --xmax 6 --ymin -6 --ymax 6 --drawColor "#ED4336"

Plotting a Face

ImplicitPlotter --relation "1/15*(6-y)+1/6400000*(8*x^2+4*(y-3)^2)^3+cos(max((x+y)*cos(y-x),(y-x)*cos(x+y)))<sin(min((x+y)*sin(y-x),(y-x)*sin(x+y)))" --output "./output.png" --width 1000 --height 1000 --xmin -8 --xmax 8 --ymin -5 --ymax 11 --drawColor "#366AAD"

Plotting Tai Chi

ImplicitPlotter --relation "(cos(a-r)-sin(a))*(r^4-2*r^2*cos(2*a+2.4)+0.9)+(0.62*r)^1000<0" --output "./output.png" --width 1000 --height 1000 --xmin -3 --xmax 3 --ymin -3 --ymax 3 --drawColor "#000000"

Plotting a Pattern

ImplicitPlotter --relation "floor(sin(x+sin(y+sin(x))))=floor(cos(y+cos(x+cos(y))))" --output "./output.png" --width 1000 --height 1000 --xmin -10 --xmax 10 --ymin -10 --ymax 10 --drawColor "#E8AC4A"

For users interested in a more interactive experience, the Relation Explorer provides a graphical version of this project with advanced plotting features and is available on the Microsoft Store.

By leveraging ImplicitPlotter, users gain a robust tool for visualizing mathematical functions and enhancing their understanding of complex relationships.