feat(graph): enhance plotting support for polar coordinates #2

[Tarun2605]

Description

This pull request enhances the plotting functionality in src/core/Core/Application.cpp by adding support for polar coordinate plots.
Functions containing the variable theta are now automatically interpreted and plotted in polar form, expanding the application's graphing capabilities.

ISSUE ADDRESSED: #2

Plotting Improvements

• Added detection for functions using the variable theta to identify polar equations and plot them using polar coordinates (r = f(theta)), converting results to (x, y) for rendering.
• Implemented a loop to evaluate and plot polar functions over a range of theta values, drawing the corresponding polyline on the canvas.

Codebase Updates

• Included the <cmath> header to support trigonometric operations required for polar plotting.

These changes enable the application to visualize both standard and polar equations seamlessly.

---

Semver Changes

• Minor (new features, no breaking changes)

---

Issues

None

---

Checklist

• I have read the [Contributing Guidelines](../Contributor_Guide/Contruting.md).

ATTACHING OUTPUT SCREENSHOTS

CARTESIAN:

POLAR:

[nsh07]

Actually after a bit of thinking, this implementation is actually quite bad at recognising whether the user actually wants to plot a polar function or not.

Say I type 1 in the expression. Do I mean y = 1 or r = 1? y = 1 is a line while r = 1 is a circle, which is a drastically different graph.

I would request you to implement the "starts with r =" approach instead of "checking for theta" for this reason.

[Tarun2605]

Yeah I just noticed that right now, you are absolutely right on that. I was just thinking of keeping functionalities same across cartesian and polar coords.

[Tarun2605]

I am attaching the screenshot of the new implementation

[nsh07]

Looks great. I'll review the code by this evening and merge it. Thanks!

[nsh07]

Really liked this PR. No obtrusive code changes, just the feature cleanly integrated into the pre-existing code. Thanks for contributing!

[Tarun2605]

Thank you !!! :)

[nsh07]

Please feel free to make any further feature requests or bug reports in this repo if you'd like

[nsh07]

Important

@Tarun2605 It seems you haven't registered on the OPCODE Discord server (at https://discord.gg/F63kqjsJ). Please join it and register your GitHub account in the #register channel for your score to show up on the leaderboard

[Tarun2605]

I am sorry but what leaderboard are you talking about?

[Tarun2605]

Ohh didnt knew this was a competition. I just do open source for fun nowadays and to kill time. Sorry if I intervened. Thank you for taking my PR though.

[nsh07]

No problem lol, you can register on the Discord anyway. We have prizes for participants, and students from outside of IIIT Bhagalpur are also allowed to participate. Now don't tell me you're not a student 😅

[Tarun2605]

Yeah yeah I am student. Final year at NSUT, Delhi.