Tool to achieve coordinates system changes in the 2d-plane (cartesian, polar, etc.). These are mathematical operations representing the same elements but in different referentials.
2D Coordinates Systems - dCode
Tag(s) : Geometry
dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!
2D Coordinates Systems
Sponsored adsChange of 2D Coordinates (plane)
Answers to Questions (FAQ)
How to convert cartesian coordinates to polar?
The base / referential change using cartesian coordinates $ (x, y) $ to another referential using polar coordinates $ (r, \theta) $ obey the equations: $$ r = \sqrt{x^2 + y^2} \\ \theta = 2\arctan\left(\frac y{x+ \sqrt{x^2+y^2}} \right) $$ with $ \arctan $ the reciprocal of the function $ \tan $ (tangent).
NB: the value of $ \theta $ calculated here is included in the inverval $ ] -\pi, \pi] $ (to have it in the interval $ ] 0, 2\pi] $ add $ 2 \pi $ if the value of the angle is negative)
If $ r = 0 $ then the angle can be defined by any real number
Example: The point of the plane in position $ (1,1) $ in Cartesian coordinates is defined by the polar coordinates $ r = \sqrt {2} $ and $ \theta = \pi/4 $
How to convert polar coordinates to cartesian?
The base / referential change from polar coordinates $ (r, \theta) $ to another referential using cartesian coordinates $ (x, y) $ follows the equations: $$ x = r \cos (\theta) \\ y = r \sin (\theta) $$
with $ r $ a positive real number and $ \theta $ an angle defined between $ ] -\pi, \pi] $
Source code
dCode retains ownership of the online "2D Coordinates Systems" source code. Except explicit open source licence (indicated CC / Creative Commons / free), the "2D Coordinates Systems" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or the "2D Coordinates Systems" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, copy-paste, or API access for "2D Coordinates Systems" are not public, same for offline use on PC, tablet, iPhone or Android ! Remainder : dCode is free to use.
Need Help ?
Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!
Questions / Comments
Thanks to your feedback and relevant comments, dCode has developed the best '2D Coordinates Systems' tool, so feel free to write! Thank you!