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2D Coordinates Systems

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.

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2D Coordinates Systems -

Tag(s) : Geometry

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2D Coordinates Systems

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Change of 2D Coordinates (plane)

Cartesian to Polar Coordinates



Polar to Cartesian Coordinates



Change of 3D Coordinates (space)

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.

Answers to Questions

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] $

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Source : https://www.dcode.fr/change-coordinates-2d
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