Coordinate Systems: 3D Angles Explained

[Trave11er]

Hi!

I see there are three 3D coordinate systems based on either 3 number (cartesian), 2 numbers and 1 angle (cylindrical) and 1 number and 2 angles (spherical). So can't there be a system based on 3 angles? Thank you.

 

[Integral]

Seems to me you would have some troubles defining the location of a point in space with 3 angles and no distances. Play with it see if you can see why.

 

[HallsofIvy]

I have to disagree with Integral here.

Given three points initially, then the angles the lines from each of those points to point p make with the plane containing the three points are unique and will establish a coordinate system.

If you already have a Cartesian coordinate system then (1, 0, 0), (0, 1, 0), and (0, 0, 1) will work nicely.

 

[Trave11er]

I have to disagree with Integral here.

Given three points initially, then the angles the lines from each of those points to point p make with the plane containing the three points are unique and will establish a coordinate system.

If you already have a Cartesian coordinate system then (1, 0, 0), (0, 1, 0), and (0, 0, 1) will work nicely.

Wow! That is very nice. Thank you a lot.

 

[CellCoree]

Hello,

Thank you for your question. While there is not a commonly used coordinate system based solely on three angles, it is possible to use three angles to define a position in 3D space. This is known as a spherical coordinate system, where the three angles represent the distance from the origin, the azimuth angle, and the inclination angle. However, this system is not as commonly used as the other three coordinate systems you mentioned, as it can be more complex and less intuitive for certain applications. Each coordinate system has its own advantages and limitations, so it is important to choose the most appropriate one for your specific needs. I hope this helps clarify the use of angles in 3D coordinate systems.