Coordinate Systems: 3D Angles Explained

In summary, the conversation discusses the concept of 3D coordinate systems and the possibility of having a system based on 3 angles. It is suggested that such a system may not be practical as it would be difficult to define the location of a point without distances. However, another participant disagrees and suggests using three points to establish a coordinate system, which would be unique and compatible with a Cartesian coordinate system. The conversation ends with gratitude for this suggestion.
  • #1
Trave11er
71
0
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.
 
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  • #2
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.
 
  • #3
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.
 
  • #4
HallsofIvy said:
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.
 
  • #5


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.
 

1. What is a coordinate system?

A coordinate system is a mathematical framework used to locate points in a 2D or 3D space. It is made up of a set of axes, typically labeled x, y, and z, that intersect at right angles and define the position of a point in relation to a reference point.

2. Why is it important to understand 3D angles in coordinate systems?

Understanding 3D angles in coordinate systems is important because it allows us to accurately describe the orientation and position of objects in 3D space. This is crucial for many fields, such as engineering, architecture, and computer graphics.

3. What are the three types of angles in a 3D coordinate system?

The three types of angles in a 3D coordinate system are pitch, roll, and yaw. Pitch is the rotation around the x-axis, roll is the rotation around the y-axis, and yaw is the rotation around the z-axis.

4. How are 3D angles measured in a coordinate system?

3D angles are typically measured in degrees or radians, and can be positive or negative depending on the direction of rotation. The angles are measured from the reference axes, with positive rotations in a counterclockwise direction and negative rotations in a clockwise direction.

5. How are 3D angles used in real-world applications?

3D angles are used in a variety of real-world applications, such as navigation systems, robotic manipulators, and 3D modeling. They are also important in understanding the movement and orientation of objects in physics and mechanics.

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