# 3D Coordinate Systems
Understanding 3D coordinate systems is fundamental to computer graphics, 3D modeling, and spatial analysis.
## Coordinate System Types
### Cartesian Coordinates
The most common system using three perpendicular axes (X, Y, Z):
- **Right-handed**: Thumb=X, Index=Y, Middle=Z
- **Left-handed**: Alternative orientation
- **Origin**: Point (0, 0, 0) where axes intersect
### Spherical Coordinates
Represents points using:
- **Radius (r)**: Distance from origin
- **Azimuth (θ)**: Angle in XY plane
- **Elevation (φ)**: Angle from Z axis
### Cylindrical Coordinates
Combines polar coordinates with height:
- **Radius (r)**: Distance from Z axis
- **Angle (θ)**: Rotation around Z axis
- **Height (z)**: Position along Z axis
## Transformations
### Translation
Moving objects in 3D space using translation vectors.
### Rotation
Rotating around axes:
- **Euler Angles**: Three rotation angles
- **Quaternions**: Four-component representation (avoids gimbal lock)
- **Rotation Matrices**: 3x3 matrices for rotation
### Scaling
Uniform or non-uniform scaling along axes.
## Homogeneous Coordinates
Using 4D representation (x, y, z, w) enables:
- Combined transformations as matrix multiplication
- Perspective projection
- Efficient computation
## Applications
- **Computer Graphics**: Rendering and animation
- **Robotics**: Kinematics and path planning
- **Medical Imaging**: 3D reconstruction and analysis
- **Game Development**: 3D world representation
## World vs. Local Coordinates
- **World Space**: Global coordinate system
- **Local Space**: Object-relative coordinates
- **View Space**: Camera-relative coordinates
- **Screen Space**: 2D projection coordinates
## Conclusion
Mastering 3D coordinate systems is essential for any work involving 3D data, graphics, or spatial computation.