A transformation rotation about the Y axis is a fundamental geometric operation in 3D space where an object spins around the vertical Y axis.
Understanding Rotation About the Y-Axis
Based on the provided information, a rotation about the y-axis involves rotating an object parallel to the y-axis (principal axis). This means the Y axis itself acts as the axis of rotation, similar to how a spinning top rotates around its central axis.
How Coordinates Change
During a rotation about the Y axis, a key characteristic is that the y coordinate remains unchanged. Only the other two coordinates, x and z, change their values as the object rotates around the Y axis.
This transformation effectively moves a point $(x, y, z)$ to a new position $(x', y', z')$, where $y' = y$. The values of $x'$ and $z'$ are recalculated based on the angle of rotation and the original $x$ and $z$ values.
Coordinate Changes During Y-Axis Rotation
| Original Coordinate | New Coordinate | Status |
|---|---|---|
| x | x' | Changes |
| y | y' | Unchanged |
| z | z' | Changes |
Key Characteristics of Y-Axis Rotation
- Axis of Rotation: The Y axis serves as the pivot point.
- Y-Coordinate Invariance: The vertical position (Y coordinate) of any point on the object does not change.
- X and Z Coordinate Alteration: The horizontal (X) and depth (Z) coordinates are updated based on the rotation angle.
- Principal Axis: The Y axis is considered the principal axis for this specific rotation type, as mentioned in the reference.
Applications of Y-Axis Rotation
Rotation about the Y axis is a common operation in various fields, including:
- 3D Computer Graphics: Used to orient objects, characters, and cameras in virtual environments.
- 3D Modeling: Essential for manipulating and positioning parts of a 3D model.
- Robotics: Used to define the movement and orientation of robotic arms or sensors.
In essence, rotating about the Y axis allows you to turn an object left or right in a standard 3D coordinate system without altering its height.
