Translation rotation refers to a combined geometric transformation where an object is both moved a certain distance and direction (translated) and turned around a fixed point (rotated).
Based on the provided definitions, a translation is a rigid movement where every point of a figure shifts the exact same distance and in the same exact direction, without being rotated, reflected, or resized. Imagine sliding a puzzle piece across a table – that's a translation.
Conversely, a rotation is the turning of a figure or object around a fixed point. Think about the hands of a clock moving – that's a rotation.
When we talk about "translation rotation," we are describing a process where an object undergoes both of these fundamental movements. The object changes both its position and its orientation in space.
Understanding the Components Separately
To grasp translation rotation, it's helpful to look at the two parts:
- Translation: This is pure shifting. The object's orientation stays the same, only its location changes. The reference states, "a scenario where every point in a figure is moved the exact same distance and in the same exact direction, without being rotated, reflected, or resized."
- Rotation: This is pure turning. The object pivots around a fixed point, changing its orientation but not its location relative to the pivot point (though its absolute position might change if the pivot point moves). The reference states, "a rotation is the turning of a figure or object around a fixed point."
The Combined Transformation
Applying both a translation and a rotation results in "translation rotation." This is a very common transformation seen in the real world and in fields like:
- Physics: Describing the motion of rigid bodies that slide and spin.
- Computer Graphics: Moving and orienting 3D models.
- Robotics: Planning the movement of robot arms or autonomous vehicles.
The final position and orientation of an object after a translation and a rotation depend on the parameters of each transformation (the distance and direction for translation, and the angle and center for rotation) and sometimes the order in which they are applied. Performing a translation followed by a rotation can lead to a different result than a rotation followed by a translation, especially if the center of rotation is not at the origin or on the object's centroid.
Key Characteristics
- Rigid Transformation: Like translation and rotation individually, the combined translation rotation is a rigid transformation. This means the shape and size of the object remain unchanged; only its position and orientation are altered.
- Combination of Movements: It involves both a straight-line shift and a turn.
Summarizing the Differences
Based on the reference and the concept of combination:
| Transformation | Description (from Reference) | Changes Position? | Changes Orientation? | Changes Size/Shape? |
|---|---|---|---|---|
| Translation | "every point in a figure is moved the exact same distance and in the same exact direction, without being rotated, reflected, or resized." | Yes | No | No |
| Rotation | "the turning of a figure or object around a fixed point." | Yes (unless pivot is object center and object doesn't move) | Yes | No |
| Translation Rotation | Combination of both a translation and a rotation | Yes | Yes | No |
In essence, translation rotation describes the general movement of a rigid object through space, incorporating both sliding and turning motions.
