- 2070 Asar · 2 marks
Short note: 2D translation
Short answer
Translation moves points by adding offsets: x'=x+tx, y'=y+ty. In homogeneous 3×3 matrix form. It preserves shape and size. Inverse is translation by (-tx,-ty). Two successive translations add: T(tx1,ty1)·T(tx2,ty2)=T(tx1+tx2,ty1+ty2).
Write a short note on 2D translation.
Translation moves an object from one position to another along a straight path without changing its shape or size. Every point P(x, y) is shifted by translation distances tx (along x) and ty (along y):
x' = x + tx, y' = y + ty
Matrix form (homogeneous coordinates):
| x' | | 1 0 tx | | x |
| y' | = | 0 1 ty | | y |
| 1 | | 0 0 1 | | 1 |
Points:
- It is a rigid-body transformation: distances and angles are preserved.
- Inverse translation is T(−tx, −ty).
- Two translations add: T(tx1, ty1)·T(tx2, ty2) = T(tx1+tx2, ty1+ty2).
Example: P(2, 3) translated by (4, −1) gives P'(6, 2).
✓ Answer checked by Claude Opus 5.5 (high effort)