2D Translation

We can move any object from one to another place without changing the shape of the object.

For Example-

Translation of a Point:If we want to translate a point from P (x₀, y₀) to Q (x₁, y₁), then we have to add Translation coordinates (Tx, Ty) with original coordinates.

We can also represent the translation in matrix form-

We can apply Translation on following objects-

• Line
• Rectangle
• Polygon
• Square

Homogeneous Coordinate Representation:

The above Translation is also shown in the form of 3 x 3 matrix-

Here, Translation coordinates (T_x, T_y) are also called “Translation or Shift Vector.”

Example- Given a Point with coordinates (2, 4). Apply the translation with distance 4 towards x-axis and 2 towards the y-axis. Find the new coordinates without changing the radius?

Solution: P = (x₀, y₀) = (2,4)

Shift Vector = (T_x, _Ty) = (4, 2)

Let us assume the new coordinates of P = (x₁, y₁)

Now we are going to add translation vector and given coordinates, then

x₁ = x₀ + T_x = (2 + 4) = 6

y₁ = y₀ + T_y = (4 + 2) = 6

Thus, the new coordinates = (6,6)