3D Translation in Computer Graphics | Definition | Examples

3D Transformation in Computer Graphics-

 

In Computer graphics, Transformation is a process of modifying and re-positioning the existing graphics.

 

• 3D Transformations take place in a three dimensional plane.
• 3D Transformations are important and a bit more complex than 2D Transformations.
• Transformations are helpful in changing the position, size, orientation, shape etc of the object.

 

Transformation Techniques-

 

In computer graphics, various transformation techniques are-

 

 

1. Translation
2. Rotation
3. Scaling
4. Reflection
5. Shear

 

In this article, we will discuss about 3D Translation in Computer Graphics.

 

3D Translation in Computer Graphics-

 

In Computer graphics, 3D Translation is a process of moving an object from one position to another in a three dimensional plane.

 

Consider a point object O has to be moved from one position to another in a 3D plane.

 

Let-

• Initial coordinates of the object O = (X_old, Y_old, Z_old)
• New coordinates of the object O after translation = (X_new, Y_new, Z_old)
• Translation vector or Shift vector = (T_x, T_y, T_z)

 

Given a Translation vector (T_x, T_y, T_z)-

• T_x defines the distance the X_old coordinate has to be moved.
• T_y defines the distance the Y_old coordinate has to be moved.
• T_z defines the distance the Z_old coordinate has to be moved.

 

 

This translation is achieved by adding the translation coordinates to the old coordinates of the object as-

• X_new = X_old + T_x     (This denotes translation towards X axis)
• Y_new = Y_old + T_y     (This denotes translation towards Y axis)
• Z_new = Z_old + T_z     (This denotes translation towards Z axis)

 

In Matrix form, the above translation equations may be represented as-

 

 

Also Read- 2D Translation in Computer Graphics

 

PRACTICE PROBLEM BASED ON 3D TRANSLATION IN COMPUTER GRAPHICS-

 

Problem-

 

Given a 3D object with coordinate points A(0, 3, 1), B(3, 3, 2), C(3, 0, 0), D(0, 0, 0). Apply the translation with the distance 1 towards X axis, 1 towards Y axis and 2 towards Z axis and obtain the new coordinates of the object.

 

Solution-

 

Given-

• Old coordinates of the object = A (0, 3, 1), B(3, 3, 2), C(3, 0, 0), D(0, 0, 0)
• Translation vector = (T_x, T_y, T_z) = (1, 1, 2)

 

For Coordinates A(0, 3, 1)

 

Let the new coordinates of A = (X_new, Y_new, Z_new).

 

Applying the translation equations, we have-

• X_new = X_old + T_x = 0 + 1 = 1
• Y_new = Y_old + T_y = 3 + 1 = 4
• Z_new = Z_old + T_z = 1 + 2 = 3

 

Thus, New coordinates of A = (1, 4, 3).

 

For Coordinates B(3, 3, 2)

 

Let the new coordinates of B = (X_new, Y_new, Z_new).

 

Applying the translation equations, we have-

• X_new = X_old + T_x = 3 + 1 = 4
• Y_new = Y_old + T_y = 3 + 1 = 4
• Z_new = Z_old + T_z = 2 + 2 = 4

 

Thus, New coordinates of B = (4, 4, 4).

 

For Coordinates C(3, 0, 0)

 

Let the new coordinates of C = (X_new, Y_new, Z_new).

 

Applying the translation equations, we have-

• X_new = X_old + T_x = 3 + 1 = 4
• Y_new = Y_old + T_y = 0 + 1 = 1
• Z_new = Z_old + T_z = 0 + 2 = 2

 

Thus, New coordinates of C = (4, 1, 2).

 

For Coordinates D(0, 0, 0)

 

Let the new coordinates of D = (X_new, Y_new, Z_new).

 

Applying the translation equations, we have-

• X_new = X_old + T_x = 0 + 1 = 1
• Y_new = Y_old + T_y = 0 + 1 = 1
• Z_new = Z_old + T_z = 0 + 2 = 2

 

Thus, New coordinates of D = (1, 1, 2).

Thus, New coordinates of the object = A (1, 4, 3), B(4, 4, 4), C(4, 1, 2), D(1, 1, 2).

 

To gain better understanding about 3D Translation in Computer Graphics,

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Next Article- 3D Rotation in Computer Graphics

 

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