2D Reflection in Computer Graphics | Definition | Examples

2D Transformations in Computer Graphics-

 

We have discussed-

• Transformation is a process of modifying and re-positioning the existing graphics.
• 2D Transformations take place in a two dimensional plane.

 

In computer graphics, various transformation techniques are-

 

 

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

 

In this article, we will discuss about 2D Reflection in Computer Graphics.

 

2D Reflection in Computer Graphics-

 

• Reflection is a kind of rotation where the angle of rotation is 180 degree.
• The reflected object is always formed on the other side of mirror.
• The size of reflected object is same as the size of original object.

 

Consider a point object O has to be reflected in a 2D plane.

 

Let-

• Initial coordinates of the object O = (X_old, Y_old)
• New coordinates of the reflected object O after reflection = (X_new, Y_new)

 

Reflection On X-Axis:

 

This reflection is achieved by using the following reflection equations-

• X_new = X_old
• Y_new = -Y_old

 

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

 

 

For homogeneous coordinates, the above reflection matrix may be represented as a 3 x 3 matrix as-

 

 

Reflection On Y-Axis:

 

This reflection is achieved by using the following reflection equations-

• X_new = -X_old
• Y_new = Y_old

 

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

 

 

For homogeneous coordinates, the above reflection matrix may be represented as a 3 x 3 matrix as-

 

 

PRACTICE PROBLEMS BASED ON 2D REFLECTION IN COMPUTER GRAPHICS-

 

Problem-01:

 

Given a triangle with coordinate points A(3, 4), B(6, 4), C(5, 6). Apply the reflection on the X axis and obtain the new coordinates of the object.

 

Solution-

 

Given-

• Old corner coordinates of the triangle = A (3, 4), B(6, 4), C(5, 6)
• Reflection has to be taken on the X axis

 

For Coordinates A(3, 4)

 

Let the new coordinates of corner A after reflection = (X_new, Y_new).

 

Applying the reflection equations, we have-

• X_new = X_old = 3
• Y_new = -Y_old = -4

 

Thus, New coordinates of corner A after reflection = (3, -4).

 

For Coordinates B(6, 4)

 

Let the new coordinates of corner B after reflection = (X_new, Y_new).

 

Applying the reflection equations, we have-

• X_new = X_old = 6
• Y_new = -Y_old = -4

 

Thus, New coordinates of corner B after reflection = (6, -4).

 

For Coordinates C(5, 6)

 

Let the new coordinates of corner C after reflection = (X_new, Y_new).

 

Applying the reflection equations, we have-

• X_new = X_old = 5
• Y_new = -Y_old = -6

 

Thus, New coordinates of corner C after reflection = (5, -6).

 

Thus, New coordinates of the triangle after reflection = A (3, -4), B(6, -4), C(5, -6).

 

 

Problem-02:

 

Given a triangle with coordinate points A(3, 4), B(6, 4), C(5, 6). Apply the reflection on the Y axis and obtain the new coordinates of the object.

 

Solution-

 

Given-

• Old corner coordinates of the triangle = A (3, 4), B(6, 4), C(5, 6)
• Reflection has to be taken on the Y axis

 

For Coordinates A(3, 4)

 

Let the new coordinates of corner A after reflection = (X_new, Y_new).

 

Applying the reflection equations, we have-

• X_new = -X_old = -3
• Y_new = Y_old = 4

 

Thus, New coordinates of corner A after reflection = (-3, 4).

 

For Coordinates B(6, 4)

 

Let the new coordinates of corner B after reflection = (X_new, Y_new).

 

Applying the reflection equations, we have-

• X_new = -X_old = -6
• Y_new = Y_old = 4

 

Thus, New coordinates of corner B after reflection = (-6, 4).

 

For Coordinates C(5, 6)

 

Let the new coordinates of corner C after reflection = (X_new, Y_new).

 

Applying the reflection equations, we have-

• X_new = -X_old = -5
• Y_new = Y_old = 6

 

Thus, New coordinates of corner C after reflection = (-5, 6).

 

Thus, New coordinates of the triangle after reflection = A (-3, 4), B(-6, 4), C(-5, 6).

 

 

To gain better understanding about 2D Reflection in Computer Graphics,

Watch this Video Lecture

 

Next Article- 2D Shearing in Computer Graphics

 

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