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 = (Xold, Yold)
  • New coordinates of the reflected object O after reflection = (Xnew, Ynew)

 

Reflection On X-Axis:

 

This reflection is achieved by using the following reflection equations-

  • Xnew = Xold
  • Ynew = -Yold

 

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-

  • Xnew = -Xold
  • Ynew = Yold

 

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 = (Xnew, Ynew).

 

Applying the reflection equations, we have-

  • Xnew = Xold = 3
  • Ynew = -Yold = -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 = (Xnew, Ynew).

 

Applying the reflection equations, we have-

  • Xnew = Xold = 6
  • Ynew = -Yold = -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 = (Xnew, Ynew).

 

Applying the reflection equations, we have-

  • Xnew = Xold = 5
  • Ynew = -Yold = -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 = (Xnew, Ynew).

 

Applying the reflection equations, we have-

  • Xnew = -Xold = -3
  • Ynew = Yold = 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 = (Xnew, Ynew).

 

Applying the reflection equations, we have-

  • Xnew = -Xold = -6
  • Ynew = Yold = 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 = (Xnew, Ynew).

 

Applying the reflection equations, we have-

  • Xnew = -Xold = -5
  • Ynew = Yold = 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

 

Get more notes and other study material of Computer Graphics.

Watch video lectures by visiting our YouTube channel LearnVidFun.

Summary
2D Reflection in Computer Graphics | Definition | Examples
Article Name
2D Reflection in Computer Graphics | Definition | Examples
Description
Reflection in Computer Graphics is a kind of rotation where the angle of rotation is 180 degree. 2D Reflection takes place in 2D plane. Reflection in Computer Graphics Definition, Solved Examples and Problems.
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Gate Vidyalay
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