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(Created page with "<div style="column-count: 2; column-gap: 20px;"> '''Subject :''' Computer Graphics '''Period:''' Fourth '''Topic:''' 2D and 3D Transformation '''Teaching Item:''' 2D and 3D Transformations: Translation, Rotation(about origin and arbitrary point) '''Level:''' Bachelor 6<sup>th</sup> sem '''Unit:''' Three '''Time:''' 50 min '''No. of Students:''' <br> </div> == Specific Objective == At the end of this lesson students will be able t...")
 
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'''Topic:''' 2D and 3D Transformation
'''Topic:''' 2D and 3D Transformation


'''Teaching Item:''' 2D and 3D Transformations: Translation, Rotation(about origin and arbitrary point)
'''Teaching Item:''' Representation of 2D and 3D Transformation in Homogeneous Coordinate System


'''Level:''' Bachelor 6<sup>th</sup> sem
'''Level:''' Bachelor 6<sup>th</sup> sem
Line 15: Line 15:


'''No. of Students:'''  
'''No. of Students:'''  
<br>
13<br>
</div>
</div>
== Specific Objective ==
== Specific Objective ==
At the end of this lesson students will be able to:
At the end of this lesson students will be able to:


* understand the concepts of translation and rotation in 2D and 3D space
* understand the concept of 2D and 3D transformations in a homogeneous coordinate system
* understand the effects of translation and rotation on 2D and 3D objects
* learn how to represent transformations using matrices in homogeneous coordinates
* apply transformation matrices to perform various 2D and 3D transformations


== Teaching Materials ==
== Teaching Materials ==
Line 32: Line 33:
== Teaching Learning Activities ==
== Teaching Learning Activities ==


# At first I will ask students what they know about 2D and 3D.
# At first I will ask students what they understand till now about previous topic.
# Then define 2D and 3D concept with example.
# Then begin the unit by defining 2D and 3D transformations in the context of computer graphics.
# Introduce the concept of transformations and their importance in computer graphics.
# Introduce the concept of homogeneous coordinate systems and their importance in computer graphics.
# Explain that transformations are used to modify the position, orientation, and size of objects in a scene.
# Explain how homogeneous coordinates are used to represent points in higher-dimensional spaces.
# Mention that translation and rotation are fundamental transformations in both 2D and 3D graphics.
# Mention that homogeneous coordinates simplify the representation and manipulation of transformations.
# Present the translation transformation for both 2D and 3D objects, explaining its mathematical foundation and implementation.
# Present the representation of 2D and 3D transformations using homogeneous coordinates, explaining the matrix-based approach.
# Discuss how translation shifts an object's position by adding/subtracting a vector.
# Discuss how translation, rotation, scaling, reflection and shearing can be represented as matrices in homogeneous coordinates.
# Present the rotation transformation for both 2D and 3D objects, explaining its mathematical foundation and implementation.
# Show examples of how different transformations affect geometric shapes in 2D and 3D space.
# Discuss how rotation changes an object's orientation around a fixed point (origin or arbitrary point).
# Discuss the advantages of using homogeneous coordinates for transformations, such as the ability to represent translations as part of matrix multiplication.
# Show how to input object vertices, perform translation and rotation transformations, and visualize the transformed objects.
# Explain how homogeneous coordinates enable the representation of affine transformations, including translations, rotations, scalings, and shears, in a unified manner.
# Highlight the importance of homogeneous coordinates in computer graphics applications.
# Divide students into groups and provide them with transformation scenarios to solve using matrices.
# Ask students if there is any confusion on today's topic and provide guidance and assistance if needed.
# Ask students if there is any confusion on today's topic and provide guidance and assistance if needed.


== Assessment ==
== Assessment ==


1. Explain how rotation about an arbitrary point differs from rotation about the origin.
1. Explain the concept of homogeneous coordinates and their role in representing transformations.  


2. Discuss the effects of translation and rotation transformations on the position and orientation of objects.
2. Given a square with vertices at (1,1), (-1,1), (-1,-1), (1,-1), perform a rotation of 45 degrees counterclockwise using a transformation matrix. Calculate the new coordinates of the square after the rotation.
 
3. Implement translation to shift a 2D square by (2, 3) units and rotate it by 45 degrees about the origin. Provide the vertices of the transformed square.

Latest revision as of 03:49, 9 May 2024

Subject : Computer Graphics

Period: Fourth

Topic: 2D and 3D Transformation

Teaching Item: Representation of 2D and 3D Transformation in Homogeneous Coordinate System

Level: Bachelor 6th sem

Unit: Three

Time: 50 min

No. of Students: 13

Specific Objective

At the end of this lesson students will be able to:

  • understand the concept of 2D and 3D transformations in a homogeneous coordinate system
  • learn how to represent transformations using matrices in homogeneous coordinates
  • apply transformation matrices to perform various 2D and 3D transformations

Teaching Materials

  • Laptop
  • Presentation slide
  • Projector
  • Whiteboard and marker

Teaching Learning Activities

  1. At first I will ask students what they understand till now about previous topic.
  2. Then begin the unit by defining 2D and 3D transformations in the context of computer graphics.
  3. Introduce the concept of homogeneous coordinate systems and their importance in computer graphics.
  4. Explain how homogeneous coordinates are used to represent points in higher-dimensional spaces.
  5. Mention that homogeneous coordinates simplify the representation and manipulation of transformations.
  6. Present the representation of 2D and 3D transformations using homogeneous coordinates, explaining the matrix-based approach.
  7. Discuss how translation, rotation, scaling, reflection and shearing can be represented as matrices in homogeneous coordinates.
  8. Show examples of how different transformations affect geometric shapes in 2D and 3D space.
  9. Discuss the advantages of using homogeneous coordinates for transformations, such as the ability to represent translations as part of matrix multiplication.
  10. Explain how homogeneous coordinates enable the representation of affine transformations, including translations, rotations, scalings, and shears, in a unified manner.
  11. Highlight the importance of homogeneous coordinates in computer graphics applications.
  12. Divide students into groups and provide them with transformation scenarios to solve using matrices.
  13. Ask students if there is any confusion on today's topic and provide guidance and assistance if needed.

Assessment

1. Explain the concept of homogeneous coordinates and their role in representing transformations.

2. Given a square with vertices at (1,1), (-1,1), (-1,-1), (1,-1), perform a rotation of 45 degrees counterclockwise using a transformation matrix. Calculate the new coordinates of the square after the rotation.

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