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CGV Module 3

This document outlines questions related to Computer Graphics and Visualization, focusing on transformations, rotations, quaternions, affine transformations, and OpenGL functions. It includes tasks such as deriving transformation matrices, demonstrating properties of transformations, and writing OpenGL code for various operations. The document also covers topics like geometric projections and hidden surface removal algorithms.

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5 views2 pages

CGV Module 3

This document outlines questions related to Computer Graphics and Visualization, focusing on transformations, rotations, quaternions, affine transformations, and OpenGL functions. It includes tasks such as deriving transformation matrices, demonstrating properties of transformations, and writing OpenGL code for various operations. The document also covers topics like geometric projections and hidden surface removal algorithms.

Uploaded by

vgamce
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Computer Graphics and Visualization (18CS602)

Module III
Qn.
Blooms
no Questions
level
1. Exemplify the basic transformations in homogeneous co-ordinates system and represent
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them in matrix form.
Illustrate with examples
2. I. Rotation about a fixed point at the origin.
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II. Rotation about an arbitrary axis.

Consider a 3D cube object, with fixed point at center of the cube and angle of rotation ‘O’
3. about an arbitrary axis defined by 2 points P1 & P2, defining the vector u. Find the final L3
rotation matrix R.
Derive the transformation that rotates an object point to theta degrees about the origin. Write
4.
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the matrix representation for this rotation.
5. Discuss the mathematical representations of quaternions. Also highlight its advantages. L2
6. How do you achieve affine transformation by concatenation? Discuss. L3
Find the transformation matrix to transform a given square ABCD to half its size with center
7. still remaining at the same position. Co-ordinates of the square are A(1,1) B(3,1) C(3,3), L4
D(1,3) and center at (2,2).
8. Show that the composition of 2D rotation followed by uniform scaling is commutative. L4
Write the OpenGL functions used for translation, scaling and rotation using the OpenGL
9. functions. Write the fragment of code to form the required matrix for a 45o rotation about L3
the line through the origin and point (1, 2, 3) with fixed points (4, 5, 6).
Consider the square A (1, 0), B (0, 0), C (0, 0), D (1, 1). Rotate the square ABCD by 45 o
10.
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clockwise about A(1,0).
Scale the given triangle with co-ordinates A,B & C using the scaling factor Sx = 1/3, Sy = ½
11.
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and the point A(3,2). The coordinates of triangle are A(3,2), B(6,2) and C(6,6).
Perform a 450 rotation of triangle A(0,0) , B (1,1), c(5,2)
12. I. About the origin
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II. About p(-1, -1)

13. Write openGL functions used in perspective projection and orthogonal projection. L2
Prove the following
14. I. Successive scaling’s are multiplicative L4
II. Successive translations are additive.
III. Successive rotations are additive

15.
Write a program using OpenGL to create a interactive mesh display. L6
16. Define the planar geometric projections. Explain orthographic projections and oblique
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projections with necessary diagrams.
17. Show that how do we position the camera in computer viewing? Also write the OpenGL
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functions used for the same with suitable example.
18. Which are the two broad classes of Hidden surface removal algorithms? Show that how Z-
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buffer algorithm aid in removing hidden surface.
19.
Illustrate various classical views with suitable sketches. L3
20. Highlight the importance of perspective and parallel viewing in OpenGL with necessary
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OpenGL functions.
Derive the following
21. I. Parallel projection matrices.
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II. Perspective projection matrix.

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