Q.1 Which of the following represents a basic 3D geometric transformation?
Translation
Scaling
Rotation
All of the above
Explanation - In 3D graphics, translation, scaling, and rotation are the fundamental geometric transformations applied to objects.
Correct answer is: All of the above
Q.2 In 3D graphics, what is the homogeneous coordinate of a 3D point (x, y, z)?
(x, y, z, 0)
(x, y, z, 1)
(x, y, z, w)
(x, y, z, -1)
Explanation - Homogeneous coordinates add a fourth component w, typically set to 1 for points, to facilitate matrix transformations.
Correct answer is: (x, y, z, 1)
Q.3 Which matrix operation is used to perform a rotation about the Z-axis in 3D?
Scaling matrix
Rotation matrix around Z-axis
Translation matrix
Reflection matrix
Explanation - Rotation about an axis is achieved using a rotation matrix specific to that axis. For Z-axis, the rotation matrix affects X and Y coordinates.
Correct answer is: Rotation matrix around Z-axis
Q.4 What is the effect of scaling a 3D object by a factor of 2 along all axes?
Object doubles in size
Object rotates
Object moves
Object disappears
Explanation - Uniform scaling multiplies each coordinate by the scaling factor, making the object larger or smaller.
Correct answer is: Object doubles in size
Q.5 Which of the following represents translation of a 3D point?
Multiplying by a matrix
Adding displacement vector
Dividing by a scalar
None of these
Explanation - Translation moves a point by adding a vector (dx, dy, dz) to its coordinates.
Correct answer is: Adding displacement vector
Q.6 Which type of transformation preserves angles but not necessarily lengths in 3D?
Translation
Rotation
Scaling
Shearing
Explanation - Rotations preserve angles between vectors but may not change the lengths if uniform scaling is not applied.
Correct answer is: Rotation
Q.7 What does a reflection transformation do to a 3D object?
Moves it along an axis
Rotates it
Flips it about a plane
Scales it
Explanation - Reflection in 3D mirrors an object about a specific plane (XY, YZ, or ZX).
Correct answer is: Flips it about a plane
Q.8 Which of the following is true about a 3D rotation matrix?
It is always symmetric
It is orthogonal
It is diagonal
It is singular
Explanation - A rotation matrix is orthogonal, meaning its transpose equals its inverse, preserving vector lengths.
Correct answer is: It is orthogonal
Q.9 Which of these transformations can be represented as a 4x4 matrix in homogeneous coordinates?
Translation
Scaling
Rotation
All of the above
Explanation - All basic 3D transformations can be represented as 4x4 matrices using homogeneous coordinates.
Correct answer is: All of the above
Q.10 What is the result of applying two successive rotations about the same axis?
Scaling
Combined rotation
Translation
Reflection
Explanation - Two successive rotations about the same axis are equivalent to a single rotation by the sum of the angles.
Correct answer is: Combined rotation
Q.11 Which 3D transformation changes the shape but preserves volume if uniform scaling is not applied?
Shearing
Translation
Rotation
Uniform Scaling
Explanation - Shearing distorts the shape, skewing objects along axes, and generally changes angles but can preserve volume depending on parameters.
Correct answer is: Shearing
Q.12 Which 3D transformation cannot be achieved by multiplying a 4x4 matrix with a point vector?
Translation
Rotation
Non-linear deformation
Scaling
Explanation - Matrix multiplication represents linear transformations, so non-linear deformations like bending cannot be achieved directly.
Correct answer is: Non-linear deformation
Q.13 What is the translation matrix in homogeneous coordinates for displacement (dx, dy, dz)?
[[1,0,0,dx],[0,1,0,dy],[0,0,1,dz],[0,0,0,1]]
[[dx,0,0,0],[0,dy,0,0],[0,0,dz,0],[0,0,0,1]]
[[1,0,0,0],[0,1,0,0],[0,0,1,0],[dx,dy,dz,1]]
[[0,0,0,dx],[0,0,0,dy],[0,0,0,dz],[1,1,1,1]]
Explanation - In homogeneous coordinates, the translation matrix places dx, dy, dz in the last column to move points accordingly.
Correct answer is: [[1,0,0,dx],[0,1,0,dy],[0,0,1,dz],[0,0,0,1]]
Q.14 Which of the following sequences is generally applied to perform rotation about an arbitrary axis?
Translate to origin, rotate, translate back
Scale, then rotate
Reflect, then translate
Shear, then scale
Explanation - To rotate about an arbitrary axis, first move the axis to the origin, perform rotation, then translate back.
Correct answer is: Translate to origin, rotate, translate back
Q.15 If a 3D object is scaled by factors (2, 1, 0.5), what happens?
It doubles in all directions
It stretches along X, unchanged along Y, shrinks along Z
It rotates
It translates
Explanation - Non-uniform scaling affects each axis differently, based on the corresponding scale factor.
Correct answer is: It stretches along X, unchanged along Y, shrinks along Z
Q.16 Which property is preserved under rigid body transformations in 3D?
Angles and lengths
Only angles
Only lengths
None
Explanation - Rigid body transformations (rotation and translation) preserve both angles and distances between points.
Correct answer is: Angles and lengths
Q.17 What does a shear transformation along the X-axis do?
Shifts Y and Z proportional to X
Shifts X proportional to Y
Scales the X-axis only
Rotates about X-axis
Explanation - Shearing along an axis moves other coordinates proportionally to that axis, causing slanting of shapes.
Correct answer is: Shifts Y and Z proportional to X
Q.18 Which transformation matrix is used to invert an object through the origin?
Rotation matrix
Scaling matrix with -1 factor
Translation matrix
Shear matrix
Explanation - Multiplying all coordinates by -1 reflects the object through the origin.
Correct answer is: Scaling matrix with -1 factor
Q.19 Which sequence of transformations would rotate an object and then move it in space?
Rotate then translate
Translate then rotate
Scale then translate
Shear then rotate
Explanation - To rotate an object in place and then move it, apply rotation first, then translation.
Correct answer is: Rotate then translate
Q.20 In homogeneous coordinates, what is the w-component of a vector?
0
1
-1
Variable
Explanation - Vectors have w = 0 in homogeneous coordinates because they represent directions, not positions.
Correct answer is: 0
Q.21 Which transformation preserves parallelism of lines in 3D?
Translation
Rotation
Scaling
All of the above
Explanation - Translation, rotation, and scaling preserve parallel lines, although angles and lengths may vary in scaling.
Correct answer is: All of the above
Q.22 What is the effect of combining two non-commuting 3D rotations?
The order of rotation does not matter
The result depends on the order
It results in translation
It results in scaling
Explanation - 3D rotations are generally non-commutative; rotating about different axes in different orders yields different results.
Correct answer is: The result depends on the order
Q.23 Which of the following is NOT a linear transformation in 3D?
Scaling
Rotation
Translation
Shearing
Explanation - Translation is not linear because it does not preserve the origin; linear transformations map the origin to itself.
Correct answer is: Translation
Q.24 Which transformation is applied to move an object from local coordinates to world coordinates?
World transformation
View transformation
Projection transformation
Screen mapping
Explanation - World transformation positions and orients an object in the global coordinate system from its local coordinates.
Correct answer is: World transformation
Q.25 Which operation is used to reverse a transformation in 3D graphics?
Transpose matrix
Inverse matrix
Scaling by 2
Rotation by 90 degrees
Explanation - Applying the inverse of a transformation matrix reverses its effect on points or objects.
Correct answer is: Inverse matrix