2-D Geometrical Transforms and Viewing MCQ Questions and Answers

1. Which operation does NOT preserve parallelism of lines in 2-D?
A. Translation
B. Rotation
C. Scaling (uniform or non-uniform)
D. Perspective projection (non-affine)
Answer: D. Perspective projection (non-affine)

2. To rotate a point about an arbitrary point P(px,py), which sequence is correct?
A. Translate by (px,py), rotate by θ, translate by (−px,−py)
B. Rotate by θ, translate by (px,py)
C. Translate by (−px,−py), rotate by θ, translate by (px,py)
D. Scale by 1 about P, then rotate about origin
Answer: C. Translate by (−px,−py), rotate by θ, translate by (px,py)

3. Which of the following is affine but not rigid (i.e., does not preserve angles)?
A. Rotation
B. Translation
C. Uniform scaling
D. Non-uniform scaling
Answer: D. Non-uniform scaling

4. The determinant of a 2×2 linear transform matrix indicates:
A. The rotation angle
B. The area scale factor (signed)
C. The translation amount
D. The shear direction
Answer: B. The area scale factor (signed)

5. Which transform will change the orientation (sign of area) of a polygon?
A. Rotation by 90°
B. Translation
C. Reflection
D. Uniform scaling by 2
Answer: C. Reflection

6. If a 2×2 linear transform has determinant −1, then it:
A. Preserves orientation and scales area by 1
B. Reverses orientation and preserves area magnitude
C. Is not invertible
D. Must be a pure rotation
Answer: B. Reverses orientation and preserves area magnitude

7. Which algorithm is parametric and computes line clipping using inequalities and param t?
A. Cohen-Sutherland
B. Liang-Barsky
C. Sutherland-Hodgman
D. Bresenham
Answer: B. Liang-Barsky

8. The Cohen-Sutherland region code for a point outside top and right of a rectangular window will have which bits set (order: top, bottom, right, left — assume top=bit3, bottom=bit2, right=bit1, left=bit0)?
A. top and right bits set
B. left and bottom bits set
C. only top set
D. none set (inside)
Answer: A. top and right bits set

9. Which clipping algorithm is suited for convex polygons clipping by a convex clip region and works edge-by-edge?
A. Cohen-Sutherland
B. Liang-Barsky
C. Sutherland-Hodgman
D. Midpoint subdivision
Answer: C. Sutherland-Hodgman

10. Window-to-viewport mapping is used to:
A. Convert world coordinates to object coordinates
B. Map coordinates from world/viewing window to device (screen) rectangle
C. Clip polygons to window
D. Compute inverse transforms only
Answer: B. Map coordinates from world/viewing window to device (screen) rectangle

11. The viewing coordinate reference frame (VCRF) in 2-D typically consists of:
A. World origin only
B. u (view right), v (view up), and origin of view coords
C. Camera focal length only
D. Device pixel grid only
Answer: B. u (view right), v (view up), and origin of view coords

12. Which transformation is NOT linear in Cartesian coordinates (without homogeneous augmentation)?
A. Rotation
B. Reflection
C. Translation
D. Scaling
Answer: C. Translation

13. Homogeneous coordinates allow translation to be represented as a:
A. Nonlinear operation
B. Linear matrix multiplication (affine transform)
C. Scaling only
D. Rotation only
Answer: B. Linear matrix multiplication (affine transform)

14. Composite transforms are best represented by:
A. Summing matrices
B. Multiplying matrices (in correct order)
C. Taking determinants
D. Concatenating as vectors
Answer: B. Multiplying matrices (in correct order)

15. Which of the following is true about matrix multiplication order for transforms?
A. It is commutative (order doesn’t matter)
B. Rightmost matrix is applied first to column vectors
C. Leftmost matrix is applied first to column vectors
D. Order only matters for reflections
Answer: B. Rightmost matrix is applied first to column vectors

16. In 2-D viewing pipeline, which step usually occurs first?
A. View volume normalization
B. Window to viewport mapping
C. World to viewing coordinate transform
D. Rasterization
Answer: C. World to viewing coordinate transform

17. Which algorithm clips polygons by iteratively clipping against each clip boundary and producing new vertex lists?
A. Liang-Barsky
B. Sutherland-Hodgman
C. Cohen-Sutherland
D. DDA line drawing
Answer: B. Sutherland-Hodgman

18. The general 3×3 homogeneous transform for 2-D affine transforms has how many independent parameters?
A. 6
B. 9
C. 4
D. 3
Answer: A. 6

19. In window-to-viewport mapping, if window and viewport have same aspect ratio, what happens to the image?
A. It gets skewed
B. It preserves aspect ratio (no distortion)
C. It flips vertically
D. It rotates 90°
Answer: B. It preserves aspect ratio (no distortion)

20. The clipping trivial accept condition in Cohen-Sutherland is:
A. Logical AND of region codes ≠ 0
B. Logical AND of region codes = 0
C. Logical OR of region codes ≠ 0
D. Region codes differ by 1
Answer: B. Logical AND of region codes = 0

21. Which of these is the disadvantage of Cohen-Sutherland?
A. It only works for polygons
B. It requires division for parameter t in all cases
C. It may perform many iterations for segments far outside window
D. It cannot clip axis-aligned lines
Answer: C. It may perform many iterations for segments far outside window

22. Which transformation can be used to convert from world coordinates to view coordinates?
A. Orthographic projection matrix only
B. A concatenation of translation and rotation aligning view axes
C. Perspective divide only
D. Rasterization
Answer: B. A concatenation of translation and rotation aligning view axes

23. In 2-D, the viewport is usually expressed in:
A. World units only
B. Normalized device coordinates or device pixels
C. Homogeneous coordinates only
D. Object local units only
Answer: B. Normalized device coordinates or device pixels

24. Which clipping algorithm is more efficient for line clipping because it uses parametric form and fewer intersection computations?
A. Cyrus-Beck
B. Liang-Barsky
C. Sutherland-Hodgman
D. Cohen-Sutherland
Answer: B. Liang-Barsky

25. Homogeneous coordinate (x, y, w) maps to Cartesian coordinates as:
A. (x, y)
B. (x/w, y/w)
C. (xw, yw)
D. (w/x, w/y)
Answer: B. (x/w, y/w)

26. Which of these is true about the Liang-Barsky algorithm?
A. It only works for circular clipping regions
B. It is based on parametric representation of line and inequalities
C. It is identical to Cohen-Sutherland in performance
D. It requires building region codes for endpoints
Answer: B. It is based on parametric representation of line and inequalities

42. In the viewing pipeline, normalization transforms the view volume to:
A. Device coordinates directly
B. A canonical view volume (e.g., unit square)
C. World coordinates
D. Clip polygons only
Answer: B. A canonical view volume (e.g., unit square)

27. Which transform is used to convert normalized device coordinates to device pixel coordinates?
A. Window to viewport mapping (scale + translate)
B. Perspective projection
C. Rotation about origin
D. Clipping algorithm
Answer: A. Window to viewport mapping (scale + translate)

28. The Sutherland-Hodgman algorithm fails (produces incorrect result) when clipping against:
A. Convex clip polygon (works fine)
B. Non-convex clip polygon
C. Axis-aligned rectangle
D. Single half-plane
Answer: B. Non-convex clip polygon

29. In 2-D coordinate transforms, to reflect about a line through origin that makes angle θ with x-axis, you can:
A. Rotate by −θ, reflect about x-axis, then rotate by θ
B. Reflect about x then y in any order
C. Translate by (θ,θ) then rotate
D. Scale by (−1,1) then shear
Answer: A. Rotate by −θ, reflect about x-axis, then rotate by θ

30. What is the effect of pre-multiplying a homogeneous transform matrix by another?
A. Applies the pre-multiplied transform last to column vectors
B. Applies the pre-multiplied transform first to column vectors
C. Adds the transforms
D. Inverts the original transform
Answer: A. Applies the pre-multiplied transform last to column vectors

31. In homogeneous 3×3 matrices, which elements encode translation?
A. Upper-left 2×2 block
B. Last column (first two entries)
C. Bottom row (first two entries)
D. Middle row only
Answer: B. Last column (first two entries)

32. Which coordinate system is typically used after applying camera/view transforms but before projection in 2-D viewing pipeline?
A. Device coordinates
B. Object coordinates
C. View coordinates (camera coordinates)
D. Screen pixel coordinates
Answer: C. View coordinates (camera coordinates)

33. For nonuniform scaling about point (px,py), which sequence is correct?
A. Translate (−px,−py), scale, translate (px,py)
B. Scale, translate (px,py)
C. Rotate about (px,py), then scale
D. Shear then translate
Answer: A. Translate (−px,−py), scale, translate (px,py)

34. The clipping window for Cohen-Sutherland must be:
A. Convex polygon only
B. Rectangular (axis aligned)
C. Circular region only
D. Non-convex polygon
Answer: B. Rectangular (axis aligned)

35. Which clipping algorithm computes entering and leaving parameter values using dot products (suitable for convex clip polygons)?
A. Liang-Barsky
B. Cohen-Sutherland
C. Cyrus-Beck
D. Sutherland-Hodgman
Answer: C. Cyrus-Beck

36. When transforming normal (for lighting in 3-D), one uses inverse transpose of transform; in 2-D which matrix is analogous for correct normal transform for non-uniform scaling?
A. The same matrix as vertices
B. Inverse transpose of the upper-left 2×2 linear matrix
C. Determinant only
D. None needed in 2-D
Answer: B. Inverse transpose of the upper-left 2×2 linear matrix

37. If an affine transform is represented by matrix (A) (2×2) and translation t, a point p transforms to:
A. (Ap + t)
B. (A + p + t)
C. (pA + t)
D. (Ap – t)
Answer: A. (Ap + t)

38. Which of these is NOT required for window to viewport mapping?
A. Window boundaries
B. Viewport boundaries
C. Projection plane distance
D. Computation of scale and translation factors
Answer: C. Projection plane distance

39. Which transform will map a line passing through origin to itself but reverse direction?
A. Reflection about origin (i.e., scale by −1)
B. Translation
C. Shear
D. Rotation by 45°
Answer: A. Reflection about origin (i.e., scale by −1)

40. In homogeneous form, which row/column indicates perspective components (if any) in 2D-to-2D projective transforms?
A. Bottom row (third row) nonzero entries besides last element
B. Top row only
C. Middle column only
D. Upper left 2×2 only
Answer: A. Bottom row (third row) nonzero entries besides last element

41. For viewport transformation, preserving center of window maps to center of viewport using:
A. Only scaling
B. Only translation
C. Scale then translate — or a single affine composed matrix
D. Rotation then scale
Answer: C. Scale then translate — or a single affine composed matrix

42. Which method computes intersections with clip edges and generates new polygon vertices one edge at a time?
A. Cyrus-Beck
B. Liang-Barsky
C. Sutherland-Hodgman
D. Cohen-Sutherland
Answer: C. Sutherland-Hodgman

43. In 2-D, a rotation by θ followed by rotation by φ is equivalent to:
A. Rotation by θ−φ
B. Rotation by θ+φ
C. Scaling by cos(θ+φ)
D. Reflection then translation
Answer: B. Rotation by θ+φ

44. Which property is preserved by all affine transforms?
A. Angles
B. Ratios of lengths along a straight line (collinearity and ratio)
C. Absolute distances
D. Orientation always (no reversal)
Answer: B. Ratios of lengths along a straight line (collinearity and ratio)

45. To rotate coordinate axes by θ (i.e., express coordinates in rotated frame), you apply:
A. The rotation matrix to point coordinates (pre-multiply) with angle +θ
B. The inverse rotation (angle −θ) to points
C. A translation only
D. Reflection then scaling
Answer: B. The inverse rotation (angle −θ) to points

46. In the viewport mapping formula, after scaling, the translation term accounts for:
A. Aligning the origins of window and viewport
B. Clipping polygons
C. Rotating the scene
D. Shearing the image
Answer: A. Aligning the origins of window and viewport

47. Which of these is a necessary step before rasterizing primitives in 2-D pipeline?
A. World to view coordinate transform and clipping to view volume
B. Ignore projection and send world coordinates directly
C. Only apply lighting calculations
D. Perform texture mapping (for 2-D)
Answer: A. World to view coordinate transform and clipping to view volume

48. The canonical view in normalized coordinates for 2-D orthographic projection is often:
A. Unit square [0,1]×[0,1] or [−1,1]×[−1,1]
B. Infinite plane
C. Circle of radius 1
D. Single point
Answer: A. Unit square [0,1]×[0,1] or [−1,1]×[−1,1]

49. The composite transform that first reflects about x-axis then rotates by 90° — which determinant sign?
A. Positive (orientation preserved)
B. Negative (orientation reversed)
C. Zero
D. Always 1
Answer: B. Negative (orientation reversed)

50. The clipping trivial reject test in Cohen-Sutherland is:
A. Logical OR of region codes = 0
B. Logical AND of region codes ≠ 0
C. Logical XOR of region codes = 0
D. Sum of region codes > 1
Answer: B. Logical AND of region codes ≠ 0

51. For polygon clipping, which case requires generating intersection points and possibly adding both intersection and entering vertex?
A. Edge from inside to outside
B. Edge from outside to inside
C. Edge fully inside
D. Edge fully outside
Answer: B. Edge from outside to inside

52. The view reference point (VRP) in 2-D determines:
A. The camera focal length only
B. The origin of the viewing coordinate system (where you look from)
C. Clipping tolerance
D. Pixel aspect ratio
Answer: B. The origin of the viewing coordinate system (where you look from)

53. Which of these is true: rotating the axes vs rotating the points by θ?
A. Rotating axes by θ is equivalent to rotating points by θ
B. Rotating axes by θ is equivalent to rotating points by −θ
C. They are unrelated
D. Rotating axes changes translation only
Answer: B. Rotating axes by θ is equivalent to rotating points by −θ

54. In computer graphics, “normalized device coordinates” (NDC) are used to:
A. Represent coordinates after projection and normalization before viewport mapping
B. Store object space coordinates only
C. Represent pixel addresses directly
D. Keep only integer coordinates for rasterization
Answer: A. Represent coordinates after projection and normalization before viewport mapping

55. Which transform will change the lengths of vectors but preserve angles between them only if scaling is uniform?
A. Uniform scaling preserves angles; nonuniform may not
B. Shear preserves angles always
C. Reflection never preserves angles
D. Translation changes angles
Answer: A. Uniform scaling preserves angles; nonuniform may not

56. When performing a sequence: translate to origin, scale, translate back — what is this accomplishing?
A. Scaling about an arbitrary point (not origin)
B. Rotation about origin
C. Shearing about x axis
D. Reflection about y axis
Answer: A. Scaling about an arbitrary point (not origin)

57. Which algorithm is line clipping that uses region codes to reject or accept lines quickly?
A. Liang-Barsky
B. Cohen-Sutherland
C. Sutherland-Hodgman
D. Cyrus-Beck
Answer: B. Cohen-Sutherland

58. The viewing transformation that aligns the view direction with the negative z-axis in 3-D has the 2-D analogue of:
A. Aligning the view axis to some canonical axis (rotate + translate)
B. Performing perspective divide
C. Rasterizing primitives
D. Generating region codes
Answer: A. Aligning the view axis to some canonical axis (rotate + translate)

59. A 2-D projective transform can map parallel lines to:
A. Always remain parallel
B. Can intersect (i.e., meet at finite point)
C. Always keep angle 90°
D. Map all to a single line only
Answer: B. Can intersect (i.e., meet at finite point)

60. When clipping against an edge in Sutherland-Hodgman, an input edge from inside to outside:
A. Output only intersection point
B. Output both vertices
C. Output nothing
D. Output outside vertex only
Answer: A. Output only intersection point

61. What does the canonical viewing transformation usually include?
A. Translation, rotation, scaling to normalize the view volume
B. Only mapping to device pixels
C. Clipping with circles
D. Spectral color mapping
Answer: A. Translation, rotation, scaling to normalize the view volume

62. If a 2×2 transform has eigenvalues 2 and 3, its area scale factor is:
A. 5
B. 6
C. 1
D. 0
Answer: B. 6

63. Which of these is NOT an affine invariant?
A. Parallelism of lines
B. Ratio of lengths on the same line segment
C. Angle between two arbitrary lines
D. Collinearity of points
Answer: C. Angle between two arbitrary lines

64. Which transform will change a square into a parallelogram?
A. Shear
B. Uniform scaling
C. Rotation about center
D. Translation
Answer: A. Shear

65. When mapping a world window to a viewport of different aspect ratio with letterboxing, what is done?
A. Add borders (blank regions) to preserve aspect ratio
B. Stretch image vertically only
C. Ignore aspect ratio and crop nothing
D. Always rotate image 90°
Answer: A. Add borders (blank regions) to preserve aspect ratio

66. The view up vector in 2-D viewing defines:
A. The direction considered “up” in the viewing coordinate system (v axis)
B. The maximum intensity of light
C. The clipping plane distance
D. The pixel density
Answer: A. The direction considered “up” in the viewing coordinate system (v axis)

67. Which of these transforms is NOT representable by a 2×2 matrix (without translation)?
A. Rotation
B. Translation
C. Shear
D. Reflection (about origin)
Answer: B. Translation

68. Which clipping algorithm is generally easiest to implement for polygon clipping against rectangular windows?
A. Sutherland-Hodgman
B. Liang-Barsky
C. Cyrus-Beck
D. Midpoint subdivision
Answer: A. Sutherland-Hodgman

69. The normalized device coordinate range often used for both axes is:
A. [−1,1] or [0,1] depending on convention
B. [−100,100] only
C. [−π,π] only
D. [1,2] only
Answer: A. [−1,1] or [0,1] depending on convention

70. In composite transforms, to rotate about point (2,3) by angle θ, what translation is needed first?
A. Translate by (−2,−3)
B. Translate by (2,3)
C. No translation needed
D. Translate by (θ,θ)
Answer: A. Translate by (−2,−3)

71. What is the key idea of parametric clipping algorithms (like Liang-Barsky)?
A. Represent line parametrically and find t interval where it lies inside clip window
B. Compute region codes for endpoints only
C. Rasterize then discard pixels outside window
D. Clip only at vertices
Answer: A. Represent line parametrically and find t interval where it lies inside clip window

72. The device coordinate origin (0,0) is usually at:
A. Top-left or bottom-left depending on system conventions
B. Always center of screen
C. Always top-right
D. Always bottom-right
Answer: A. Top-left or bottom-left depending on system conventions

73. Which of these is true about Sutherland-Hodgman when clipping a concave polygon against a convex clip region?
A. It works correctly (concave subject is OK)
B. It fails for concave subject polygons only
C. It only works for convex subjects
D. It requires region codes
Answer: A. It works correctly (concave subject is OK)

74. The clipping of a line segment completely inside the clipping window by Liang-Barsky:
A. Returns original segment unchanged quickly
B. Always subdivides the segment
C. Always returns empty segment
D. Requires computing region codes
Answer: A. Returns original segment unchanged quickly

75. Which transformation changes orientation and area sign but preserves line straightness?
A. Reflection (an affine transform with negative determinant)
B. Shear with determinant 0
C. Singular scaling
D. Translation only
Answer: A. Reflection (an affine transform with negative determinant)

76. Which step is NOT part of 2-D view pipeline for rendering to screen?
A. World-to-view transform
B. Clipping to viewport
C. Lighting and shading calculations for 3-D (not in basic 2-D pipeline)
D. Viewport mapping and rasterization
Answer: C. Lighting and shading calculations for 3-D (not in basic 2-D pipeline)

77. In 2D graphics, a transformation that changes the size of an object but not its shape is called
A) Rotation
B) Translation
C) Scaling
D) Reflection

78. Which transformation is used to mirror an object about the X-axis?
A) Scaling
B) Reflection
C) Translation
D) Shearing

79. The homogeneous coordinate representation of a point (x, y) is
A) (x, y, 0)
B) (x, y, 1)
C) (x, y, z)
D) (x, y, 1)

80. The determinant of a pure rotation matrix in 2D is always
A) -1
B) 0
C) 1
D) 2

81. In a 2D translation, which of the following remains unchanged?
A) Position
B) Orientation
C) Shape and Size
D) Both position and shape

82. A scaling factor less than 1 results in
A) Enlargement
B) Shrinkage
C) Reflection
D) Rotation

83. A transformation that alters the shape of an object such that rectangles become parallelograms is called
A) Rotation
B) Translation
C) Shear
D) Scaling

84. In homogeneous coordinates, translation can be represented using
A) 2×2 matrix
B) 3×3 matrix
C) 4×4 matrix
D) None

85. Which transformation moves every point of an object by the same distance in a specified direction?
A) Translation
B) Scaling
C) Rotation
D) Shear

86. The product of two rotation matrices is another rotation matrix because
A) They are symmetric
B) They are upper triangular
C) Rotation matrices are orthogonal
D) They are diagonal

87. The reflection about line y = x can be achieved by
A) Interchanging x and y
B) Negating x
C) Negating y
D) Adding both coordinates

88. The scaling matrix is uniform if
A) sx ≠ sy
B) sx = sy
C) sx = 0
D) sy = 0

89. Which transformation can be reversed by applying the same operation again?
A) Scaling
B) Shear
C) Reflection
D) Translation

90. The composite of two translations results in
A) Reflection
B) Scaling
C) Another translation
D) Rotation

91. If a point is rotated by 90° twice about the origin, the result is equivalent to
A) No change
B) Reflection
C) 180° rotation
D) Translation

92. The homogeneous coordinate system is mainly used to
A) Increase computation time
B) Simplify matrix representation of transformations
C) Reduce memory usage
D) Represent 3D only

93. The 3×3 matrix representation allows combination of
A) Only rotations
B) All 2D affine transformations
C) Only translations
D) Only scaling

94. To rotate a point about an arbitrary point (x₁, y₁), one must
A) Rotate directly about (x₁, y₁)
B) Translate → Rotate → Translate back
C) Reflect then rotate
D) Scale then rotate

95. In window-to-viewport mapping, the primary purpose is
A) Clipping
B) Scaling only
C) To map a portion of world coordinates to screen coordinates
D) Projection

96. The viewing pipeline does NOT include
A) Clipping
B) Projection
C) Transformation
D) Z-buffering

97. The line clipping algorithm proposed by Cohen–Sutherland uses
A) Parametric equations
B) Region codes
C) Polar coordinates
D) Transformation matrices

98. In Cohen–Sutherland line clipping, a line with both endpoints inside the window has
A) Logical AND of region codes ≠ 0
B) Logical OR of region codes = 1
C) Logical AND of region codes = 0
D) Logical OR of region codes = 0

99. The Liang–Barsky algorithm is based on
A) Parametric line representation
B) Region coding
C) Midpoint method
D) Bresenham’s approach

100. The polygon clipping algorithm commonly used is
A) Cohen–Sutherland
B) Bresenham
C) Sutherland–Hodgman
D) Liang–Barsky