3-D Object Representation, Geometric Transformations and Viewing MCQ Questions and Answers

1. Which data structure is most natural for representing the faces of a 3D polyhedral model when rapid traversal of adjacent faces is required?
A. Vertex list
B. Adjacency matrix
C. Winged-edge structure
D. Edge list
Answer: C. Winged-edge structure

2. What is the principal advantage of using triangular meshes over polygonal faces with many sides in 3D modelling?
A. Triangles can approximate curves exactly
B. Triangles guarantee planarity and are always convex
C. Triangles require more storage but fewer computations
D. Triangles cannot represent curved surfaces
Answer: B. Triangles guarantee planarity and are always convex

3. In homogeneous coordinates for 3D, a translation is represented by which property in a 4×4 matrix?
A. Nonzero elements in the top-left 3×3 submatrix
B. Nonzero elements in the last column (except bottom element)
C. Nonzero elements in the bottom row (except rightmost element)
D. Nonzero elements on the main diagonal only
Answer: B. Nonzero elements in the last column (except bottom element)

4. A rigid transformation in 3D consists of which of the following?
A. Rotation + uniform scaling
B. Rotation + translation
C. Shear + rotation
D. Non-uniform scaling + translation
Answer: B. Rotation + translation

5. The normal vector of a polygon face is used primarily for which of the following tasks?
A. Defining vertex coordinates
B. Texture coordinate generation only
C. Back-face culling and shading calculations
D. Memory allocation for the polygon
Answer: C. Back-face culling and shading calculations

6. Which algorithm is commonly used to test if a point lies inside a convex polygon by checking half-spaces?
A. Ray casting algorithm
B. Winding number algorithm
C. Half-plane intersection test
D. Cohen–Sutherland algorithm
Answer: C. Half-plane intersection test

7. The standard equation of a quadric surface includes which highest degree term?
A. Linear terms only
B. Quadratic terms in x, y, z
C. Cubic terms in x, y, z
D. Exponential terms
Answer: B. Quadratic terms in x, y, z

8. Which of the following is not a quadric surface?
A. Sphere
B. Torus
C. Ellipsoid
D. Hyperboloid
Answer: B. Torus

9. A general second-degree equation in x, y, z describes a quadric. Which matrix form is useful for classifying quadrics?
A. 2×2 matrix
B. 3×3 rotation matrix
C. Symmetric 4×4 matrix in homogeneous coordinates
D. Diagonal 1×1 matrix
Answer: C. Symmetric 4×4 matrix in homogeneous coordinates

10. Which property distinguishes a parametric surface representation (like Bézier) from an implicit surface?
A. Parametric surfaces are always closed
B. Parametric surfaces map a 2D parameter domain to 3D points
C. Implicit surfaces always use polygon meshes
D. Parametric surfaces cannot represent smooth surfaces
Answer: B. Parametric surfaces map a 2D parameter domain to 3D points

11. What is the degree of a cubic Bézier curve?
A. 1
B. 2
C. 3
D. 4
Answer: C. 3

12. A cubic Bézier curve uses how many control points?
A. 2
B. 3
C. 4
D. 5
Answer: C. 4

13. Which of the following properties does a Bézier curve always satisfy?
A. It interpolates all control points.
B. It lies within the convex hull of its control points.
C. It is invariant under perspective projection.
D. It has C2 continuity regardless of control points.
Answer: B. It lies within the convex hull of its control points.

14. The De Casteljau algorithm is used for what operation on Bézier curves?
A. Converting to B-spline basis
B. Evaluating and subdividing Bézier curves
C. Implicit surface extraction
D. Computing normals for shading
Answer: B. Evaluating and subdividing Bézier curves

15. The Bernstein polynomials form the basis functions for which curve representation?
A. B-spline curves
B. Bézier curves
C. Catmull-Rom splines
D. Fourier series
Answer: B. Bézier curves

16. Which parameterization property is true for uniform cubic B-splines?
A. They always pass through every control point.
B. They are C2 continuous across the entire curve.
C. They use Bernstein polynomials as basis functions.
D. They have local support: each control point affects the entire curve.
Answer: B. They are C2 continuous across the entire curve.

17. What is a key advantage of B-splines over Bézier curves for interactive modelling?
A. B-splines are always lower degree than Bézier curves
B. B-splines provide local control so a single control point affects only a portion of the curve
C. B-splines do not require basis functions
D. B-splines cannot be converted to Bézier pieces
Answer: B. B-splines provide local control so a single control point affects only a portion of the curve

18. The knot vector in a B-spline primarily controls which aspect?
A. The color of the curve when rendered
B. The parameterization and continuity at joins
C. The dimensionality of control points
D. The metric used for curve length
Answer: B. The parameterization and continuity at joins

19. A uniform cubic B-spline of n control points produces how many curve segments (in terms of polynomial pieces) when clamped appropriately?
A. n
B. n−1
C. n−3
D. 3n
Answer: C. n−3

20. What is the effect of repeating a knot value multiple times in a B-spline’s knot vector?
A. Increasing the smoothness at that parameter value
B. Decreasing continuity at that parameter value (possibly to interpolation)
C. Increasing degree of the spline
D. Converting the spline to Bézier globally
Answer: B. Decreasing continuity at that parameter value (possibly to interpolation)

21. For Bézier surfaces, control points are organized in what structure?
A. A single vector
B. A 2D grid (control net)
C. A triangular mesh only
D. A binary tree
Answer: B. A 2D grid (control net)

22. How is a bicubic Bézier surface evaluated?
A. By evaluating two 1D Bézier curves sequentially in u and v directions
B. By solving a system of linear equations for x, y, z
C. Using Laplace transforms
D. By rasterization only
Answer: A. By evaluating two 1D Bézier curves sequentially in u and v directions

23. What is one advantage of using B-spline surfaces versus tensor-product Bézier surfaces?
A. B-spline surfaces have global control only
B. B-spline surfaces cannot be made continuous
C. B-spline surfaces allow local refinement without changing the entire surface
D. B-spline surfaces always interpolate boundary control points
Answer: C. B-spline surfaces allow local refinement without changing the entire surface

24. Which continuity type indicates the first derivative is continuous across a surface patch join?
A. C0
B. C1
C. C2
D. G0
Answer: B. C1

25. Geometric (G) continuity differs from parametric (C) continuity because it focuses on:
A. Parameter values only
B. Visual smoothness (direction/shape) rather than parameter derivative equality
C. Color continuity across textures
D. Memory layout of control points
Answer: B. Visual smoothness (direction/shape) rather than parameter derivative equality

26. The Phong illumination model decomposes light into which three types?
A. Ambient, diffuse, specular
B. Global, local, texture
C. Emissive, transmissive, reflective
D. Rough, smooth, glossy
Answer: A. Ambient, diffuse, specular

27. Lambert’s cosine law is the basis for which component of Phong shading?
A. Ambient component
B. Diffuse component
C. Specular component
D. Emissive component
Answer: B. Diffuse component

28. Which shading method computes lighting per-vertex and interpolates colors across polygon surfaces?
A. Flat shading
B. Gouraud shading
C. Phong shading (per-pixel)
D. Ray tracing only
Answer: B. Gouraud shading

29. In Phong shading (per-pixel interpolation of normals), what is interpolated across the polygon?
A. Color values
B. Vertex indices
C. Surface normals (and then lighting computed per-pixel)
D. Texture coordinates only
Answer: C. Surface normals (and then lighting computed per-pixel)

30. Specular highlights in the Phong model depend primarily on:
A. Surface roughness only
B. The angle between reflected view vector and specular exponent
C. The normal only
D. Background color
Answer: B. The angle between reflected view vector and specular exponent

31. Which polygon rendering method relies on sorting polygons by depth and painting them from farthest to nearest?
A. Z-buffer algorithm
B. Scanline polygon fill
C. Painter’s algorithm
D. Bresenham algorithm
Answer: C. Painter’s algorithm

32. The Z-buffer algorithm stores which value per pixel?
A. Color only
B. Depth (z) value and color
C. Object ID only
D. Edge list of polygons intersecting the pixel
Answer: B. Depth (z) value and color

33. What is a key drawback of the basic Painter’s algorithm?
A. It always requires hardware acceleration
B. Requires sorting and doesn’t handle cyclic overlap without splitting polygons
C. It uses more memory than Z-buffer by an order of magnitude
D. It cannot draw triangles
Answer: B. Requires sorting and doesn’t handle cyclic overlap without splitting polygons

34. Back-face culling uses which test on a triangle to determine if it should be culled?
A. Dot product between view vector and surface normal
B. Cross product of vertex positions only
C. Length of normal vector
D. Texture coordinate orientation
Answer: A. Dot product between view vector and surface normal

35. Scanline polygon filling proceeds primarily by iterating across which of the following?
A. Columns of the framebuffer
B. Rows (scanlines) of the framebuffer
C. Depth slices in z-order
D. Random pixel sets
Answer: B. Rows (scanlines) of the framebuffer

36. Which acceleration technique reduces the number of triangles processed by clipping them to the view frustum early?
A. Deferred shading
B. View frustum culling
C. Shadow mapping
D. Bloom filter
Answer: B. View frustum culling

37. Which coordinate is not part of the canonical view volume in normalized device coordinates (after projection and perspective divide)?
A. x between -1 and +1
B. y between -1 and +1
C. z between -1 and +1 (or 0 and 1 depending on convention)
D. w between -1 and +1
Answer: D. w between -1 and +1

38. Which pipeline stage converts object coordinates into eye (camera) coordinates?
A. Projection transform
B. View (camera) transform
C. Model transform only
D. Clipping stage
Answer: B. View (camera) transform

39. The view matrix (camera transform) is typically formed by combining which pieces?
A. Scaling, projection, rasterization
B. Camera orientation (rotation) and camera position (translation) inverse
C. Texture mapping matrices
D. Light-space transforms
Answer: B. Camera orientation (rotation) and camera position (translation) inverse

40. Perspective projection differs from orthographic projection in that perspective:
A. Preserves parallelism of lines
B. Produces depth-dependent foreshortening (objects farther appear smaller)
C. Is linear in screen coordinates for z
D. Uses no projection center
Answer: B. Produces depth-dependent foreshortening (objects farther appear smaller)

41. Which general projection transform maps 3D points onto a plane through lines passing through a fixed center of projection?
A. Orthographic projection
B. Perspective projection
C. Shear projection
D. Parallel projection
Answer: B. Perspective projection

42. In perspective projection with homogeneous coordinates, what operation follows applying the projection matrix to obtain normalized device coordinates?
A. Adding the w component
B. Perspective divide (divide by w)
C. Multiplying by w again
D. Taking the square root of coordinates
Answer: B. Perspective divide (divide by w)

43. Cohen–Sutherland and Liang–Barsky are algorithms for which problem?
A. Hidden surface removal
B. Line clipping against a rectangular clipping window
C. Polygon triangulation
D. Spline subdivision
Answer: B. Line clipping against a rectangular clipping window

44. Sutherland–Hodgman algorithm is primarily used for:
A. Line clipping in 3D cubes
B. Clipping polygons against a convex clipping region (e.g., rectangular window)
C. Hidden-surface removal by z-ordering
D. Converting polygons to triangles
Answer: B. Clipping polygons against a convex clipping region (e.g., rectangular window)

45. Which clipping algorithm uses outcodes for endpoints to quickly trivial-accept or trivial-reject line segments?
A. Liang–Barsky
B. Sutherland–Hodgman
C. Cohen–Sutherland
D. Weiler–Atherton
Answer: C. Cohen–Sutherland

46. In Liang–Barsky clipping, the parametric form of the line is used. What benefit does this give?
A. It avoids division operations entirely
B. It gives exact intersection parameter values and can be more efficient than Cohen–Sutherland
C. It generalizes to curved clipping windows easily
D. It always outputs fewer segments than any other algorithm
Answer: B. It gives exact intersection parameter values and can be more efficient than Cohen–Sutherland

47. What does “homogeneous clipping” refer to in graphics pipelines?
A. Clipping after perspective divide only
B. Clipping in homogeneous (clip) coordinates before perspective divide, so planes are linear
C. Clipping only objects of the same material
D. Clipping performed in world coordinates only
Answer: B. Clipping in homogeneous (clip) coordinates before perspective divide, so planes are linear

48. Which of the following is true about the canonical view volume for orthographic projection?
A. It is a cube in normalized device coordinates
B. It is an inverted pyramid
C. It is always a sphere
D. It depends on the light direction
Answer: A. It is a cube in normalized device coordinates

49. The term “view frustum” refers to:
A. The clipping planes for orthographic maps only
B. The truncated pyramidal (or parallelepiped for orthographic) volume that defines the visible region in perspective projection
C. The transformation matrix used to view textures
D. The list of lights visible to the camera
Answer: B. The truncated pyramidal (or parallelepiped for orthographic) volume that defines the visible region in perspective projection

50. In the graphics pipeline, after transforming vertices to clip coordinates, the next mandatory step is:
A. Rasterization
B. Clipping to the canonical view volume
C. Texture mapping
D. Blending colors
Answer: B. Clipping to the canonical view volume

51. Which of the following is a CUDA/GPU-friendly approach to handle visibility per pixel?
A. Painter’s algorithm with software sorting
B. Z-buffer implemented in hardware
C. Sutherland–Hodgman polygon clipping
D. Liang–Barsky function calls per fragment
Answer: B. Z-buffer implemented in hardware

52. Which polygon attribute interpolation method is perspective-correct and avoids affine artifacts?
A. Linear interpolation in screen space of attribute values directly
B. Interpolation of attribute divided by clip-space w and then correcting by 1/w
C. Interpolating texture coordinates without depth modification
D. No interpolation: use nearest neighbor only
Answer: B. Interpolation of attribute divided by clip-space w and then correcting by 1/w

53. Which of the following best describes Gouraud shading’s primary limitation?
A. It produces extremely expensive per-pixel lighting calculations
B. It can miss small specular highlights because it interpolates vertex colors rather than computing per-pixel lighting
C. It requires non-linear texture coordinates
D. It cannot be used on triangles
Answer: B. It can miss small specular highlights because it interpolates vertex colors rather than computing per-pixel lighting

54. Which of the following is not part of the standard graphics viewing pipeline?
A. Model transform
B. View (camera) transform
C. Illumination model
D. Projection transform
Answer: C. Illumination model
(Illumination is usually part of shading stage; pipeline stages vary, but model/view/projection are core transformations.)

55. The view volume clipping planes include which of the following sets?
A. Near, far, left, right, top, bottom
B. Near, focus, chroma, alpha
C. Front, back, diagonal, tangent
D. Ambient, diffuse, specular
Answer: A. Near, far, left, right, top, bottom

56. For a perspective camera, increasing field of view (FOV) causes which visual effect?
A. Objects appear larger and less depth distortion
B. Objects appear smaller and more perspective distortion (wide-angle)
C. No change in perspective, only z-buffer resolution changes
D. Colors shift due to gamma correction
Answer: B. Objects appear smaller and more perspective distortion (wide-angle)

57. Which transformation matrix would you apply to convert from world coordinates to camera (eye) coordinates?
A. Model matrix
B. Inverse of camera’s world transform (translation and rotation)
C. Projection matrix
D. Viewport transformation
Answer: B. Inverse of camera’s world transform (translation and rotation)

58. The viewport transforms maps normalized device coordinates to:
A. World coordinates
B. Device (screen) pixel coordinates
C. Texture coordinates
D. Eye coordinates
Answer: B. Device (screen) pixel coordinates

59. Which of the following is a local illumination model?
A. Global illumination with radiosity and path tracing
B. Phong reflection model (ambient + diffuse + specular computed at the surface point)
C. Photon mapping with multiple bounces
D. Full Monte Carlo light transport
Answer: B. Phong reflection model (ambient + diffuse + specular computed at the surface point)

60. Which lighting term accounts for indirect light uniformly present across a scene (often approximated simply)?
A. Specular term
B. Ambient term
C. Diffuse term
D. Emissive term
Answer: B. Ambient term

61. In the Phong reflection model the specular term commonly uses what parameter to control highlight tightness?
A. Albedo
B. Specular exponent (shininess)
C. Ambient coefficient
D. Diffuse coefficient
Answer: B. Specular exponent (shininess)

62. The half-vector used in some specular models is defined as:
A. The average of eye and light directions normalized
B. Exactly equal to the surface normal always
C. The direction to the nearest light only
D. The vector halfway between surface normal and tangent
Answer: A. The average of eye and light directions normalized

63. Which rendering method computes color by following many random light paths and is used for global illumination?
A. Scanline algorithm
B. Ray tracing / Path tracing
C. Z-buffer rasterization only
D. Gouraud shading
Answer: B. Ray tracing / Path tracing

64. In hierarchical bounding volume techniques, which bounding shape is best for tight fitting but slower to test?
A. Axis-aligned bounding box (AABB)
B. Bounding sphere
C. Oriented bounding box (OBB)
D. Infinite plane
Answer: C. Oriented bounding box (OBB)

65. A mesh is manifold if:
A. Every edge belongs to at most two faces and the faces around each vertex form a single fan
B. Edges can belong to any number of faces
C. Faces may be degenerate arbitrarily
D. The mesh is 2D only
Answer: A. Every edge belongs to at most two faces and the faces around each vertex form a single fan

66. What is the Euler characteristic (V − E + F) used for in 3D meshes?
A. To compute shading coefficients
B. To check topological properties and genus of the surface
C. To accelerate rasterization
D. To compress mesh data
Answer: B. To check topological properties and genus of the surface

67. When tessellating a parametric surface for rendering, increasing tessellation density affects which of the following?
A. Decreases memory usage
B. Increases geometric fidelity and computational cost
C. Eliminates the need for shading
D. Converts the surface into an implicit form
Answer: B. Increases geometric fidelity and computational cost

68. Which method creates a smooth surface by interpolating a triangular mesh using barycentric coordinates and smooth basis functions?
A. Bézier triangle patches (Bezier on triangles)
B. Tensor-product Bézier surfaces only
C. Implicit blobby surfaces only
D. Z-buffer interpolation
Answer: A. Bézier triangle patches (Bezier on triangles)

69. What is the main idea behind subdivision surfaces (e.g., Catmull–Clark)?
A. Replace polygons with spheres recursively
B. Repeatedly refine a coarse mesh into a smoother mesh by subdivision rules
C. Convert polygons to NURBS directly
D. Merge small faces into larger ones
Answer: B. Repeatedly refine a coarse mesh into a smoother mesh by subdivision rules

70. Catmull–Clark subdivision generalizes which 2D method to surfaces?
A. Chaikin’s corner-cutting subdivision (for curves)
B. De Casteljau algorithm
C. Fast Fourier Transform
D. Dijkstra’s shortest path
Answer: A. Chaikin’s corner-cutting subdivision (for curves)

71. NURBS stands for:
A. Non-Uniform Rational B-Spline
B. Non-Uniform Regular Binary Spline
C. Normalized Uniform Radial Basis Spline
D. Nonlinear Uniform Rational Basis Set
Answer: A. Non-Uniform Rational B-Spline

72. Which advantage do NURBS have over regular B-splines?
A. They cannot represent circles or conics
B. They include rational weights so they can represent conic sections exactly (e.g., circles)
C. They require uniform knot vectors only
D. They are always linear
Answer: B. They include rational weights so they can represent conic sections exactly (e.g., circles)

73. Which of the following is true about a cubic B-spline basis function?
A. It is nonzero across the entire real line
B. It has compact support over at most four knot intervals for cubic case
C. It cannot be evaluated by de Boor’s algorithm
D. It equals a Bernstein polynomial directly
Answer: B. It has compact support over at most four knot intervals for cubic case

74. The de Boor algorithm is used to:
A. Evaluate B-splines at a parameter value
B. Convert Bézier curves to implicit surfaces
C. Compute ray-surface intersections analytically
D. Determine the Euler characteristic of a mesh
Answer: A. Evaluate B-splines at a parameter value

75. In curve modeling, “parametric continuity” C2 vs “geometric continuity” G2 differ because:
A. C2 requires second derivatives equal; G2 requires curvature (shape) continuity but allows reparameterization
B. They are identical definitions
C. G2 requires discrete sampling only
D. C2 is weaker than G0
Answer: A. C2 requires second derivatives equal; G2 requires curvature (shape) continuity but allows reparameterization

76. For a Bézier curve of degree n, how many non-zero Bernstein basis polynomials exist?
A. n
B. n+1
C. 2n
D. n−1
Answer: B. n+1

77. Which of the following operations on Bézier curves is stable and commonly used to split a curve into two sub-curves?
A. Knot insertion only for B-splines
B. De Casteljau subdivision
C. Fourier transform subdivision
D. Direct matrix inversion
Answer: B. De Casteljau subdivision

78. What is a common reason to convert a B-spline curve into a sequence of Bézier segments?
A. To reduce the number of control points
B. To allow GPU hardware that uses Bézier patch evaluation or simpler tessellation
C. To change the curve degree to zero
D. To perform implicit surface extraction
Answer: B. To allow GPU hardware that uses Bézier patch evaluation or simpler tessellation

79. Bézier curves do not have local control because:
A. Each control point affects the entire curve due to global Bernstein basis support
B. They require knot vectors
C. Their basis functions have local compact support
D. They are evaluated only at integer parameters
Answer: A. Each control point affects the entire curve due to global Bernstein basis support

80. Which of the following surface representations is naturally suited for sweep operations (e.g., extrude, revolve)?
A. Implicit scalar fields only
B. Parametric surfaces like NURBS and swept surfaces (surface of revolution and extrusion)
C. Voxel grids exclusively
D. Displacement maps only
Answer: B. Parametric surfaces like NURBS and swept surfaces (surface of revolution and extrusion)

81. Which is the correct order for rasterization pipeline steps (high level)?
A. Vertex processing → Clipping → Perspective divide → Viewport transform → Fragment processing → Framebuffer write
B. Fragment processing → Vertex processing → Rasterization → Clipping
C. Viewport transform → Vertex processing → Clipping → Fragment processing
D. Rasterization → Vertex processing → Framebuffer write
Answer: A. Vertex processing → Clipping → Perspective divide → Viewport transform → Fragment processing → Framebuffer write

82. Which of the following is a fast per-pixel visibility test commonly used in GPUs?
A. Depth peeling in software only
B. Hardware Z-buffer test
C. Euler characteristic test
D. Polygon winding test per pixel
Answer: B. Hardware Z-buffer test

83. In texture mapping, perspective-correct interpolation corrects an artifact that arises because:
A. Attributes are inherently linear in clip-space divided by w, not in screen space
B. Textures are 3D images only
C. Mipmapping uses wrong colors by default
D. Bilinear filtering is always perspective-correct
Answer: A. Attributes are inherently linear in clip-space divided by w, not in screen space

84. What is a common technique to avoid aliasing when rasterizing lines or polygons?
A. Depth testing
B. Anti-aliasing using supersampling or multisample anti-aliasing (MSAA)
C. Clipping only
D. Using integer arithmetic only
Answer: B. Anti-aliasing using supersampling or multisample anti-aliasing (MSAA)

85. Which of the following is a frame-coherent visibility algorithm used for order-independent transparency?
A. Z-buffer only
B. Depth peeling
C. Cohen–Sutherland
D. Gouraud shading
Answer: B. Depth peeling

86. What does “order-independent transparency” aim to solve?
A. The problem of sorting translucent fragments by depth at render time to correctly blend them without per-object sorting
B. The buffering order of triangular meshes on disk
C. Converting polygons to textures
D. Reducing polygon count to zero
Answer: A. The problem of sorting translucent fragments by depth at render time to correctly blend them without per-object sorting

87. Which of the following is a correct definition of an affine transformation in 3D?
A. A transformation that preserves straight lines and parallelism but not necessarily angles or lengths (can include translation, rotation, scaling, shear)
B. A transformation that only rotates and translates
C. A non-linear projection from 3D to 2D
D. Only perspective divisions are affine transformations
Answer: A. A transformation that preserves straight lines and parallelism but not necessarily angles or lengths (can include translation, rotation, scaling, shear)

88. The determinant of the linear part (3×3) of an affine transform indicates:
A. The color change applied to textures
B. The scaling factor of volumes (negative means orientation reversal)
C. The number of vertices in a mesh
D. Nothing of importance
Answer: B. The scaling factor of volumes (negative means orientation reversal)

89. To correctly transform normals under a non-uniform scaling transform, which matrix should be applied to the normal?
A. The same model matrix as vertices
B. The inverse transpose of the linear part of the model matrix
C. The transpose of the full 4×4 matrix including translation
D. Identity matrix only
Answer: B. The inverse transpose of the linear part of the model matrix

90. Shear transformations are used in computer graphics to:
A. Preserve angles and lengths always
B. Slant objects, changing angles while preserving parallelism of lines
C. Reduce polygon count
D. Change color saturation
Answer: B. Slant objects, changing angles while preserving parallelism of lines

91. Which of the following best describes “view space” (eye coordinates)?
A. Coordinates with origin at world origin always
B. Coordinates after the model-view transform, with camera at origin looking along a canonical axis (e.g., −z)
C. Coordinates in texture parameter space
D. Coordinates after rasterization only
Answer: B. Coordinates after the model-view transform, with camera at origin looking along a canonical axis (e.g., −z)

92. Clipping in homogeneous coordinates allows clipping against which geometric primitives to remain linear?
A. Spheres only
B. Planes (like frustum planes) because they become linear in homogeneous space
C. Arbitrary curved windows only
D. Pixel grids only
Answer: B. Planes (like frustum planes) because they become linear in homogeneous space

93. The homogeneous coordinate w encodes what geometric concept for perspective projection?
A. Lighting intensity
B. Reciprocal of depth scaling that leads to perspective division
C. Texture index
D. Vertex ID
Answer: B. Reciprocal of depth scaling that leads to perspective division

94. A common approach for robust polygon clipping to the view frustum is to:
A. Ignore near-plane clipping entirely
B. Clip polygons in clip space (homogeneous coords) against each frustum plane using Sutherland–Hodgman per-plane
C. Convert polygons to spheres first
D. Only clip vertices, not edges
Answer: B. Clip polygons in clip space (homogeneous coords) against each frustum plane using Sutherland–Hodgman per-plane

95. In hardware pipelines, vertex attributes are typically transformed and lit in which stage?
A. Fragment shader stage only
B. Vertex shader stage
C. Rasterizer only
D. Framebuffer write stage
Answer: B. Vertex shader stage

96. Which interpolation qualifier in shading languages indicates that a varying should be interpolated perspective-correct across a triangle?
A. flat
B. noperspective (or no perspective correction)
C. smooth (default – perspective-correct interpolation)
D. centroid only
Answer: C. smooth (default – perspective-correct interpolation)

97. For anti-aliasing, multisample anti-aliasing (MSAA) saves computation by:
A. Sampling depth and coverage at multiple sub-pixel locations but shading interpolants only once per pixel sample group
B. Computing lighting millions of times per pixel
C. Replacing textures with blurred versions only
D. Performing no depth test at all
Answer: A. Sampling depth and coverage at multiple sub-pixel locations but shading interpolants only once per pixel sample group

98. What is a primary cause of z-fighting artifacts when rendering polygons?
A. Two surfaces with nearly equal depth values compete due to limited depth buffer precision
B. Texture coordinates are outside [0,1]
C. The polygon is convex
D. The vertex shader returns NaN for position
Answer: A. Two surfaces with nearly equal depth values compete due to limited depth buffer precision

99. Which technique reduces aliasing when sampling textures displayed at greatly reduced sizes?
A. Anisotropic filtering and mipmapping
B. Gouraud shading only
C. Phong shading only
D. Point sampling only
Answer: A. Anisotropic filtering and mipmapping

100. The Weiler–Atherton algorithm is primarily used for:
A. Clipping complex polygons (possibly concave) and polygons with holes against clipping polygons
B. Line clipping only
C. Texture filtering only
D. Sorting transparent polygons only
Answer: A. Clipping complex polygons (possibly concave) and polygons with holes against clipping polygons