Mid-Point Circle Algorithms in Computer Graphics MCQ Questions and Answers
1. The midpoint circle algorithm is used to
A) Fill polygons
B) Draw ellipses only
C) Rasterize circles using integer arithmetic and symmetry
D) Compute polygon normals
Answer: C
2. The midpoint circle algorithm is a variant of which family of algorithms?
A) Scanline polygon fill
B) Bresenham-like incremental algorithms
C) Clipping algorithms
D) Texture mapping algorithms
Answer: B
3. For a circle centered at the origin with radius r, the initial point usually used is
A) (r, 0)
B) (r, r)
C) (0, r)
D) (r, −r)
Answer: C
4. The midpoint decision parameter p₀ for a circle of radius r (starting at x=0, y=r) is commonly initialized as
A) r − 1
B) 1 − r
C) r + 1
D) −r
Answer: B
5. In the midpoint circle algorithm, if the decision parameter p < 0 at a step, the next pixel chosen is
A) (x+1, y−1)
B) (x+1, y)
C) (x, y−1)
D) (x−1, y)
Answer: B
6. If the decision parameter p ≥ 0, the midpoint algorithm chooses next pixel as
A) (x, y+1)
B) (x+1, y−1)
C) (x−1, y−1)
D) (x+2, y)
Answer: B
7. The update formula for the decision parameter when p < 0 (choosing (x+1, y)) is often written as
A) p = p − 2x − 2y + 1
B) p = p + 2x + 3
C) p = p + 2y − 3
D) p = p + 1
Answer: B
8. When p ≥ 0 and we select (x+1, y−1), the decision parameter update is usually
A) p = p + 2x + 5
B) p = p + 2(x − y) + 5
C) p = p − 2x + 3
D) p = p − 1
Answer: B
9. The midpoint test evaluates the value of the circle implicit function at
A) The pixel center only
B) The midpoint between two candidate pixel centers
C) The origin only
D) The previous plotted pixel
Answer: B
10. The implicit equation of a circle centered at (0,0) is
A) x + y = r
B) x² − y² = r²
C) x² + y² − r² = 0
D) x² + y = r
Answer: C
11. The midpoint algorithm exploits circle symmetry. One octant’s computed points are replicated to produce how many total points on the circle?
A) 4
B) 6
C) 8
D) 16
Answer: C
12. The eight-way symmetry maps a point (x, y) to which of these?
A) (x+y, y−x)
B) (−x, −y) only
C) (±x, ±y) and (±y, ±x) combinations
D) Rotations by 30° increments
Answer: C
13. The midpoint algorithm uses only additions and subtractions in its main loop because it avoids
A) Memory access
B) Branching
C) Multiplications and divisions
D) Pixel color setting
Answer: C
14. The midpoint circle algorithm is most efficient when implemented with integer arithmetic because it avoids costly
A) Comparisons
B) Floating-point multiplications/divisions
C) Additions
D) Memory writes
Answer: B
15. If the circle has radius r = 5, the initial decision parameter p₀ = 1 − r equals
A) 4
B) −4
C) 6
D) 0
Answer: B
16. The algorithm terminates when x > y because beyond this point
A) Circle color changes
B) We switch to a different algorithm
C) Further stepping would duplicate points already plotted in other octants
D) The circle is filled
Answer: C
17. The midpoint algorithm is equivalent to Bresenham’s circle algorithm because both
A) Use trigonometric functions
B) Use incremental integer decision updates and symmetry
C) Use raster scanline filling primitives
D) Use parametric t stepping exclusively
Answer: B
18. The per-step complexity of the midpoint circle algorithm for radius r is approximately
A) O(r²)
B) O(r)
C) O(1)
D) O(log r)
Answer: B
19. For a point (x, y) on the circle, the next step in the first octant increments x by 1. The y coordinate either stays same or decreases by 1 depending on
A) Color depth
B) Decision parameter sign
C) Pixel aspect ratio
D) Memory size
Answer: B
20. The midpoint algorithm tests the function f(x + 1, y − ½) where f(x, y) = x² + y² − r². The fractional sample y − ½ is chosen because it lies
A) At the pixel edge
B) At the midpoint between two candidate pixels in vertical direction
C) At the circle center
D) At the previous pixel center
Answer: B
21. If pₖ < 0 at step k, which change to p is correct (using integer increments) when moving to x+1?
A) p ← p − 2x + 1
B) p ← p + 2x + 3
C) p ← p + 2y + 3
D) p ← p + 2(x − y) + 5
Answer: B
22. The initial values before the loop for x and y are typically set to
A) x = r, y = 0
B) x = 1, y = 1
C) x = 0, y = r
D) x = r, y = r
Answer: C
23. Using symmetry, if you compute points for 0 ≤ x ≤ y, you cover the full circle by reflecting these points across octants. True or false?
A) False for all r
B) True
C) Only true if r is even
D) Only true for unit circles
Answer: B
24. For large radii, the midpoint circle algorithm is preferred over naive parametric sampling because parametric sampling may suffer from
A) Integer arithmetic only
B) Uneven pixel spacing and floating-point inefficiency
C) Too much symmetry
D) Using 8-way reflection
Answer: B
25. When implementing midpoint circle for a circle centered at (xc, yc), computed points (x, y) are converted to screen coordinates by
A) Rotating by 90°
B) Adding the center coordinates: (xc ± x, yc ± y), etc.
C) Multiplying by center values
D) Subtracting the center coordinates
Answer: B
26. If the decision parameter p becomes zero exactly at some step, most implementations will choose which pixel and update how?
A) Always choose (x+1, y) and add 1 to p
B) Choose (x+1, y−1) or (x+1, y) depending on convention, but both choices are valid symmetry-wise
C) Terminate algorithm immediately
D) Increase radius by 1
Answer: B
27. The implicit circle function f(x, y) = x² + y² − r² increases when a point moves
A) Toward circle center
B) Away from the circle towards outside
C) Along the circle exactly
D) Only along x axis
Answer: B
28. The midpoint algorithm is derived by evaluating f at the midpoint between candidate pixels. This derivation ensures that the decision depends on
A) Pixel color
B) Relative distances to the true circle
C) Memory layout
D) Anti-aliasing factor
Answer: B
29. The midpoint circle algorithm can be adapted to draw filled circles by
A) Drawing only octant edges and leaving interior blank
B) Drawing horizontal or vertical spans between symmetric points for each scanline
C) Replacing decisions with color interpolation only
D) Using Wu’s intensities instead
Answer: B
30. In hardware implementations (FPGA/ASIC), midpoint circle algorithm is attractive because
A) It uses floating-point units heavily
B) It uses simple adders and comparators with predictable timing
C) It requires large LUTs only
D) It requires slow division units
Answer: B
31. Which of these is a correct pair of updates for p when choosing (x+1, y) and (x+1, y−1) respectively?
A) p += 2y + 1; p += 2x − 3
B) p += 2x + 3; p += 2(x − y) + 5
C) p += x + y; p += x − y
D) p -= 2x + 3; p -= 2(x − y) + 5
Answer: B
32. The midpoint algorithm plots integer pixel centers that best approximate circle — this sampling can still exhibit aliasing because
A) It uses 8-way symmetry
B) Discrete sampling of continuous boundary causes jaggedness at low resolution
C) It uses integer arithmetic only
D) It plots too many pixels
Answer: B
33. The midpoint circle algorithm is exact in the sense that it samples points that are the closest integer lattice points to the true circle boundary only when
A) r is prime
B) Using the midpoint decision yields pixels that approximate minimal distance in the chosen sample geometry
C) r = 1 only
D) Only for even radii
Answer: B
34. Which of the following modifies midpoint algorithm to draw ellipses?
A) Increase symmetry to 16-way
B) Use midpoint ellipse algorithm with separate Δ calculations for x and y increments
C) Use Bresenham for circles only
D) Use Wu’s anti-aliasing only
Answer: B
35. To plot the circle centered at (xc, yc), one of the octant reflections of pixel (x, y) is (xc − y, yc + x). This is obtained by
A) Rotation by 30°
B) Scaling by two
C) Swapping and sign changes (symmetry)
D) Adding radii
Answer: C
36. The midpoint algorithm evaluates f at non-integer positions (half integer) but maintains integer updates because the initial p and updates are scaled appropriately. This scaling avoids needing to evaluate which function type exactly?
A) Exponential functions
B) Floating-point square computations at every step
C) Memory copies
D) Lookup tables
Answer: B
37. The reason the midpoint algorithm only computes octant 0 (0≤x≤y) is that beyond x>y the other octant points would be symmetric duplicates — true or false?
A) False for all circles
B) True
C) True only for r odd
D) True only for integer r
Answer: B
38. Which of the following statements is true about initial decision p₀ = 1 − r?
A) It applies only for unit circle r=1
B) It is positive for r > 1 always
C) It is negative for r > 1 and provides correct sign to decide first step
D) It must be computed as r² − 1 always
Answer: C
39. The midpoint method is robust under integer arithmetic because the decision function can be scaled by constants without changing the sign. This property is called
A) Discretization invariance
B) Scale invariance of sign tests
C) Linear interpolation
D) Convolution property
Answer: B
40. When drawing circle on a display with non-square pixels, one must adjust algorithm to account for pixel aspect ratio by
A) Using Wu only
B) Scaling coordinates according to pixel aspect ratio before decision tests
C) Doubling r always
D) Using octant duplication only
Answer: B
41. In an implementation where x and y are integers, the term 2x + 3 arises in p update because it equals the difference between f(x+1,y) and f(x,y) scaled appropriately. True or false?
A) False for all x
B) True — derived from incremental evaluation of f
C) Only true if r is zero
D) Only true for negative x
Answer: B
42. When p becomes positive, the y coordinate is decremented because the midpoint lies
A) Inside the circle
B) Exactly on the circle
C) Outside the circle, so the vertical step is necessary to move closer
D) At origin
Answer: C
43. The midpoint algorithm can be used to rasterize arcs by restricting the octant reflections and plotting only desired angle ranges. True or false?
A) False, midpoint cannot draw arcs
B) True
C) Only if r is integer
D) Only if circle centered at origin
Answer: B
44. The memory requirement for midpoint circle algorithm is minimal because it only needs to store
A) Entire pixel buffer
B) All computed octant points before plotting
C) Current x, y, decision parameter and circle center (constant space)
D) Complex lookup tables for sin/cos
Answer: C
45. For a circle radius r = 10, initial p₀ = 1 − r = −9. After first step (x=1) if p₀ < 0, the new p₁ becomes p₀ + 2*0 + 3 = −6. This represents correct integer update assuming initial x=0. True or false?
A) False — computation wrong
B) True — p₁ = −9 + 3 = −6
C) False — should add 5
D) False — should subtract 3
Answer: B
46. The midpoint circle algorithm’s plotted pixels approximate the true circle boundary in which metric?
A) Taxicab (L1) only
B) Euclidean distance metric (approximately)
C) Infinity norm only
D) Hamming distance
Answer: B
47. Which of the following is NOT a correct reason to prefer midpoint algorithm for circle drawing?
A) Uses integer arithmetic
B) Exploits symmetry to reduce computations
C) Produces exact antialiased curve without extra work
D) Low memory overhead
Answer: C
48. A common improvement to midpoint algorithm to produce smoother circles is to combine it with
A) Larger integer steps only
B) Anti-aliasing methods (e.g., Xiaolin Wu style intensity blending)
C) Clipping exclusively
D) Rotation transforms only
Answer: B
49. The midpoint algorithm is derived from comparing f(midpoint) to zero. If f(midpoint) < 0, the midpoint is inside the circle. Which pixel is closer in that case?
A) (x+1, y−1)
B) (x+1, y)
C) (x, y)
D) (x−1, y)
Answer: B
50. When integrating midpoint algorithm into higher level graphics functions (line/arc/circle editors), care must be taken to handle clipping, transformations and
A) Pixel refreshing only
B) Attribute interpolation (color/line-width) if required
C) Division by zero only
D) None — midpoint handles all cases automatically
Answer: B
51. The midpoint algorithm is often presented as an instance of which numerical technique?
A) Newton–Raphson root finding
B) Incremental difference evaluation (finite differences)
C) Simpson’s rule integration
D) Least squares fitting
Answer: B
52. When implementing midpoint circle algorithm for a circle centered at (xc, yc) with radius r, what is the first pixel plotted (before octant reflections)?
A) (xc + r, yc)
B) (xc, yc + r)
C) (xc + 1, yc)
D) (xc, yc)
Answer: B
53. Suppose r = 7 and starting p₀ = 1 − r = −6. If p < 0 for several steps, which coordinate changes occur?
A) x remains constant, y increases
B) x increments by 1 each step while y remains the same until p ≥ 0
C) y decrements each step while x remains same
D) Both x and y remain unchanged
Answer: B
54. The midpoint test f(x+1, y−½) uses y−½ as a half-integer sample. The rationale for half-integer sampling is to sample the midpoint between the centers of which two candidate pixels?
A) Left and right pixels
B) The E (east) and SE (south-east) candidate pixel centers vertically
C) North and south only
D) Origin and current pixel
Answer: B
55. The midpoint algorithm can be modified to draw circles with sub-pixel offsets (non-integer centers) by adjusting which value(s)?
A) Radius only
B) The center coordinates in decision test (use offsets in f evaluation or pre-shift coordinates)
C) Use Wu algorithm only
D) Octant reflection rules only
Answer: B
56. If one wants to draw only the upper-right quadrant of a circle, one would compute octant points for 0 ≤ x ≤ y and then reflect only into which octants?
A) All eight octants
B) Lower-left octants only
C) The two or more octants corresponding to upper-right quadrant (i.e., x≥0,y≥0)
D) None — full circle must be drawn
Answer: C
57. In implementing midpoint circle algorithm on an integer-only platform, the variable types should be chosen to avoid overflow. The magnitude of intermediate values is roughly on the order of
A) r only
B) r² (e.g., f(x,y) involves r²)
C) log r
D) 1/r
Answer: B
58. A performance optimization for drawing many concentric circles of increasing radius is to reuse
A) The same p exactly for all radii
B) Precomputed incremental steps where possible or use symmetry of radii increments
C) Wu’s algorithm for each only
D) Use random dithering instead
Answer: B
59. The midpoint algorithm for a circle can also be formulated in terms of differential equations approximations — true or false?
A) False — cannot be related
B) True — incremental difference is a discrete analog of continuous derivative behavior
C) Only for r prime
D) Only when using floating point
Answer: B
60. Which of the following is a correct reason that midpoint algorithm uses y−½ in the midpoint test instead of y?
A) To reduce branching in code
B) Because the midpoint between candidate pixel centers lies halfway between integer y coordinates
C) To avoid symmetry usage
D) To increase radius value
Answer: B
61. If you wanted to add anti-aliasing weight to the plotted pixel at (x,y) using midpoint information, you could base the weight on
A) The integer x coordinate only
B) The absolute value of f(midpoint) normalized by some factor (distance estimate)
C) The color palette index
D) Octant index only
Answer: B
62. The midpoint update formulas are derived by substituting (x+1, y) and (x+1, y−1) into f(x,y) and computing the difference; this approach is an example of using which property?
A) Polynomial regression
B) Finite difference of the implicit function
C) Fourier transform
D) Monte Carlo sampling
Answer: B
63. A naive parametric sampling of circle points using x = xc + r cos θ, y = yc + r sin θ with Δθ constant can miss pixels or cluster pixels due to non-uniform spacing in θ. The midpoint algorithm avoids this by stepping in
A) Angular increments only
B) Cartesian increments (x stepping) ensuring approximately uniform pixel coverage along octant
C) Random t increments
D) Color increments only
Answer: B
64. The midpoint circle algorithm can be adapted to rasterize circular arcs defined between angles θ₁ and θ₂ by restricting reflection and plotting only points whose angle lies in that interval. Which practical test is used to determine if a given (x,y) lies within the angle interval after reflection?
A) Compare x only
B) Compute atan2(y, x) and test angle range (or use cross-product sign tests without floating trig if desired)
C) Compare with radius only
D) Use color value to encode inclusion
Answer: B
65. The midpoint algorithm assumes an isotropic grid. On anisotropic sampling grids plotting will be distorted unless you
A) Multiply r by 2 always
B) Pre-scale the coordinates to square pixel aspect ratio before running the algorithm
C) Use Bresenham instead only
D) Use Wu’s algorithm only
Answer: B
66. The midpoint algorithm’s correctness relies on that f(x+1,y−½) sign uniquely identifies which candidate pixel is closer in Euclidean sense (given the step geometry). This is true because f is proportional to what geometric quantity?
A) Angle to center
B) Twice the signed distance (approximately) from the midpoint to the circle boundary
C) Hamming distance
D) Color intensity
Answer: B
67. When writing code for midpoint circle, developers often increment p by expressions involving 2x and 2y. Why are these doubled quantities used rather than x and y alone?
A) For aesthetics only
B) Because the difference formulas produce factors of 2 from (x+1)² − x² expansions
C) To use only even numbers
D) To avoid negative values entirely
Answer: B
68. Which of the following is a direct advantage of using midpoint algorithm over floating parametric methods in embedded displays?
A) Requires trig lookup tables
B) Deterministic performance and reduced computational overhead (no sin/cos)
C) Produces anti-aliased output automatically
D) Uses more memory but less CPU
Answer: B
69. A midpoint-based circle rasterizer that increments x until x > y will produce how many iterations approximately for radius r?
A) r² iterations
B) ~r iterations (one per x step in an octant)
C) log r iterations
D) Constant iterations only
Answer: B
70. The midpoint decision parameter p can be made to stay integer-valued throughout by multiplying original half-integer tests by 4. This is valid because sign comparisons are invariant under positive scaling. This technique is primarily used to avoid which operation?
A) Addition
B) Division or fractional arithmetic
C) Bit shifting
D) Symmetry transformations
Answer: B
71. The midpoint circle algorithm is best described as which of these numerical strategies?
A) Global optimization solver
B) Local incremental test at each step using finite differences
C) Monte Carlo approximation
D) Frequency domain filter
Answer: B
72. When implementing circle drawing for many small radii, which approach is often faster?
A) Parametric cos/sin every time
B) Use incremental midpoint updates for each radius or precompute small circle templates
C) Use Wu anti-aliasing always
D) Use giant LUT for all radii up to max only
Answer: B
73. If you implement midpoint algorithm and find a one-pixel bias (systematic offset), likely cause is
A) Wrong octant reflections only
B) Off-by-one initial conditions or incorrect choice when p==0
C) Hardware failure only
D) Using Wu’s algorithm instead
Answer: B
74. The midpoint circle algorithm can be used to rasterize circle outlines; filling the interior efficiently typically uses scanline filling between symmetric x pairs for each y. Which cost is then dominant?
A) Per-pixel trig cost
B) Per-scanline span drawing (proportional to radius)
C) Octant reflection only
D) Memory copying only
Answer: B
75. In many textbooks, the update when choosing (x+1, y−1) is simplified to p += 2*(x − y) + 5. If one implements a variant adding p += 2*(x − (y−1)) + 3, the result is
A) Totally different algorithm
B) Algebraically equivalent (different derivation but same integer effect) if arithmetic consistent
C) Always incorrect
D) Only valid for even r
Answer: B
76. The midpoint algorithm’s reflection into octants requires plotting (xc ± x, yc ± y) and (xc ± y, yc ± x). For x=y these may duplicate; implementations often guard against double-plotting by checking equality — true or false?
A) False — duplicates don’t occur
B) True — check avoids plotting same pixel twice
C) True only if r is even
D) False only for r odd
Answer: B
77. If one wants to estimate actual Euclidean error between the plotted pixel center and the true circle boundary, one can compute |f(x,y)|/√(A²+B²) where f(x,y)=x²+y²−r² and A,B are coefficients of linearization. This provides approximate distance. True or false?
A) False — not related
B) True — provides signed distance approximation when linearized
C) Only true for ellipses
D) Only true after scaling by r
Answer: B
78. The midpoint circle algorithm will produce identical pixels as Bresenham’s circle algorithm if both are implemented with the same choice for the equality case p==0 and same step order. True or false?
A) False always
B) True
C) Only for odd radii
D) Only for radii > 10
Answer: B
79. In a GPU fragment shader approach, drawing antialiased circles might evaluate distance to circle per-pixel; compared to midpoint, this approach:
A) Uses integer-only math
B) Provides smoother output but at higher per-pixel computational cost
C) Requires no per-pixel tests
D) Is identical in speed and quality to midpoint always
Answer: B
80. When plotting many circles of varying centers and radii, which data structure can accelerate repeated plotting of same-radius circles?
A) No data structure helps
B) Precomputed circle point tables indexed by radius (cache)
C) Binary search trees only
D) Hashing on centers only
Answer: B
81. The midpoint algorithm is sometimes used to draw thick stroking of circular arcs by drawing adjacent concentric circle offsets — the downside of naive concentric approach is
A) Perfect joins always
B) Imperfect joins and potential holes at joins requiring polygonal stroke handling
C) Faster rendering always
D) No need for anti-aliasing
Answer: B
82. Which of the following best describes the midpoint method’s decision function f evaluated at the midpoint sample?
A) A non-linear trigonometric test
B) A linearized test of the implicit quadratic circle function at a half-step sample
C) A random noise value
D) The gradient of color intensity
Answer: B
83. The midpoint integer updates rely on binomial expansions like (x+1)² − x² = 2x + 1. Because of such identities the algorithm avoids repeated squaring. True or false?
A) False — repeated squaring required
B) True — finite differences use these expansions
C) True only for odd x
D) False only for y
Answer: B
84. Implementing midpoint algorithm in fixed-point arithmetic rather than integer-only can help represent subpixel centers—this is useful when
A) Display always integer centers only
B) You need sub-pixel accuracy for translation or high-resolution rendering
C) Avoiding any arithmetic entirely
D) Reducing memory usage only
Answer: B
85. A corner case to consider in midpoint algorithm is r = 0. The correct plotting behavior should be to plot
A) Nothing
B) Single pixel at center (xc,yc)
C) Entire display filled
D) A line only
Answer: B
86. In some formulations, decision parameter initial p₀ is taken as 5/4 − r for better symmetry when using integer rounding. This is algebraically equivalent to 1 − r when scaled appropriately. True or false?
A) False — entirely different
B) True — equivalent under scaling and integer rounding conventions
C) Only for even r
D) Only in floating point
Answer: B
87. For radius r small (e.g., r=1 or 2), midpoint algorithm still functions but must handle duplicates accordingly; the plotted set is identical to analytical circle points under chosen sampling. True or false?
A) False — algorithm fails for small r
B) True — works for small r with proper handling
C) Only works for r≥3
D) Only works for odd r
Answer: B
88. The midpoint algorithm plotted point density tends to be more uniform around the circle than naive parametric θ-stepping because it increments in x leading to approximately unit x spacing and near-uniform arc coverage in octant — true or false?
A) False — θ-stepping is superior always
B) True
C) True only for r even
D) False for large r only
Answer: B
89. Which of the following best describes the role of the variable ‘y’ in the loop of midpoint algorithm?
A) It is always increased
B) It is decremented sometimes to maintain closeness to the circle as x increases
C) It is used only for plotting symmetric points and not updated
D) It stores color index only
Answer: B
90. When plotting circle pixels on a display with gamma correction, the perceived radius could vary visually if plotted intensities are not gamma-corrected. For midpoint algorithm which plots single full-intensity pixels, one might need to apply gamma correction when combining with anti-aliasing — true or false?
A) False — gamma not relevant
B) True — gamma affects perceived brightness and blending
C) Only true for CRTs
D) Only true for even radii
Answer: B
91. The midpoint formula can be rearranged to produce an update that only depends on previous p and x or y, avoiding recomputing full function. This is an instance of which programming technique?
A) Lazy evaluation
B) Dynamic incremental update (recursive relation)
C) Divide and conquer
D) Backtracking
Answer: B
92. Using the midpoint algorithm in integer arithmetic, plotting speed is roughly proportional to which factor?
A) r²
B) r (number of steps in an octant)
C) log r
D) constant independent of r
Answer: B
93. Drawing circles using midpoint algorithm in real-time graphics (e.g., GUI cursor outline) is efficient because algorithm supports incremental updates when radius changes by ±1 by recomputing from scratch or reusing previous calculations — true or false?
A) False — must recompute completely every time
B) True — incremental strategies and caching can accelerate small radius changes
C) Only true if radius increases
D) Only true for even radii
Answer: B
94. If you want to rasterize a circle with line width greater than 1, a robust approach is to treat the stroke as a filled annulus and fill between two radii using scanline spans; midpoint algorithm can be used to compute outer and inner boundaries. True or false?
A) False — cannot be used for annulus
B) True
C) Only true for integer radii multiples
D) Only works with Wu’s algorithm
Answer: B
95. Which statement about midpoint algorithm and computational error is correct?
A) It accumulates large floating errors by design
B) Using integer finite-difference updates avoids cumulative floating drift typical of parametric methods
C) It uses trigonometry so no errors occur
D) It produces exact analytic circle points always
Answer: B
96. For performance on CPUs with vector instructions, one may vectorize plotting multiple octant reflections simultaneously; main challenge is
A) Lack of symmetry
B) Branch divergence and scatter writes to framebuffer (non-contiguous memory writes)
C) No available registers
D) Too many floating multiplications
Answer: B
97. The midpoint algorithm’s update constants (3, 5, etc.) arise from algebraic simplification of squared differences; the constant ‘3’ specifically comes from which expansion?
A) (x+1)³ − x³
B) (x+1)² − x² = 2x + 1, combined with other terms yields small constants like 3
C) sin(1) expansion
D) log(2) approximation
Answer: B
98. Which of the following is a good test to validate an implementation of midpoint circle algorithm?
A) Compare with Bresenham circle results and analytic distance checks for multiple radii and centers
B) Only test r=1
C) Only verify symmetry but not distances
D) Ensure no pixel is ever plotted twice only
Answer: A
99. The midpoint algorithm can be extended to draw circles in 3D voxel grids (discrete sphere surface intersection) by analogous incremental tests; however complexity increases because you must consider which additional factor?
A) 2D symmetry still applies directly
B) Additional dimension introduces more neighbor candidates and octant/voxel symmetry complexity
C) No change necessary — same as 2D
D) Use Wu’s algorithm only
Answer: B
100. Which property best summarizes the midpoint circle algorithm for use in exam answers?
A) Uses trigonometry for exact samples
B) An efficient integer incremental method using midpoint tests and octant symmetry to rasterize circles
C) Requires floating-point sin/cos tables
D) Only suitable for circles centered at origin
Answer: B