Ellipse Algorithms in Computer Graphics MCQ Questions and Answers
1. The main purpose of ellipse drawing algorithms is to
A) Draw straight lines
B) Generate rasterized ellipses efficiently using integer arithmetic
C) Compute 3D models
D) Fill polygons
Answer: B
2. The midpoint ellipse algorithm is conceptually similar to which other algorithm?
A) DDA
B) Wu’s algorithm
C) Midpoint circle algorithm
D) Scanline polygon fill
Answer: C
3. The general equation of an ellipse centered at the origin is
A) x² + y² = r²
B) (x² / a²) + (y² / b²) = 1
C) x + y = a
D) x² − y² = 1
Answer: B
4. In an ellipse, the parameter ‘a’ represents
A) Minor axis length
B) Focal distance
C) Semi-major axis length
D) Total axis length
Answer: C
5. The parameter ‘b’ in an ellipse represents
A) Circle radius
B) Axis ratio
C) Semi-minor axis length
D) Perimeter
Answer: C
6. The midpoint ellipse algorithm divides the drawing process into
A) One region
B) Two regions (Region 1 and Region 2)
C) Four regions
D) Eight regions
Answer: B
7. In Region 1 of the ellipse, which slope condition holds true?
A) dy/dx < 1
B) dy/dx > 1
C) dy/dx = 0
D) dy/dx = ∞
Answer: A
8. In Region 2 of the ellipse, which slope condition holds true?
A) dy/dx < 1
B) dy/dx > 1
C) dy/dx = 0
D) dy/dx = constant
Answer: B
9. The implicit equation used in the midpoint ellipse algorithm is
A) f(x, y) = x² + y² − r²
B) f(x, y) = b²x² + a²y² − a²b²
C) f(x, y) = x² − y² − a²
D) f(x, y) = ax + by + c
Answer: B
10. The midpoint ellipse algorithm starts drawing from
A) (a, 0)
B) (0, 0)
C) (0, b)
D) (b, 0)
Answer: C
11. The initial decision parameter for Region 1 is
A) p₀ = 1 − a
B) p₀ = b² − a²b + ¼a²
C) p₀ = a² − b²
D) p₀ = b² + a²
Answer: B
12. The Region 1 decision parameter tests the midpoint between which two pixels?
A) East and South pixels
B) East and South-East pixels
C) North and South pixels
D) West and East pixels
Answer: B
13. When p₁ < 0 in Region 1, the next point chosen is
A) (x+1, y)
B) (x+1, y−1)
C) (x, y−1)
D) (x−1, y)
Answer: A
14. When p₁ ≥ 0 in Region 1, the next point chosen is
A) (x, y+1)
B) (x+1, y−1)
C) (x−1, y−1)
D) (x+2, y)
Answer: B
15. In Region 2, the algorithm increments which coordinate at each step?
A) x only
B) y only
C) Both x and y
D) None
Answer: B
16. The decision parameter for Region 2 is initialized at the point where
A) x = y
B) 2b²x = 2a²y
C) x = a
D) y = b
Answer: B
17. The midpoint ellipse algorithm exploits which symmetry?
A) 2-way
B) 4-way symmetry about major and minor axes
C) 8-way
D) 16-way
Answer: B
18. To obtain all points of an ellipse, computed points are reflected across
A) X-axis only
B) Both X and Y axes
C) 45° line
D) Origin
Answer: B
19. The stopping condition in Region 1 occurs when
A) x > y
B) 2b²x ≥ 2a²y
C) x < y
D) y > b
Answer: B
20. The per-step update formula for Region 1 when p < 0 is
A) p = p + 2b²x + b²
B) p = p − 2a²y
C) p = p + a²b
D) p = p + 2a²y
Answer: A
21. For Region 1, when p ≥ 0, the update is
A) p = p + b²
B) p = p + 2b²x − 2a²y + b²
C) p = p − a²
D) p = p + 2a²y
Answer: B
22. In Region 2, if p < 0, the next pixel is
A) (x+1, y)
B) (x+1, y−1)
C) (x, y−1)
D) (x, y+1)
Answer: B
23. In Region 2, when p ≥ 0, the next pixel is
A) (x+1, y)
B) (x−1, y)
C) (x, y−1)
D) (x−1, y−1)
Answer: C
24. The decision parameter in Region 2 is updated using
A) p = p + a² − 2a²y + 2b²x
B) p = p − 2b²
C) p = p + 2a²x + 3
D) p = p − a²b
Answer: A
25. The algorithm terminates when
A) y > 0
B) y = 0
C) x > y
D) x = 0
Answer: B
26. The ellipse function value f(x, y) > 0 means the midpoint is
A) Outside the ellipse
B) Inside the ellipse
C) On the ellipse
D) Undefined
Answer: A
27. When f(x, y) < 0, the midpoint lies
A) Outside ellipse
B) Inside ellipse
C) On the ellipse
D) Undefined
Answer: B
28. The midpoint ellipse algorithm is more efficient than the parametric approach because it avoids
A) Integer arithmetic
B) Trigonometric computations (sin, cos)
C) Coordinate updates
D) Symmetry
Answer: B
29. The major advantage of midpoint ellipse algorithm is
A) Requires many divisions
B) No symmetry used
C) Only uses addition, subtraction, and multiplication
D) Uses floating point
Answer: C
30. Ellipse algorithms are commonly implemented using
A) Tangent functions
B) Finite difference incremental methods
C) Recursive subdivision
D) Monte Carlo sampling
Answer: B
31. The initial point of the ellipse (0, b) is chosen because
A) It minimizes error
B) The slope at that point is 0
C) f(x,y)=0 there
D) It lies on x-axis
Answer: B
32. The implicit function for the ellipse is used for
A) Texture mapping
B) Lighting
C) Deciding which pixel is closer to the true ellipse
D) Clipping
Answer: C
33. The ellipse function f(x, y) = b²x² + a²y² − a²b² = 0 represents points
A) Inside the ellipse
B) On the ellipse boundary
C) Outside ellipse
D) Undefined
Answer: B
34. Which ellipse algorithm divides computation into regions based on slope?
A) Midpoint ellipse algorithm
B) Parametric ellipse
C) DDA
D) Bresenham ellipse
Answer: A
35. The Region 2 initialization uses the last point from
A) Region 1
B) Region 3
C) Circle
D) Axis
Answer: A
36. For a circle, a = b. The midpoint ellipse algorithm reduces to
A) Wu’s line algorithm
B) Midpoint circle algorithm
C) Liang–Barsky clipping
D) Polygon filling
Answer: B
37. The midpoint ellipse algorithm is best suited for
A) Thick lines
B) Raster ellipse outlines
C) Clipping polygons
D) Texture generation
Answer: B
38. If a > b, the ellipse is
A) Horizontally stretched
B) Vertically stretched
C) Circular
D) None
Answer: A
39. If b > a, the ellipse is
A) Horizontal
B) Vertically stretched
C) Circular
D) Oblique
Answer: B
40. The midpoint ellipse algorithm uses what type of arithmetic?
A) Floating point
B) Integer or fixed-point arithmetic
C) Fractional
D) Binary-coded decimal
Answer: B
41. In Region 1, the slope magnitude |dy/dx| is
A) Less than 1
B) Equal to 1
C) Greater than 1
D) Infinity
Answer: A
42. In Region 2, the slope magnitude |dy/dx| is
A) Less than 1
B) Greater than 1
C) Equal to 1
D) Zero
Answer: B
43. The major reason the ellipse algorithm splits into two regions is to
A) Handle color intensity
B) Handle the change in slope (>1 vs <1)
C) Reduce memory
D) Add anti-aliasing
Answer: B
44. The ellipse is symmetric in
A) One quadrant only
B) All four quadrants
C) X-axis only
D) Y-axis only
Answer: B
45. The incremental computation of ellipse points is based on evaluating
A) The difference between f at successive midpoints
B) The sum of slopes
C) The parametric angle θ
D) Random samples
Answer: A
46. The midpoint ellipse algorithm is a special case of
A) Numerical integration
B) Finite difference methods for implicit curves
C) DDA
D) Recursive functions
Answer: B
47. The Region 1 condition 2b²x < 2a²y ensures the slope remains
A) Less than 1
B) Greater than 1
C) Constant
D) Undefined
Answer: A
48. The Region 2 condition 2b²x ≥ 2a²y ensures slope becomes
A) Less than 1
B) Greater than 1
C) Constant
D) Zero
Answer: B
49. If both a and b are equal, ellipse becomes a
A) Parabola
B) Circle
C) Line
D) Rectangle
Answer: B
50. The time complexity of midpoint ellipse algorithm is
A) O(a² + b²)
B) O(max(a, b))
C) O(a × b)
D) Constant
Answer: B
51. To draw filled ellipses, one can modify the algorithm by
A) Using Wu’s method
B) Drawing horizontal spans between symmetric points
C) Using polygon clipping
D) Scaling a circle
Answer: B
52. The midpoint ellipse algorithm can be adapted for
A) Lines only
B) Arcs and partial ellipses
C) Circles only
D) Curves of order 3
Answer: B
53. If the ellipse is centered at (xc, yc), the plotted points are offset as
A) (±x + xc, ±y + yc)
B) (x − xc, y − yc)
C) (x, yc) only
D) (xc, yc)
Answer: A
54. Which variable decreases in both regions of the ellipse algorithm?
A) x
B) y
C) p
D) None
Answer: B
55. Which variable always increases per iteration in Region 1?
A) x
B) y
C) a
D) b
Answer: A
56. The ellipse equation in integer form helps avoid
A) Addition
B) Subtraction
C) Floating-point multiplications
D) Division by zero
Answer: C
57. The decision variable in ellipse algorithm decides
A) Which pixel is closer to the ellipse boundary
B) The color intensity
C) The radius
D) The speed
Answer: A
58. The midpoint ellipse algorithm draws only
A) One quadrant
B) One quadrant then reflects across axes
C) The entire ellipse directly
D) Half ellipse
Answer: B
59. The primary difference between circle and ellipse midpoint algorithms is
A) Use of sine/cosine
B) Two-region handling due to different slopes
C) No symmetry
D) Floating arithmetic
Answer: B
60. The point (a, 0) corresponds to
A) Minor axis end
B) Major axis end
C) Center
D) None
Answer: B
61. The point (0, b) corresponds to
A) Major axis end
B) Minor axis end
C) Origin
D) Focal point
Answer: B
62. The algorithm stops when
A) x = a
B) y = 0
C) p = 0
D) x = 0
Answer: B
63. The slope of tangent at (x, y) on an ellipse is
A) −x/y
B) −(b²x)/(a²y)
C) x/y
D) (a²x)/(b²y)
Answer: B
64. Ellipse algorithm output is approximate because
A) It uses exact floating values
B) Rasterization rounds continuous coordinates to pixel grid
C) It ignores symmetry
D) It doesn’t use p
Answer: B
65. The decision parameter is initialized using
A) Trial and error
B) Substitution of midpoint into ellipse equation
C) Circle approximation
D) Pixel averaging
Answer: B
66. The midpoint ellipse algorithm belongs to which generation category?
A) Non-incremental
B) Incremental (raster scan) algorithms
C) Recursive
D) Analytical
Answer: B
67. The implicit ellipse function f(x,y)=b²x²+a²y²−a²b²=0 represents
A) A hyperbola
B) The set of all ellipse boundary points
C) Straight lines
D) Circle
Answer: B
68. A circle is a special case of an ellipse with
A) a = 0
B) b = 0
C) a = b
D) a ≠ b
Answer: C
69. The midpoint ellipse algorithm draws symmetric points about
A) 45° line
B) Both coordinate axes
C) Only Y-axis
D) Diagonal
Answer: B
70. Ellipse rasterization algorithms are necessary because computer screens are
A) Analog
B) Discrete pixel grids
C) Infinite resolution
D) Non-digital
Answer: B
71. The midpoint ellipse algorithm starts drawing from which axis?
A) X-axis
B) Y-axis (top of ellipse)
C) Origin
D) Random point
Answer: B
72. The ellipse can be represented parametrically as
A) x = r cos θ, y = r sin θ
B) x = a cos θ, y = b sin θ
C) x = a + b, y = a − b
D) x = a sin θ, y = b cos θ
Answer: B
73. The parametric representation of an ellipse is inefficient for raster plotting because
A) It uses integer arithmetic
B) It involves trigonometric computations (sin, cos)
C) It cannot plot symmetric points
D) It has only one region
Answer: B
74. The midpoint ellipse algorithm replaces trigonometric operations with
A) Incremental integer updates
B) Division and exponentiation
C) Complex numbers
D) Floating logarithms
Answer: A
75. The slope of the ellipse at (a,0) is
A) Infinite
B) −1
C) 0
D) Undefined
Answer: C
76. The slope of the ellipse at (0,b) is
A) 0
B) Infinite (vertical tangent)
C) 1
D) −1
Answer: B
77. Which of the following statements is true about midpoint ellipse algorithm?
A) It computes points for all regions simultaneously
B) It processes Region 1 and Region 2 separately due to changing slope
C) It needs sin θ tables
D) It starts from (a,0) only
Answer: B
78. The implicit function for ellipse is used in midpoint algorithm because
A) It simplifies pixel coloring
B) It allows decision-making using only arithmetic signs
C) It defines parametric coordinates
D) It eliminates need for axes
Answer: B
79. The decision parameter in Region 2 decreases faster because
A) a < b
B) y changes faster than x
C) It uses small increments
D) It stops early
Answer: B
80. The midpoint ellipse algorithm maintains numerical stability because it
A) Uses exponential growth
B) Avoids cumulative floating errors via integer arithmetic
C) Uses large lookup tables
D) Ignores slope changes
Answer: B
81. Which step ensures the midpoint ellipse algorithm correctly transitions from Region 1 to Region 2?
A) When p = 0
B) When 2b²x ≥ 2a²y
C) When x = 0
D) When y = 0
Answer: B
82. The midpoint ellipse algorithm ensures even distribution of pixels along the ellipse by
A) Random selection
B) Using incremental slope-based region changes
C) Using sine lookup tables
D) Increasing radius dynamically
Answer: B
83. The midpoint ellipse algorithm computes points for which part of the ellipse before reflection?
A) Half ellipse
B) First quadrant only
C) Full ellipse
D) Random region
Answer: B
84. The implicit equation f(x, y) = b²x² + a²y² − a²b² is zero for
A) Points inside ellipse
B) Points outside ellipse
C) Points exactly on the ellipse boundary
D) Points on x-axis
Answer: C
85. The midpoint ellipse algorithm chooses the next pixel based on
A) Distance from origin
B) Angle with x-axis
C) Sign of the decision parameter
D) Major axis orientation
Answer: C
86. The midpoint ellipse algorithm is called “midpoint” because
A) It uses midpoint of the line segment
B) It evaluates the ellipse function at the midpoint between two candidate pixels
C) It starts at middle of the ellipse
D) It calculates average of a and b
Answer: B
87. The primary output of the midpoint ellipse algorithm is
A) Analytical equation
B) Angle data
C) Discrete pixel coordinates approximating ellipse
D) Vector equations
Answer: C
88. When plotting an ellipse, which axis is considered the “major” axis?
A) The longer axis of the two (a > b)
B) The y-axis only
C) The x-axis only
D) The minor axis
Answer: A
89. When a < b, the major axis is
A) X-axis
B) Y-axis
C) 45° line
D) None
Answer: B
90. If ellipse parameters a = 10, b = 5, the ellipse is
A) Circular
B) Horizontally elongated
C) Vertically elongated
D) Parabolic
Answer: B
91. The decision parameter for Region 1 is initialized by substituting which coordinates into f(x,y)?
A) (x+1, y−½)
B) (x, y−1)
C) (x−½, y)
D) (x+½, y+½)
Answer: A
92. The decision parameter for Region 2 is initialized by substituting which coordinates into f(x,y)?
A) (x−1, y)
B) (x+½, y−1)
C) (x, y−½)
D) (x+1, y+1)
Answer: B
93. The ellipse rasterization process is slower than a line rasterization because
A) It uses double buffering
B) It needs trigonometric functions
C) It involves more conditional regions and symmetry calculations
D) It uses floating-point division
Answer: C
94. When a and b are large, the ellipse appears visually close to
A) A circle
B) A rectangle
C) A parabola
D) A line
Answer: A
95. The ellipse algorithm can be generalized to arbitrary rotation by applying
A) Shear transformation
B) Rotation transformation using rotation matrix
C) Translation only
D) Clipping
Answer: B
96. The midpoint ellipse algorithm assumes axes are aligned with
A) Arbitrary lines
B) Coordinate axes (no rotation)
C) Diagonals
D) None
Answer: B
97. The midpoint ellipse algorithm stops after how many reflections?
A) 2
B) 4 (using quadrant symmetry)
C) 8
D) 1
Answer: B
98. To optimize drawing, many implementations precompute
A) Trigonometric tables
B) Random numbers
C) a² and b² constants used in updates
D) Line equations
Answer: C
99. Which of the following algorithms draws ellipses efficiently without floating point computation?
A) DDA
B) Parametric ellipse method
C) Midpoint ellipse algorithm
D) Wu’s algorithm
Answer: C
100. The midpoint ellipse algorithm is widely used in
A) Data encryption
B) Raster graphics systems for ellipse and arc generation
C) Audio processing
D) Database indexing
Answer: B