Q.1 Which of the following is a parametric curve representation commonly used in computer graphics?
Hermite Curve
Fourier Series
Laplace Transform
Discrete Cosine Transform
Explanation - Hermite curves are widely used in computer graphics as a parametric representation of curves using endpoints and tangent vectors.
Correct answer is: Hermite Curve
Q.2 Bézier curves are defined using which type of points?
Control Points
Grid Points
Sample Points
Boundary Points
Explanation - Bézier curves use control points to determine the shape of the curve without necessarily passing through all of them.
Correct answer is: Control Points
Q.3 Which property of Bézier curves ensures they lie within the convex hull of their control points?
Convex Hull Property
Affine Invariance
Local Control
Symmetry
Explanation - The convex hull property ensures that Bézier curves stay within the polygon formed by their control points.
Correct answer is: Convex Hull Property
Q.4 In cubic Bézier curves, how many control points are required?
2
3
4
5
Explanation - Cubic Bézier curves require four control points: two endpoints and two handles for shaping the curve.
Correct answer is: 4
Q.5 Which curve representation provides local control over the shape when modifying a control point?
Hermite Curve
B-spline Curve
Bezier Curve
Lagrange Interpolation Curve
Explanation - B-splines allow local control, meaning adjusting one control point affects only part of the curve.
Correct answer is: B-spline Curve
Q.6 What does NURBS stand for in computer graphics?
Non-Uniform Rational B-Splines
Normalized Uniform Rational B-Splines
Non-Uniform Random Basis System
Normal Unitary Rational Basis Surfaces
Explanation - NURBS stands for Non-Uniform Rational B-Splines, a mathematical model for generating and representing curves and surfaces.
Correct answer is: Non-Uniform Rational B-Splines
Q.7 Which of the following is NOT a solid modeling technique?
Boundary Representation (B-Rep)
Constructive Solid Geometry (CSG)
Voxel Representation
Rasterization
Explanation - Rasterization is a rendering process, not a solid modeling technique. B-Rep, CSG, and voxels are solid modeling methods.
Correct answer is: Rasterization
Q.8 A bicubic surface patch requires how many control points?
4
8
12
16
Explanation - A bicubic surface patch is defined by a 4×4 grid of control points, totaling 16 points.
Correct answer is: 16
Q.9 Which blending function is used in Bézier curves?
Bernstein Polynomials
Legendre Polynomials
Chebyshev Polynomials
Hermite Polynomials
Explanation - Bézier curves use Bernstein polynomials as blending functions to interpolate between control points.
Correct answer is: Bernstein Polynomials
Q.10 The process of representing a solid object by its vertices, edges, and faces is called?
Boundary Representation
Constructive Geometry
Wireframe Modeling
Parametric Surface Modeling
Explanation - Boundary Representation (B-Rep) models solids using their boundary elements like vertices, edges, and faces.
Correct answer is: Boundary Representation
Q.11 In B-spline curves, the degree of the polynomial is determined by?
Number of Control Points
Knot Vector
Interpolation Method
Curve Length
Explanation - The knot vector determines the degree of polynomial basis functions in B-splines.
Correct answer is: Knot Vector
Q.12 Which curve passes through all of its control points?
Lagrange Interpolation Curve
Bezier Curve
B-spline Curve
NURBS
Explanation - Lagrange interpolation curves are designed to pass exactly through all specified control points.
Correct answer is: Lagrange Interpolation Curve
Q.13 Which method of solid modeling uses Boolean operations like union, intersection, and difference?
Boundary Representation
Constructive Solid Geometry
Voxel Modeling
Mesh Modeling
Explanation - Constructive Solid Geometry (CSG) builds complex solids using Boolean set operations on primitives.
Correct answer is: Constructive Solid Geometry
Q.14 What is the main advantage of NURBS over B-splines?
NURBS can represent exact circles and ellipses
NURBS require fewer control points
NURBS have lower computational cost
NURBS avoid numerical errors
Explanation - Unlike B-splines, NURBS can exactly represent conic sections like circles and ellipses using rational functions.
Correct answer is: NURBS can represent exact circles and ellipses
Q.15 In parametric surfaces, two parameters are typically denoted as?
x and y
u and v
p and q
m and n
Explanation - Parametric surfaces are defined in terms of two parameters, usually denoted as u and v.
Correct answer is: u and v
Q.16 Which is an example of a primitive solid used in CSG?
Sphere
B-spline
Bezier Curve
NURBS Surface
Explanation - CSG uses primitive solids like spheres, cubes, and cylinders to build complex models.
Correct answer is: Sphere
Q.17 What is the role of a knot vector in B-spline curves?
Defines curve color
Defines curve smoothness and continuity
Defines curve shading
Defines rendering speed
Explanation - Knot vectors in B-splines influence how smoothly the curve transitions between segments.
Correct answer is: Defines curve smoothness and continuity
Q.18 Which of the following representations uses voxels?
Boundary Representation
Constructive Solid Geometry
Volume Representation
Parametric Surfaces
Explanation - Volume representation divides 3D objects into small cubes (voxels) to model internal and external structures.
Correct answer is: Volume Representation
Q.19 In a quadratic Bézier curve, how many control points are used?
2
3
4
5
Explanation - Quadratic Bézier curves require three control points: two endpoints and one control point shaping the curve.
Correct answer is: 3
Q.20 Which surface type can be generated by rotating a curve around an axis?
Sweep Surface
Surface of Revolution
Ruled Surface
Bezier Surface
Explanation - A surface of revolution is formed by rotating a curve around a fixed axis in 3D.
Correct answer is: Surface of Revolution
Q.21 What is the degree of a Bézier curve with 5 control points?
3
4
5
6
Explanation - The degree of a Bézier curve is one less than the number of control points, so 5 points yield a 4th-degree curve.
Correct answer is: 4
Q.22 Which property ensures B-splines are invariant under affine transformations?
Convex Hull Property
Affine Invariance
Local Control
Continuity
Explanation - B-splines are affine invariant, meaning translation, scaling, or rotation of control points transforms the curve consistently.
Correct answer is: Affine Invariance
Q.23 What is the purpose of blending functions in curve generation?
To determine shading
To interpolate curve points
To reduce rendering time
To define surface textures
Explanation - Blending functions determine how control points influence the final curve or surface shape.
Correct answer is: To interpolate curve points
Q.24 Which of these is a ruled surface?
Cylinder
Sphere
Torus
Cone
Explanation - Ruled surfaces are generated by moving a straight line along two guiding curves. Cylinders and cones are ruled surfaces.
Correct answer is: Cylinder
Q.25 Which surface is formed by linearly interpolating between two curves?
Sweep Surface
Ruled Surface
Revolved Surface
Bezier Surface
Explanation - Ruled surfaces are generated by joining corresponding points of two curves using straight lines.
Correct answer is: Ruled Surface