# Solid Modelling MCQ (Multiple Choice Questions)

1. Which solid modelling method does solid structure manipulation through high level?
a) Parametric solid modelling
b) Constructive Solid Geometry (CSG)
c) Feature based modeling
d) Analytical solid modelling

Explanation: Parametric solid modelling does solid structure manipulation through high level with parameterized steps. These steps are modified by users and instantiated to specific parameter values and constraint configurations. The system allows designer to modify entire families of shapes which makes the manipulation level higher compared to other solid modelling methods.

2. Which of the following option defines parametric solid more accurately?
a) Shape and geometry
b) Set of parameters and constraints
c) Fixed script
d) Algebraic coefficients

Explanation: Parametric solid is accurately defined by function of set of parameters and constraints. Whereas fixed script is used to define variant designs, algebraic coefficients define tricubic solids, shape and geometry are used to define constructive solids.

3. In 3-D parametric solids, edge curve comes under which form of function?
a) One parametric variable function
b) Two parametric variable function
c) Three parametric variable functions
d) Constant function

Explanation: Edge curves is one parametric variable function. In order to obtain them, one of the variables out of (u, v, w) is kept free while fixing combination of other two variables at their limiting values and that’s why edge curve comes under one parametric variable function.

4. Which of the following is the correct function to represent parametric solid model?
a) x = x (u, v), y = y (u, v), z = z (u, v)
b) x = x (u), y = y (v), z = z (w)
c) x = x (u, v), y = y (v, w), z = z (w, u)
d) x = x (u, v, w), y = y (u, v, w), z = z (u, v, w)

Explanation: Parametric solid model is represented by x = x (u, v, w), y = y (u, v, w), z = z (u, v, w), three parameter, single valued functions. These functions define the coordinates of the set of points comprising the solid. Here, the parametric variables u, v, w are constrained to the interval [0, 1].

5. What is the main feature of parametric solid modelling?
a) It offers ease to produce flexible designs
b) It has reduced engineering cycle time
c) It gives better integration
d) It allows designer to define entire classes of shapes, not just specific instances

Explanation: Parametric solid modelling allows designer to define entire classes of shapes, not just specific instances. If a designer wants to change all the parameters, in parametric modelling, the designer needs to alter only one parameter and other parameters change accordingly. This is the main advantage offered by parametric modelling over other techniques.

6. Which of the following is two parametric variable function in parametric solids?
a) Edge curve
b) Bounding faces
c) Surfaces
d) Corner points

Explanation: In parametric solids, bounding faces comes under two parametric variable functions as two variables are kept free which results in six possible points. Whereas edge curve is one parametric variable function. Corner points and surfaces are not defined by any functions.

7. What is isoparametric surface in parametric solids?
a) Surface parallel to patch faces of solid
b) Surface perpendicular to patch faces of solid
c) Surface which passes through each point of solid
d) Surface which passes through complete solid

Explanation: Isoparametric surface is the surface which passes through each point of solid. It is a surface within the solid on which one of the three parametric variables is kept constant while other two are fixed. There is single surface of each family that passes through each point.

8. Ordinary parametric solid always has eight and only eight corner points.
a) True
b) False

Explanation: Ordinary parametric solid consists of the 8 corner points with coordinates (0, 0, 0), (1, 0, 0), (0, 1, 0), (0, 0, 1), (1, 1, 0), (1, 0, 1), (0, 1, 1), (1, 1, 1) along with 12 curves that define the edges, and 6 patches that define the faces. A rectangular solid is very simple example of it.

9. Which of the following statement is not true about constraint system of parametric solid?
a) In variational geometric constraint, several geometric entities need to be placed simultaneously in relation to each other
b) In parametric geometric constraint, several elements are placed simultaneously in relation to other elements
c) For planar geometric constraint efficient solver is provided
d) For spatial constraint there is no mature technology developed to solve problems

Explanation: In parametric geometric constraint, only a single element is placed simultaneously in relation to other elements that are already placed. While several elements are placed in case of variational geometric constraint system which is not possible in case of constraint system of parametric solid.

10. Which of the following software is not used for parametric solid modelling?
a) Solidworks
b) Creo
c) MATLAB
d) CATIA

Explanation: Solidworks, Creo, CATIA are used to generate parametric solid model. These software are used in manufacturing industries for 3-D parametric modelling. MATLAB is used to create scripts which include programming language for mathematical computations.

11. The parametric equation defines only the points comprising the boundary elements of the solid.
a) True
b) False

Explanation: The parametric equation defines not only the points comprising the boundary elements of the solid but also all the points interior to it. The parametric functions are used to define interior and exterior of the solid which include coordinate of the set of the points.

## Solid Modelling MCQ on Tricubic Solid

12. Which of the following equation is the algebraic form of the tricubic solid?
a) p (u, v, w) = $$∑_{i=0}^3 ∑_{j=0}^3 ∑_{k=0}^3$$ aijk ui vj wk
b) p (u, v, w) = $$∑_{i=0}^1 ∑_{j=0}^1 ∑_{k=0}^1$$ aijk ui vj wk
c) p (u, v, w) = $$∑_{i=0}^3 ∑_{j=0}^3 ∑_{k=0}^3$$ aijk u3 v3 w3
d) p (u, v, w) = $$∑_{i=0}^3 ∑_{j=0}^3 ∑_{k=0}^3$$ aijk u v w

Explanation: The algebraic form of the tricubic solid is given by the equation p (u, v, w) = $$∑_{i=0}^3 ∑_{j=0}^3 ∑_{k=0}^3$$ aijk ui vj wk. The аijk vectors are the algebraic coefficients of the solid and u, v, w are the parametric variables which are restricted in the interval 0 to 1.

13. What is the result of manipulation of tangent and twist vectors of tricubic solid provided that corner points of the solid are fixed?
a) Generation of flat faces
b) Generation of irregular faces
c) Generation of concave and convex faces
d) Generation of curved faces

Explanation: In tricubic solid, by manipulating tangent and twist vectors provided that corner points of the solid are fixed, we get concave and convex faces generated as these vectors provide variety of ways to control the exterior shape of the solid. Here, the shape formed is concave and convex.

14. Which vectors define the boundary conditions for tricubic solid?
a) Tangent vectors, twist vectors
b) Corner point, tangent vectors, twist vectors
c) Corner point, triple mixed partial vector
d) Corner point, tangent vectors, twist vectors, triple mixed partial vector

Explanation: There are 8 vectors defining boundary conditions at each of the 8 corners, resulting in total of 64 vectors of tricubic solid. The boundary conditions found are; a corner point, three tangent vectors, three twist vectors and a triple mixed partial vector.

15. Tangent vectors and twist vectors control the shape of tricubic solid in solid modelling.
a) True
b) False

Explanation: In solid modelling, tangent vectors and twist vectors change and control the shape of Hermite curves and surfaces, so do they also control the shape of tricubic solid. The interior distribution of parametric variable is also controlled by these vectors.

16. Which of the following mathematician developed a relationship between patches and hyperpatches of the tricubic solid?
a) Gauss
b) Euler and Lagrange
c) Stanton and Crain
d) Ron Goldman

Explanation: Stanton and Crain developed a relationship between patches and hyperpatches of the tricubic solid, treating 64 hyperpatch parameters as 4 sets of 16 parameter which allows user to understand more easily the basis-function properties. They also defined the algebraic and geometric forms for the same.

17. Which of the following is the correct patch function for tricubic solid?
a) G(w) = Fi (w) Bi
b) G(w) = Fib (w) Bi
c) G(w) = Fib (w) Bib
d) G(w) = Fi (w) Bib

Explanation: The patch function for tricubic solid is defined as G(w) = Fib (w) Bi, it is used to transform equations from point form to geometric form. The equation defines a bicubic patch corresponding to a specific value of w for given hyperpatch array.

18. What is the tricubic Hermite solid in solid modelling?
a) Natural continuation of the cubic forms for curves only
b) Natural continuation of the cubic and bicubic forms for curves only
c) Natural continuation of the cubic and bicubic forms for curves and surfaces
d) Natural continuation of the bicubic forms for curves and surfaces

Explanation: Tricubic Hermite solid in solid modelling is defined as the natural continuation of the cubic and bicubic forms for curves and surfaces. Parametric and tricubic Hermite solid model forms of multivariate interpolation functions on the lower dimensions form.

19. Which of the following are the tangent vectors of the tricubic solid?
a) $$(\frac{\partial}{\partial u} , \frac{\partial}{\partial v} , \frac{\partial}{\partial w})$$
b) $$(\frac{\partial^2}{\partial u \partial v} , \frac{\partial^2}{\partial v \partial w} , \frac{\partial^2}{\partial w \partial u})$$
c) $$\frac{\partial^3}{\partial u \partial v \partial w}$$
d) $$\frac{\partial}{\partial u \partial v} , \frac{\partial}{\partial v \partial w}$$

Explanation: Boundary conditions for tricubic solid are defined by 8 vectors naming tangent, twist and triple mixed partial vectors. Tangent vectors are given by $$(\frac{\partial}{\partial u} , \frac{\partial}{\partial v} , \frac{\partial}{\partial w})$$. Twist vectors are given by $$(\frac{\partial^2}{\partial u \partial v} , \frac{\partial^2}{\partial v \partial w} , \frac{\partial^2}{\partial w \partial u})$$ and triple mixed partial vectors are given by $$\frac{\partial^3}{\partial u \partial v \partial w}$$.

20. Computing the parametric derivatives of the tricubic solid is different process than those for the bicubic patch.
a) True
b) False

Explanation: Computing the parametric derivatives of the tricubic solid involves similar process to those for the bicubic patch. Tricubic function is expressed as three independent variables and partial derivative is computed and for the bicubic patch, same process is followed to compute parametric derivative.

21. Which mathematician widely worked on the tricubic interpolation method used in solid modelling?
a) Leonhard Euler
b) John Conway
c) Stanton and Crain
d) Lekien and Marsden

Explanation: From the inspiration of studies of ocean dynamics, Lekien and Marsden provided their tricubic technique. It is used for either time dependent two-dimensional flows or three-dimensional time independent flows.

22. Which of the following interpolation method is defined on a regular grid to obtain the values at points in 3-D space of the tricubic solid?
a) Bicubic interpolation
b) Tricubic interpolation
c) Cubic interpolation
d) Hermite interpolation

Explanation: Tricubic interpolation method is defined on a regular grid to obtain the values at points in 3-D space of the tricubic solid. The interpolation function is given by the form p (u, v, w) = $$∑_{i=0}^3 ∑_{j=0}^3 ∑_{k=0}^3$$ aijk ui vj wk. It is used to interpolate values and the measured derivatives at the grid points.

23. In solid modelling, what does the parameter space of a solid consist of?
a) Three-dimensional parameter spaces
b) Four-dimensional parameter spaces
c) Two-dimensional parameter spaces
d) One-dimensional parameter spaces

Explanation: In solid modelling, the parameter space of a solid consists of four-dimensional parameter spaces defined by (u, v, w, x), (u, v, w, y) and (u, v, w, z) coordinates. This parameter space differs from that of curve or surface because we must account for an additional parametric variable.

## Solid Modelling MCQ on Curves and Surfaces Embedded in a Solid

24. Which mathematician introduced the term curvilinear coordinate system for solids?
a) Gauss
b) Euler
c) Euclid
d) Lamé

Explanation: French mathematician Lamé introduced the term curvilinear coordinate system for solids. The term is derived from the fact that coordinate surfaces of curvilinear system are curved. The example can be spherical and cylindrical polar coordinates.

25. Which of the following curve is the result of holding two of the tricubic parametric variables fixed at some constant values for a solid?
a) Parametric curve
b) Isoparametric curve
c) Hermite cubic curve
d) Bezier curve

Explanation: An isoparametric curve is the result of holding two of the tricubic parametric variables fixed at some constant values for a solid. Two parametric variables u and v are assigned to some constants which also generates two isoparametric surfaces.

26. Which coordinate system is required to define both curves and surfaces in parametric solids?
a) Translational coordinate system
b) 1-D curvilinear coordinate system
c) 2-D curvilinear coordinate system
d) 3-D curvilinear coordinate system

Explanation: In parametric solids, 3-D curvilinear coordinate system is required to define both curves and surfaces. Whereas with the help of 2-D curvilinear coordinate system, only curves can be defined in case of parametric surfaces. Isoparametric curves and surfaces defined using 3-D curvilinear coordinate system is one of the examples of it.

27. Which of the following equation defines the nonisoparametric curve in model space?
a) c (t) = u (t) + v (t) + w (t)
b) c (x, y, z) = p [u (t), v (t), w (t)
c) c (t) = u (t) – v (t) – w (t)
d) c (u, v, w) = p [u (t), v (t), w (t)

Explanation: The nonisoparametric curve mapped in a tricubic solid in model space is expressed as c (x, y, z) = p [u (t), v (t), w (t)]. The curvilinear vector components of points on the curve are c (t) = u (t) + v (t) + w (t). The additional parametric variable t is used to define the curve.

28. A parametric cell is a sub element of the solid with six boundary surfaces.
a) True
b) False

Explanation: A parametric cell is bounded by six isoparametric boundary surfaces. Such a cell is orthogonal if the curve nets of the three families of isoparametric surfaces. This cell is defined on the orthogonal parametric curve nets.

29. Which of the following expression gives the vector components of the surface patch in parameter space?
a) t (s, t) = u (s, t) + v (s, t) + w (s, t)
b) r (x, y, z) = p [u (s, t), v (s, t), w (s, t)
c) t (s, t) = u (s, t) – v (s, t) – w (s, t)
d) r (u, v, w) = p [u (s, t), v (s, t), w (s, t)

Explanation: A surface patch is mapped in both the unit cube of parameter space and model space. The surface patch in parameter space is expressed as t (s, t) = u (s, t) + v (s, t) + w (s, t) while in model space the expression is r (x, y, z) = p [u (s, t), v (s, t), w (s, t)].

30. What are the trimmed boundaries in solid modelling?
a) Regular and nonisoparametric boundaries
b) Irregular and isoparametric boundaries
c) Irregular and nonisoparametric boundaries
d) Regular or isoparametric boundaries

Explanation: In solid modelling, trimmed boundaries basically are irregular and nonisoparametric boundaries. Variety of complex solids can be modeled if they are permitted to have trimmed boundaries. Solids with clipped corners can be one of the examples of trimmed boundaries.

31. What do the isoparametric curves of parametric solid system consist of?
a) Network of crossing solids
b) Network of crossing surfaces
c) Network of crossing curves
d) Network of crossing lines

Explanation: An isoparametric curves of parametric solid system consist of network of crossing curves. These curves help the user to visualize the shape of surface. When the respective surface is selected, all of the isoparametric curves highlight.

32. What does spatial occupancy enumeration refer to in solid modelling?
a) Spatial cells occupied by the solid
b) Spatial cells occupied by the surface
c) Spatial cells occupied by the curve
d) Spatial cells occupied by the line

Explanation: Spatial occupancy enumeration refer to spatial cells occupied by the solid. These cells are called as voxels which are arranged in a fixed spatial grid. Each cell is represented by the coordinates of a single point in that particular solid model.

33. In parametric solid modelling, the solid surface is undefined initially in either parameter space or model space.
a) True
b) False

Explanation: In parametric solid modelling, the solid surface is need to be defined initially in either parameter space or model space, depending on the modelling situation. It is conventionally required to define the surface in order to express the vector components of it, so the rest of the computation can be done correctly.

## Solid Modelling MCQ on Instances and Parameterized Solids

34. Which of the following statement is incorrect about group technology in solid modelling?
a) It is easy to validate and use
b) Models are unquestionably concise
c) Modeling system based on it is highly specialized
d) Number of useful generic primitives is unlimited

Explanation: In group technology, numbers of useful generic primitives are limited, though large. A large range of generic primitives is required in order to have wide application but the available count for these primitives is limited.

35. What is the initial shape of the solid in simple scaling transformation called as?
a) Instance
b) Primitive
c) Unit
d) Domain

Explanation: The initial or original shape of the solid is called as primitive shape and the new shape obtained from transformation is called as an instance. While domain is the region of presentation and unit is used to determine the quantity of the respective solid.

36. Which of the following operation in solid modelling is used to transform the unit cube into a new shape?
a) Translation
b) Rotation
c) Scaling
d) Reflection

Explanation: There are several ways of transforming the unit cube into a new shape by using scaling operation. Equal scaling of all three-dimensional components gives new cubes while differential scaling gives a variety of rectangular solids. Each new cube or rectangular solid is a particular instance of the initial cube.

37. What is the main advantage of group technology in part designing?
a) Models are easy to validate and use
b) Many manufactured parts can be grouped into classes of same shapes
c) The standardization in production is encouraged
d) It uses Boolean combination of instances

Explanation: The central thesis and main advantage of group technology is, many manufactured parts can be grouped into classes of same shapes, where individual members are distinguished by different key dimensions. A single family of shapes is called as generic primitive, and individual members are primitive instances.

38. Which of the following is the correct condition applied while transforming Z section into instances, where a, b, h, l, t are the dimensions of the Z section of solid model?
a) a, b, h, l, t < 0
b) a < 2t, h < 4t
c) a, b, h, l, t > 0
d) a < 2t, h > 4t

Explanation: For any solid model, while transforming Z section into instances following conditions are applied and easily checked: a, b, h, l, t > 0, b <= a, a > 2t and h > 4t. It is used to verify the validity of data specifying a model and provides better representation of instances.

39. What type of topology is used to restrict the most parameterized-shape procedures in solid modelling?
a) Single topology
b) Variable topology
c) Dual topology
d) Mesh topology

Explanation: Most of the parameterized-shape procedures are restricted by a single topology. We can develop parameterized shapes with variable topologies, such as n-called structure but single topology is used to develop the most parameterized shapes.

40. Which of the following option is used to compute complete mathematical representation of solid?
a) Domain
b) Transformation
c) Algorithm
d) Dimension

Explanation: Geometric modelling algorithms are used to compute complete mathematical representation of solid. Dimensions are used to define the shapes of simple objects. Transformation is used to define new shapes and domain gives the area of representation for solids.

41. What is the main drawback of primitive instancing technique in parameterized solids?
a) Lack of means for combining instances
b) Difficulty of writing algorithms for computing properties of represented solids
c) Complex technique to create solid models
d) Difficult to obtain the instances from algorithms

Explanation: In parameterized solids, the main drawback of primitive instancing technique is the difficulty of writing algorithms for computing properties of represented solids. There is need to build family specific information into the algorithms and therefore each generic primitive is supposed to treated as a special case.

42. Simple transformations affect the geometry and topology of a shape of solid.
a) True
b) False

Explanation: Simple transformations create an unlimited variety of specific instances of an original shape. But such transformations only affect the geometry of a shape of solid and not the topology of that respective shape.

More MCQs on Solid Modelling:

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