This set of Solid Modelling Multiple Choice Questions & Answers (MCQs) focuses on “Controlled Deformation Solids”.

1. Which mathematician developed a technique in solid modelling to deform solid by deforming the space in which it is embedded?

a) Barr

b) Coquillart

c) Chang and Rockwood

d) Sederberg and Parry

View Answer

Explanation: Sederberg and Parry developed a technique in solid modelling to deform solid by deforming the space in which it is embedded. The technique deforms solid geometric modes in free form manner. It is based on trivariate Bernstein polynomials and used for sculpturing models.

2. What’s the purpose of axial deformation technique in controlled deformation solids?

a) To control transformations

b) To control size of domain

c) To control shaping operations

d) To control orientations

View Answer

Explanation: Axial deformation is used to control shaping operations such as scaling, bending, twisting, and stretching by reference to some convenient axis in which user induce the desired deformations subsequently to be passed on to the model.

3. Which of the following transformation is used to deform shapes in a controlled way in solid modelling?

a) Linear transformation

b) Nonlinear transformation

c) Rigid transformation

d) Rotation transformation

View Answer

Explanation: Nonlinear transformation is used to deform shapes in a controlled way in order to create new shapes. To deform any curve, a deformation of the x axis is defined first and then relationship between parametric variables involved is defined. The deformed curve is then written in terms of unit vector.

4. Which of the following expression is used to map the curve for trivariate solid?

a) pi = p [u(t), v(t), w(t)]

b) pi = p [u(t), v(t)]

c) p’= mm’ + nn’

d) p’= r[t(u)] +pm

View Answer

Explanation: In three-dimensions, expression used to map the curve for trivariate solid p (u, v, w) is pi = p [u(t), v(t), w(t)]. The curve for solid is defined first and then embedded in a normalized parametric space u, v, w. For bivariate surface, expression pi = p [u(t), v(t)] is used to map the curve. Deformed shape given by equation p’= r[t(u)] +pm is mapped by p’= mm’ + nn’ with respect to a transformed basis.

5. The hyperpatch is used as a solid modelling primitive.

a) True

b) False

View Answer

Explanation: The hyperpatches are represented using surfaces and curves in two-dimensional space similar to lines, circles, etc. All two-dimensional contours are counted as valid primitives. Therefore, hyperpatch is also a solid modelling primitive.

6. Which of the following statement is incorrect about free-form deformation (FFD) technique in solid modelling?

a) It can be used with any solid modelling scheme

b) It works with surfaces of any formulation or degree

c) It is cheaper technique relatively

d) It can be applied to surfaces or polygonal models

View Answer

Explanation: Free-form deformation technique is quite costly. In this method, local FFD forms a planar boundary with undeformed portion of the object. In order to create one arbitrary boundary curve, it is required to begin with FFD which is already in deformed orientation and deform it to more extent, which costs relatively higher.

7. What are the two major components of axial deformation in solid modelling?

a) Axial curve, set of global coordinate frames

b) Axial curve, set of local coordinate frames

c) Set of global coordinate frames, shape functions

d) Axial curve, shape functions

View Answer

Explanation: In solid modelling, the two major components of axial deformation are axial curve and set of local coordinate frames. An object can be deformed using this axial curve. By adjusting this curve and set of user defined local coordinate frames, the new position of the object can be computed.

8. Which of the following mathematicians described a method for sculpting B-Spline surfaces in solid models?

a) Gleicher and Witkin

b) Light and Gossard

c) Bartels and Beatty

d) Celniker and Welch

View Answer

Explanation: Celniker and Welch described a method for sculpting B-Spline surfaces that leaves a set of local geometric constraints invariant such as interpolated points and curves. While Gleicher and Witkin, Light and Gossard, Bartels and Beatty worked on direct manipulation of geometric properties and relationships to control surface shapes.

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