This set of Solid Modelling Multiple Choice Questions & Answers (MCQs) focuses on “Generalized Notation Scheme and Higher-Dimension Elements”.

1. To which of the following interpolation, generalized notation convention is applied in solid modelling?

a) Tricubic interpolation

b) Hermite interpolation

c) Isometric interpolation

d) Polycubic interpolation

View Answer

Explanation: Generalized notation convention is explicitly applied to polycubic interpolation involving an arbitrary number of independent parametric variables in solid modelling. It suggests a system that can directly extend to any odd-ordered polynomial form.

2. Who first laid the foundation for D geometry in higher-dimensional modelling?

a) Riemann

b) Descartes

c) Euclid

d) Poincaré

View Answer

Explanation: Descartes laid the foundation for D geometry by putting coordinates to space, allowing the numerical description of geometric primitives and the use of algebraic methods. Riemann developed theories of D geometry. Poincaré developed algebraic topology with a dimension-independent formulation.

3. What is the stress matrix for higher order elements such as quadratic bar?

a) {σ} = E [ε] {d}

b) {σ} = ε [B] {d}

c) {σ} = E [B] {d}

d) {σ} = [B] {d}

View Answer

Explanation: For higher order elements, such as quadratic bar stress matrix is given by {σ} = E [B] {d}, where E is the modulus of elasticity, [B] is a function of natural coordinates s and d is the displacement. The expression is determined by Hooke’s law.

4. Which of the following is the general notation for elements of the transformation matrix M in solids?

a) u

b) m_{jk}

c) a_{j1, j2,…..jn}

d) e_{jk}

View Answer

Explanation: The general notation for elements of the transformation matrix M is m

_{jk}. These elements correspond to the various transformations taking place in the matrix. u is the notation for parametric variable while the notation a

_{j1, j2,…..jn}is used for vector elements of the geometric coefficient array A.

5. For Hermite bicubic patch in three-space, what are the values of m and n?

a) m=1, n=2

b) m=2, n=3

c) m=1, n=3

d) m=3, n=2

View Answer

Explanation: For Hermite bicubic patch in three-space, m=3, n=2. Here, m is number of dependent variables and n is independent or parametric variables. The equation for Hermite bicubic patch contains 4n terms.

6. Which of the following sentence is incorrect about higher-dimensional representations used in solid modelling?

a) It is structured to deal with simple cases

b) It offers a solution to the integration of parametrisable characteristics

c) It makes possible to store all the topological relationships

d) It is space intensive

View Answer

Explanation: Higher-dimensional representations used in solid modelling are based on long-standing and profound mathematical theories proved. So, it is able to deal with complex cases as well as with the special requirements of each dimension more robustly in comparison with other representation techniques.

7. What are the aspects used to construct spatial data structures of higher-dimensional modelling?

a) Domain and embedding

b) Operators and embedding

c) Domain and primitives

d) Set of primitives and embedding

View Answer

Explanation: Spatial data structures of higher-dimensional modelling consist of a set of primitives and some topological relationships between these primitives and embedding which links these primitives to their geometry and attributes. It is important to understand the topological relations in higher-dimension.

**Sanfoundry Global Education & Learning Series – Solid Modelling.**

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