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Mechanical - Computer Aided Design - Geometric Modeling

GEOMETRIC MODELING

**1. ****What are
the two types of equations for curve representation? **

(1) Parametric
equation x, y, z coordinates are related by a parametric variable (*u* or θ)

(2) Nonparametric
equation x, y, z coordinates are related by a function

**Example:
Circle (2-D)**

**Name some
types of curves used in geometric modelling.**

Hermite curves

Bezeir curves

B-spline curv es

NURBS curv es

**3 ****What are
the desirable properties of Bezier Curve? **

** ****4 Write any
Two Drawbacks of Bezier Curves.**

**5. List the
advantages of B -spline curves.**

**6. What are the functions of Geometric Modelling
in design analysis?**

Evaluation of are a, volume, mass and inertia properties
Interference chec king in assemblies

Analysis of tolerance build-up in assemblies Kinematic analys
is of mechanisms and robots Automatic mesh generation for finite element
analysis

**7. What are the functions of Geometric Modelling
in Manufacturing??**

Parts classification Process planning

NC data generatio n and verification Robot program ge neration
Scheduling

**8. ****List the
Properties of a Geometric Modeling System. **

The geometric model must stay invariant with regard to its
location and o rientation The solid must have an in terior and must not have
isolated parts

The solid must be finite a nd occupy only a finite shape

The application of a trans formation or Boolean operation must
produce another solid The solid must have a finite number of surfaces which can
be described

The boundary of the solid must not be ambiguous

**9. What are called 2 ½ - D Wire frame models?**

Two classes of shape for which a simple wire-frame
representation is often adequate are those shapes defined by projecting a plane
profile along its normal or by rotating a planar profile about an axis. Such
shapes are not two-dimensional, but neither do they require sophisticated
three-dimensional schemes for their representation. Such representation is
called 2 ½ - D.

**10. Draw
an example for 2 ½ - D Wire frame model.**

**11.
****Catalog Techniques In Surface Modelling. **

i.
Surface Patch

ii.
Coons Patch

iii.
Bicubic Patch

iv.
Be’zier Surface

v.
B-Spline Surfaces

**12.
****What are the Solid Modeling Techniques? **

The various methods for representing the solids are:

1. Half-space
method

2. Boundary
representation method (B-rep)

3. Constructive
solid geometry (CSG and C-rep)

4. Sweep
representation

5. Analytical
solid modeling (ASM)

6. Primitive
instancing

7. Spatial
partitioning representation

a. Cell
decomposition

b. Spatial
occupancy enumeration

c. Octree
encoding

**13.
****Write short note on Be’zier Surface.**

The
Be’zier s urface formulation use a characteristic polygon

Points the Be zier surface
are given by

**14.
****Write any topological te rms used Boundary
representation method (B-rep).**

Vertex
(V) : It is a unique point (an ordered triplet) in space

Edge
(E): It is finite, non-self intersecting, directed space c urve bounded by t wo
vertices that are not necessarily distinct

Face
(F) : It is defined as a finite connected, non-self-intersecting, region of a
closed oriented surface bounded by one or mor e loops

Loop
(L) : It is an ordered alternating sequence of vertices and edges

Genus
(G) : It is the topological name for the number of handles or through holes in
an object

Body/Shell(B)
: It is a set of faces that bound a single connected c losed volume. A m inimum
body is a point

**15. What
is called singular body in b-rep?**

A minimum body is a point;
topologically this body has one face, one vertex, and no edges. It is called a
seminal or singular body

**16.
****Sketch some open polyhedral objects used in
B-rep.**

**17. Write Euler’s formula for open and closed
objects used in b-rep.**

Euler –
Poincare Law for closed objects :

*F – E + V
– L = 2 (B – G)*

Euler –
Poincare Law for open objects :

*F – E + V
– L = B – G*

**18.
****What are Advantages and Disadvantages of
b-rep? **

**Advantages **

O Appropriate
to construct solid models of unusual shapes

O Relatively
simple to convert a b-rep model to wireframe model

**Disadvantages
of b-rep**

O Requires more storage

O Not suitable for applications
like tool path generation

O
Slow manipulation

**19.
****How solids are created using CSG? **

**20. Give an example for CS G Tree.**

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Mechanical : Computer Aided Design : Geometric Modeling : Important Questions and Answers: Geometric Modeling |

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