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Solid Modeling Techniques
The various methods for representing the solids are:
1. Half-space m ethod
2. Boundary rep resentation method (B-rep)
3. Constructive solid geometry (CSG and C-rep)
4. Sweep repres entation
5. Analytical solid modeling (ASM)
6. Primitive inst ancing
7. Spatial partiti oning representation
a. Cell d ecomposition
b. Spatial occupancy enumeration
c. Octree encoding

**Solid Modeling Techniques **

The various methods for representing the solids are:

1. Half-space
m ethod

2. Boundary
rep resentation method (B-rep)

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

4.
Sweep repres entation

5.
Analytical solid modeling (ASM)

6.
Primitive inst ancing

7.
Spatial partiti oning representation

a. Cell d
ecomposition

b. Spatial
occupancy enumeration

c. Octree
encoding

**Boundary representation method (B-rep)**

The main topological ite ms / primitives of b-rep
are:

In solid modeling and computer-aided design,
boundary representation often abbreviated as B-rep or BREP—is a method for
representing shapes using the limits.

A solid is represented as a collection of connected
surface elements, the boundary between solid and non-so lid.

Boundary representation models are composed of two
parts:

O Topology,
and

O Geometry
(surfaces, curves and points).

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

A minimum body is a p oint; topologically this body has one
face, one vertex, and no edges. It is called a semin al or singular body.

*Geometry*

**Open polyhedral objects**

**Curved Objects**

**Euler’s formula**

Euler – Poinc are Law for closed objects : *F – E + V – L = 2 (B – G)*

Euler – Poinc are Law for open objects : *F – E + V – L
= B
– G*

**Some Euler Operations**

**Solid Model Generation using B-rep**

**Advantages
of b-rep**

O Appropriate to construct solid
models of unusual shapes

O Relatively simple to c onvert 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

** **

**Constructive Solid Geometry (CSG and C-rep)**

Constructive solid geometry (CSG) (formerly
called computational binary solid geometry) is a techni que used in solid
modeling.

Constructive solid ge ometry allows a modeler to
create a complex surface or object by using Boolean ope rators to combine
objects.

Often CSG presents a model or surface that appears
visually comple x, but is actually little more than cleve rly combined or
de-combined objects

The
simplest solid objects
used for the
representation are c alled primitives.

Typically they are the objects of simple shape:

O cuboids

O cylinders

O prisms

O pyramids

O spheres

O cones

The set of allowable primitives
is limited by each software packag e. Some software packages allow CSG on
curved objects while other packages do not

It is said that an object is constructed from primitives by
means of allowable operations , which are typically Boolean o perations on
sets: union, intersection an d difference, as well as geometric transformati
ons of those sets

**Boolean
Operations**

**CSG Tree**

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