This document discusses solid modeling techniques used in CAD software. It describes boundary representation, which stores solid objects as sets of polygon surfaces defined by topological and geometric information. Constructive solid geometry builds solids by combining 3D primitive shapes using Boolean operations. Sweep representation involves sweeping a 2D cross-section along a trajectory to form an object. Cell decomposition and spatial occupancy enumeration subdivide solids into primitive cells or voxels for applications like finite element analysis.

1. Solids
Solid modeling:-
Solid Modeling is a tool for generating a 3D representation of an object.
Most of the applications in CAD software’s contains task for creating solid
part model geometry. A CAD Solid Modeling System should satisfy the
following requirement:-
1. Rigidity
2. Homogenous
3. Finite volume
4. Finite description
Need of Solid modeling:-
 Need for analysis
1. To evaluate mass & inertia properties.
2. Checking in assemblies.
3. To evaluate surface area and volume of solids model.
 In Drafting application:-
1. Automatic dimensioning.
2. Automatic projections.
 Manufacturing:-
1. Parts classification.
2. Process planning.

2. 3. Numeric control.
 Production Engineering:-
1. MRP
2. Scheduling
 Inspection & Quality Control:-
*Boundary Representation:-
B-Representation is a method of generating a Solid Model in which
a solid axis described by the elements which form its boundary. B-
representation is done by a set-up of surfaces that enclose the
object’s interiors-
 The graphic system store all object descriptions as a set of
polygon surfaces.
 Linear equations are used to describe the surface mathematically.
 A Polygon defines the surface feature.
 There are two types of information include in B- Representation:-
 Topological information.
 Geometric information.

3. Topological Information:-
Topological information includes the relationship among edges ,
surface and the faces. It is similar to the wireframe Model.
Geometric Information:-
Geometric equation includes the equation of edge and surface. The
faces are region of closed and orient table surface.
Topology and geometry are interrelated and cannot be separated.
Both are comfortable otherwise non-scenic object may be resulted.
It is further shown below with the help of diagrams:-

4. Different type of data structure used to store coordinates is given
below:-
 Edge is a function of start vertex & finish vertex & surface is the
function of n edges.
E=f(Vs,Vf) and s=f(E1,E2,E3,……,En)
 Surface is a function of n vertices & edge is function of start &
finish vertex.
S=f(V1,V2,V3,……Vn) and E=f(Vs,Vf)
 Surface is a function of n vertices and edge is a function of two
surfaces.
S=f(V1,V2,V3,…..,Vn) and E=f(S1,S2)
Constructive Solid Geometry (CSG):-
In CSG technique, a solid object is created by combining the
volumes occupied by overlapping 3D Objects called primitives
using Boolean operations. The Boolean operations used are union,
intersection or difference. The primitives used by CSG are simple
blocks, spheres, torus, wedges etc.

5.  TYPES OF SWEEP:-
There are three types of sweep:-
 Linear Sweep
 Non-Linear sweep
 Hybrid sweep
Linear Sweep:-
A linear sweep is described by the linear equation. It can be
translation sweep and rotation sweep.
Non-Linear Sweep:-
Non-linear sweep is described by the higher order equations i.e.
Quadratic and Cubic Equations.
Hybrid Sweep:-
Hybrid sweep is the combination of linear & non-linear (quadratic
& cubic) equations.
SWEEP REPRESENTATION:-
Sweeping an object or a cross section along a specified trajectory
through space, forms a new object often called sweep. This
technique can be used for creating 3D objects that have
translational, rotational or other symmetries.
 A simple sweep can be created by a 2D cross-section being swept
along Normal plane of cross-section area, is called translational
sweep.

6.  Rotational sweep is created by rotating a cross-section about its
axis.
APPLICATIONS:-
1. Useful in modeling.
2. Determination of region swept out by root.
CELL DECOMPOSITION:-
Cell decompositioning technique decomposes the solid into a set of
primitive cells that are parameterized. Cell decomposition makes
use of bottom up construction in which complex shapes are created
from simple primitives by sticking them together but the cells must
not intersect while sharing single point, edge or face.
Cell decomposition has potential use in finite element analysis in
which, system to be analyzed into smaller elements called finite
elements with the condition that the element should not overlap each
other.

7. SPATIAL OCCUPANCY ENUMERATION:-
It is the technique of spatial portioning representation analogues to
cell decomposition but the difference is that in spatial occupancy
enumeration, the solid is subdivided into identical cells. These cells
are called Voxels. Representation of solid as regular array of cubes
is known as Cabrille.
 Various solid shapes such as cube, pyramid, prism etc. can be
used as voxels but the most commonly type is the cube.
ADVANTAGES OF SOLID MODELLING:-
 Complete modelling.
 Unambiguous.
 Best suitable for calculating mass properties.
 Very much suitable for automated applications.
 Fast creation.
 Gives huge information about solid.

8. DISADVANTAGES OF SOLID MODELLING:-
 Requires large memory.
 Slow manipulation.
APPLICATIONS OF SOLID MODELING:-
 Manufacturing planning applications.
 Automatic cutting tool path generation.