The document discusses solid modeling, emphasizing its advantages over wireframe and surface modeling by providing complete geometric and topological representations of objects. It highlights various methods of solid modeling, including boundary representation (b-rep) and constructive solid geometry (csg), along with their respective strengths and limitations. Solid modeling is integral to design and analysis, offering tools for visualization, property calculations, and effective manufacturing applications.

1. Solid Modeling

2. Solid models give designers a complete, valid and
unambiguous representation of geometry, shape, surface,
volume, and density of an object.
🞭 weakness of wireframe and surface
modeling
🞭 confusing geometric description
🞭 incomplete geometric description
🞭 lack topological information
🞭 Tedious modeling process
🞭 Improper visualization
Solid modeling

3. In this approach complete solid
model can be generated from
basic building block (primitives)
which are combined together in
various way to create specific
shapes.
Primitives used in solid modeling
are cylinder, cone, block, sphere,
torus, etc.

4. Solid models are created by using 3-dimensional geometric
entities, known as primitives
Wire frame and surface
models, which contain
only geometric data, solid
model contains both
geometric and
topological information
of the object.

5. GEOMETRY AND TOPOLOGY
GEOMETRY- Geometry is the actual dimensions that define the entities of the
object
It consist – length of lines L1,L2,L3
Angle between the lines.
Radius R of circle.
Center P1 of circle.
TOPOLOGY – Topology is the connectivity and associativity of the of the different
entities of the object. It describe the way in which the different entities of the
object are connected.
It consist –
Line L1 shares a point (vertex) with line L2 and circle C1.
Line L2 shares a vertex with lines L1 and L3
Line L3 Shares a vertex with L2& circle C1
Point P1 lies outside the object

7. Advantages of solid modeling
1.It is easiest and most advanced method of geometric modeling.
2. It contain both geometric data and topological data thus solid models store
more information than wireframe or surface models.
3.It provide better visualization as compared to the wire frame and surface model.
4. Using solid model, it is possible to calculate the properties such as
mass,volume,moment of inertia.
5.Solid modeling produces accurate designs, improves the quality of design
provides complete three- dimensional definition of the objects.

8. limitation
1. It is not possible to create the solid models automatically from the wire
frame or surface model.
2. Solid model require more CPU time to retrieve, edit or update the model.

9. In CAD systems there are a number of representation schemes for solid modeling
include:
1. Constructive Solid Geometry (CSG)
2. Boundary Representation (BREP)
3. Sweeping
4. Parametric solid modeling
5. Primitive Instancing.
6. Feature Based Modeling.
7. Cell Decomposition.
8. Spatial Enumeration
9. Octree Encoding.
10. Quadtree Encoding
Methods of solid modeling

10. Boundary Representation (B-Rep)
The boundary representation model is based on the principal that any physical object can
be considered to be bounded by a set of faces.
Solid model is defined by their enclosing surfaces or boundaries. And object is created by
using a set of faces, each face is bounded by the edges, and each edge is bounded by the
vertices. This technique consists of the geometric information about the faces, edges and
vertices of an object with the topological data on how these are connected.
Object is defined in terms of its surface boundaries, vertices, edges and faces. Curved surfaces
are always approximated with polygons –piecewise linear/planar.
Not only planar but also convex polygon boundaries are used.

11. Boundary Representation (B-Rep)
• The database of a boundary model contains both its topology and geometry.
• Topology is created by performing Euler operations.
• Geometry is created by performing Euclidean calculations.
• Primitives of B-Rep scheme:
– A Vertex is unique point in a space.
– An Edge is a finite, non-self-intersecting, directed space curve bounded by two vertices that
are not necessarily distinct.
– A Face is defined as a finite connected, non-self-intersecting, region of a closed oriented
surface bounded by one or more loops.
– A Loop is an ordered alternating sequence of vertices and edges.
– A Handle (or through hole) is defined as a passageway that pierces the object completely. The
topological name for the number of handles in an object is genus.
– A Body (or Shell) is a set of faces that bound a single connected closed volume.

12. Euler’s equation
Euler’s equation is used to verify the validity of the topology of the boundary representation
models.
Valid vertices, edges, faces are connected properly.
The B-rep models topologically valid only if it satisfy Euler’s equation, else it is not valid.
Euler’s equation for 3D object (Closed polyhedral) given by
F-E+V-L = 2(B-G)
Euler’s equation for 3D object (Open polyhedral) given by
F-E+V-L = B-G
And the simplest version of this equations is F-E+V = 2.
F =Number of faces
E =Number of edges .
V =Number of vertices
L =Number of inner loops on faces (All faces combined)
G=Genus (no of handles or through holes)
B= Number of Bodies
V = 5, E = 8, F = 5
5 – 8 + 5 = 2
f4
E4
f2 E3
E7
E8
E5
f5 E2 E6
v2
v3
f1
f3
E1 v4
v5
v1

16. f4
E4
f2 E3
E7
E8
E5
f5 E2 E6
v2
v3
f1
f3
E1 v4
v5
B-Rep data structure
A database method that defines and stores a solid as a set
of vertices, edges and faces (point,line,curve,and surface)
which encloses its volume completely

17. Boundary Representation (B-Rep) validity
• System must validate topology of created solid.
• B-Rep has to fulfill certain conditions to disallow self intersecting and open objects.
This condition include:
– Each edge should adjoin exactly two faces and have a vertex at each end.
– Vertices are geometrically described by point coordinates.
– At least three edges must meet at each vertex.
– Faces are described by surface equations.
– The set of faces forms a complete skin of the solid with no missing parts.
– Each face is bordered by an ordered set of edges forming a closed loop.
– Faces must only intersect at common edges or vertices.
– The boundaries of faces do not intersect themselves.

18.  Valid B-Reps are unambiguous.
 Not fully unique, but much more so than CSG
 Potential difference exists in division of
– Surfaces into faces.
– Curves into edges
 Capability to construct unusual shapes that would not be possible with the available
CSG. Ex: aircraft fuselages, swing shapes
 Less computational time to reconstruct the image
 Requires more storage
 More prone to validity failure than CSG
 Model display limited to planar faces and linear edges
 complex curve and surfaces only approximated
Advantages and limitations

19. Constructive Solid Geometry (CSG)
• CSG is the most popular and widely used approach to create the solid model of the
object.
• A CSG model is based on the topological notion that a physical object can be
divided into a set of primitives (basic elements or shapes) that can be combined in a
certain order following a set of rules (Boolean operations) to form the object.
• In CSG approach, a solid model of an object is created by using three dimensional
geometric entities, known as primitives. Objects are represented as a combination of
simpler solid objects (primitives).
• The primitives are such as cube, cylinder, cone, torus, sphere, blocks etc.
• These primitives (two or more) can be combined by a mathematical SET of Boolean
operation to create a desired model.

20. Solid models are created by using 3-dimensional geometric
entities, known as primitives

21. • Structuring and combining the primitives of the solid model in graphics data base
is achieved by the use of Boolean operations.
• The Boolean operation are-
• Union(U) –used to combine two primitives.
• Intersection(∩) - used to get common volume in two primitives.
• Subtraction(-) – used to subtract one primitive from the other.

22. 🞭 Union
🞭 The sum of all points in each
of two defined sets. (logical
“OR”)
🞭 Also referred to as Add,
Combine, Join, Merge
• Intersection
– Those points common to each of
two defined sets (logical “AND”)
– Set must share common volume
– Also referred to as common,
conjoin
• Difference
– The points in a source set minus the points common to a second set. (logical “NOT”)
– Also referred to as subtraction, remove, cut

25. The database of a CSG model contains both its topology and geometry. the topology is
created by performing Boolean operation that combine primitives, whereas the geometry is
created from parameter configuration of primitives and rigid motion and transformation.
The data structure of the CSG model is represented by the CSG tree (or Graph). The data of the
solid model is stored in its database in the form of CSG tree (or Graph).
CSG tree gives the complete information about the process of combining individual
primitives by Boolean operation to generate the solid model.

29. +
-
CONSTRUCTIVE SOLID GEOMETRY (CSG)- CSG TREE

30. Advantage
• CSG is powerful with high level command.
• Easy to construct a solid model – minimum step.
• CSG modeling techniques leads to a concise database
• less storage.
• Complete history of model is retained and can be altered at any point.
• Can be converted to the corresponding boundary representation.
Disadvantage
• Only Boolean operations are allowed in the modeling process
• With Boolean operation alone, the range of shapes to be modelled is severely
restricted, i.e. not possible to construct unusual shape.
• Requires a great deal of computation to derive the information on the boundary,
faces and edges which is important for the interactive display/ manipulation of solid.
Constructive Solid Geometry (CSG) – Advantage and Disadvantage

31. 2. SWEEPING
In sweeping approach, a solid model is created by
moving a surface along a given path.
There are three type of sweeps.
1.Linear sweep .
2.Non –Linear sweep.
3.Hybrid sweep.

33. LINEAR SWEEP
In linear sweep ,a surface is
moved in a linear or circular
path .
Linear further divided in two
types- translational and
rotational sweep.
In translational sweep a surface
is moved by a given
distance in space in a
direction perpendicular to
the plane of a surface.
it is also know as extrusion
In rotational sweep ,a surface is rotated about an axis of
rotation by a given angle

34. Non linear sweep
In non linear sweep a surface (curve ) is moved along
the curved path .

35. Hybrid sweep
In a hybrid sweep ,the two surface are swept in two
different direction and the two resulting swept
volume are combined to form the object model .

36. 3.Parametric solid modeling
In a parametric modeling the solid object are described
mathematically in three dimensional space by the
parametric equation.

37. The solid object is represented as assembly of non –overlapping
hyperpatches.
Any point in the interior or on the boundary of the hyperpatch is expressed by
a parametric equation containing three variables u,v,w is given by
P(u,v,w) = (x,y,z)= (x(u,v,w),y(u,v,w),z(u,v,w)

38. 4.Feature based modeling
Now a day feature based modeling is most widely
used method of creating models.
This approach is more general than the CSG
approach ,it allow the designer create the complex
parts.
Feature is defined as the combination of shape and
operation to build the part.
The shape is two dimensional sketch .e.g of the
shape are rectangle,square,triangle ,circle, ellipse
etc.

39. Steps in feature based modeling
1. Create shape (sketches)- first step is to
create the shapes (sketches) .A shape is a two
dimensional profile or cross-section .
2. Create feature- In second step apply, feature
operations to the shape(sketch) to create the
features e.g. – extrude ,revolve,sweep,loft.
3. Combine feature are combine to form the
solid model of the object.

40. different feature operation are .
1.Extrude
2.Resolve
3.Sweep
4.Loft
5.Shaft
6.Pipe
7.Boss
8.Cut
9.Slot
10.Shell
11.Fillet
12. Fillet
13. chamfer
14. Draft
15. Spiral
16. Spring
17. Thread

41. extrude
Extrude model is solid model of the object with uniform
thickness.
It requires a sketch and an extrusion vector. The extrusion
vector is always perpendicular to the plane of sketch.

42. revolve
Resolve feature is used to create axis symmetric objects.
It require a sketch and a revolution vector

43. sweep
Sweep feature sweep a
sketch or cross section
along a guide curve .
It require a sketch and a
guide curve .
Linear sweep- guide
curve is straight line.
Non-Linear sweep- guide
curve is any curve
other than straight
line.

44. Loft is a generalization of sweep .Loft blends multiple cross sections
along a guide curve Types- linear and non linear.
1.Linear loft- Linear loft ,guide curve is a straight line .
2. Non Linear loft – guide curve is any curve other than straight line
LOFT

45. boss
Boss is an addition of an extrude or revolved
feature to a base feature.

46. CUT
CUT is the subtraction of an extruded or
revolved feature from a base feature

47. slot
Slot is subtraction of an extruded feature from
a solid or a base feature

48. Shell
Shell feature is used
to create a thin
walled hollow solid.
Fillet - Fillet feature is
used to round off
or smoothen the
sharp corners and
edges of the solids.

49. Chamfer – chamfer feature
is used to remove sharp
edges and corners from the
solid by creating beveled
edges.
Draft - Draft feature is
used to create a taper on
the surface of the object.
Input to create draft is face
to be drafted ,draft angle
and neutral angle from
which the draft angle is
measured.

50. Spiral – spiral feature is
used to create spiral
springs.
Input parameter for
spiral operation are : a
profile to sweep and
sweeping helix curve.
Spring -Spring Feature is
used to create helical
springs.
Input parameter for
spring operation are
profile to sweep and
sweeping helix.

51. This technique is used to define
families of object ,which is called
generic primitive.
The primitive are defined in term of a
parameter group for e.g a block
primitive is defined by parameter ;
height(h) ,width(w),and depth(D).
By inputting the values of parameter
defining the primitive ,model can
be generated.
In addition to basic primitives ,the
library of generic primitives
(shapes) which are commonly
used is created.
The generic primitive called from
library by its assigned name and
it can be created by inputting the
values of parameters.
PRIMITIVE INSTANCING

52. Constraint Based Modeling
• A constraint is defined as the geometric condition that
relates two or more entities of model.
• In constrain based modeling ,the designer can add certain
constrains in modeling .for e.g. adding the constraint of
the symmetry to the modeling allows the designer to
modify the part of the model on one side of the
symmetrical axis, then the part of the model on other
side of the symmetrical axis gets modified automatically.

53. Various constraint are –
Coincident,collinear,concetric,horizontal
,vertical,midpoint,parallel,perpendicular,tangent,symmetry

54. Solid modeling based application
1. Graphics – solid models can be used to generate
automatically the orthographic view of the object.
It can also be converted into wire-frame models.
2. Design and analysis -
Solid models are used for automatic mass property
calculations .
Other design and analysis applications of solid model
include : finite element analysis, kinematic analysis,
dynamic analysis,

55. 3. Manufacturing- most significance application of
the solid models in this group is the automatic
tool path generation and verification ,dimension
inspection.
4. Inspection and testing : solid model is used in
computer aided inspection (CAI) and computer
aided testing.

56. • Modeling Facilities Desired
– The geometric modeling features
– The editing or manipulation features
– The display control facilities
– The drafting features
– The programming facility
– The analysis features
– The connecting features

57. • The geometric modeling features
– Cartesian and polar coordinates
– 2D analytical features
• Points
• Lines
• Arcs
• Circles
• Conics
• Splines
• Fillets
• Chamfers …

58. • The editing or manipulation features
– Transformations like move, rotate, copy,
scale…
– Editing features like trim, intersection, stretch,
…

59. • Display control facilities
– Window
– Zoom
– Pan
– Hidden
– Shading
– Animation
– Clipping

60. • Drafting features
– The facilities can be utilised for the purpose of
transmitting the information in hard copy
• The ability to get various types of lines
• Text handling capacity interms of font
• To store the large number of views such as isometric,
orthographic, section views,…
• It should have automatic or semi-automatic
dimensioning

61. • programming facility
– The MACRO programming within a CAD system is
useful to program specifically for an application,
making use of all the features available in the
system for either modelling or for any specific
application based on the information generated
during modeling
• GRIP in Unigraphics
• GLUE in CAM-X

62. • analysis features
– Calculating Area, perimeter, volume, mass, …
– General purpose analyses like FEA
– Assembly facility with the interference or
clearance analysis
– Ability to explode an assembly for manual
preparation

63. • connecting features
– The internal data format should be well connected
with other allied modules, i.e, an integrated data
base structure would be useful wherein all the
various modules share the common database