This document provides an overview of solid modeling schemes and techniques. It discusses six common solid modeling representations: spatial enumeration, cell decomposition, boundary representation, sweep methods, primitive instancing, and constructive solid geometry. It focuses on the last three techniques, which are most commonly used in modeling packages. Constructive solid geometry uses basic shapes combined with Boolean operations. Boundary representation describes a solid using its enclosing faces, edges and vertices. The document provides examples of both techniques and discusses how solid models allow designers to determine important properties and make design changes more easily compared to other modeling types.

1. Solid Modeling Schemes
University of Koya Graduate Course
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Ali Ahmed
Department OF Manufacturing Engineering,
Faculty of Engineering,
Danielle Mitterrand Boulevard, Koya
2nd semester 2017
a.a_agha@yahoo.co.uk

2. SOLID MODELING
The representation of solid models uses the fundamental idea that a
physical object divides the 3-D Euclidean space into two regions, one
exterior and one interior, separated by the boundary of the solid. Solid
models are:
• bounded
• homogeneously three dimensional
• finite
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3. There are six common representations in solid modeling.
• Spatial Enumeration: In this simplest form of 3D volumetric raster model, a
section of 3D space is described by a matrix of evenly spaced cubic volume
elements called voxels.
• Cell Decomposition: This is a hierarchical adaptation of spatial enumeration. 3D
space is sub-divided into cells. Cells could be of different sizes. These simple cells
are glued together to describe a solid object.
• Boundary Representation: The solid is represented by its boundary which consists
of a set of faces, a set of edges and a set of vertices as well as their topological
relations.
• Sweep Methods: In this technique a planar shape is moved along a curve.
Translational sweep can be used to create prismatic objects and rotational sweep
could be used for axisymmetric components.
• Primitive Instancing: This modeling scheme provides a set of possible object
shapes which are described by a set of parameters. Instances of object shape can
be created by varying these parameters.
• Constructive Solid Geometry (CSG): Primitive instances are combined using
Boolean set operations to create complex objects.
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4. In most of the modeling packages, the approach used for modeling uses
any one of the following three techniques:
i. Constructive solid geometry (CSG or C-Rep)
ii. Boundary representation (B-Rep)
iii. Hybrid method which is a combination of B-Rep and CSG.
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Constructive Solid Geometry (CSG)
In a CSG model, physical objects are created by combining basic elementary shapes
known as primitives like blocks, cylinders, cones, pyramids and spheres. The
Boolean operations like union (+), difference (–) and intersection are used to carry
out this task. For example, let us assume that we are using two primitives, a block
and a cylinder which are located in space as shown in Fig 1.

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Figure 1: CSG Operation
A “union” operation (A B) will combine the two
to convert them into a new solid.(Fig. 1 (c)) The
difference operation (A – B) will create a block
with a hole (Fig. 1 (D)). An intersection
operation (A B) will yield the portion common
to the two primitives. (Fig. 1 (E)).

6. Boundary Representation
Boundary representation is built on the concept that a physical object is
enclosed by a set of faces which themselves are closed and orientable
surfaces. Fig. 2 shows a B-rep model of an object. In this model, face is
bounded by edges and each edge is bounded by vertices. The entities
which constitute a B-rep model are:
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Fig. 2 B-Rep Model
A solid model is a 3-D representation of an object. It is an accurate geometric description which
includes not only the external surfaces of part, but also the part’s internal structure. A solid model
allows the designer to determine information like the object’s mass properties, interferences, and
internal cross sections.

8. Solid models differ from wire frame and surface models in the kind of geometric
information they provide. Wire frame models only show the edge geometry of an
object. They say nothing about what is inside an object. Surface models provide
surface information, but they too lack information about an object’s internal
structure. Solid models provide complete geometric descriptions of objects.
Engineers use solid models in different ways at different stages of the design
process. They can modify a design as they develop it. Since computer-based solid
models are a lot easier to change and manipulate than the physical mock-ups or
prototypes, more design iterations and modifications can be easily carried out as a
part of the design process. Using solid modeling techniques a design engineer can
modify a design several times while optimizing geometry. This means that designers
can produce more finished designs in less time than by using traditional design
methods or 2-D CAD drafting tools.
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9. Solid models can be used for quick and reliable design analysis. Solid models apart
from geometric information provide important data such as volume, mass, mass
properties and center of gravity. The designer can also export models created to
other applications for finite element analysis (FEA), rapid prototyping and other
special engineering applications.
Finally designers can generate detailed production drawings directly from the solid
model. This capability increases design productivity considerably. Another
important feature of solid modeling is associativity. Detailed drawings are linked to
solid model through the associativity feature. This is a powerful function - as an
engineer modifies a design, the drawings get updated automatically. In bidirectional
associativity, any modifications made to geometry in the drawing are reflected in the
model. In more advanced design and manufacturing environments, solid
models are used for rapid prototyping and automated manufacturing
applications.
The salient features of the solid modeling approach to design are discussed in the
following sections.
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10. SALIENT FEATURES OF SOLID MODELING
• FEATURE-BASED DESIGN
The most fundamental aspect in creating a solid model is the concept of feature-based
design. In typical 2-D CAD applications, a designer draws a part by adding basic geometric
elements such as lines, arcs, circles and splines. Then dimensions are added. In solid
modeling a 3-D design is created by starting a base feature and then adding other features,
one at a time, until the accurate and complete representation of the part’s geometry is
achieved.
A feature is a basic building block that describes the design, like a keyway on a shaft. Each
feature indicates how to add material (like a rib) or remove a portion of material (like a cut
or a hole). Features adjust automatically to changes in the design thereby allowing the
capture of design intent. This also saves time when design changes are made. Because
features have the ability to intelligently reference other features, the changes made will
navigate through design, updating the 3-D model in all affected areas. Figure 3 shows a
ribbed structure. It consists of feature like ribs and holes.
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Fig. 3 A Ribbed Structure

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Similarly, if a flanged part shown in Fig. 4 (A) is to be created, the one approach is
to sketch the cross section as shown in Fig. 4 (B) and then revolve through 360°.
Fig. 4 Flanged Part
In typical solid modeling software the designer can
create a feature in two basic ways. One is to sketch
a section of the shape to be added and then
extrude, revolve, or sweep it to create the shape.
These are called sketched features.
Another type of feature is the pick-and-place
feature. Here the designer simply performs an
engineering operation such as placing a hole,
chamfering or rounding a set of edges, or shelling
out the model.

13. This process represents true design. Unlike many CAD applications in which designing means
drawing a picture of the part, working with the feature-based solid modeling method is more like
sculpting designs from solid material. Features/available in typical solid modeling software are:
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An important component of every feature is its dimensions. Dimensions are the variables that one changes in
order to make the design update automatically. When a dimension is changed the solid modeling software
recalculates the geometry.
Design of a part always begins with a base feature. This is a basic shape, such as a block or a cylinder that
approximates the shape of the part one wants to design. Then by adding familiar design features like protrusions,
cuts, ribs, keyways, rounds, holes, and others the geometry of a part is created.

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Thank you for attention