This document discusses different types of geometric modeling methods including wireframe, surface, and solid modeling. Wireframe modeling uses points and lines to define objects but does not represent actual surfaces or volumes. Surface modeling defines the outer surfaces of an object. Solid modeling precisely defines the enclosed volume of an object using its faces, edges, and vertices. Constructive solid geometry and boundary representation are two common solid modeling techniques. CSG uses Boolean operations to combine primitive shapes, while boundary representation precisely defines the boundaries and topology of a model.
CAD software can be divided based on the modeling technique used, including 2D, basic 3D, sculpted surfaces, and 3D solid modeling. Geometric modeling is a fundamental part of CAD tools and refers to techniques for developing efficient representations of a design's geometric aspects. The main geometric modeling approaches are wireframe modeling, surface modeling, and solid modeling. Solid modeling provides the most complete description of an object's shape, surface, volume, and density.
Geometric modeling is an important part of CAD systems. There are several techniques for geometric modeling including wireframe modeling, surface modeling, and solid modeling. Solid modeling uses half-spaces and boolean operations to define objects by their volume and boundaries. Constructive solid geometry (CSG) and boundary representation (B-rep) are two common solid modeling techniques. CSG uses predefined geometric primitives and boolean operations to combine them. B-rep represents solids as collections of boundary surfaces and records the geometry and topology of the surfaces.
Geometric modeling is a fundamental CAD technique that allows for the complete representation of parts, including their geometry and topology. There are several techniques for geometric modeling, including wireframe modeling, surface modeling, and solid modeling. Solid modeling uses half-spaces and Boolean operations to represent parts as volumes. Common solid modeling techniques are Constructive Solid Geometry (CSG) and Boundary Representation (B-rep). CSG uses primitives and Boolean operations to combine them into a modeling tree, while B-rep represents parts using their boundary surfaces and connectivity. Feature-based, parametric modeling further advanced modeling by using modeling features instead of basic primitives. Geometric modeling continues to evolve with new challenges like modeling porous media and biomedical
1) Geometric modeling is a fundamental CAD technique that represents objects using points, lines, curves, surfaces or solids.
2) Early techniques included wireframe and surface modeling but they were ambiguous and could not fully support engineering activities like stress analysis.
3) Solid modeling uses half-spaces and Boolean operations to unambiguously represent objects spatially and allow full engineering analysis.
1) Geometric modeling is a fundamental CAD technique that represents objects using points, lines, curves, surfaces or solids.
2) Early techniques included wireframe and surface modeling but they were ambiguous and lacked topological data.
3) Solid modeling techniques like CSG and B-Rep overcome these issues by representing objects unambiguously using their volume and topology.
4) Feature-based modeling further advanced CAD by modeling objects parametrically using high-level features like holes and rounds.
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.
Geometric modeling is a fundamental technique in CAD. There are several techniques including wireframe modeling, surface modeling, and solid modeling. Wireframe models only use points and curves, while surface models add topology. Solid models provide complete spatial representations using half-spaces and boundary representations (B-rep). Constructive solid geometry (CSG) builds models from primitives using Boolean operations, while B-rep defines models by their surfaces. Parametric, feature-based modeling in systems like Pro/E uses sketches, extrusions, and features to efficiently generate complex models.
CAD software can be divided based on the modeling technique used, including 2D, basic 3D, sculpted surfaces, and 3D solid modeling. Geometric modeling is a fundamental part of CAD tools and refers to techniques for developing efficient representations of a design's geometric aspects. The main geometric modeling approaches are wireframe modeling, surface modeling, and solid modeling. Solid modeling provides the most complete description of an object's shape, surface, volume, and density.
Geometric modeling is an important part of CAD systems. There are several techniques for geometric modeling including wireframe modeling, surface modeling, and solid modeling. Solid modeling uses half-spaces and boolean operations to define objects by their volume and boundaries. Constructive solid geometry (CSG) and boundary representation (B-rep) are two common solid modeling techniques. CSG uses predefined geometric primitives and boolean operations to combine them. B-rep represents solids as collections of boundary surfaces and records the geometry and topology of the surfaces.
Geometric modeling is a fundamental CAD technique that allows for the complete representation of parts, including their geometry and topology. There are several techniques for geometric modeling, including wireframe modeling, surface modeling, and solid modeling. Solid modeling uses half-spaces and Boolean operations to represent parts as volumes. Common solid modeling techniques are Constructive Solid Geometry (CSG) and Boundary Representation (B-rep). CSG uses primitives and Boolean operations to combine them into a modeling tree, while B-rep represents parts using their boundary surfaces and connectivity. Feature-based, parametric modeling further advanced modeling by using modeling features instead of basic primitives. Geometric modeling continues to evolve with new challenges like modeling porous media and biomedical
1) Geometric modeling is a fundamental CAD technique that represents objects using points, lines, curves, surfaces or solids.
2) Early techniques included wireframe and surface modeling but they were ambiguous and could not fully support engineering activities like stress analysis.
3) Solid modeling uses half-spaces and Boolean operations to unambiguously represent objects spatially and allow full engineering analysis.
1) Geometric modeling is a fundamental CAD technique that represents objects using points, lines, curves, surfaces or solids.
2) Early techniques included wireframe and surface modeling but they were ambiguous and lacked topological data.
3) Solid modeling techniques like CSG and B-Rep overcome these issues by representing objects unambiguously using their volume and topology.
4) Feature-based modeling further advanced CAD by modeling objects parametrically using high-level features like holes and rounds.
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.
Geometric modeling is a fundamental technique in CAD. There are several techniques including wireframe modeling, surface modeling, and solid modeling. Wireframe models only use points and curves, while surface models add topology. Solid models provide complete spatial representations using half-spaces and boundary representations (B-rep). Constructive solid geometry (CSG) builds models from primitives using Boolean operations, while B-rep defines models by their surfaces. Parametric, feature-based modeling in systems like Pro/E uses sketches, extrusions, and features to efficiently generate complex models.
The document discusses different types of geometric models used in modeling including wireframe models, surface models, and solid models. It provides details on each type of model, including their advantages and disadvantages. Wireframe models are the simplest but use the least amount of memory and are easy to create. Surface models are more complex but provide more geometric constraints for engineering applications. Solid models provide the most complete representation and allow calculation of mass properties. The document also discusses different modeling approaches like constructive solid geometry (CSG) and boundary representation (B-rep) used for solid modeling.
All physical objects have 3D boundaries that define their shape. Surface modeling uses points, lines, and faces to define these boundaries mathematically. There are several types of surfaces, including plane, ruled, revolved, and freeform surfaces. Revolved surfaces are created by rotating a profile around an axis, generating surfaces like cylinders and cones. Curves and surfaces are essential for modeling complex shapes encountered in engineering designs.
This document discusses computer integrated manufacturing and CAD/CAM modeling techniques. It introduces wireframe, surface, and solid modeling approaches used in geometric modeling. Wireframe models represent objects with edges, while surface modeling uses surfaces defined by vertices and edges. Solid modeling represents objects as bounded 3D volumes divided space into interior and exterior regions. The document then discusses modeling primitives, drawing entities, and algorithms for drawing lines and circles in computer graphics. It concludes by introducing the concept of representing curves and surfaces through implicit and parametric equations.
The document discusses different methods for modeling solid objects in 3D, including constructive solid geometry (CSG) and boundary representation (B-Rep). CSG uses boolean operations on primitive solids, represented as a tree structure, while B-Rep defines solids by their enclosing faces, edges and vertices with topological connectivity. Both have advantages such as unambiguous definitions but also challenges around complexity, storage or modeling restrictions. Hybrid approaches combine benefits of both methods.
This document discusses different methods for representing 3D models, including:
- Traditional representations using engineering drawings had weaknesses like ambiguity.
- Computer representations include wireframe geometry, surface representations using tabulated, ruled or swept surfaces, and solid modeling using constructive solid geometry (CSG) or boundary representation (B-rep).
- Surface modeling overcomes some ambiguities of wireframes by specifying surfaces, but is computationally demanding.
- Solid modeling with CSG uses primitives and boolean operations, while B-rep ensures topological consistency of faces, edges and vertices.
- B-rep is more popular than CSG due to limitations of CSG for displays and easier conversion from CSG to
2D drawings are not ideal for representing 3D objects as they lack a Z axis. There are three main types of 3D models: wireframe, surface, and solid models. Wireframe models only contain edges and vertices and cannot represent complex surfaces. Surface models include edges, vertices and exterior surfaces but provide no interior details. Solid models are the current standard as they contain edges, vertices, exterior surfaces and interior details, providing an unambiguous representation of an object that can be used for engineering analysis.
Unit 2-ME8691 & COMPUTER AIDED DESIGN AND MANUFACTURINGMohanumar S
This document discusses different geometric modeling techniques. It describes wireframe modeling where object edges are represented by lines. Surface modeling uses techniques like patches to represent curved surfaces. Solid modeling represents objects as solids to avoid misinterpretation. Constructive solid geometry and boundary representation are two common solid modeling techniques. CSG uses primitives and Boolean operations while boundary representation uses edges, vertices and faces to define boundaries.
Solid models in mechanical engineering are used for graphics, design, manufacturing, and assembly applications. There are three forms of solid model representation: wireframe, surface, and solid models. Solid models are the preferred form as they can calculate mass properties and perform other analyses. Solid models must be bounded, three-dimensional, and finite. They can be created using constructive solid geometry (CSG), boundary representation (B-rep), or sweeping schemes. CSG combines primitives like blocks and cylinders using operations like union and subtraction. B-rep models surfaces and calculates volumetric properties. Sweeping extrudes a 2D sketch along a path.
Geometric modeling involves creating mathematical representations of geometric objects using CAD software. There are three main types of geometric models: wireframe models using lines and curves, surface models representing an object's surface, and solid models representing the complete volumetric shape. Solid modeling is now the most common approach as it allows for properties like mass to be calculated and enables applications like finite element analysis. Geometric models can be created using set operations in constructive solid geometry or parametric modeling techniques.
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.
The document discusses geometric modeling which plays a crucial role in CAD/CAM/CAE systems. It describes three main types of geometric modeling: wireframe, surface, and solid modeling. Wireframe modeling uses lines and curves to represent an object, while surface modeling uses surfaces like planes. Solid modeling generates the most complete representation and provides all information for engineering analysis and manufacturing. The document also covers curve representation techniques, order of continuity between curves, and cubic spline modeling which uses piecewise cubic polynomials to smoothly join data points.
The document discusses geometric modeling which plays a crucial role in CAD/CAM/CAE systems. It describes three main types of geometric modeling: wireframe, surface, and solid modeling. Wireframe modeling uses lines and curves to represent an object, surface modeling uses surfaces like planes, and solid modeling creates a complete 3D representation of an object. Parametric curves and issues of continuity between curves are also covered. Cubic spline curves are discussed as an example of synthetic curves used in surface modeling.
COMPUTER CONTROL IN PROCESS PLANNING Unit 2 (ME CAD/CAM)Avt Shubhash
This document provides information on part design preparation for computer control process planning (CCPP). It discusses topics like computer-aided drafting and design (CADD), basic dimensions, geometric characteristic controls, characteristics and symbols, CAD input/output devices, topology, geometric transformations, data structures, geometric modeling for process planning, GT coding principles and examples, and part classification coding systems like Opitz and MICLASS. The document is an educational reference for the concepts and methodologies used in part design preparation for computer-based process planning.
This document provides a summary of important two-mark questions and answers related to the topics covered in a Computer Aided Design (CAD) course. It includes questions from five units:
1. Fundamentals of computer graphics including the design process, applications of CAD, geometric transformations, and homogeneous coordinates.
2. Geometric modeling covering curves, wireframe modeling, boundary representation vs constructive solid geometry.
3. Visual realism such as visualization techniques, lighting models, shading methods and color models.
4. Assembly of parts including assembly modeling, mating conditions, tolerancing, mass properties and interference checking.
5. CAD standards including the need for data exchange standards and important standards for exchange
Geometric modeling uses software to mathematically describe an object's geometry. There are three main methods: wireframe modeling represents edges as lines; surface modeling depicts objects' surfaces clearly but provides no interior data; and solid modeling displays whole solids realistically without misinterpretation risk. Boundary representation is a popular solid modeling technique where views are sketched and connected via lines. Constructive solid geometry also constructs solids using primitives combined through Boolean operations.
TOWARDS A UNIFIED IN-PROCESS GEOMETRIC MODEL FOR MULTIPLE MACHINING AND Layer...Liu PeiLing
There are many fabrication processes in modern manufacturing, but current modeling and simulation tools only simulate a few unit processes based on different geometry models. To overcome the data exchange problem between different models, this paper studies various in-process geometry models together with their working systems / prototypes for traditional manufacturing processes. Novel hybrid multiple-machining and layered manufacturing processes are presented to identify critical issues. Working towards a vision of pervasive modeling and simulation, a unified Voxel-based in-process geometry model for multiple-machining and layered manufacturing simulations is proposed and discussed.
Geometric modeling involves mathematically describing an object's geometry using software. There are three main methods: wireframe modeling uses lines to represent edges; surface modeling represents objects' surfaces; and solid modeling displays models as solids to avoid misinterpretation. Solid modeling is most effective as it makes objects most realistic and eliminates ambiguity.
This document discusses different types of 3D modeling including wireframe models, surface models, and solid models. It focuses on solid modeling which provides a complete, valid, and unambiguous geometric representation of physical objects. Solid models contain geometric and topological data and can be represented using constructive solid geometry (CSG) which constructs objects by combining simpler solid objects called primitives using Boolean set operations like union, intersection, and difference. CSG starts with basic primitives that are combined and recombined to model complex objects.
The document discusses geometric modeling and surface modeling techniques used in computer-aided design (CAD). It describes how geometry, topology, and other attributes are used to model engineering objects. Common surface modeling techniques include extruded, revolved, swept, fill, blended, spherical, cylindrical, and offset surfaces. Boundary representation is introduced as a method to represent solid objects using the boundaries between solid and non-solid areas.
The document discusses automated guided vehicles (AGVs). It provides three key points:
1) AGVs increase efficiency and reduce costs by automating material transport in manufacturing facilities and warehouses, carrying loads, towing trailers, and storing objects. They are used across many industries.
2) The first AGV was introduced in the 1950s and followed wires in floors, but now they mainly use laser navigation. AGVs communicate to ensure smooth product flow through warehouses.
3) AGVs use different navigation systems like wired, taped, or laser guidance. They transport a variety of materials for raw material handling, work-in-process movement, pallet handling, and finished good transport.
The document summarizes a seminar topic on group technology presented by Muhammed Sarfan. Group technology is a manufacturing philosophy that identifies similar parts and groups them to take advantage of similarities in design or manufacturing. Parts are classified into part families that are alike geometrically, in size, or require similar processing steps. Methods for forming part families include visual inspection of parts, production flow analysis of route sheets to group parts with similar machine operations, and classification coding systems based on design attributes, manufacturing attributes, or both.
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This document discusses different methods for representing 3D models, including:
- Traditional representations using engineering drawings had weaknesses like ambiguity.
- Computer representations include wireframe geometry, surface representations using tabulated, ruled or swept surfaces, and solid modeling using constructive solid geometry (CSG) or boundary representation (B-rep).
- Surface modeling overcomes some ambiguities of wireframes by specifying surfaces, but is computationally demanding.
- Solid modeling with CSG uses primitives and boolean operations, while B-rep ensures topological consistency of faces, edges and vertices.
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2D drawings are not ideal for representing 3D objects as they lack a Z axis. There are three main types of 3D models: wireframe, surface, and solid models. Wireframe models only contain edges and vertices and cannot represent complex surfaces. Surface models include edges, vertices and exterior surfaces but provide no interior details. Solid models are the current standard as they contain edges, vertices, exterior surfaces and interior details, providing an unambiguous representation of an object that can be used for engineering analysis.
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This document discusses different geometric modeling techniques. It describes wireframe modeling where object edges are represented by lines. Surface modeling uses techniques like patches to represent curved surfaces. Solid modeling represents objects as solids to avoid misinterpretation. Constructive solid geometry and boundary representation are two common solid modeling techniques. CSG uses primitives and Boolean operations while boundary representation uses edges, vertices and faces to define boundaries.
Solid models in mechanical engineering are used for graphics, design, manufacturing, and assembly applications. There are three forms of solid model representation: wireframe, surface, and solid models. Solid models are the preferred form as they can calculate mass properties and perform other analyses. Solid models must be bounded, three-dimensional, and finite. They can be created using constructive solid geometry (CSG), boundary representation (B-rep), or sweeping schemes. CSG combines primitives like blocks and cylinders using operations like union and subtraction. B-rep models surfaces and calculates volumetric properties. Sweeping extrudes a 2D sketch along a path.
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This document provides a summary of important two-mark questions and answers related to the topics covered in a Computer Aided Design (CAD) course. It includes questions from five units:
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2. Geometric modeling covering curves, wireframe modeling, boundary representation vs constructive solid geometry.
3. Visual realism such as visualization techniques, lighting models, shading methods and color models.
4. Assembly of parts including assembly modeling, mating conditions, tolerancing, mass properties and interference checking.
5. CAD standards including the need for data exchange standards and important standards for exchange
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imaging, emphasizing addressing false positives and resource efficiency.
Electric vehicle and photovoltaic advanced roles in enhancing the financial p...IJECEIAES
Climate change's impact on the planet forced the United Nations and governments to promote green energies and electric transportation. The deployments of photovoltaic (PV) and electric vehicle (EV) systems gained stronger momentum due to their numerous advantages over fossil fuel types. The advantages go beyond sustainability to reach financial support and stability. The work in this paper introduces the hybrid system between PV and EV to support industrial and commercial plants. This paper covers the theoretical framework of the proposed hybrid system including the required equation to complete the cost analysis when PV and EV are present. In addition, the proposed design diagram which sets the priorities and requirements of the system is presented. The proposed approach allows setup to advance their power stability, especially during power outages. The presented information supports researchers and plant owners to complete the necessary analysis while promoting the deployment of clean energy. The result of a case study that represents a dairy milk farmer supports the theoretical works and highlights its advanced benefits to existing plants. The short return on investment of the proposed approach supports the paper's novelty approach for the sustainable electrical system. In addition, the proposed system allows for an isolated power setup without the need for a transmission line which enhances the safety of the electrical network
3. Why Geometric modeling is needed
Geometric (3D) models are easier to interpret.
Simulation under real-life conditions.
Less expensive than building a physical model.
3D models can be used to perform finite element analysis
(stress, deflection, thermal)
3D models can be used directly in manufacturing,
Computer Numerical Control (CNC).
Can be used for presentations and marketing.
4. Wireframe Modeling
Wire-frame modelling uses points and curves (i.e. lines,
circles, arcs) to define objects.
The user uses edges and vertices of the part to form a 3-D
object
Wireframe model Part
5. Wireframe modeling - Advantages
Can quickly and efficiently convey information than
multiview drawings.
Can be used for finite element analysis.
Can be used as input for CNC machines to generate
simple parts.
Contain most of the information needed to create surface,
solid and higher order models
6. Tend to be not realistic
Do not represent an actual solids (no surface and volume).
Cannot model complex curved surfaces.
Cannot be used to calculate dynamic properties.
Ambiguity
complex model difficult to interpret.
Wireframe modeling -
Disadvantages
8. “ A surface model represents the skin of an object,
these skins have no thickness or material type ”
Surface modeling is more sophisticated than wireframe
modeling in that it defines not only the edges of a 3D
object, but also its surfaces.
In surface modeling, objects are defined by their
bounding faces.
Surface Modeling
9. Eliminates ambiguity and non-uniqueness present in wireframe
models by hiding lines not seen.
Renders the model for better visualization and presentation,
objects appear more realistic.
Provides the surface geometry for CNC machining.
Provides the geometry needed for mold and die design.
Can be used to design and analyze complex free-formed
surfaces (car bodies)
Surface properties such as roughness, color and reflectivity can
be assigned and demonstrated.
Surface modeling - Advantages
10. Surface models provide no information about the inside of
an object.
Cannot be used to calculate dynamic properties.
Surface modeling - Disadvantages
11. Surface Entities
Analytic entities include :
• Plane surface,
• Ruled surface,
• Surface of revolution, and
• Tabulated cylinder.
Synthetic entities include
• Hermite Cubic spline surface,
• B-spline surface,
• Bezier surface, and
• Coons patches.
13. Ruled (lofted) surface. This is a linear surface. It interpolates
linearly between two boundary curves that define the surface.
14. Surface of revolution. This is an axisymmetric surface that can
model axisymmetric objects. It is generated by rotating a planar
wireframe entity in space about the axis of symmetry a certain
angle.
15. Tabulated cylinder. This is a surface generated by translating a
planar curve a certain distance along a specified direction (axis of
the cylinder).
16. Bezier surface. This is a surface that approximates given input
data. It is different from the previous surfaces in that it is a synthetic
surface. Similarly to the Bezier curve, it does not pass through all
given data points. It is a general surface that permits, twists, and
kinks . The Bezier surface allows only global control of the surface.
17. B-spline surface. This is a surface that can approximate or
interpolate given input data. It is a synthetic surface. It is a general
surface like the Bezier surface but with the advantage of permitting
local control of the surface.
19. Solid Modeling
In the solid modeling, the solid definitions include
vertices (nodes), edges, surfaces, weight, and volume. The
model is a complete and unambiguous representation of a
precisely enclosed and filled volume
20. Methods of Creating Solid Models
Constructive Solid Geometry (CSG), CAD packages;
Unigraphics, AutoCAD – 3D modeler.
Boundary Representation (B-rep), mostly used in finite
element programs.
Parametric Modeling, CAD packages: SolidWorks,
Pro/Engineer
21. Primitive solids
Primitive creation functions:
These functions retrieve a
solid of a simple shape
from among the primitive
solids stored in the
program in advance and
create a solid of the same
shape but of the size
specified by the user
22. Constructive Solid Geometry, CSG
CSG defines a model in terms of combining basic and
generated (using extrusion and sweeping operation) solid
shapes.
Objects are represented as a combination of simpler solid
objects (primitives).
CSG uses Boolean operations to construct a model.
There are three basic Boolean operations:
Union (Unite, join) - the operation combines two
volumes included in the different solids into a single solid.
Subtract (cut) - the operation subtracts the volume of
one solid from the other solid object.
Intersection - the operation keeps only the volume
common to both solids
24. Union
Plan your modeling strategy
before you start creating the
solid model
Solid Modeling Example Using CSG
Cut
Cut
25. (CSG)- data structure
Data structure does not define model shape explicitly but
rather implies the geometric shape through a procedural
description
E.g: object is not defined as a set of edges & faces but by
the instruction : union primitive1 with primitive 2
This procedural data is stored in a data structure referred to as
a CSG tree
The data structure is simple and stores compact data easy to
manage
26. CSG tree stores the history of
applying boolean operations on the
primitives.
Stores in a binary tree format
The outer leaf nodes of tree
represent the primitives
The interior nodes represent the
boolean operations performed.
CSG Tree
+
-
27. CSG – Nonuniqueness of solid model
More than one procedure (and hence database) can be used to
arrive at the same geometry.
∪
-
28. CSG is powerful with high level command.
Easy to construct a solid model – minimum step.
CSG modeling techniques lead 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.
CSG - Advantage
29. Only boolean operations are allowed in the modeling process
with boolean operation alone, the range of shapes to be
modeled is severely restricted 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.
CSG - Disadvantage
30. Boundary Representation (B-rep)
Solid model is defined by their enclosing surfaces or
boundaries. 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.
B-rep model is created using Euler operation
Data structure :
B-Rep graph store face, edge and vertices as nodes, with
pointers, or branches between the nodes to indicate
connectivity.
33. Boundary representation-
validity
System must validate topology of created solid.
For topology consistency, certain rules have to be followed
Faces should be bound by a simple loop of edges and
should be not intersected by itself.
Each edge should exactly adjoin two faces and each edge
should have a vertex at each ends.
At least three edges should meet at each vertex.
34. Validity also checked through mathematical evaluation
Evaluation is based upon Euler’s Law (valid for simple
solid – no hole)
V – E + F = 2 V- number of vertices
E- number of edges
F- number of faces
Boundary representation-
validity
f1
f2
f3
f4 f5
E1
E2
E3
E4
E5
E6
E7
E8
v2
v3
v4
v5 V = 5, E = 8, F = 5
5 – 8 + 5 = 2
v1
35. Expanded Euler’s law for complex polyhedrons (with holes)
Euler-Poincare Law:
V-E+F-H+2P=2B
H – number of holes in face, P- number of passages or through
holes, B- number of separate bodies.
Boundary representation-
validity
V = 24, E=36, F=15, H=3, P=1,B=1
36. “ Feature” --- (shape & operation)
Operation --- (Sweep, extrude, Revolve, Boolean)
Operation performed
(Extrude Feature, Revolve Feature, Sweep, Loft, Fillet,
Chamfer)
Sketched Feature
Create a feature from the sketch by extruding, revolving,
sweeping, lofting and blending.
Create a 2D sketch.
Revolved
feature
Extruded (Protruded)
feature
37. Sweeping
Linear
Extrusion
Non – linear
1. Sweep a cross section along a guide curve
2. “BLEND” two cross section linearly.(linear sweep between
two section)
3. Sweep two cross section along a guide curve.
4. “LOFT” – to blend two cross section. (like 2 & 3))
38. Operation performed
Sweeping: Sweeping is a modeling
function in which a planar closed
domain is translated or revolved to form
a solid. When the planar domain is
translated, the modeling activity is called
translational sweeping; when the planar
region is revolved, it is called swinging,
or rotational sweeping.
39.
40. Applied Feature
• Applied feature does not require a sketch.
• They are applied directly to the model.
• Fillets and chamfers are very common applied features.
Chamfer
Fillet
41. Capability to construct unusual shapes that would not be
possible with the available CSG aircraft
Less computational time to reconstruct the image
Boundary representation-
advantages
42. • 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
Boundary representation-
disadvantages
43. Has all the advantages of surface models (uniqueness, non-
ambiguous, realistic, surface profile) plus volumetric
information.
Allows the designer to create multiple options for a design.
2D standard drawings, assembly drawing and exploded views
are generated form the 3D model.
Can easily be exported to different Finite Element Methods
programs for analysis.
Mass and volumetric properties of an object can be easily
obtained; total mass, mass center, area and mass moment of
inertia, volume, radius of gyration
Solid modeling - Advantages
44. More intensive computation than wireframe and surface
modeling.
Requires more powerful computers (faster with more memory
and good graphics)
Solid modeling - Disadvantages
45. Creating Solid Models
Parametric Modeling Concept
Parametric is a term used to describe a dimension’s ability to
change the shape of model geometry if the dimension value is
modified.
Feature-based is a term used to describe the various components
of a model. For example, a part can consists of various types of
features such as holes, grooves, fillets, and chamfers.
Parametric modeler are featured-based, parametric, solid
modeling design program: SolidWorks, Pro-Engineer,
Unigraphics (CSG and parametric), …..
46. Design Intent
In parametric modeling, dimensions control the
model.
Design intent is how your model will react when
dimension values are changed.
47. Remember that the placement of dimensions is very important because
they are being used to drive the shape of the geometry. If the 2.5 in.
vertical dimension increases, the 2.5 in. flat across the chamfer will be
maintained, but its angle will change.
The drawing shows the intent of the
designer that the inclined plane
(chamfer) should have a flat area
measuring 2.5 inches and that it should
start at a point 1.25 inches from the
base of the drawing. These parameters
are what the designer deemed
significant for this model.
2.50
4.00
1.25
2.50
Example:
48. In this drawing, what is important to
the designer is the vertical location and
horizontal dimension of the chamfer,
rather than the flat of the chamfer.
2.50
4.00
1.2
5
2.125
In the last drawing, the designer calls
for a specific angle for the chamfer.
In this case the angle of the chamfer
should be dimensioned.
2.50
4.00
1.75
30.0O
49.
50. Design Notes
Keep in mind that dimensioning scheme can be changed at
any time. You are not locked into a specific design. You
can also design without dimensioning, rough out a sketch,
and then later go back and fully define it.
51. The ability to go back on some earlier stage in the design
process and make changes by editing a sketch or changing
some dimensions is extremely important to a designer. This is
the main advantage of a parametric (SolidWorks, Unigraphics,
Inventor, Pro-Engineer) over a non-parametric modeler
(AutoCAD 3D modeler – Boolean operation)
52. Example:
Let’s assume that it is desired to design a part consisting
of a ring with a certain thickness and a series of counter
bore holes along the perimeter.
53. Boolean operation
Make the base part by creating two
cylinders and subtract the small one
from the large one
Create the solid geometry that will become the
counterbore holes and generate the pattern.
54. Position the pattern about the perimeter of the base part.
Locating the holes is critical to creating an accurate solid
model.
What would happen if you had to come back to this part to change the
thickness of the ring or size of the counterbore holes?
Since Boolean operation was used to create the part, changing the thickness would not
increase the height of the holes. There is no association between the thickness and the
hole pattern location.
Subtract the pattern from the base part to create the actual
holes.
55. Parametric modeling (SolidWorks, ProE, UG, …)
Create the initial base, the ring, by extruding the
profile (circles) in a particular direction (Pro/E or
SolidWorks) or use primitive solids and Boolean
operation (UG).
Create the counterbore as a feature. Select the
top surface of the ring and either sketch the two
holes and extrude at different depth or use the
hole feature option.
56. The next step would be to pattern the hole. The
pattern would actually be considered a feature in
itself, and would have its set of parametric
variables, such as the number of copies and the
angle between copies.
The model created would be identical to the one created using Boolean
operation, but with intelligence built into the model.
57. Ken Youssefi Mechanical Engineering Dept. 57
The true power of parametric modeling shines through when design changes need to
be made. The design modification is made by simply changing a dimension.
Since the counterbore is associated with the top surface of the ring, any changes in the
thickness of the ring would automatically be reflected on the counterbore depth.
58. Sketching and Features
Take the word sketch literally. A sketch should be just
that, a sketch.
When sketching, it is not necessary to create geometry
with accuracy. Lines, arcs, and additional geometry need
not be created with exact dimensions in mind.
When the dimensions are added, the sketch will change
size and shape. This is the essence of Parametric
Modeling.
When discussing the mind-set needed for working with parametric modelers,
there are two topics that need to be expanded: Sketching and Features
Sketching
In short, the sketch need only be the approximate size and shape of the part being
designed. When dimensions and constraints are added, they will drive the size and the
shape of the geometry.
59. Summary – Solid Modeling
Methods
Primitive creation modeling
A solid model is created by retrieving primitive solids
and performing Boolean operations
Sweeping function
Creates a solid by translating, revolving or sweeping a
predefined 2D shape (Sketching).
If geometric and dimensional constraints are imposed,
it is called Parametric Modeling.
Feature-based Modeling
Models a solid by using familiar shapes; holes, slots,
grooves, pockets, chamfers, fillets…..