Week 5 – MSE508/LIleana Costea, Ph.D.

Spring 2008

Solid Modeling/Data ExchangesChapter 4 and part of Ch. 5 (pp. 169 - 177)

(Chang textbook)

Week 5Parametric/Variational/Feature-Based Modeling

• Solid Model Software Systems

• Parametric Design Modeling

• Feature-Based Modeling

Source: Computer Integrated Manufacturing, 2nd Edition by James a Rehg and Henry W. Kraebber, Prentice-Hall 2001, pp. 120-124 and

Your textbook (SP08-I. Costea, Tien-Chien Chang et. al.)

Surface Modeling

• Section 4.6.2 in Chang textbook• Ruled surface• Tabulated surface• Free-form surface

• Analytical 3D surfaces (sphere, etc.) vs. free form

• Parametric polynomial curves developed for free form surfaces (p. 111 in Chang)

Free form surface modeling

• Easiest way : meshes p. 111 (Chang text)• Coon’s surface p. 111 (Chang text)• And Fig. 4. 20 p. 115 in Chang text• Bezier’s surface• B-spline surface• NURBS p. 112 in Chang text – best for free

surface• http://www.3drender.com/jbirn/ea/HeadModel.ht

mlTUTORIAL: NURBS Head Modeling

Topology vs. Geometry

• Topology (p. 172 Chang text) represents the basic relationships of the

geometric entities within an object.• Each geometric entity, such as point, line,

surface has a topological element, such as vertex, edge, face.

• Topology of a 3D object is bounded by several faces. (See figure 5.41 p. 175 Chang textbook);

• The same topological relationship remain the same for any tetrahedron, of any size or orientation.

Topology p. 172, 174 Chang text

• Face = described by a surface equation (e.g. planar, conic, free form, etc). A face is bounded by edges.

• Edge = given by an equation (line, circle, curve)

• Loop = a set of edges = a topological element between

face and edge• Vertex = its geometric counterpart point

Object is represented by:

• Geometric entities (lines, curves, surfaces;represented by coordinates, equations, parameters)

• Topological elements (vertices, edges, faces;represented by linkage in the data structure)

• Auxiliary information (color, tolerances, etc.)

• Both geometry and topology is needed in order to manipulate and display object correctly. In 3D modeling topology is critical.

Euler’s Formula – p. 176 Chang textbook

Question: How do we know that the structure represents a valid or invalid object?

Look at formulae for object without and with a hole and at the example p. 176

Euler operators are used to edit a solid by adding or deleting vertices, edges and faces. Euler operators ensure that the object edited respects the Euler-Poincare formula (eq. 5.64 p. 176)

(More details studied later in the semester)

Solid Model Software Systems

• Solid model: A mathematically complete and unambiguous representation of part geometry

• Two most commonly used techniques for creating software:– Constructive Solid Geometry (CSG)

most used

– Boundary Representation (B-Rep)

Two most commonly used techniques for creating Solid Model Software Systems (cont’d):

Constructive Solid Geometry (CSG)

• Build solid geometry from a primitive shape (Figure 4-17, 4-18)

• Can’t be used in complex designs such as automotive design

Two most commonly used techniques for creating Solid Model Software Systems (cont’d):

Constructive Solid Geometry (CSG)

• Build solid geometry from a primitive shape (cont’d):

Two most commonly used techniques for creating Solid Model Software Systems (cont’d): Boundary Representation (B-Rep)

• Represent objects by describing the bounding faces. (Figure 4-19)

• B-rep solid modeler can represent any object regardless of surface contour complexity.

• Difficult to build

• Uses a lot of vector-based memory

B-rep

• 3D objects can be manifold and non-manifold (see Fig. 5.40 p. 175 Chang text)

• A manifold model does not allow any dangling faces or edges.

• In a 3D manifold model the dimensionality is retained.

• B-rep consists only of bounded faces, with no loose edge or face. (p. 172 – Chang text)

Solid Model Software Systems3rd type is not used as commonly: Sweeping

• Used for cutter path simulation (Figure 4-20) (Figure 5.36 in Chang textbook, p. 171)

• Two types of sweeping actions are translation and rotation

• Difficult to build

• Uses a lot of memory

Parametric Design Modeling

• Parametric design approaches include:– Variant programming: the generation of programs for

parts using macros or API’s– Expert Systems: Knowledge Based Engineering

(KBE) that uses repetitive rule-driven design tasks– Constructive Solid Schemes: Use of the sequence or

history of operations by the user to build a part to record the object definition

– Numerical Constant Solvers: Allow the part to be defined in terms of relationships and constraints, then generate part variants by applying some sort of constraint satisfaction algorithm

Parametric Design Modeling

• Two main views:– Parametric modeling: Solve constraints by applying assignments

to model variables sequentially where each assigned value is computed as a function of previously assigned values

– Variational modeling: Construct a system of equations representing the constraints, and then solve all the equations simultaneously using a numerical solving procedure or some equivalent method

• In addition:– Associativity: There is a relationship between the solid model

part and the 2D drawing. If a dimension is changed on the 2D drawing, the solid model is updated or vice-versa

Parametric Design Modeling

• Variational constraint problem solver UGS ??

http://www.cc.gatech.edu/~turk/my_papers/schange.pdf

(the article is rather difficult reading with much mathematics)

Parametric/Variational Design Modeling

• Good explanation on p. 123 of your textbook (Tien-Chien Chang et al.)

(Instructor uses notes and does on the board)

Parametric/Variational Modeling

Differences:

Parametric

Sequential solution

Variational

Simultaneous set of equations

• Evaluate models fast

• No complex equations

• slow

• complex

• Can not deal with constraints that

are mutually coupled

• Can handle …

• Limited capabilities to handle

inconsistencies and

incompletely satisfied models

Parametric/Variational Modeling

• Look at picture p. 124 Fig. 4.29 in textbook (Chang)

Feature-Based Modeling

• There are many definitions of features … Some take it to mean a part of the model, and some think it can be something such as a hole or a boss.

• Feature: Any special geometric or functional element or property of an object useful in understanding the function, behavior, or performance of that object

• Feature recognition: The process of identifying features in a CAD model

Feature-Based Modeling

• Feature recognition: The process of identifying features in a CAD model

– Syntactic pattern methods– Rule-based methods– Graph-based methods

See next slide…

Feature-Based Modeling

– Syntactic pattern methods: 2D geometric searching for features

– Rule-based methods: Use production rules to describe features, then for patterns that match those rule. (Figure 8.20)

Feature-Based Modeling

– Graph-based methods: Use either boundary representation or other graph such as a face-edge graph (FEG) to represent the model… then that graph is searched for similar feature graphs

Feature-Based Modeling

• Volume decomposition: Determines the material that has been removed from a base part to get the required object, and then decomposes this material into features generally corresponding to machining operations

Feature-Based Modeling

• Design by features: An alternative to feature recognition, where a model is constructed from a library of features rather than geometric primitives– Destructve-solid geometry– Constructional design by features

See following slides …

Feature-Based Modeling Design by features

– Destructive-solid geometry: Features representing machining operations are subtracted from the material (Figure 8.22)

Feature-Based ModelingDesign by features

– Constructional design by features: The user assembles a representation of the object as a collection of features by adding or subtracting features from the model (Figure 8.23)

Feature-Based Modeling

• Design by features include:– Library or user-defined features classified as:

• Elementary: Simple features that can’t be composed into simpler features

• Composite: Constructed from two or more elementary features

• Composite features include:– Pattern: Have repeated instances of simpler features

such as a pattern of bolt holes– Compound: Features such as counter-bored holes

Feature-Based Modeling

• Design by features include: (cont’d)– Explicit Evaluated, or Enumerated features: All the

geometric details of the feature are explicitly defined– Implicit or Unevaluated: Contain information (such as

defining parameters) which may be used to define part geometry, the full details of which need to be calculated when required … such as threads, knurls, and gear

CAD/CAM Principles, Practice, and Manufacturing, 2nd Edition by Chris McMahon, and Jimmie Browne,

Addison Wesley Longman Limited 1998, pp. 270-271, 275-282.

Design Data exchange

• IGES

• STEP (ISO 10303) former PDES

pp. 124 -128 in Chang textbook.

Taught on the board.