Week 5 – MSE508/L Ileana Costea, Ph.D.

1. Week 5 – MSE508/LIleana Costea, Ph.D. Spring 2008 Solid Modeling/Data Exchanges Chapter 4 and part of Ch. 5 (pp. 169 - 177) (Chang textbook)

2. 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.)

3. 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)

4. 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.html TUTORIAL: NURBS Head Modeling

5. 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.

6. 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

7. 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.

8. 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)

9. 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)

10. 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

11. 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):

12. 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

13. 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)

14. 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

15. 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

16. 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

17. 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)

18. 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)

19. Parametric/Variational Modeling Differences:

20. Parametric/Variational Modeling • Look at picture p. 124 Fig. 4.29 in textbook (Chang)

21. 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

22. 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…

23. 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)

24. 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

25. 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

26. 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 …

27. Feature-Based Modeling Design by features • Destructive-solid geometry: Features representing machining operations are subtracted from the material (Figure 8.22)

28. 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)

29. 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

30. 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.

31. Design Data exchange • IGES • STEP (ISO 10303) former PDES pp. 124 -128 in Chang textbook. Taught on the board.