Geometric Modeling
- 1. IE 605 Fall 2006 UW-Madison Section 2-1-1 Geometric Modeling Introduction Courtesy of Alyn Alyn Rockwood, SGI Ardy Ardy Goshtasby, Wright State Wright State U.
- 2. IE 605 Fall 2006 UW-Madison Field warranty service Production system Prototyping Process design GD&T Quality control Product design GD&T Engineering Modeling Market analysis, R&D Computer Aided Design (CAD) Computer Aided Manufacturing (CAM) Rapid Prototyping Cell, Quick Response Manufacturing Statistic Process Control (SPC) Geometric Modeling FEM (ME601) SOVA (IE655) CAD design DFMA AXIOM QFD FMEA CNC CAPP Machining calculation Tolerance design (IE 655) Rapid prototyping Rapid Prototyping (ME 601) Manufacturing process (IE 415) Facility Planning (IE 510) QRM (IE 641) SPC (IE 512) DOE(IE 575) QRM (IE 641) Information Sensing and Analysis (IE6 12 ) Manufacturing Map: Where we are? Topics and related classes
- 3. Geometric Modeling: The Foundation of CAD Why do we want to model the physical world (e.g., an object) ? Model is: Extract/represent: George Box: Model & simulation What does CAD do? What information does it represent? What does CAD don’t do? IE 605 Fall 2006 UW-Madison
- 4. Geometric Modeling: The Foundation of CAD A Geometric Modeling System can be characterized as an application component responsible for creating, inspecting, analyzing and distributing geometric models. Geometric Modeling Studies computer-based representation of geometry and related information needed for supporting various computer-based applications in engineering design, analysis, manufacturing and related areas. IE 605 Fall 2006 UW-Madison Approaches to geometric modeling vary in content and capability of supporting the full range of geometric computations.
- 5. Geometric Modeling (contd.) Involves study of data structures, algorithms and formats for creating, representing, communicating and manipulating geometric information of parts and processes. There are 4 major types of geometric models: Graphical models Wireframe Model Curve models Hermite Cubic Splines; Bezier Curves; B-Splines, NURBS Surface models Non-parametric; Parametric Surfaces (Bicubic, Bezier, …., Ruled Surfaces) Solid models Quadtrees/Octrees (2D/3D, orthogonal partitioning); Binary Space Partitioning (BSP; Non-orthogonal lines/surfaces); Constructive Solid Geometry (CSG: Primitives/Boolean operations) Boundary Representation (B-Rep: Primitives/Euler Operations: Example: The Winged-Edge Data Structure) IE 605 Fall 2006 UW-Madison
- 6. For a long time CAD stood for Computer Aided Drafting. Many industries use CAD for such applications even today. Such CAD packages are based primarily on graphical modelers. Two basic kind: 2D Graphical Models 3D Graphical Models Graphical Models IE 605 Fall 2006 UW-Madison
- 7. Graphical Models (contd.) 2D Graphical Models Graphical primitive lines, points, arcs, etc. used Each entity may have graphical attributes (color, display, etc.) Models can be composed of independent layers 3D Graphical Models Graphical primitives and parts are defined in 3D space Resulting representation frequently referred to as “Wire Frame” model “ Graphically deficient” models - possible to create meaningless designs IE 605 Fall 2006 UW-Madison
- 8. Graphical Models (contd.) IE 605 Fall 2006 UW-Madison
- 9. Geometric Modeling: Validation IE 605 Fall 2006 UW-Madison A good geometric modeling representation should address the following seven issues: Domain : While no representation can describe all possible solids, a representation should be able to represent a useful set of geometric objects. Unambiguity : When you see a representation of a solid, you will know what is being represented without any doubt. An unambiguous representation is usually referred to as a complete one. Uniqueness : That is, there is only one way to represent a particular solid. If a representation is unique, then it is easy to determine if two solids are identical since one can just compare their representations.
- 10. Geometric Modeling: Validation IE 605 Fall 2006 UW-Madison R R Object (Reality) Representation (Model) M M1 M2 R1 Unambiguous, complete, unique scheme Unambiguous, complete, Non-unique scheme Ambiguous, incomplete scheme M1 R2
- 11. Geometric Modeling: Validation IE 605 Fall 2006 UW-Madison A good geometric modeling representation should address the following seven issues: Accuracy : A representation is said accurate if no approximation is required. Validness : This means a representation should not create any invalid or impossible solids. More precisely, a representation will not represent an object that does not correspond to a solid. Closure : Solids will be transformed and used with other operations such as union and intersection. "Closure" means that transforming valid solids always yields valid solids. Compactness and Efficiency : A good representation should be compact enough for saving space and allow for efficient algorithms to determine desired physical characteristics .
- 12. Curve Models: Boundary Conditions Start & end points of the curve The tangent vectors at the start & end points of the curve IE 605 Fall 2006 UW-Madison p(0)/ u u = 0 p 0 p(1)/ u u = 1 p 1
- 13. In many cases, it is necessary to synthesize a curve from several curves, for modeling shapes & features. When 2 curves are joined, 3 continuity conditions are possible: C0 Continuity or Point Continuity C1 Continuity or Tangent Continuity C2 Continuity or Curvature Continuity Composite Curves IE 605 Fall 2006 UW-Madison u 5 u 1 O u 2 u 3 u 4
- 14. Composite Curves (contd.) C0 Continuity or Point Continuity Two curves are joined end to end with no restriction on the end slope or curvature. IE 605 Fall 2006 UW-Madison A B
- 15. Composite Curves (contd.) C1 Continuity or Tangent Continuity: This implies that two curves joined end to end have the same slope at the common meeting point. IE 605 Fall 2006 UW-Madison A B
- 16. Composite Curves (contd.) C2 Continuity or Curvature Continuity: The two curves not only have the same slope at the common point but also the same curvature too. IE 605 Fall 2006 UW-Madison A B