1. 1 Special Topics in Computer Science Computational Modeling for Snake-Based Robots Computer-Aided Design Crash Course Week 1, Lecture 2 William Regli Geometric and Intelligent Computing Laboratory Department of Computer Science Drexel University http://gicl.cs.drexel.edu

2. 2 Building Multidisciplinary Model Class Goal: create multidisciplinary engineering models Challenge: Learn enough about each discipline to create integrated models! Today: The role of 3D models and CAD

3. 3 Computer Aided Design: A Brief History In The Beginning… 1963 Ivan Sutherland’s Sketchpad Modified oscilloscope for drawing The original CAD system Courtesy Marc Levoy @ Stanford U

4. 4 History of the 3D graphics industry 1960s: –Line drawings, hidden lines, parametric surfaces (B-splines…) –Automated drafting & machining for car, airplane, and ships manufacturers 1970’s: –Mainframes, Vector tubes (HP…) –Software: Solids, (CSG), Ray Tracing, Z-buffer for hidden lines 1980s: –Graphics workstations ($50K-$1M): Frame buffers, rasterizers, GL, Phigs –VR: CAVEs and head-mounted displays –CAD/CAM & GIS: CATIA, SDRC, PTC –Sun, HP, IBM, SGI, E&S, DEC 1990s: –PCs ($2K): Graphics boards, OpenGL, Java3D –CAD+Videogames+Animations: AutoCAD, SolidWorks…, Alias-Wavefront –Intel, many board vendors 2000s: –Laptops, PDAs, Cell Phones: Parallel graphic chips –Everything will be graphics, 3D, animated, interactive –Nvidia, Sony, Nokia

5. 5 Buzzword Deconfliction Computer Aided Geometric Design (CAGD): Curves/surfaces Solid Modeling: Representations and Algorithms for solids Computational Geometry: Provably efficient algorithms Computer-Aided Design (CAD): Automation of Shape Design Computer-Aided Manufacturing (CAM): NC Machining Finite Element Meshing (FEM): Construction and simulation Animation: Capture, Design, Simulation of shape behavior Visualization: Graphical interpretations of (large) nD datasets Rendering: Making (realistic) pictures of 3D geometric shapes Image-Based Rendering (IBR): Mix images and geometry Computer Vision: Reconstruction of 3D models from images Reverse Engineering: Fitting surfaces to scanned 3D points Virtual Reality (VR): Immersion in interactive environments Augmented Reality (AR): Track and mark-up what you see

6. 6 What is CAD? Primary authoring tool for the geometry and topology data associated with a product (plan, train, auto, building, etc) CAD software is central to Product Lifecycle Management and is often integrated with manufacturing, analysis, simulation and other engineering and business functions

7. 7 Different Aspects of CAD

8. 8 2D Graphics Raster: Pixels –X11 bitmap, XBM –X11 pixmap, XPM –GIF –TIFF –PNG –JPG Lossy, jaggies when transforming, good for photos. Vector: Drawing instructions –Postscript –CGM –Fig –DWG Non-lossy, smooth when scaling, good for line art and diagrams.

9. 9 Representing 3D Objects Approximate –Facet / Mesh Just surfaces –Voxel Volume info Exact –Wireframe –Parametric Surface –Solid Model CSG BRep Implicit Solid Modeling

10. 10 Representing 3D Objects Exact –Precise model of object topology –Mathematically represent all geometry Approximate –A discretization of the 3D object –Use simple primitives to model topology and geometry

11. 11 Negatives when Representing 3D Objects Exact –Complex data structures –Expensive algorithms –Wide variety of formats, each with subtle nuances –Hard to acquire data –Translation required for rendering Approximate –Lossy –Data structure sizes can get HUGE, if you want good fidelity –Easy to break (i.e. cracks can appear) –Not good for certain applications Lots of interpolation and guess work

12. 12 Positives when Representing 3D Objects Exact –Precision Simulation, modeling, etc –Lots of modeling environments –Physical properties –Many applications (tool path generation, motion, etc.) –Compact Approximate –Easy to implement –Easy to acquire 3D scanner, CT –Easy to render Direct mapping to the graphics pipeline –Lots of algorithms

13. 13 Two Major Types to Care About (for this class) Mesh-based representations Solid Models –As generated from CAD or modeling systems

14. 14 3D Mesh File Formats Some common formats STL SMF OpenInventor VRML

15. 15 Minimal Vertex + Face No colors, normals, or texture Primarily used to demonstrate geometry algorithms

16. 16 Full-Featured Colors / Transparency Vertex-Face Normals (optional, can be computed) Scene Graph Lights Textures Views and Navigation

17. 17 Subdivision Surfaces Coarse Mesh & Subdivision Rule –Define smooth surface as limit of sequence of algorithmic refinements Modify topology & interpolate neighboring vertices Used in graphics, animation and digital arts applications

18. 18 Simple Mesh Format (SMF) Michael Garland http://graphics.cs.uiuc.edu/~garland/ Triangle data Vertex indices begin at 1

19. 19 Stereolithography (STL) Triangle data + Face Normal The de-facto standard for rapid prototyping

20. 20 How STL Works

21. 21 Open Inventor Developed by SGI Predecessor to VRML –Scene Graph

22. 22 Virtual Reality Modeling Language (VRML) SGML Based Scene-Graph Full Featured

23. 23 Issues with 3D “mesh” formats Easy to acquire Easy to render Harder to model with Error prone –split faces, holes, gaps, etc

24. 24 Scanned Data From Exact Representation Single Scan360° Scan

25. 25 How to scan (1)

26. 26 How to scan (2)

27. 27 Issues with Scanning Error and noise Time consuming –Lots of human editing required to create clean models Models can be very large –Much larger than original BRep

28. 28 Solid Models

29. 29 3D solid model representations Implicit models Super/quadrics Blobbies Swept objects Boundary representations Spatial enumerations Distance fields Quadtrees/octrees Stochastic models

30. 30 3D solid model representations Implicit models Super/quadrics Blobbies Swept objects Boundary representations Spatial enumerations Distance fields Quadtrees/octrees Stochastic models

31. 31 Boundary Representation Solid Modeling The de facto standard for CAD since ~1987 –BReps integrated into CAGD surfaces + analytic surfaces + boolean modeling Models are defined by their boundaries Topological and geometric integrity constraints are enforced for the boundaries –Faces meet at shared edges, vertices are shared, etc.

32. 32 Solids and Solid Modeling Solid modeling introduces a mathematical theory of solid shape –Domain of objects –Set of operations on the domain of objects –Representation that is Unambiguous Accurate Unique Compact Efficient

33. 33 Solid Objects and Operations Solids are point sets –Boundary and interior Point sets can be operated on with boolean algebra (union, intersect, etc) Foley/VanDam, 1990/1994

34. 34 Solid Object Definitions Boundary points –Points where distance to the object and the object’s complement is zero Interior points –All the other points in the object Closure –Union of interior points and boundary points

35. 35 Let’s Start Simple: Polyhedral Solid Modeling Definition –Solid bounded by polygons whose edges are each a member of an even number of polygons –A 2-manifold: edges members of 2 polygons

36. 36 BRep Data Structure Vertex structure –X,Y,Z point –Pointers to n coincident edges Edge structure –2 pointers to end-point vertices –2 pointers to adjacent faces –Pointer to next edge –Pointer to previous edge Face structure –Pointers to m edges

37. 37 BRep Data Structures Winged-Edge Data Structure (Weiler) Vertex –n edges Edge –2 vertices –2 faces Face –m edges Pics/Math courtesy of Dave Mount @ UMD-CP

38. 38 State of the Art: BRep Solid Modeling … but much more than polyhedra Two main (commercial) alternatives –All NURBS, all the time Pro/E, SDRC, … –Analytic surfaces + parametric surfaces + NURBS + …. all stitched together at edges Parasolid, ACIS, …

39. 39 Issues in Boundary Representation Solid Modeling Very complex data structures –NURBS-based winged-edges, etc Complex algorithms –manipulation, booleans, collision detection Robustness Integrity Translation Features Constraints and Parametrics

40. 40 Other Issues in Boundary Representation Solid Modeling What’s the surface? Foley/VanDam, 1990/1994

41. 41 Issues with 3D Set Operations Ops on 3D objects can create “non-3D objects” or objects with non-uniform dimensions Objects need to be “Regularized” –Take the closure of the interior Foley/VanDam, 1990/1994 Input set Closure Interior Regularized

42. 42 Regularized Boolean Operations 3D Example –Two solids A and B –Intersection leaves a “dangling wall” A 2D portion hanging off a 3D object –Closure of interior gives a uniform 3D result Pics/Math courtesy of Dave Mount @ UMD-CP

43. 43 Boolean Operations Other Examples: (c) ordinary intersection (d) regularized intersection –AB - objects on the same side –CD objects on different sides Foley/VanDam, 1990/1994

44. 44 Boolean Operations Foley/VanDam, 1990/1994

45. 45 Constructive Solid Geometry (CSG) A tree structure combining primitives via regularized boolean operations Primitives can be solids or half spaces

46. 46 A Sequence of Boolean Operations Boolean operations Rigid transformations Pics/Math courtesy of Dave Mount @ UMD-CP

47. 47 The Induced CSG Tree Pics/Math courtesy of Dave Mount @ UMD-CP

48. 48 The Induced CSG Tree Can also be represented as a directed acyclic graph (DAG) Pics/Math courtesy of Dave Mount @ UMD-CP

49. 49 Issues with Constructive Solid Geometry Non-uniqueness Choice of primitives How to handle more complex modeling? –Sculpted surfaces? Deformable objects?

50. 50 Issues with Constructive Solid Geometry Non-Uniqueness –There is more than one way to model the same artifact –Hard to tell if A and B are identical

51. 51 Issues with CSG Minor changes in primitive objects greatly affect outcomes Shift up top solid face Foley/VanDam, 1990/1994

52. 52 Uses of CSG Constructive Solid Geometry Found (basically) in every CAD system Elegant, conceptually and algorithmically appealing Good for –Rendering, ray tracing, simulation –BRL CAD

53. 53 CAD: Feature-Based Design CSG is the basic machinery behind CAD features Features are –Local modifications to object geom/topo with engineering significance –Often are additive or subtractive mods to shape Hole, pocket, etc…

54. 54 Parametric Modeling in CAD Foley/VanDam, 1990/1994 Feature relationships Constraints

55. 55 CAD Formats

56. 56 Common CAD Formats Standards –STEP (ISO 103033) –IGES Industry –Solid Model (mostly just geom/topo) ACIS.sat, Parasolid.xmt, OpenCascade –CAD Model Vendor specific

57. 57 CAD Vendor Formats Pro/ENGINEER –.prt (part) and.asm (assembly) UG/SDRC –.mf1 (model file),.arc (archive),.xmt (transmit file) AutoCAD –DXF, DWG Bentley –DGN Etc etc

58. 58 CAD Vendor Format Comments Some systems do not produce ‘solids’ by default –i.e. AutoCAD AEC models, while 3D, are not solids Formats are complex Translation is difficult Going from –System #1 Native file  STEP (neutral file)  System #2 Native file … creates data loss and can introduce error

59. 59 A brief history IGES V1.0 was released in 1981, the current version V5.3 was released in 1996 –Geometry-based standard –Non-unique definition for many entities –Many IGES flavoring tools for repair STEP v1.0 was released in 1994 –Product-based –Have not heard about “step flavoring” tools –An issue in both IGES and STEP: different CAD systems have different tolerance, therefore a trim surface may become untrimmed after translation. –A very popular application of IGES/STEP is not data translation, it is long term data retention.

60. 60 IGES & STEP history IGES v.1 IGES v5.3 STEP AP203 STEP AP203 E2 1980 2010 2000 1990 Multiple definitions for the same entity. Many IGES flavoring tools CAD system tolerance issues Parametrics Need construction history, GD&T Many commercial direct translators A very successful application of IGES/STEP is long term data retention. Full interoperability?

61. 61 Getting CAD Model for Legos

62. 62 CAD Systems Drexel is site licensed for MicroStation –https://software.drexel.eduhttps://software.drexel.edu Other tools available at GICL and MEM –I-DEAS –Pro/E –SolidWorks –AutoCAD

63. 63 Spatial Occupancy Enumerations

64. 64 Spatial Occupancy Enumeration Brute force –A grid Pixels –Picture elements Voxels –Volume elements Quadtrees –2D representation Octrees –3D representation –Extension of quadtrees

65. 65 Brute Force Spatial Occupancy Enumeration Impose a 2D/3D grid –Like graph paper or sugar cubes Identify occupied cells Problems –High fidelity requires many cells “Modified” –Partial occupancy Foley/VanDam, 1990/1994

66. 66 Quadtree Hierarchically represent spatial occupancy Tree with four regions –NE, NW, SE, SW –“dark” if occupied Foley/VanDam, 1990/1994

67. 67 Octree 8 octants 3D space –Left, Right, Up, Down, Front, Back Foley/VanDam, 1990/1994

68. 68 Applications for Spatial Occupancy Enumeration Many different applications –GIS –Medical –Engineering Simulation –Volume Rendering –Video Gaming –Approximating real-world data –….

69. 69 Issues with Spatial Occupancy Enumeration Approximate –Kind of like faceting a surface, discretizing 3D space –Operationally, the combinatorics (as opposed to the numerics) can be challenging –Not as good for applications wanting exact computation (e.g. tool path programming)

70. 70 END

71. 71 MBD or Model Based Definition 3D model is the sole data authority No more 2D drawings The 3D model should contain everything needed from design to manufacturing, in particular, GD&T (Geometry Dimensions and Tolerance). Therefore we need GD&T in data translation STEP 203 E2 implementation will help

72. 72 MBD – Model Based Definition Boeing is transitioning rapidly to a model based environment. Data Delivery to supplier must be formatted robustly and efficiently and in a standard open format. Data must be “purposed” to the downstream activity to protect IP and KBE. Relational design chains must be preserved for interoperability. Attribute and Meta data must be passed in a Xlation and purposed. New materials will bring new requirements for data exchange.

73. 73 The Design CyclePROCESS DATAFORMAT REQ’sREQ’sREQ’sREQ’s TOOLSTOOLSTOOLSTOOLS Process drives out requirements Requirements are accommodated by data structure Data format enables the tool Tools accomplish the process INNOVATION!

74. 74 Feature-based translation Users expect translated model to be modifiable at the receiving site Feature-based translation or construction history or STEP AP203 E2 Feature-reconstruction bypasses CAD system tolerance issues, however, it brings in another set of problems – – There are many incompatible features between CAD systems – There are many construction methods for the same feature on the same CAD system (e.g.hole) – Different CAD system employs different algorithms to computer intersection curves, therefore, we need translation validation.

75. 75 CAD Data Translation Validation Users have been asking for it since Day 1. What to validate? Do you care about these changes? – geometry or shape – topology – one sphere becomes two semi-spheres – entity count – math – exact representation of a circle by a NURBS spline – mass property – color changes – layer changes Challenges – Need to recognize that this is a new field – How to communicate changes to a general user in a “general” language? – Need a tool developed for this purpose

76. 76 Factors influence the quality of data translation Design standards Design methodology Design quality control Release process with a model quality check

77. 77 Design processes influence data translation needs paper drawing – no need for data translation 2D CAD drawing – dxf or IGES 3D CAD design – IGES or STEP 3D CAD solid design - STEP PLM – Product Lifecycle Management Data management is the center of the universe Designers must go to PDM to get appropriate CAD models CAD is one of many tools within PLM CAD data translation must go with PDM (CAD model + data maturity level + BOM + relational design…+etc)

78. 78 CAD Data Translation Challenges CAD systems were design for CAD, not data translation Data translation is a step-child of a CAD system Do CAD vendors care about data translation? No, this is a step-child. Yes, make sure it does not work well to export my data. STEP AP203 E2 implementation – How to get all major CAD vendors involved?

79. 79 What we do not want to translate Company intellectual property embedded in CAD models – KBE (Knowledge Based Engineering) data – Specific math formulas to create curves and surfaces – Third party application software data - engineering notes – in-house developed macros This is not a problem with current IGES, STEP or other direct translators. However, we are concerned with data exchange with suppliers in native CAD files such as CATIA V5 via a PDM system.

80. 80 How does Boeing perform data translation? Point solution Xlators tailored for specific native formats are utilized at Boeing Healthy use of iges and STEP for exchange of data. Validation shares equal priority with Xlation Boeing has adopted a common native toolset from Dassault Systems’ as a go forward strategy. Process>Requirements>DataStructure>T ool,----} Paradigm Single source master definition, vaulted data, distributed and repurposed for the target downstream activity. Highly reusable data sets.

81. 81 Introduction Past – STEP expectations not met, what has accomplished, weak areas, work arounds, etc. Present – New standards evolving, current capabilities, limitations, work arounds, etc. Future – Full relational design expectations, dreams,

82. 82 Surface Models Basic idea: –Represent a model as a set of faces/patches Limitations: –Topological integrity; how do faces “line up”?; which way is ‘inside’/ ‘outside’? Used in many CAD applications –Why? They are fine for drafting and rendering, not as good for creating true physical models

83. 83 Implicit Solid Modeling Computer Algebra meets CAD Idea: –Represents solid as the set of points where an implicit global function takes on certain value F(x,y,z) < val –Primitive solids are combined using CSG –Composition operations are implemented by functionals which provide an implicit function for the resulting solid From M.Ganter, D. Storti, G. Turkiyyah @ UW

84. 84 Quadratic Surfaces Sphere Ellipsoid Torus General form

85. 85 Superellipsoid Surfaces Generalization of ellipsoid Control parameters s 1 and s 2 If s 1 = s 2 =1 then regular ellipsoid Has an implicit and parametric form! s2s2 s1s1

86. 86 CSG with Superquadrics

87. 87 CSG with Superellipsoids

88. 88 End