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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 1

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

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 3

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

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) n. D datasets Rendering: Making (realistic) pictures of 3 D geometric shapes Image-Based Rendering (IBR): Mix images and geometry Computer Vision: Reconstruction of 3 D models from images Reverse Engineering: Fitting surfaces to scanned 3 D points Virtual Reality (VR): Immersion in interactive environments Augmented Reality (AR): Track and mark-up what you see 5

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 6

Different Aspects of CAD 7

2 D Graphics • Raster: Pixels – – – X 11 bitmap, XBM X 11 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. 8

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

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

Negatives when Representing 3 D 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 11

Positives when Representing 3 D 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 • 3 D scanner, CT – Easy to render • Direct mapping to the graphics pipeline – Lots of algorithms 12

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

3 D Mesh File Formats Some common formats • STL • SMF • Open. Inventor • VRML 14

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

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

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 17

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

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

How STL Works 20

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

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

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

Scanned Data 360° Scan Single Scan From Exact Representation 24

How to scan (1) 25

How to scan (2) 26

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 27

Solid Models 28

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

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

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. 31

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 32

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

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 34

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 35

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 36

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

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, … 38

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 39

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

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

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

Boolean Operations 44 Foley/Van. Dam, 1990/1994

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

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

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

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

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

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 50

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

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 52

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… 53

Parametric Modeling in CAD • Feature relationships • Constraints 54 Foley/Van. Dam, 1990/1994

CAD Formats 55

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

CAD Vendor Formats • Pro/ENGINEER –. prt (part) and. asm (assembly) • UG/SDRC –. mf 1 (model file), . arc (archive), . xmt (transmit file) • Auto. CAD – DXF, DWG • Bentley – DGN • Etc etc 57

CAD Vendor Format Comments • Some systems do not produce ‘solids’ by default – i. e. Auto. CAD AEC models, while 3 D, 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 58

A brief history • IGES V 1. 0 was released in 1981, the current version V 5. 3 was released in 1996 – Geometry-based standard – Non-unique definition for many entities – Many IGES flavoring tools for repair • STEP v 1. 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 59 long term data retention.

IGES & STEP history STEP AP 203 E 2 2010 Full interoperability? IGES v 5. 3 STEP AP 203 2000 Parametrics Need construction history, GD&T A very successful application of IGES/STEP is long term data retention. IGES v. 1 1980 1990 Many commercial direct translators CAD system tolerance issues Multiple definitions for the same entity. Many IGES flavoring tools 60

Getting CAD Model for Legos 61

CAD Systems • Drexel is site licensed for Micro. Station – https: //software. drexel. edu • Other tools available at GICL and MEM – I-DEAS – Pro/E – Solid. Works – Auto. CAD 62

Spatial Occupancy Enumerations 63

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

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

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

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

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

Issues with Spatial Occupancy Enumeration • Approximate – Kind of like faceting a surface, discretizing 3 D 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) 69

END 70

MBD or Model Based Definition • 3 D model is the sole data authority • No more 2 D drawings • The 3 D 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 E 2 implementation will help 71

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. 72

The Design Cycle PROCESS Tools accomplish the process T O O L S Data format enables the tool INNOVATION! DATA FORMAT Process drives out requirements R E Q ’s Requirements are accommodated by data structure 73

Feature-based translation • Users expect translated model to be modifiable at the receiving site • Feature-based translation or construction history or STEP AP 203 E 2 • Feature-reconstruction bypasses CAD system tolerance issues, however, it brings in another set of problems – – There are many incompatible features between CAD systems 74

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 75 – mass property

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

Design processes influence data translation needs • paper drawing – no need for data translation • 2 D CAD drawing – dxf or IGES • 3 D CAD design – IGES or STEP • 3 D 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) 77

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 AP 203 E 2 implementation – How to get all major CAD vendors involved? 78

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 79 are concerned with data exchange with

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>Data. Structure>80

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 81

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 82

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 83 From M. Ganter, D. Storti, G. Turkiyyah @ UW

Quadratic Surfaces • Sphere • Ellipsoid • Torus • General form 84

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

CSG with Superquadrics 86

CSG with Superellipsoids 87

End 88