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 3D 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

• • • • • 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 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: Rendering:

Graphical interpretations of (large) nD datasets 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

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

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.

8

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

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 10

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 11

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 12

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

3D Mesh File Formats Some common formats • STL • SMF • OpenInventor • 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.cs.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 3D “mesh” formats • Easy to acquire • Easy to render • Harder to model with • Error prone – split faces, holes, gaps, etc 23

360 ° Scan Scanned Data 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

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

3D 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/VanDam, 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 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 Input set Closure Interior Regularized 41 Foley/VanDam, 1990/1994

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 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/VanDam, 1990/1994

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

CAD Formats 55

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

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 57

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 System #2 Native file … creates data loss and can introduce error  STEP (neutral file)  58

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.

59

IGES & STEP history STEP AP203 IGES v5.3

STEP AP203 E2 2000 2010 Full interoperability?

Parametrics Need construction history, GD&T IGES v.1

A very successful application of IGES/STEP is long term data retention.

1990 Many commercial direct translators CAD system tolerance issues 1980 Multiple definitions for the same entity. Many IGES flavoring tools 60

Getting CAD Model for Legos 61

CAD Systems • Drexel is site licensed for MicroStation – https://software.drexel.edu

• Other tools available at GICL and MEM – I-DEAS – Pro/E – SolidWorks – AutoCAD 62

Spatial Occupancy Enumerations 63

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

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 65 Foley/VanDam, 1990/1994

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

Octree • 8 octants 3D space – Left, Right, Up, Down, Front, Back 67 Foley/VanDam, 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 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) 69

END 70

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 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

Tools accomplish the process The Design Cycle PROCESS Process drives out requirements T O O L S INNOVATION!

R E Q ’s Data format enables the tool DATA FORMAT 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 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 74 – There are many construction methods for

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 75 – color changes

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 • paper drawing – translation needs 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) 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 AP203 E2 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 suppliers in native CAD files such as CATIA

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 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 – expectations, dreams,

81

Full relational design

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

Quadratic Surfaces  • Sphere

x

2 

y

2 

z

2 

r

2 • Ellipsoid  

r x x

  2 • Torus     

r

  

r x x

   2 

y



r y

   2 

y



r y

• General form    2  

r z z

    2   2   1  

r z z

  2  1 

a



x

2 

b



y

2 

c



z

2  2

f



yz

 2

g



xz

 2

h



xy

 2

p



x

 2

q



y

 2

r



z



d

 0  84

 Superellipsoid Surfaces • Generalization of ellipsoid • Control parameters s 1 and s 2     

x r x

  2 /

s

2   

y



r y

  2 /

s

2   

s

2 /

s

1   

r z z

  2 /

s

1  1 • If s 1 = s 2 =1 ellipsoid then regular • Has an implicit and parametric form!

s 1 s 2 85

CSG with Superquadrics 86

CSG with Superellipsoids 87

End 88