Special Topics in Computer Science Computational Modeling for SnakeBased Robots ComputerAided Design

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Special Topics in Computer ScienceComputational
Modeling for Snake-Based RobotsComputer-Aided
Design Crash CourseWeek 1, Lecture 2

• William Regli
• Geometric and Intelligent Computing Laboratory
• Department of Computer Science
• Drexel University
• http//gicl.cs.drexel.edu

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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

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Computer Aided Design A Brief History

• In The Beginning1963Ivan SutherlandsSketchpad
  
• Modified oscilloscope for drawing
• The original CAD system

Courtesy Marc Levoy _at_ Stanford U
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
• 1970s
• 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, ES, DEC
• 1990s
• PCs (2K) Graphics boards, OpenGL, Java3D
• CADVideogamesAnimations 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

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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

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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

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Different Aspects of CAD
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2D Graphics

• RasterPixels
• X11 bitmap, XBM
• X11 pixmap, XPM
• GIF
• TIFF
• PNG
• JPG
• Lossy, jaggies when transforming, good for photos.

• VectorDrawing instructions
• Postscript
• CGM
• Fig
• DWG
• Non-lossy, smooth when scaling, good for line art
  and diagrams.

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Representing 3D Objects

• Approximate
• Facet / Mesh
• Just surfaces
• Voxel
• Volume info

• Exact
• Wireframe
• Parametric Surface
• Solid Model
• CSG
• BRep
• Implicit Solid Modeling

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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

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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

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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

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Two Major Types to Care About(for this class)

• Mesh-based representations
• Solid Models
• As generated from CAD or modeling systems

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3D Mesh File Formats

• Some common formats
• STL
• SMF
• OpenInventor
• VRML

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Minimal

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

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Full-Featured

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

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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

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Simple Mesh Format (SMF)

• Michael Garland http//graphics.cs.uiuc.edu/garla
  nd/
• Triangle data
• Vertex indices begin at 1

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Stereolithography (STL)

• Triangle data Face Normal
• The de-facto standard for rapid prototyping

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How STL Works
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Open Inventor

• Developed by SGI
• Predecessor to VRML
• Scene Graph

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Virtual Reality Modeling Language (VRML)

• SGML Based
• Scene-Graph
• Full Featured

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Issues with 3D mesh formats

• Easy to acquire
• Easy to render
• Harder to model with
• Error prone
• split faces, holes, gaps, etc

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Scanned Data
From Exact Representation
Single Scan
360 Scan
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How to scan (1)
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How to scan (2)
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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

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Solid Models
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3D solid model representations

• Implicit models
• Super/quadrics
• Blobbies
• Swept objects
• Boundary representations
• Spatial enumerations
• Distance fields
• Quadtrees/octrees
• Stochastic models

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3D solid model representations

• Implicit models
• Super/quadrics
• Blobbies
• Swept objects
• Boundary representations
• Spatial enumerations
• Distance fields
• Quadtrees/octrees
• Stochastic models

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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.

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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

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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
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Solid Object Definitions

• Boundary points
• Points where distance to the object and the
  objects complement is zero
• Interior points
• All the other points in the object
• Closure
• Union of interior points and boundary points

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Lets Start SimplePolyhedral 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

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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

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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 _at_ UMD-CP
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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,

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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

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Other Issues in Boundary Representation Solid
Modeling

• Whats the surface?

Foley/VanDam, 1990/1994
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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
Foley/VanDam, 1990/1994
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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 _at_ UMD-CP
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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
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Boolean Operations
Foley/VanDam, 1990/1994
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Constructive Solid Geometry (CSG)

• A tree structure combining primitives via
  regularized boolean operations
• Primitives can be solids or half spaces

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A Sequence of Boolean Operations

• Boolean operations
• Rigid transformations

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

• Can also be represented as a directed acyclic
  graph (DAG)

Pics/Math courtesy of Dave Mount _at_ UMD-CP
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Issues with Constructive Solid Geometry

• Non-uniqueness
• Choice of primitives
• How to handle more complex modeling?
• Sculpted surfaces? Deformable objects?

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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

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Issues with CSG

• Minor changes in primitive objects greatly affect
  outcomes
• Shift up top solid face

Foley/VanDam, 1990/1994
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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

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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

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Parametric Modeling in CAD

• Feature relationships
• Constraints

Foley/VanDam, 1990/1994
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CAD Formats
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Common CAD Formats

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

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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

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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

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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.

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

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Spatial Occupancy Enumerations
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Spatial Occupancy Enumeration

• Brute force
• A grid
• Pixels
• Picture elements
• Voxels
• Volume elements
• Quadtrees
• 2D representation
• Octrees
• 3D representation
• Extension of quadtrees

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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
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Quadtree

• Hierarchically represent spatial occupancy
• Tree with four regions
• NE, NW, SE, SW
• dark if occupied

Foley/VanDam, 1990/1994
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Octree

• 8 octants 3D space
• Left, Right, Up, Down, Front, Back

Foley/VanDam, 1990/1994
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Applications for Spatial Occupancy Enumeration

• Many different applications
• GIS
• Medical
• Engineering Simulation
• Volume Rendering
• Video Gaming
• Approximating real-world data
• .

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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)

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END
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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, GDT
  (Geometry Dimensions and Tolerance).
• Therefore we need GDT in data translation
• STEP 203 E2 implementation will help

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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.

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The Design Cycle
PROCESS
Process drives out requirements
Tools accomplish the process
INNOVATION!
TOOLS
REQs
Requirements are accommodated by data structure
DATA FORMAT
Data format enables the tool
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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.

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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

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Factors influence the quality of data translation

• Design standards
• Design methodology
• Design quality control
• Release process with a model quality check

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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 designetc)

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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?

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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.

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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.
• ProcessgtRequirementsgtDataStructuregtTool,----
  Paradigm
• Single source master definition, vaulted data,
  distributed and repurposed for the target
  downstream activity.
• Highly reusable data sets.

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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,

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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

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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) lt 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 _at_ UW
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Quadratic Surfaces

• Sphere
• Ellipsoid
• Torus
• General form

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Superellipsoid Surfaces

• Generalization of ellipsoid
• Control parameters s1 and s2
• If s1 s2 1 then regular ellipsoid
• Has an implicit and parametric form!

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CSG with Superquadrics
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CSG with Superellipsoids
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End