11. Implicit Surfaces for Geometric Modeling and Computer Graphics
Full Day / Intermediate
In this course, researchers from academia and industry introduce the basic
concepts and uses of implicit surfaces in geometric modeling and computer
graphics. In particular, the course covers techniques for modeling,
visualizing, and animating implicit algebraic patches, skeletal surfaces,
and fractal surfaces. Also covered: new twists related to dual boundary and
constructive solid geometry representation schemes, parallel hardware for
direct processing, and implicit techniques for non-manifold
geometry.
Who Should Attend
Engineers involved with CAD, scientists involved with visualization,
animators, programmers, or managers who use or build computer animation or
geometric modeling tools.
Organizers
Jai Menon
IBM T. J. Watson Research Center
Brian Wyvill
University of Calgary
Lecturers
Chandrajit Bajaj
Purdue University
Jules Bloomenthal
Microsoft Corporation
Baining Guo
York University
John Hart
Washington State University
Geoff Wyvill
University of Otago
Schedule
Implicit Surfaces for Geometric Modeling and Computer Graphics
Course syllabus
8:30 am: Introduction - J. Menon, B. Wyvill
Welcome
Evolution of the field
Course history: 1990, 1993, 1996 (what's new)
What we will (and will not) cover
SECTION 1: Basic Building Blocks
8:40 am: Fundamentals of Implicit Surfaces - J. Menon
Contrast with parametric surfaces
General categorization and range of implicit surfaces
(algebraic to skeletal, and now emerging R-function based
methods)
A math primer using quadratic algebraic surfaces
(algebraic/geometric reps, classification, transformation,
etc.)
Introduction to low degree implicit algebraics in shape modeling
(both "prismatic", e.g. pistons, and "free-form", e.g. bones)
9:00 am: Intuitive Implicit Skeletal Design - J. Bloomenthal
Implicit primitives as distance functions
Blends as combination of implicit primitives
Integration vs. polynomial blends
9:30 am: Representation Schemes and Impact on Rendering - J. Menon
Boundary representation
Constructive Solid Geometry
Representation Conversion (problems of separation and
describability)
Rendering methods (polygonal Brep vs. direct CSG rendering)
RayCasting Engine (RCE) and ray-rep applications
(custom-VLSI highly parallel direct CSG hardware raycaster
with)
(applications: rendering, boolean, blending and Minkowski
operations)
10:00 am: Break
SECTION 2: Implicit Algebraic Methods
10:15 am: A-Patches and Deformations - C. Bajaj
Definition of A-Patches, Barycentric, Tensor
Topology of A-patches
Interpolatory fitting schemes (C1 with cubics, C2 with quintics)
Subdivision based approximation scheme (C1 with cubics, C2 with
quintics)
Fast Display, Animation and Interactive Control
Free-form implicit deformations
Surface fitting
11:05 am: Dual Free-form Brep/CSG with Algebraic Patches - J. Menon
Algebraic patches, halfspaces, and trunctets
Constructive Shell Representation (CSR: new hybrid Brep/CSG)
Exact CSG from polyhedral smoothing
Coupling problems (e.g. separation and subshell-overlaps)
Finite extent decompositions
Incremental CSG updates during surface tweaking
Direct rendering on the RCE
11:25 am: Shape Creation and Control with Low Degrees - B. Guo
Polyhedral smoothing
Degree vs. continuity (e.g. lifting schemes for finite elements)
Topological anomalies and single-sheetedness
Dual control polygon model
Control points computation (Kuhn-Tucker conditions)
Local and global effects (hard vs. soft constraints,
interactivity)
Shape control analogy with NURBS patches
12:00 noon: Break
SECTION 3: Beyond Low Degree Algebraics
1:30 pm: Tiling Techniques for Implicit Skeletal Models - B. Wyvill
Uniform and adaptive space subdivision
Table driven polygonization
Shrink-wrapped adaptive polygonization
Optimization techniques including skeletal pre-sort and frame
coherence
Surface following vs. space subdivision
1:50 pm: Animation and Design Systems for Skeletal Models - B. Wyvill
Global and local functions
Conforming a surface to its surroundings
Heuristics for metamorphosis
Dynamic and kinematic control of shape distortion
Changing skeleton positions over time
Collision detection
Skeletal design: advantages, changes over time
2:20 pm: Blends in Implicit Skeletal Methods - J. Bloomenthal
Relation of skeleton to bulge-free blends
Blend of volume to surface
Non-manifold surface techniques
Distance to a surface patch
2:40 pm: Implicit Skeletal Models and CSG - G. Wyvill
Principles of CSG modeling and rendering
Distinction between CSG subtraction and negative fields
Direct CSG ray tracing (why polygons are unsuitable)
Multiple intersections, signatures and mailboxes
Space division for efficient CSG rendering
Blended objects as CSG primitives
3:00 pm: Break
3:15 pm: Texturing Implicit Seletal Models - G. Wyvill
Parameterization (constructing surface uv coordinates)
Establishing the object coordinate system
Accounting for geometrical and topological changes
Abstract texture space coordinates and alternative methods
Clipping volumes to determine vertex color
Embedded particles
Displaced surfaces by noise addition
Inheritance of color and texture
Solid texturing (fhc coordinates, cases where this fails)
3:45 pm: Implicit Representations of Rough Surfaces - J. Hart
IFS and RIFS fractal models
Hypertexture fractal models
Ray tracing
Sphere tracing
Blending
4:25 pm: Interactive Modeling - J. Hart
Interactive techniques for implicit surfaces
Oriented particle systems
Critical points
Maintaining correct topology
DEMO of this system
ANNOUNCEMENT of code availability
4:45 pm: Conclusions - All Presenters
Unifying it all (e.g. tiling skeletal models with algebraic patches)
Commerical ventures/viability (yesterday, today, and tomorrow)
Impact on modeling and graphics (both software and hardware)
What's next? (dynamic implicit surfaces, wavelets, ...)
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