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.

Jai Menon
IBM T. J. Watson Research Center

Brian Wyvill
University of Calgary

Chandrajit Bajaj
Purdue University

Jules Bloomenthal
Microsoft Corporation

Baining Guo
York University

John Hart
Washington State University

Geoff Wyvill
University of Otago


Implicit Surfaces for Geometric Modeling and Computer Graphics Course syllabus

8:30 am: Introduction - J. Menon, B. Wyvill

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

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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