## 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 CenterBrian Wyvill

University of Calgary

Lecturers

Chandrajit Bajaj

Purdue UniversityJules Bloomenthal

Microsoft CorporationBaining Guo

York UniversityJohn Hart

Washington State UniversityGeoff Wyvill

University of Otago

ScheduleImplicit 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, ...)

Courses | This Web Site

Final SIGGRAPH 96 Web site update: 25 October 1996.

For complete information on the next conference and exhibition, see: http/www.siggraph.org/s97/