Course Syllabus

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Lecture 1: Introduction

• Overview
• Graphical Objects
• Multiresolution Representation
• Construction Techniques
• Motivation
• Visualization
• Compression
• Computation
• Modeling
• Areas of Application
• GIS / Cartographyy
• Virtual Reality / Simulation
• Graphics / Scientific Visualzation
• Vision / Image Processing
• CAD / Engineering
• Types of Geometry
• Surface Classes
• Data Description
• Products
• Graphics Libraries / Formats
• Graphics Systems
• Modeling Systems

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Lecture 2: Basic Concepts

• Space Decompositions
• Cell Complexes
• Simplicial Complexes
• Triangulations
• Mesh Structures
• Geometry and Topology
• Elements of a Mesh
• Topological Graphs
• Operations on Meshes
• Construction Primitives
• Structure Traversal
• Surfaces and Meshes
• Polygonization
• Sparse Data Interpolation
• Free-Form Patches
• Surface Approximation
• Error Metrics
• Local and Global Analysis
• Posing the Optimation Problem
• Evaluating Results

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Lecture 3: Multiresolution Meshes

• Hierarchical Structures
• Pyramids
• Restricted Trees
• Progressive Sequences
• Multi-Triangulation
• A General Framework
• Fragments
• Compatible Triangulations
• Definition
• Elements
• Representation
• DAG / Data Structure
• Explicit Representation
• Implicit Representation
• Properties
• Non-Redundancy
• Expressive Power
• Monotonicity
• Growth / Height
• Operations
• Mesh Extraction
• Structure Navigation
• Spatial Search

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Lecture 4: Simplification Methods

• Simplification Mechanisms
• Decimation
• Clustering
• Other operations
• Simplification Criteria
• Local Error
• Global Error
• Computational Framework
• Basic Algorithms
• Restrictions and Features
• Topology Preservation
• Parallel Simplication Methods
• Grid Baed
• Wavelet Based
• Sequential Simplification Methods
• Decimation
• Clustering
• Relaxation Methods
• Resampling with Simplification

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Lecture 5: Refinement Methods

• Subdivision Templates
• Uniform Templates
• Adaptive Templates
• General Templates
• Base Mesh Generation
• Parametric Surfaces
• Implicit Surfaces
• Sampled Data
• Computational Framework
• Basic Algorithm
• Sampling Criteria
• Maintaining Mesh Consistency
• Uniform Refinement
• Rectangular
• Triangular
• Non-Uniform Refinement
• Restricted
• Edge Coherence
• Hybrid Refinement
• Retriangulation
• Cuts

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Lecture 6: Conclusion

• Research Groups
• CNUCE / DISI
• CMU
• SUNY
• Microsoft
• UNC
• Caltech
• Companies
• InnovMetric
• SGI
• IBM
• Research Issues
• Open Problems