From Continuous Parametrizations to Discrete Hexahedral Meshes : Reliable Algorithms for a Versatile Pipeline / Hendrik Brückler ; Supervisor: Prof. Dr. Marcel Campen. Paderborn, 2026
Inhalt
- Abstract
- Zusammenfassung
- Acknowledgements
- Introduction
- Academic Interest
- Physical simulation
- Volume Meshes
- The Hex Meshing Problem
- Common Hex Meshing Approaches
- Thesis Structure and Contributions
- Preliminaries
- Volume Meshes
- Integer-Grid Maps for Hex Meshing
- T-meshes as Proxy Domains
- Input Map Sanitization
- Map-guided Cuboid Decomposition
- Surface Case
- Related Work: Structured Decomposition
- Generalizing the Problem
- Generalizing the Solution
- The 3D Motorcycle Complex
- Construction in Practice
- Results: Motorcycle Complexes
- Formalization as Embedded T-meshes
- Robust Volume Quantization
- T-mesh Quantization
- Notation
- Formulation as an Integer Program
- Efficient Constraint Formulation
- Local q-Charts
- Type item:link Conditions: Link collapse prevention
- Type item:criti Conditions: Critical Entity separation
- Type item:bound and item:noncon Conditions: Topology preservation
- Lazy Constraint Strategy
- Algorithm Summary
- Results: T-Mesh Quantizations
- Discussion
- Global Map Reparametrization
- Notation
- Constraint Extraction from a Quantized T-Mesh
- Results: Integer-Grid Maps and Hex Meshes
- Discussion
- T-mesh Collapsing for Guaranteed-Injective Maps
- Towards Versatility and Efficiency
- Flexible Singularities
- New Problem Statement
- Structure Preservation with Flexible Singularities
- Flexible Quantization Objective
- Results
- Discussion
- Replacing Integer Solvers
- Synopsis