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Interactive Design and Visualization of Branched Covering Spaces.
IEEE Transactions on Visualization and Computer Graphics
|September 4, 2017
Summary
We introduce a framework for designing and visualizing branched covering spaces (BCS), crucial for tensor field topology and geometry processing. Our system aids in understanding BCS properties and their geometric realization on mesh surfaces.
Area of Science:
- Mathematics
- Computer Science
- Geometry Processing
Background:
- Branched covering spaces (BCS) are fundamental in complex analysis and topology.
- They have critical applications in tensor field topology and geometry remeshing.
- Understanding BCS is vital for researchers in tensor field visualization and geometry processing.
Purpose of the Study:
- To present an interactive framework for designing and visualizing branched covering spaces (BCS).
- To enable users to explore the construction process and geometric realization of BCS.
- To facilitate verification of key BCS properties, including manifold properties and the Riemann-Hurwitz formula.
Main Methods:
- Development of an interactive system for BCS design and visualization.
- Utilizing mesh deformation techniques for geometric realization of BCS.
- Incorporating connecting tubes to aid in visualizing BCS structure.
Main Results:
- A functional framework allowing interactive design and visualization of BCS for mesh surfaces.
- The system visualizes both the final BCS and its step-by-step construction.
- Users can manipulate the geometric realization of BCS and verify mathematical properties.
Conclusions:
- The developed framework effectively supports the design and visualization of branched covering spaces.
- The system aids in understanding complex topological and geometric concepts.
- Evaluations confirm the utility for researchers and educators in relevant fields.
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