One-forms and Tutte-like Embeddings

Channel:
Microsoft Research
Subscribers:
344,000
Published on ● Video Link: https://www.youtube.com/watch?v=AJNA-qII8o4


Duration: 1:01:38
546 views
6

In 1962, Tutte presented a simple algorithm to draw a planar graph using straight lines. This algorithm has become the primary method that is used in computer graphics for flattening meshes. Mesh flattening is the first step in many geometric processing algorithms, such as texture mapping. Though Tutte's algorithm is simple, his proof of correctness was anything but. In this talk, I will describe some properties of one-forms on meshes, and show how this can be used to provide an elementary proof of the correctness of Tutte's algorithm. These properties will also allow us to analyze some natural generalizations of Tutte's algorithm such as flattening closed meshes of arbitrary genus.



Other Videos By Microsoft Research


2016-09-05Efficient and Robust Routing in the Presence of Competing Interests
2016-09-05Load Management and Fault-Tolerance in a Distributed Stream Processing System [1/2]
2016-09-05The Case for Technology for Developing Regions
2016-09-05Constructing Broad-Coverage Knowledge Repositories by Collecting Knowledge from Volunteers
2016-09-05Controlling Overlap in Content-Oriented XML Retrieval
2016-09-05Inferring Class Invariants in object-oriented languages via abstract interpretation
2016-09-05Technology Design to Foster Collaboration: A Multidisciplinary Approach
2016-09-05Towards Concept-Based Text Understanding and Mining
2016-09-05Component Programming with Object-Oriented Signals
2016-09-05On the Capacity of Information Networks
2016-09-05One-forms and Tutte-like Embeddings
2016-09-05Personal Passion and Professional Excellence ΓÇô You canΓÇÖt have one without the other!
2016-09-05Social Mobile Applications, Location, Privacy and the Capital of Nevada [1/16]
2016-09-05Search Engines Considered Harmful: In Search of an Unbiased Web Ranking
2016-09-05Science Friction: Where the Known Meets the Unknown
2016-09-05Concave utility functions on finite sets
2016-09-05Exploring Mars by 4-Wheel Drive
2016-09-05Computing with Selfish Agents [1/2]
2016-09-05Opportunities and Challenges in End-to-End Verification of Software Systems
2016-09-05Tools and Techniques for Prototyping Future Interactions [1/2]
2016-09-05Mathematical Sketching: A New Approach for Creating and Exploring Dynamic Illustrations


Tags:
microsoft research