Works (43)
Updated: April 4th, 2024 12:53
2023 article
Guest editorial: Special issue on the 33rd Canadian Conference on Computational Geometry (CCCG)
He, M., & Sheehy, D. (2024, January). COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, Vol. 116.
Sources: Web Of Science, NC State University Libraries
Added: September 11, 2023
2020 journal article
Adaptive Metrics for Adaptive Samples
ALGORITHMS, 13(8).
author keywords: surface reconstruction; homology inference; adaptive sampling; topological data analysis
TL;DR:
The local-feature size definition of adaptive sampling used in surface reconstruction is generalized to relate it to an alternative metric on Euclidean space, making it simpler both to give adaptive sampling versions of homological inference results and to prove topological guarantees using the critical points theory of distance functions.
(via Semantic Scholar)
open access via www.mdpi.com (publisher PDF)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: September 21, 2020
2020 journal article
Efficient Algorithm for the Topological Characterization of Worm-like and Branched Micelle Structures from Simulations
JOURNAL OF CHEMICAL THEORY AND COMPUTATION, 16(7), 4588–4598.
UN Sustainable Development Goal Categories
9. Industry, Innovation and Infrastructure
(OpenAlex)
Sources: Web Of Science, NC State University Libraries
Added: February 8, 2021
2018 conference paper
Computing the Shift-Invariant Bottleneck Distance for Persistence Diagrams
CCCG: The Canadian Conference in Computational Geometry. Presented at the Canadian Conference in Computational Geometry, Winnipeg, Canada.
Event: Canadian Conference in Computational Geometry at Winnipeg, Canada on August 8-10, 2018
Source: NC State University Libraries
Added: November 15, 2020
2018 chapter
Fréchet-Stable Signatures Using Persistence Homology
In Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms (pp. 1100–1108).
TL;DR:
The algorithm for computing the signatures in Euclidean spaces uses a new method for computing persistent homology of convex functions on simplicial complexes and exploits the natural invariance of persistence diagrams of functions to homeomorphisms of the domain.
(via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: January 7, 2020
2018 conference paper
When Can We Treat Trajectories as Points?
CCCG: The Canadian Conference in Computational Geometry. Presented at the Canadian Conference in Computational Geometry, Winnipeg, Canada.
Event: Canadian Conference in Computational Geometry at Winnipeg, Canada on August 8-10, 2018
Source: NC State University Libraries
Added: November 15, 2020
2017 conference paper
Supporting Ruled Polygons
CCCG: The Canadian Conference in Computational Geometry. Presented at the Canadian Conference in Computational Geometry, Ottawa, Ontario.
Event: Canadian Conference in Computational Geometry at Ottawa, Ontario on July 26-28, 2017
Source: NC State University Libraries
Added: November 15, 2020
2017 conference paper
When and Why the Topological Coverage Criterion Works
Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms. Presented at the Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms.
Event: Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms
TL;DR:
A new, simpler proof of the de Silva-Ghrist Topological Coverage Criterion is given that eliminates any assumptions about the smoothness of the boundary of the underlying space, allowing the results to be applied to much more general problems.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(OpenAlex)
Sources: Crossref, NC State University Libraries
Added: January 7, 2020
2016 conference paper
Adaptive Metrics for Adaptive Samples
CCCG: The Canadian Conference in Computational Geometry. Presented at the Canadian Conference in Computational Geometry, Vancouver, British Columbia, Canada.
Event: Canadian Conference in Computational Geometry at Vancouver, British Columbia, Canada on August 3-5, 2016
Source: NC State University Libraries
Added: November 15, 2020
2016 journal article
Efficient and robust persistent homology for measures
Computational Geometry, 58, 70–96.
author keywords: Persistent homology; Topological data analysis; Distance to a measure; Power distance; Sparse rips filtration
TL;DR:
An efficient and reliable scheme to approximate the topological structure of the family of sublevel-sets of the distance to a measure and an algorithm for approximating the persistent homology of thedistance to an empirical measure that works in arbitrary metric spaces are obtained.
(via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: January 14, 2020
2016 conference paper
Exploring Circle Packing Algorithms
SOCG: Symposium on Computational Geometry (Multimedia Session). Presented at the 32nd International Symposium on Computational Geometry, Boston, MA.
Event: 32nd International Symposium on Computational Geometry at Boston, MA on June 14-18, 2016
TL;DR:
This work presents an interactive tool for visualizing and experimenting with different circle packing algorithms and shows how these algorithms can be modified to suit the needs of the user.
(via Semantic Scholar)
Sources: NC State University Libraries, NC State University Libraries
Added: November 15, 2020
2016 conference paper
Interactive Geometric Algorithm Visualization in a Browser
SOCG: Symposium on Computational Geometry (Multimedia Session). Presented at the 32nd International Symposium on Computational Geometry (SoCG 2016), Boston, MA.
Event: 32nd International Symposium on Computational Geometry (SoCG 2016) at Boston, MA on June 14-18, 2016
Source: NC State University Libraries
Added: November 15, 2020
2016 conference paper
Transforming Hierarchical Trees on Metric Spaces
CCCG: The Canadian Conference in Computational Geometry,2016. Presented at the Canadian Conference in Computational Geometry, Vancouver, British Columbia, Canada.
Event: Canadian Conference in Computational Geometry at Vancouver, British Columbia, Canada on August 3-5, 2016
Source: NC State University Libraries
Added: November 15, 2020
2016 conference paper
kth Nearest Neighbor Sampling in the Plane
CCCG: The Canadian Conference in Computational Geometry. Presented at the Canadian Conference in Computational Geometry, Vancouver, British Columbia, Canada.
Event: Canadian Conference in Computational Geometry at Vancouver, British Columbia, Canada on August 3-5, 2016
Source: NC State University Libraries
Added: November 15, 2020
2015 conference paper
A Geometric Perspective on Sparse Filtrations
CCCG: The Canadian Conference in Computational Geometry. Presented at the Canadian Conference in Computational Geometry, Kingston, Ontario.
Event: Canadian Conference in Computational Geometry at Kingston, Ontario on August 10-12, 2015
Source: NC State University Libraries
Added: November 15, 2020
2015 conference paper
An Output-Sensitive Algorithm for Computing Weightedα-Complexes
CCCG: The Canadian Conference in Computational Geometry. Presented at the Canadian Conference in Computational Geometry, Kingston, Ontario.
Event: Canadian Conference in Computational Geometry at Kingston, Ontario on August 10-12, 2015
Source: NC State University Libraries
Added: November 15, 2020
2015 chapter
Approximating Nearest Neighbor Distances
In Lecture Notes in Computer Science (pp. 200–211).
TL;DR:
Several researchers proposed using non-Euclidean metrics on point sets in Euclidean space for clustering noisy data to assign smaller costs to the paths that stay close to the input points.
(via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: January 14, 2020
2015 conference paper
Persistent Homology and Nested Dissection
Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms. Presented at the Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms.
Event: Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms
Sources: Crossref, NC State University Libraries
Added: January 14, 2020
2015 conference paper
Visualizing Sparse Filtrations
SOCG: Symposium on Computational Geometry (Multimedia Session). Presented at the 31st International Symposium on Computational Geometry, Eindhoven, Netherlands.
Event: 31st International Symposium on Computational Geometry at Eindhoven, Netherlands on June 22-25, 2015
TL;DR:
A geometric perspective on sparse filtrations that leads to simpler proofs, more general theorems, and a more visual explanation is illustrated.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(OpenAlex)
Sources: NC State University Libraries, NC State University Libraries
Added: November 15, 2020
2014 journal article
A New Approach to Output-Sensitive Construction of Voronoi Diagrams and Delaunay Triangulations
Discrete & Computational Geometry, 52(3), 476–491.
author keywords: Voronoi diagram; Delaunay triangulation; Output-sensitive algorithms; Mesh generation; Kinetic data structures
TL;DR:
The key idea is to first build the Voronoi diagram of a superset of the input points using ideas from Voronoi refinement mesh generation, then the extra points are removed in a straightforward way that allows the total work to be bounded in terms of the output complexity, yielding the output sensitive bound.
(via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: January 14, 2020
2014 conference paper
Efficient and Robust Persistent Homology for Measures
Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms. Presented at the Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms.
Event: Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms
Sources: Crossref, NC State University Libraries
Added: January 14, 2020
2014 conference paper
The Persistent Homology of Distance Functions under Random Projection
SOCG: Symposium on Computational Geometry. Presented at the 30th International Symposium on Computational Geometry, Kyoto, Japan.
Event: 30th International Symposium on Computational Geometry at Kyoto, Japan on June 8-11, 2014
TL;DR:
This paper shows that the persistent homology of the distance function to P is also preserved up to a comparable constant factor, and proves these results in the more general setting of weighted kth nearest neighbor distances.
(via Semantic Scholar)
Sources: NC State University Libraries, NC State University Libraries
Added: November 15, 2020
2014 journal article
Zigzag Zoology: Rips Zigzags for Homology Inference
Foundations of Computational Mathematics, 15(5), 1151–1186.
author keywords: Topological inference; Persistent homology; Vietoris-Rips complex; Quiver representations; Reflections
Sources: Crossref, NC State University Libraries
Added: January 14, 2020
2013 conference paper
A fast algorithm for well-spaced points and approximate delaunay graphs
Proceedings of the 29th annual symposium on Symposuim on computational geometry - SoCG '13. Presented at the the 29th annual symposium.
Event: the 29th annual symposium
TL;DR:
A new algorithm is presented that produces a well-spaced superset of points conforming to a given input set in any dimension with guaranteed optimal output size and provides an approximate Delaunay graph on the output points.
(via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: January 14, 2020
2013 conference paper
A new approach to output-sensitive voronoi diagrams and delaunay triangulations
Proceedings of the 29th annual symposium on Symposuim on computational geometry - SoCG '13. Presented at the the 29th annual symposium.
Event: the 29th annual symposium
TL;DR:
A new algorithm for computing the Voronoi diagram of a set of n points in constant-dimensional Euclidean space is described, which improves on the state of the art for all inputs with polynomial spread and near-linear output size.
(via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: January 14, 2020
2013 conference paper
Geometric Separators and the Parabolic Lift
CCCG: The Canadian Conference in Computational Geometry. Presented at the Canadian Conference in Computational Geometry, Waterloo, Ontario.
Event: Canadian Conference in Computational Geometry at Waterloo, Ontario on August 8-10, 2013
Source: NC State University Libraries
Added: November 15, 2020
2013 journal article
Linear-Size Approximations to the Vietoris–Rips Filtration
Discrete & Computational Geometry, 49(4), 778–796.
author keywords: Persistent Homology; Vietoris-Rips filtration; Net-trees
Sources: Crossref, NC State University Libraries
Added: January 14, 2020
2013 conference paper
Zigzag zoology
Proceedings of the 29th annual symposium on Symposuim on computational geometry - SoCG '13. Presented at the the 29th annual symposium.
Event: the 29th annual symposium
TL;DR:
Several species of Rips-like zigzags are presented and compare them with respect to the signal-to-noise ratio, a measure of how well the underlying homology is represented in the persistence barcode relative to the noise in the barcode at the relevant scales.
(via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: January 14, 2020
2012 conference paper
A Multicover Nerve for Geometric Inference
CCCG: The Canadian Conference in Computational Geometry. Presented at the Canadian Conference in Computational Geometry, Charlottetown, Prince Edward Island.
Event: Canadian Conference in Computational Geometry at Charlottetown, Prince Edward Island on August 8-10, 2012
Source: NC State University Libraries
Added: November 15, 2020
2012 conference paper
Linear-size approximations to the vietoris-rips filtration
Proceedings of the 2012 symposuim on Computational Geometry - SoCG '12. Presented at the the 2012 symposuim.
Event: the 2012 symposuim
TL;DR:
For the first time, it is shown how to construct an O(n) size filtered simplicial complex on an n-point metric space such that its persistence diagram is a good approximation to that of the Vietoris–Rips filtration.
(via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: January 14, 2020
2012 conference paper
Minimax Rates for Homology Inference
AISTATS: AI and Statistics. Presented at the 15th International Conference on Artificial Intelligence and Statistics, La Palma, Canary Islands.
Event: 15th International Conference on Artificial Intelligence and Statistics at La Palma, Canary Islands on April 21-23, 2012
Source: NC State University Libraries
Added: November 15, 2020
2012 journal article
New Bounds on the Size of Optimal Meshes
Computer Graphics Forum, 31(5), 1627–1635.
TL;DR:
A way to bound the feature size integral in terms of an easy to compute property of a suitable ordering of the point set, which tightens bounds from several previous results and provides matching lower bounds.
(via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: January 14, 2020
2011 conference paper
Beating the spread
Proceedings of the 27th annual ACM symposium on Computational geometry - SoCG '11. Presented at the the 27th annual ACM symposium.
Event: the 27th annual ACM symposium
TL;DR:
NetMesh is a new algorithm that produces a conforming Delaunay mesh for point sets in any fixed dimension with guaranteed optimal mesh size and quality with constants depending only on the dimension and the desired element quality.
(via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: January 14, 2020
2010 journal article
Approximate centerpoints with proofs
Computational Geometry, 43(8), 647–654.
TL;DR:
The IteratedTverberg algorithm is presented, the first deterministic algorithm for computing an approximate centerpoint of a set [email protected]?R^d with running time sub-exponential in d.
(via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: January 14, 2020
2010 conference paper
Topological inference via meshing
Proceedings of the 2010 annual symposium on Computational geometry - SoCG '10. Presented at the the 2010 annual symposium.
Event: the 2010 annual symposium
author keywords: topological inference; persistent homology; mesh generation; sparse Voronoi refinement
TL;DR:
These ideas from mesh generation are applied to improve the time and space complexities of computing the full persistent homological information associated with a point cloud P in Euclidean space ℜd, and a new collection of filtrations, based on the Delaunay triangulation of a carefully-chosen superset of P, whose sizes are reduced to 2O(d2)n.
(via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: January 14, 2020
2009 conference paper
Approximate center points with proofs
Proceedings of the 25th annual symposium on Computational geometry - SCG '09. Presented at the the 25th annual symposium.
Event: the 25th annual symposium
author keywords: centerpoints; derandomization; approximation algorithms; Tverberg's Theorem
TL;DR:
The Iterated-Tverberg algorithm is presented, the first deterministic algorithm for computing an approximate centerpoint of a set S ∈ Rd with running time sub-exponential in d and returns a polynomial-time checkable proof of the approximation guarantee, despite the coNP-Completenes of testing centerpoints in general.
(via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: January 14, 2020
2009 conference paper
Size Complexity of Volume Meshes vs. Surface Meshes
Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms. Presented at the Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms.
Event: Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
TL;DR:
This work analyzes the number of scaffold vertices in a setting that encompasses many existing volume meshing algorithms and shows that under simple preconditions, theNumber of scaffolding vertices will be linear in thenumber of surface vertices.
(via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: January 14, 2020
2009 conference paper
The Centervertex Theorem for Wedge Depth
CCCG: The Canadian Conference in Computational Geometry. Presented at the Canadian Conference in Computational Geometry, Vancouver, British Columbia, Canada.
Event: Canadian Conference in Computational Geometry at Vancouver, British Columbia, Canada on August 17-19, 2009
Source: NC State University Libraries
Added: November 15, 2020
2008 conference paper
Achieving Spatial Adaptivity while Finding Approximate Nearest Neighbors
CCCG: The Canadian Conference in Computational Geometry. Presented at the Canadian Conference in Computational Geometry, Montreal, Quebec, Canada.
Event: Canadian Conference in Computational Geometry at Montreal, Quebec, Canada on August 13-15, 2008
Source: NC State University Libraries
Added: November 15, 2020
2008 conference paper
Linear-size meshes
CCCG: The Canadian Conference in Computational Geometry. Presented at the Canadian Conference in Computational Geometry, Montreal, Quebec, Canada.
Event: Canadian Conference in Computational Geometry at Montreal, Quebec, Canada on August 13-15, 2008
Source: NC State University Libraries
Added: November 15, 2020
2008 journal article
Shape deformation in continuous map generalization
GeoInformatica, 13(2), 203–221.
author keywords: Continuous generalization; Scale change; Homotopy; Cartograms
TL;DR:
An application of this method is used to provide an algorithm to obtain cartograms and to preserve topology, area-ratios, and relative position as they change over time.
(via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: January 14, 2020
2007 chapter
Size Competitive Meshing Without Large Angles
In Automata, Languages and Programming (pp. 655–666).
TL;DR:
A new meshing algorithm for the plane, Overlay Stitch Meshing (OSM), accepting as input an arbitrary Planar Straight Line Graph and producing a triangulation with all angles smaller than 170°, which has competitive size with any optimal size mesh having equally bounded largest angle.
(via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: January 14, 2020
2006 journal article
Compatible triangulations and point partitions by series-triangular graphs
Computational Geometry, 34(3), 195–202.
author keywords: compatible triangulations; Steiner points; series-triangular graphs
TL;DR:
This work introduces series-triangular graph embeddings and shows how to partition point sets with them, and proves an upper bound on the number of Steiner points needed to obtain compatible triangulations of point sets.
(via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: January 14, 2020
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