Computational geometry: an introduction
Computational geometry: an introduction
Computational-geometric methods for polygonal approximations of a curve
Computer Vision, Graphics, and Image Processing
Reporting points in halfspaces
Computational Geometry: Theory and Applications
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
On approximating polygonal curves in two and three dimensions
CVGIP: Graphical Models and Image Processing
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Handbook of discrete and computational geometry
Handbook of discrete and computational geometry
Efficiently computing the closest point to a query line
Pattern Recognition Letters
Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
Queries with segments in Voronoi diagrams
Computational Geometry: Theory and Applications
Space-Time Tradeoffs for Emptiness Queries
SIAM Journal on Computing
Efficient Algorithms for the Smallest Enclosing Cylinder Problem
Proceedings of the 8th Canadian Conference on Computational Geometry
Using simplicial partitions to determine a closest point to a query line
Pattern Recognition Letters
SIAM Journal on Computing
Approximating extent measures of points
Journal of the ACM (JACM)
High-Dimensional Shape Fitting in Linear Time
Discrete & Computational Geometry
Ray shooting amid balls, farthest point from a line, and range emptiness searching
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
An O(N) algorithm for polygonal approximation
Pattern Recognition Letters
Face recognition using the nearest feature line method
IEEE Transactions on Neural Networks
Stabbing balls and simplifying proteins
International Journal of Bioinformatics Research and Applications
Farthest segments and extremal triangles spanned by points in R3
Information Processing Letters
Semialgebraic Range Reporting and Emptiness Searching with Applications
SIAM Journal on Computing
| Hi-index | 0.00 |
We address a number of extremal point query problems when P is a set of n points in R^d, d=3 a constant, including the computation of the farthest point from a query line and the computation of the farthest point from each of the lines spanned by the points in P. In R^3, we give a data structure of size O(n^1^+^@?), that can be constructed in O(n^1^+^@?) time and can report the farthest point of P from a query line segment in O(n^2^/^3^+^@?) time, where @?0 is an arbitrarily small constant. Applications of our results also include: (1) Sub-cubic time algorithms for fitting a polygonal chain through an indexed set of points in R^d, d=3 a constant, and (2) A sub-quadratic time and space algorithm that, given P and an anchor point q, computes the minimum (maximum) area triangle defined by q with P@?{q}.