Topic
General position
About: General position is a research topic. Over the lifetime, 1077 publications have been published within this topic receiving 12681 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: If the points are added one by one, then flipping in a topological order will succeed in constructing this triangulation and the algorithm takes expected time at mostO(nlogn+n[d/2]).
Abstract: A set ofn weighted points in general position in źd defines a unique regular triangulation. This paper proves that if the points are added one by one, then flipping in a topological order will succeed in constructing this triangulation. If, in addition, the points are added in a random sequence and the history of the flips is used for locating the next point, then the algorithm takes expected time at mostO(nlogn+n[d/2]). Under the assumption that the points and weights are independently and identically distributed, the expected running time is between proportional to and a factor logn more than the expected size of the regular triangulation. The expectation is over choosing the points and over independent coin-flips performed by the algorithm.
442 citations
TL;DR: A survey of results in the problem of describing diffeomorphism rearrangements of fronts and caustics in one-parameter families of general position in spaces of low dimension is given in this paper.
Abstract: A survey of results is presented in the problem of describing up to diffeomorphism rearrangements of fronts and caustics in one-parameter families of general position in spaces of low dimension.
153 citations
1 May 1996
TL;DR: Any triangulation of a set of n points in general position contains at least \(\lceil (n-4)/2 \rceil\) edges that can be flipped, and it is proved that O(n + k2) flips are sufficient to transform any triangulations of an n -gon with k reflex vertices into any other triangulated.
Abstract: In this paper we study the problem of flipping edges in triangulations of polygons and point sets. One of the main results is that any triangulation of a set of n points in general position contains at least \(\lceil (n-4)/2 \rceil\) edges that can be flipped. We also prove that O(n + k2) flips are sufficient to transform any triangulation of an n -gon with k reflex vertices into any other triangulation. We produce examples of n -gons with triangulations T and T' such that to transform T into T' requires Ω(n2) flips. Finally we show that if a set of n points has k convex layers, then any triangulation of the point set can be transformed into any other triangulation using at most O(kn) flips.
146 citations
03 Jan 1988-Graphical Models \/graphical Models and Image Processing \/computer Vision, Graphics, and Image Processing
TL;DR: A simple method for computing the general position based on the line data is presented and the algorithms of computing the most general eye position by solving this maximin problem are presented.
Abstract: In 3D graphics, the selection of the location of the center of projection (eye) is very important in order to obtain the pictures by which the original shapes of 3D objects can be comprehended easily. The eye position from which the picture of 3D objects with the maximum shape information is obtained is called the “general position”. In the current practice of making pictures, the most general eye position is determined in ad hoc ways, because it is very difficult to determine the view, foreseeing the resultant display image. In this paper, a simple method for computing the general position is presented. First the general position problem based on the line data is formulated as a maximin problem. Then the algorithms of computing the most general eye position by solving this maximin problem are presented. Some examples of performing these algorithms yielding satisfactory results are also presented.
145 citations
TL;DR: In this article, an embedding of the original polynomial system is presented, which leads to a sequence of homotopies, with solution paths leading to generic points of all components as the isolated solutions of an auxiliary system.
118 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 5 |
| 2024 | 14 |
| 2023 | 39 |
| 2022 | 87 |
| 2021 | 68 |
| 2020 | 63 |