Two-dimensional line segment–triangle intersection test: revision and enhancement

2018 ◽  
Vol 35 (10) ◽  
pp. 1347-1359
Author(s):  
Simo Jokanovic
Keyword(s):  
Line Segment ◽  
Two Dimensional ◽  
Intersection Test

scholarly journals A line segment extraction algorithm using laser data based on seeded region growing

2018 ◽  
Vol 15 (1) ◽  
pp. 172988141875524 ◽  
Author(s):  
Haiming Gao ◽  
Xuebo Zhang ◽  
Yongchun Fang ◽  
Jing Yuan
Keyword(s):  
Line Segment ◽  
Region Growing ◽  
Superior Performance ◽  
Two Dimensional ◽  
Line Segments ◽  
Seeded Region Growing ◽  
Extraction Algorithm ◽  
Laser Data ◽  
Split And Merge ◽  
2D Data

This article presents a novel line segment extraction algorithm using two-dimensional (2D) laser data, which is composed of four main procedures: seed-segment detection, region growing, overlap region processing, and endpoint generation. Different from existing approaches, the proposed algorithm borrows the idea of seeded region growing in the field of image processing, which is more efficient with more precise endpoints of the extracted line segments. Comparative experimental results with respect to the well-known Split-and-Merge algorithm are presented to show superior performance of the proposed approach in terms of efficiency, correctness, and precision, using real 2D data taken from our hallway and laboratory.

A lower bound for electrostatic capacity in the plane

1981 ◽  
Vol 88 (3-4) ◽  
pp. 267-273 ◽  
Author(s):  
L. E. Fraenkel
Keyword(s):  
Lower Bound ◽  
Line Segment ◽  
Diameter Ratio ◽  
Two Dimensional ◽  
Steiner Symmetrization

SynopsisThis note presents a lower bound, in terms of the diameter ratio of the inner and outer conductors, for the electrostatic capacity of certain two-dimensional condensers. We use double Steiner symmetrization to prove that the minimizing condenser consists of a line segment placed symmetrically within a circle; the capacity of this condenser is known explicitly.

Transition Probabilities for Markov Process on a Line Segment Located within a Quarter-Plane

2021 ◽  
pp. 4-24
Author(s):  
A.V. Kalinkin
Keyword(s):  
Markov Process ◽  
Random Process ◽  
Generating Function ◽  
Line Segment ◽  
Transition Probabilities ◽  
Special Functions ◽  
Transition Probability ◽  
Separation Of Variables ◽  
Two Dimensional ◽  
Quarter Plane

The paper considers a quadratic birth-death Markov process. The points on a line segment located within a quarter-plane represent the states of the random process. We designate the set of vectors that have integer non-negative coordinates as our quarter plane. The process is defined by infinitesimal characteristics, or transition probability densities. These characteristics are determined by a quadratic function of the coordinates at the segment points with integer coordinates. The boundary points of the segment are absorbing; at these points, the random process stops. We investigated a critical case when process jumps are equally probable at the moment of exiting a point. We derived expressions describing transition probabilities of the Markov process as a spectral series. We used a two-dimensional exponential generating function of transition probabilities and a two-dimensional generating function of transition probabilities. The first and second systems of ordinary differential Kolmogorov equations for Markov process transition probabilities are reduced to second-order mixed type partial differential equations for a double generating function. We solve the resulting system of linear equations using separation of variables. The spectrum obtained is discrete. The eigen-functions are expressed in terms of hypergeometric functions. The particular solution constructed is a Fourier series, whose coefficients are derived by means of expo-nential expansion. We employed sums of functional series known in the theory of special functions to construct the exponential expansion required

A three‐dimensional perspective on two‐dimensional dip moveout

Geophysics ◽  
1988 ◽  
Vol 53 (5) ◽  
pp. 604-610 ◽  
Author(s):  
David Forel ◽  
Gerald H. F. Gardner
Keyword(s):  
Line Segment ◽  
Constant Velocity ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Prestack Migration ◽  
Standard Normal ◽  
Ellipsoidal Surface ◽  
Zero Offset

Prestack migration in a constant‐velocity medium spreads an impulse on any trace over an ellipsoidal surface with foci at the source and receiver positions for that trace. The same ellipsoid can be obtained by migrating a family of zero‐offset traces placed along the line segment from the source to the receiver. The spheres generated by migrating the zero‐offset impulses are arranged to be tangent to the ellipsoid. The resulting nonstandard moveout equation is equivalent to two consecutive moveouts, the first requiring no knowledge of velocity and the second being standard normal moveout (NMO). The first of these is referred to as dip moveout (DMO). Because this DMO-NMO algorithm converts any trace to an equivalent set of zero‐offset traces, it can be applied to any ensemble of traces no matter what the variations in azimuth and offset may be. In particular, this three‐dimensional perspective on DMO can be used with multifold inline data. Then it becomes clear that velocity‐independent DMO operates on radial‐trace profiles and not on constant‐offset profiles. Inline data over a three‐dimensional subsurface will be properly stacked by using DMO followed by NMO.

scholarly journals Hyers–Ulam Stability of Two-Dimensional Flett’s Mean Value Points

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 733
Author(s):  
Soon-Mo Jung ◽  
Ji-Hye Kim ◽  
Young Woo Nam
Keyword(s):  
Differentiable Function ◽  
Line Segment ◽  
Mean Value ◽  
Two Dimensional ◽  
Ulam Stability ◽  
Intermediate Point

If a differentiable function f : [ a , b ] → R and a point η ∈ [ a , b ] satisfy f ( η ) - f ( a ) = f ′ ( η ) ( η - a ) , then the point η is called a Flett’s mean value point of f in [ a , b ] . The concept of Flett’s mean value points can be generalized to the 2-dimensional Flett’s mean value points as follows: For the different points r ^ and s ^ of R × R , let L be the line segment joining r ^ and s ^ . If a partially differentiable function f : R × R → R and an intermediate point ω ^ ∈ L satisfy f ( ω ^ ) - f ( r ^ ) = ω ^ - r ^ , f ′ ( ω ^ ) , then the point ω ^ is called a 2-dimensional Flett’s mean value point of f in L. In this paper, we will prove the Hyers–Ulam stability of 2-dimensional Flett’s mean value points.

Sign in / Sign up

Export Citation Format

Share Document