Polynomial triangle centers on the line at infinity

Kimberling, Clark

doi:10.1007/s00022-020-0522-y

Cited by 8 publications

(10 citation statements)

References 4 publications

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“…Triangle is in perspective with the medial triangle of the incentral triangle of , and the perspector is the Grinberg point. This is point X(37) in [6].…”

Section: Proofmentioning

confidence: 97%

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102.14 A Note on the Feuerbach triangle

Grozdev¹,

Okumura²,

Dekov³

2018

Math. Gaz.

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“…Triangle is in perspective with the medial triangle of the incentral triangle of , and the perspector is the Grinberg point. This is point X(37) in [6].…”

Section: Proofmentioning

confidence: 97%

“…]) and the perspector is known as the Feuerbach perspector. (Point in[1, Chap.21], point X(12) in[6]). …”

mentioning

confidence: 99%

102.14 A Note on the Feuerbach triangle

Grozdev¹,

Okumura²,

Dekov³

2018

Math. Gaz.

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“…The two concurrent points are called parallelogic (orthologic) centres. Parallelogy, orthology relations are used to construct many triangle centres [1].…”

Section: Median-parallelogic and Median-orthologic Trianglesmentioning

confidence: 99%

105.11 Median-parallelogic and median-orthologic triangles

Vu¹

2021

Math. Gaz.

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“…We design a back-routing avoidance method to address the moving path backpropagation problem for the greedy-based path planning algorithm calculation for the ICPPA, where L k is the location of sensor node k and r is the radius of the communication range of the sensor node. Let I k I k x , I k y be the inner center for sensor node k. According to the distances among L k-1 , L k and L k+1 , I k x and I k y are calculated by [34][35][36] where a is the distance between L k and L k+1 , b is the distance between L k+1 and L k-1 , and c is the distance between L k-1 and L k . According to the circle center at L k L k x , L k y and the radius r, the equation of the circle can be calculated by According to the path from I k to L k , the equation of the line can be calculated by (1) Fig.…”

Section: Is K Greater Than N?mentioning

confidence: 99%

An efficient data collection path planning scheme for wireless sensor networks with mobile sinks

Chang

Jeng

Sheu

et al. 2020

J Wireless Com Network

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Wireless sensor networks with mobile sinks enable a mobile device to move into the sensing area for the purpose of collecting the sensing data. Mobile sinks increase the flexibility and convenience of data gathering in such systems. Taking the energy consumption of the mobile sink into account, the moving distance of the mobile sink must be reduced efficiently. Hence, it is important and necessary to develop an efficient path planning scheme for mobile sinks in large-scale wireless sensor network systems. According to several greedy-based algorithms, we adopt an angle bisector concept to create the moving path for the mobile sink. In this paper, a novel and efficient data collection path planning scheme is proposed to reduce the moving distances and to prolong the lifetimes of mobile sinks in wireless sensor networks. Considering the communication range limitations of sensor nodes and the obstacles within sensing areas, we design an inner center path planning algorithm to reduce the moving distance for the mobile sink. A back-routing avoidance method is included to address the moving path backpropagation problem. We account for the obstacles in sensing area. The reference point of obstacle avoidance is employed to address the obstacle problem. The proposed scheme makes an adaptive decision for creating the moving path of the mobile sink. A suitable moving path planning scheme can be achieved, and the moving distance of the mobile sink can be reduced. The proposed scheme is promising in large-scale wireless sensor networks. When the number of sensor nodes in the sensing area is increased by 50, the proposed scheme yields an average moving distance that is 1.1 km shorter than that of the heuristic tour-planning algorithm, where the sensing area is 5 km × 5 km. Simulation results demonstrate that the proposed data collection path planning scheme outperforms the previously developed greedy-based scheme in terms of the moving paths and moving distances of mobile sinks in wireless sensor networks.

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Polynomial triangle centers on the line at infinity

Cited by 8 publications

References 4 publications

102.14 A Note on the Feuerbach triangle

102.14 A Note on the Feuerbach triangle

105.11 Median-parallelogic and median-orthologic triangles

An efficient data collection path planning scheme for wireless sensor networks with mobile sinks

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