Triangle centers and central triangles , by Clark Kimberling. Pp. 295. $42.90. 1998. ISSN 0316 1282 ( Congressum Numerantium , Vol. 129, Winnipeg).
About: This article is published in The Mathematical Gazette.The article was published on 2001-03-01. It has received 168 citations till now. The article focuses on the topics: Triangle center.
Citations
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TL;DR: This work describes a method to automatically calculate portion size of a variety of foods through volume estimation using an image, utilizing camera parameter estimation and model reconstruction to determine the volume of food items, from which nutritional content is then extrapolated.
Abstract: As concern for obesity grows, the need for automated and accurate methods to monitor nutrient intake becomes essential as dietary intake provides a valuable basis for managing dietary imbalance. Moreover, as mobile devices with built-in cameras have become ubiquitous, one potential means of monitoring dietary intake is photographing meals using mobile devices and having an automatic estimate of the nutrient contents returned. One of the challenging problems of the image-based dietary assessment is the accurate estimation of food portion size from a photograph taken with a mobile digital camera. In this work, we describe a method to automatically calculate portion size of a variety of foods through volume estimation using an image. These "portion volumes" utilize camera parameter estimation and model reconstruction to determine the volume of food items, from which nutritional content is then extrapolated. In this paper, we describe our initial results of accuracy evaluation using real and simulated meal images and demonstrate the potential of our approach.
55 citations
18 Jun 2007
TL;DR: A novel range-free localization technique, called HCRL, which uses only the ratios of anchor-to-node hop-counts, and satisfies low-cost with a single flooding from a small number of anchor nodes, and subdivides one-hop into several sub-hops by transmission power control to improve localization accuracy.
Abstract: Determining the positions of nodes is essential in many applications and geographic routing protocols of Wireless Sensor Networks. Since localization is a fundamental component of sensor networks, the cost for localization itself should be minimized. In this paper, we focus on developing a localization algorithm which provides both low-cost and accuracy. Considering these requirements, we propose a novel range-free localization technique, called HCRL, which uses only the ratios of anchor-to-node hop-counts. HCRL satisfies low-cost with a single flooding from a small number of anchor nodes, and subdivides one-hop into several sub-hops by transmission power control to improve localization accuracy. Unlike previous work, we have conducted real experiments, which were made possible by using an external antenna with an omni-directional radiation pattern. The experimental results show that the performance of HCRL is superior to the conventional DV-Hop scheme with a small transmission overhead.
55 citations
Cites background from "Triangle centers and central triang..."
...Hence we have two intersection points P and P’, which are the isodynamic points of the triangle ABC Δ [ 11 ]....
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TL;DR: In this article, it was proved that if any two of the traditional centers of an orthocentric simplex (in any dimension) coincide, then the simplex is regular.
Abstract: A simplex is said to be orthocentric if its altitudes intersect in a common point, called its orthocenter. In this paper it is proved that if any two of the traditional centers of an orthocentric simplex (in any dimension) coincide, then the simplex is regular. Along the way orthocentric simplices in which all facets have the same circumradius are characterized, and the possible barycentric coordinates of the orthocenter are described precisely. In particular these barycentric coordinates are used to parametrize the shapes of orthocentric simplices. The substantial, but widespread, literature on orthocentric simplices is briefly surveyed in order to place the new results in their proper context, and some of the previously known results are given with new proofs from the present perspective.
32 citations
Cites result from "Triangle centers and central triang..."
...It is well-known that for d = 2 the coincidence of any two of the four mentioned centers yields a regular (or equilateral) triangle; see [37], page 78, and for triangle centers in general we refer to [5] and [ 32 ]....
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01 Jan 2011
TL;DR: In this article, the porisitic 1 system of triangles with common incircle and circumcircle is described and the orbits of centers and some other points of the poristic system are described.
Abstract: The one-parameter family of triangles with common incircle and circumcircle is called a porisitic 1 system of triangles. The triangles of a poristic system can be rotated freely about the common incircle. However this motion is not a rigid body motion for the sidelengths of the triangle are changing. Surprisingly many triangle centers associated with the triangles of the poristic family trace circles while the triangle traverses the poristic family. Other points move on conic sections, some points trace more complicated curves. We shall describe the orbits of centers and some other points. Thereby we are able to answer open questions and verify some older results.
32 citations
Cites background from "Triangle centers and central triang..."
...For some centers the loci are given in [11], especially the trace of the Gergonne point is treated in [1]....
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...The circumcenter and the incenter shall be denoted by X3 and X1, see [10, 11]....
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...[10, 11]) and it remains fixed while ∆ goes through the poristic family....
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...[10, 11]) is the centroid of ∆i and therefore X354 = [d(3R+ r)/(3R), 0]....
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19 Sep 2012
TL;DR: It is proved that every planar graph with maximum degree three has a planar drawing in which the edges are drawn as circular arcs that meet at equal angles around every vertex.
Abstract: We prove that every planar graph with maximum degree three has a planar drawing in which the edges are drawn as circular arcs that meet at equal angles around every vertex. Our construction is based on the Koebe---Andreev---Thurston circle packing theorem, and uses a novel type of Voronoi diagram for circle packings that is invariant under Mobius transformations, defined using three-dimensional hyperbolic geometry. We also use circle packing to construct planar Lombardi drawings of a special class of 4-regular planar graphs, the medial graphs of polyhedral graphs, and we show that not every 4-regular planar graph has a planar Lombardi drawing. We have implemented our algorithm for 3-connected planar cubic graphs.
31 citations
Cites background from "Triangle centers and central triang..."
...Hundreds of triangle centers are known, and include many well-known points determined from a triangle, such as its centroid, circumcenter, incenter, and orthocenter [18]....
[...]
References
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TL;DR: This work describes a method to automatically calculate portion size of a variety of foods through volume estimation using an image, utilizing camera parameter estimation and model reconstruction to determine the volume of food items, from which nutritional content is then extrapolated.
Abstract: As concern for obesity grows, the need for automated and accurate methods to monitor nutrient intake becomes essential as dietary intake provides a valuable basis for managing dietary imbalance. Moreover, as mobile devices with built-in cameras have become ubiquitous, one potential means of monitoring dietary intake is photographing meals using mobile devices and having an automatic estimate of the nutrient contents returned. One of the challenging problems of the image-based dietary assessment is the accurate estimation of food portion size from a photograph taken with a mobile digital camera. In this work, we describe a method to automatically calculate portion size of a variety of foods through volume estimation using an image. These "portion volumes" utilize camera parameter estimation and model reconstruction to determine the volume of food items, from which nutritional content is then extrapolated. In this paper, we describe our initial results of accuracy evaluation using real and simulated meal images and demonstrate the potential of our approach.
55 citations
18 Jun 2007
TL;DR: A novel range-free localization technique, called HCRL, which uses only the ratios of anchor-to-node hop-counts, and satisfies low-cost with a single flooding from a small number of anchor nodes, and subdivides one-hop into several sub-hops by transmission power control to improve localization accuracy.
Abstract: Determining the positions of nodes is essential in many applications and geographic routing protocols of Wireless Sensor Networks. Since localization is a fundamental component of sensor networks, the cost for localization itself should be minimized. In this paper, we focus on developing a localization algorithm which provides both low-cost and accuracy. Considering these requirements, we propose a novel range-free localization technique, called HCRL, which uses only the ratios of anchor-to-node hop-counts. HCRL satisfies low-cost with a single flooding from a small number of anchor nodes, and subdivides one-hop into several sub-hops by transmission power control to improve localization accuracy. Unlike previous work, we have conducted real experiments, which were made possible by using an external antenna with an omni-directional radiation pattern. The experimental results show that the performance of HCRL is superior to the conventional DV-Hop scheme with a small transmission overhead.
55 citations
01 Jan 2011
TL;DR: In this article, the porisitic 1 system of triangles with common incircle and circumcircle is described and the orbits of centers and some other points of the poristic system are described.
Abstract: The one-parameter family of triangles with common incircle and circumcircle is called a porisitic 1 system of triangles. The triangles of a poristic system can be rotated freely about the common incircle. However this motion is not a rigid body motion for the sidelengths of the triangle are changing. Surprisingly many triangle centers associated with the triangles of the poristic family trace circles while the triangle traverses the poristic family. Other points move on conic sections, some points trace more complicated curves. We shall describe the orbits of centers and some other points. Thereby we are able to answer open questions and verify some older results.
32 citations
19 Sep 2012
TL;DR: It is proved that every planar graph with maximum degree three has a planar drawing in which the edges are drawn as circular arcs that meet at equal angles around every vertex.
Abstract: We prove that every planar graph with maximum degree three has a planar drawing in which the edges are drawn as circular arcs that meet at equal angles around every vertex. Our construction is based on the Koebe---Andreev---Thurston circle packing theorem, and uses a novel type of Voronoi diagram for circle packings that is invariant under Mobius transformations, defined using three-dimensional hyperbolic geometry. We also use circle packing to construct planar Lombardi drawings of a special class of 4-regular planar graphs, the medial graphs of polyhedral graphs, and we show that not every 4-regular planar graph has a planar Lombardi drawing. We have implemented our algorithm for 3-connected planar cubic graphs.
31 citations
03 Mar 2011
TL;DR: The result shows that the approach can provide about 90% accuracy for bi-directional people counting with an angle of 45° to the scene.
Abstract: In this paper, an object based bi-directional counting system is proposed, which comprises of an advanced object detection and tracking algorithm to count the people flow in the monitoring scene. The result of which shows that the approach can provide about 90% accuracy for bi-directional people counting with an angle of 45° to the scene.
30 citations