Problem 71. An Angle Bisector

1979 ◽  
pp. 186-187
Keyword(s):  
Angle Bisector

scholarly journals Maxillomandibular Plane Angle Bisector (MM) Adjunctive to Occlusal Plane to evaluate Anteroposterior Measurement of Dental Base

2012 ◽  
Vol 13 (4) ◽  
pp. 539-544
Author(s):  
Chanamallappa R Ganiger ◽  
KU Cariappa ◽  
AR Yusuf Ahammed
Keyword(s):  
Clinical Significance ◽  
Orthodontic Treatment ◽  
Clinical Usefulness ◽  
Occlusal Plane ◽  
Reference Plane ◽  
Plane Angle ◽  
B Values ◽  
Angle Bisector ◽  
Lateral Cephalograms ◽  
Relationship Of

ABSTRACT Aim This study was undertaken to analyze the clinical usefulness of the maxillomandibular bisector, its reproducibility, its validity and its relationship to the functional occlusal plane, the bisecting occlusal plane and the nature of its cant. Materials and methods Thirty pretreatment lateral cephalograms, each of adolescents (above 18 years of age) and children (10- 12 years), seeking orthodontic treatment were randomly selected and the Wits technique of anteroposterior measurement was used to compare A-B values measured to the new plane with those measured to the functional occlusal plane (FOP) and to the traditional or bisecting occlusal plane (BOP). Results Present study showed that MM bisector plane is more reproducible and valid reference plane, than the FOP and BOP. Conclusion A new plane, geometrically derived from the dental base planes, has been tested as an occlusal plane substitute for the measurement of anteroposterior jaw relationships. It lies close to but at an angle and inferior to the traditional occlusal planes and is highly reproducible at all times. Clinical significance Maxillomandibular planes angle bisector may be a useful adjunct for the cephalometric assessment of sagittal relationship of the patient. How to cite this article Ganiger CR, Nayak USK, Cariappa KU, Ahammed ARY. Maxillomandibular Plane Angle Bisector (MM) Adjunctive to Occlusal Plane to evaluate Anteroposterior Measurement of Dental Base. J Contemp Dent Pract 2012; 13(4):539-544.

scholarly journals Angle Bisector Algorithm and Modified Dynamic Programming Algorithm for Dubins Traveling Salesman Problem

2021 ◽  
Author(s):  
Eswara Venkata Kumar Dhulipala
Keyword(s):  
Euclidean Distance ◽  
Travelling Salesman Problem ◽  
Dynamic Programming Algorithm ◽  
Constant Factor ◽  
Programming Algorithm ◽  
Worst Case ◽  
Angle Bisector ◽  
Set Of Points ◽  
The Given ◽  
Tour Length

A Dubin's Travelling Salesman Problem (DTSP) of finding a minimum length tour through a given set of points is considered. DTSP has a Dubins vehicle, which is capable of moving only forward with constant speed. In this paper, first, a worst case upper bound is obtained on DTSP tour length by assuming DTSP tour sequence same as Euclidean Travelling Salesman Problem (ETSP) tour sequence. It is noted that, in the worst case, \emph{any algorithm that uses of ETSP tour sequence} is a constant factor approximation algorithm for DTSP. Next, two new algorithms are introduced, viz., Angle Bisector Algorithm (ABA) and Modified Dynamic Programming Algorithm (MDPA). In ABA, ETSP tour sequence is used as DTSP tour sequence and orientation angle at each point $i_k$ are calculated by using angle bisector of the relative angle formed between the rays $i_{k}i_{k-1}$ and $i_ki_{k+1}$. In MDPA, tour sequence and orientation angles are computed in an integrated manner. It is shown that the ABA and MDPA are constant factor approximation algorithms and ABA provides an improved upper bound as compared to Alternating Algorithm (AA) \cite{savla2008traveling}. Through numerical simulations, we show that ABA provides an improved tour length compared to AA, Single Vehicle Algorithm (SVA) \cite{rathinam2007resource} and Optimized Heading Algorithm (OHA) \cite{babel2020new,manyam2018tightly} when the Euclidean distance between any two points in the given set of points is at least $4\rho$ where $\rho$ is the minimum turning radius. The time complexity of ABA is comparable with AA and SVA and is better than OHA. Also we show that MDPA provides an improved tour length compared to AA and SVA and is comparable with OHA when there is no constraint on Euclidean distance between the points. In particular, ABA gives a tour length which is at most $4\%$ more than the ETSP tour length when the Euclidean distance between any two points in the given set of points is at least $4\rho$.

scholarly journals LEARNING HYPERPLANES THAT CAPTURES THE GEOMETRIC STRUCTURE OF CLASS REGIONS

2013 ◽  
pp. 7-12
Author(s):  
PRAMOD PATIL ◽  
ALKA LONDHE ◽  
PARAG KULKARNI
Keyword(s):  
Decision Tree ◽  
Decision Trees ◽  
Geometric Structure ◽  
Gini Index ◽  
Decision Tree Algorithm ◽  
Top Down ◽  
Angle Bisector ◽  
Eigen Value ◽  
Tree Algorithms ◽  
Left And Right

Most of the decision tree algorithms rely on impurity measures to evaluate the goodness of hyperplanes at each node while learning a decision tree in a top-down fashion. These impurity measures are not differentiable with relation to the hyperplane parameters. Therefore the algorithms for decision tree learning using impurity measures need to use some search techniques for finding the best hyperplane at every node. These impurity measures don’t properly capture the geometric structures of the data. In this paper a Two-Class algorithm for learning oblique decision trees is proposed. Aggravated by this, the algorithm uses a strategy, to evaluate the hyperplanes in such a way that the (linear) geometric structure in the data is taken into consideration. At each node of the decision tree, algorithm finds the clustering hyperplanes for both the classes. The clustering hyperplanes are obtained by solving the generalized Eigen-value problem. Then the data is splitted based on angle bisector and recursively learn the left and right sub-trees of the node. Since, in general, there will be two angle bisectors; one is selected which is better based on an impurity measure gini index. Thus the algorithm combines the ideas of linear tendencies in data and purity of nodes to find better decision trees. This idea leads to small decision trees and better performance.

The paramagnetic germanium–sodium impurity centres and in α-quartz

1991 ◽  
Vol 69 (7) ◽  
pp. 761-779 ◽  
Author(s):  
R. S. Dickson ◽  
J. A Weil ◽  
P. H. Davis
Keyword(s):  
Bond Angle ◽  
Resonance Spectroscopy ◽  
Crystallographic Axis ◽  
Paramagnetic Resonance ◽  
Angle Bisector ◽  
X Band ◽  
Ca 50 ◽  
X Irradiation ◽  
Na Ions ◽  
Sodium Impurity

Centres [Formula: see text] formed in α-quartz by 77 K x irradiation and warming above ca. 165 K, both exhibit a reversible change in symmetry of the centres from C1 at 75 K to C2 at 295 K, as observed by X-band electronic paramagnetic resonance spectroscopy. Each centre contains a Ge3+ ion (S = 1/2) substituted for a Si4+ ion, with a nearby Na+ interstitial ion. Spin-Hamiltonian electronic Zeeman, 73Ge and 23Na nuclear hyperfine and quadrupole parameter matrices for these centres were measured at temperatures 75, 190, and 295 K. They show that the change is associated with the defect reorienting between sites related by a two-fold crystallographic axis a, with energy barrier 0.223(6) eV for A and 0.178(14) eV for C. In both centres, ca. 50% of the spin density is located in a Ge sp orbital; in A, the sp orbital is oriented close to a, while in C it is nearly parallel to an O–Si–O bond-angle bisector that is nearly normal to a. Theoretical hyperfine matrices indicate that the Na ions are located near a, in a c-axis channel near the Ge site. Above ca. 270 K, A and C are observably in equilibrium, and are thus deemed to be isomeric species.

Development and Analysis of Hilly Power Chassis With Vari-Ground Clearance and Vari-Wheel Track Mechanism

2013 ◽  
Author(s):  
Qiaoming Gao ◽  
Feng Gao ◽  
Guoyan Xu ◽  
Nenggen Ding
Keyword(s):  
Power Transmission ◽  
Design Method ◽  
Steering System ◽  
Middle Part ◽  
Full Time ◽  
Angle Bisector ◽  
Ground Clearance ◽  
Wheel Drive ◽  
Line Spacing ◽  
Wheel Track

A kind of Hilly Power Chassis with Vari-ground Clearance and Vari-wheel Track Mechanism (VII-HPC) is designed to be adapted to various types of crops grown ridge section and height. It consists of the middle part, balancing system, two driving axles and steering system. These assemblies form an H-type chassis structure where both sides of the driving axle and the middle part are connected for power transmission, ground clearance varying and wheel track adjustable function, which ensures full-time four-wheel drive in a complex road environment and confirms that the middle part is always in the angle bisector of the two driving axles. According to the various agricultural ground clearance and line spacing of different crops in the hilly areas, the ground clearance and the wheel track can be adjusted continuously and smoothly driven by hydraulic system. According to VII-HPC Structural Characteristic without Ackerman Steering Linkage, the hydraulic four wheel steering scheme has been proposed. The related analysis is presented to verify the feasibility of VII-HPC, including the relationship between the ground clearance and parameters like centroid height, and the ride analysis at different speeds on the pulse road. The results and the subsequent experimental results show the design method and the concept of VII-HPC are proved reasonable, feasible and practical.

Algorithm for Detecting and Solving the Problem of Under-Filled Pointed Ends Based on 3D Printing Plastic Droplet Generation

2014 ◽  
Author(s):  
Jelena Prša ◽  
Franz Irlinger ◽  
Tim C. Lueth
Keyword(s):  
3D Printing ◽  
Droplet Generation ◽  
Generation Process ◽  
Critical Area ◽  
Final Shape ◽  
Angle Bisector ◽  
Critical Areas ◽  
3D Printed ◽  
Plastic Parts ◽  
Initial Geometry

In this paper the problem of under-filled pointed ends is introduced and mathematically defined. To tackle this problem, we present a new algorithm that detects and fills the critical areas, which arise at the 3D printed plastic parts. While printing the contours and/or infill lines, due to the limitations based on the width of the extruded material, narrow edges and pointed ends remain improperly filled. This eventually results in 3D printed objects with the final geometry that differs greatly from the initial geometry. This paper presents the fundamentals for solving the problem of 3D printing of geometries which contain narrow pointed ends. The critical area of the pointed ends is mathematically defined and, depending on the angle, the formulae for the calculation of under-filled and over-filled areas are given. The newly developed algorithm, based on the 3D Printing plastic droplet generation process, assures that the droplets of the repeating contours are placed at the edges of the contour-segments and by that minimises the potential under-fills. Furthermore, an additional number of droplets is defined, that are either printed in or removed from the under-filled areas in the angle bisector. The proposed algorithm is applied on parts, whose geometry describes pointed ends. The final 3D printed parts are very appealing and their shape resembles the original geometry more than the final shape of the parts without applying the algorithm.

scholarly journals Comprehensive evaluation model of wind power accommodation ability based on macroscopic and microscopic indicators

2019 ◽  
Vol 4 (1) ◽  
Author(s):  
Gengyin Li ◽  
Guodong Li ◽  
Ming Zhou
Keyword(s):  
Wind Power ◽  
Index System ◽  
Comprehensive Evaluation ◽  
Evaluation Model ◽  
Evaluation Index System ◽  
Angle Bisector ◽  
Evaluation Indexes ◽  
Study Results ◽  
Comprehensive Evaluation Model ◽  
Radar Chart

Abstract This article explores and establishes comprehensive evaluation index system of wind power accommodation ability considering microscopic index and macroscopic index, and the index system includes conventional evaluation indexes such as forecast deviation, simultaneity factor and anti-peak rate, also newly introduced evaluation indexes such as installed capacity, power adequacy and accommodation space. Bayesian weight modified method is used for solving index weights of 8 wind power accommodation indexes. The paper puts forward a comprehensive evaluation model of wind power accommodation ability based on improved radar chart method, and this model changes traditional radar chart fan-shaped sector to quadrilateral evaluation region, and increasing angle bisector can solve the problem that evaluation results are not unique. It constructs new area and perimeter vectors of radar chart, which make the evaluation results give consideration to level of aggregation and balance degree of evaluation objectives, and case study results show that this model has a certain practical value.

Sign in / Sign up

Export Citation Format

Share Document