scholarly journals Piecewise Curve Fitting Based on Least Square Method in 3D Space

2020 ◽  
Vol 3 (1) ◽  
Author(s):  
Lihong Xue
Keyword(s):  
Least Squares ◽  
Curve Fitting ◽  
Dimensional Space ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Least Square Method ◽  
Least Square ◽  
Least Square Fitting ◽  
Fitting In ◽  
Three Dimensional Space

Least squares curve fitting is widely used in various neighborhoods, such as industry, agriculture, and economy. The method of piecewise curve fitting is used to deal with some experimental studies with large amounts of data. It can not only be used for plane space points, but also for three-dimensional space points. Firstly, this article introduces the principles of curve fitting and least squares. Secondly, it clarifies the steps based on least square fitting and gives examples of improvements made based on the principle of least square fitting functions by some scientists. Finally, the piecewise curve fitting in the three-dimensional space is obtained using the least squares piecewise curve fitting. It lays a certain theoretical foundation for drawing the laws between data in three-dimensional space.

Railroad track modeling based on the results of mobile laser scanning

2018 ◽  
pp. 408-413
Author(s):  
Elena Lenchenkova
Keyword(s):  
Mathematical Model ◽  
Laser Scanning ◽  
Dimensional Space ◽  
Practical Importance ◽  
Three Dimensional ◽  
Least Square Method ◽  
Least Square ◽  
Railroad Track ◽  
Railway Line ◽  
Type Data

Objective: To develop a mathematical model of the railroad track based on the initial progressive-type data (laser scanning) in railroad design. Methods: Regression analysis (least-square method), as well as coordinate methods of calculating point position in space were applied. Results: The mathematical model, which could describe the position of the railroad track in three-dimensional space by means of mathematical relations, was obtained. Applicability of approximating models was established. The models make it possible to provide smoothing of laser survey data. Regularization and globalization algorithms of initial data were developed. Practical importance: The introduced model is universal when describing the position of the track at all stages of life cycle of the railway line. It is reasonable to apply the presented model in design engineering in order to balance survey errors, maintain the track in coordinates, as well as to calculate design and profile parameters.

A 3D stable trot of a quadruped robot over uneven terrains

2016 ◽  
Vol 231 (3) ◽  
pp. 555-573 ◽  
Author(s):  
Mahdi Khorram ◽  
S Ali A Moosavian
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Quadruped Robot ◽  
Legged Robots ◽  
Whole Body ◽  
Main Body ◽  
Stable Gait ◽  
Three Dimensional Space

Legged robots have superior advantages rather than wheeled robots for moving over uneven terrains in the presence of various obstacles. The design of an appropriate path for the main body and legs is an important issue for such robots especially on the uneven terrains. In this paper, the focus is to develop a stable gait for a quadruped robot to trot on uneven terrains. First, a stability condition is developed for a whole-body quadruped robot over uneven terrains based on avoiding the tumbling. By using a simple model, a point with zero moments is calculated in the three-dimensional space. Then, the reference path of this point is determined so that the tumbling moments become zero. The path of the main body will be calculated by using an optimal controller. The main feature of the proposed gait generation framework is that the height of robot can change continuously and stably on uneven terrains. To evaluate the robot stability, the tumbling moments around diagonal lines are calculated and some methods are proposed to reduce these moments to improve the robot stability. The tip of swing foot is also planned to avoid any collision with the environment. The proposed method will be demonstrated using an 18-Degrees of freedom (DOF) quadruped robot in simulation and experimental studies. The experimental setup is a small-size quadruped robot, which is composed of a rectangular plate as its main body with four legs that each one has three active joints with DC servo motors. Obtained results reveal that the robot can trot on uneven terrains stably. Besides, the comparison with the previous methods approves the merits of proposed algorithm on uneven terrains.

MAP FORMATION IN PROPRIOCEPTIVE CORTEX

1994 ◽  
Vol 05 (02) ◽  
pp. 87-101 ◽  
Author(s):  
SUNGZOON CHO ◽  
JAMES A. REGGIA
Keyword(s):  
Primary Motor Cortex ◽  
Dimensional Space ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Muscle Length ◽  
Muscle Group ◽  
Feature Maps ◽  
Organizational Issues ◽  
Muscle Groups ◽  
Three Dimensional Space

Current understanding of feature maps in proprioceptive cortex is quite limited. To complement experimental studies, we developed a computational model of map formation in proprioceptive cortex. Muscle length and tension from six muscle groups controlling the position of a model arm in three-dimensional space served as input to the simulated cortex. The resultant feature map consisted of regularly spaced clusters of cortical columns representing individual muscle lengths and tensions. Cortical units became tuned to plausible combinations of tension and length, and multiple representations of each muscle group were present. The map was organized such that compact regions within which all muscle group lengths and tensions are represented could be identified. Most striking was the observation that, although not explicitly present in the input, the cortical map developed a representation of the three-dimensional space in which the arm moved. These findings represent testable predictions about proprioceptive cortex, and may also help clarify some organizational issues concerning primary motor cortex.

scholarly journals Improved Total Least Square Algorithm

2015 ◽  
Vol 9 (1) ◽  
pp. 394-399 ◽  
Author(s):  
Deng Yonghe
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Least Square ◽  
Error Equation ◽  
Virtual Observation ◽  
Straight Line ◽  
Condition Equation ◽  
Total Least Square ◽  
Three Dimensional Space ◽  
Improved Algorithm

Aim to blemish of total least square algorithm based on error equation of virtual observation,this paper proposed a sort of improved algorithm which doesn’t neglect condition equation of virtual observation,and considers both error equation and condition equation of virtual observation.So,the improved algorithm is better.Finally,this paper has fitted a straight line in three-dimensional space based on the improved algorithm.The result showed that the improved algorithm is viable and valid.

Determination of Arbitrary Tooth Displacements

1978 ◽  
Vol 57 (5-6) ◽  
pp. 663-674 ◽  
Author(s):  
R.J. Pryputniewicz ◽  
C.J. Burstone ◽  
W.W. Bowley
Keyword(s):  
Dimensional Space ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Double Exposure ◽  
Maxillary Central Incisor ◽  
Modern Technique ◽  
Hologram Interferometry ◽  
Component Loading ◽  
Three Dimensional Space

The noninvasive, modern technique based on the method of double-exposure hologram interferometry was used to measure arbitrary displacements of teeth in the three dimensional space. The experimental studies were carried out on an idealized model of the maxillary central incisor. The results show that the experimental data, based on component loading, are inadequate to accurately predict tooth displacement from an arbitrary force acting in the three dimensional space.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

A Peptoid with Extended Shape in Water

2019 ◽  
Author(s):  
Jumpei Morimoto ◽  
Yasuhiro Fukuda ◽  
Takumu Watanabe ◽  
Daisuke Kuroda ◽  
Kouhei Tsumoto ◽  
...  
Keyword(s):  
Spectroscopic Analysis ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Biomolecular Recognition ◽  
Biological Application ◽  
New Class ◽  
Proteolytic Resistance ◽  
Pharmacokinetic Properties ◽  
Optically Pure ◽  
Three Dimensional Space

<div> <div> <div> <p>“Peptoids” was proposed, over decades ago, as a term describing analogs of peptides that exhibit better physicochemical and pharmacokinetic properties than peptides. Oligo-(N-substituted glycines) (oligo-NSG) was previously proposed as a peptoid due to its high proteolytic resistance and membrane permeability. However, oligo-NSG is conformationally flexible and is difficult to achieve a defined shape in water. This conformational flexibility is severely limiting biological application of oligo-NSG. Here, we propose oligo-(N-substituted alanines) (oligo-NSA) as a new peptoid that forms a defined shape in water. A synthetic method established in this study enabled the first isolation and conformational study of optically pure oligo-NSA. Computational simulations, crystallographic studies and spectroscopic analysis demonstrated the well-defined extended shape of oligo-NSA realized by backbone steric effects. The new class of peptoid achieves the constrained conformation without any assistance of N-substituents and serves as an ideal scaffold for displaying functional groups in well-defined three-dimensional space, which leads to effective biomolecular recognition. </p> </div> </div> </div>

Sign in / Sign up

Export Citation Format

Share Document