Cubic Polynomial Space Curve Splines

2000 ◽  
pp. 77-93
Author(s):  
Gary D. Knott
Keyword(s):  
Space Curve ◽  
Polynomial Space ◽  
Cubic Polynomial

The projective geometry of ambiguous surfaces

1990 ◽  
Vol 332 (1623) ◽  
pp. 1-47 ◽  
Keyword(s):  
Projective Geometry ◽  
Space Curve ◽  
Scene Reconstruction ◽  
Original Surface ◽  
Twisted Cubic ◽  
Straight Line ◽  
Cubic Polynomial ◽  
Ambiguous Case ◽  
Polynomial Constraint

The projective geometry underlying the ambiguous case of scene reconstruction from image correspondences is developed. The am biguous case arises when reconstruction yields two or more essentially different surfaces in space, each capable of giving rise to the image correspondences. Such surfaces naturally occur in complementary pairs. Ambiguous surfaces are examples of rectangular hyperboloids. Complementary ambiguous surfaces intersect in a space curve of degree four, which splits into two components, namely a twisted cubic (space curve of degree three), and a straight line. For each ambiguous surface compatible with a given set of image correspondences, a complementary surface compatible with the same image correspondences can always be found such that both the original surface and the twisted cubic contained in the intersection of the two surfaces are invariant under the same rotation through 180°. In consequence, each ambiguous surface is subject to a cubic polynomial constraint. This constraint is the basis of a new proof of the known result that there are, in general, exactly ten scene reconstructions compatible with five given image correspondences. Ambiguity also arises in reconstruction based on image velocities rather than on image correspondences. The two types of ambiguity have m any sim ilarities because image velocities are obtained from image correspondences as a limit, when the distances between corresponding points become small. It is shown that the amount of similarity is restricted, in that when passing from image correspondences to image velocities, some of the detailed geometry of the ambiguous case is lost.

Path Planning of Mobile Robot Using Improved Artificial Bee Colony Algorithm

2020 ◽  
Vol 38 (9A) ◽  
pp. 1384-1395
Author(s):  
Rakaa T. Kamil ◽  
Mohamed J. Mohamed ◽  
Bashra K. Oleiwi
Keyword(s):  
Mobile Robot ◽  
Comparative Research ◽  
Artificial Bee Colony Algorithm ◽  
Artificial Bee Colony ◽  
Dynamic Control ◽  
Computational Time ◽  
Bee Colony ◽  
Shortest Distance ◽  
Minimum Number ◽  
Cubic Polynomial

A modified version of the artificial Bee Colony Algorithm (ABC) was suggested namely Adaptive Dimension Limit- Artificial Bee Colony Algorithm (ADL-ABC). To determine the optimum global path for mobile robot that satisfies the chosen criteria for shortest distance and collision–free with circular shaped static obstacles on robot environment. The cubic polynomial connects the start point to the end point through three via points used, so the generated paths are smooth and achievable by the robot. Two case studies (or scenarios) are presented in this task and comparative research (or study) is adopted between two algorithm’s results in order to evaluate the performance of the suggested algorithm. The results of the simulation showed that modified parameter (dynamic control limit) is avoiding static number of limit which excludes unnecessary Iteration, so it can find solution with minimum number of iterations and less computational time. From tables of result if there is an equal distance along the path such as in case A (14.490, 14.459) unit, there will be a reduction in time approximately to halve at percentage 5%.

A Combinatorial Problem Which Is Complete in Polynomial Space

1976 ◽  
Vol 23 (4) ◽  
pp. 710-719 ◽  
Author(s):  
S. Even ◽  
R. E. Tarjan
Keyword(s):  
Combinatorial Problem ◽  
Polynomial Space

Geometry Design and Contact Ratio Analysis for Circular Arc Parallel-Axis Helical Gears

2016 ◽  
Author(s):  
Z. Chen ◽  
B. Lei ◽  
Q. Zhao
Keyword(s):  
Rolling Process ◽  
Helical Gear ◽  
Space Curve ◽  
Impact Factors ◽  
Contact Ratio ◽  
Circular Arc ◽  
Practical Applications ◽  
Geometry Design ◽  
Gear Mechanism ◽  
The Impact

Based on space curve meshing theory, in this paper, we present a novel geometric design of a circular arc helical gear mechanism for parallel transmission with convex-concave circular arc profiles. The parameter equations describing the contact curves for both the driving gear and the driven gear were deduced from the space curve meshing equations, and parameter equations for calculating the convex-concave circular arc profiles were established both for internal meshing and external meshing. Furthermore, a formula for the contact ratio was deduced, and the impact factors influencing the contact ratio are discussed. Using the deduced equations, several numerical examples were considered to validate the contact ratio equation. The circular arc helical gear mechanism investigated in this study showed a high gear transmission performance when considering practical applications, such as a pure rolling process, a high contact ratio, and a large comprehensive strength.

Cubic polynomial patches through geodesics

2008 ◽  
Vol 40 (1) ◽  
pp. 56-61 ◽  
Author(s):  
Marco Paluszny
Keyword(s):  
Cubic Polynomial

Special Bishop Motion and Bishop Darboux Rotation Axis of the Space Curve

2008 ◽  
Vol 6 (1) ◽  
pp. 27-34 ◽  
Author(s):  
Bahaddin Bukcu ◽  
Murat Kemal Karacan
Keyword(s):  
Rotation Axis ◽  
Space Curve

scholarly journals Development of a semi-parametric PAR (Photosynthetically Active Radiation) partitioning model for the United States, version 1.0

2014 ◽  
Vol 7 (5) ◽  
pp. 2477-2484 ◽  
Author(s):  
J. C. Kathilankal ◽  
T. L. O'Halloran ◽  
A. Schmidt ◽  
C. V. Hanson ◽  
B. E. Law
Keyword(s):  
United States ◽  
Elevation Angle ◽  
Model Performance ◽  
Diffuse Radiation ◽  
The United States ◽  
Polynomial Model ◽  
Coefficient Of Determination ◽  
Data Set ◽  
Cubic Polynomial ◽  
Solar Elevation Angle

Abstract. A semi-parametric PAR diffuse radiation model was developed using commonly measured climatic variables from 108 site-years of data from 17 AmeriFlux sites. The model has a logistic form and improves upon previous efforts using a larger data set and physically viable climate variables as predictors, including relative humidity, clearness index, surface albedo and solar elevation angle. Model performance was evaluated by comparison with a simple cubic polynomial model developed for the PAR spectral range. The logistic model outperformed the polynomial model with an improved coefficient of determination and slope relative to measured data (logistic: R2 = 0.76; slope = 0.76; cubic: R2 = 0.73; slope = 0.72), making this the most robust PAR-partitioning model for the United States currently available.

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