It is illustrated that there exists an inflection circle on the linkage rigid body by the principle of relative motion. Confirmed methods of the inflection circle, curvature radius and curvature center of the point tr...It is illustrated that there exists an inflection circle on the linkage rigid body by the principle of relative motion. Confirmed methods of the inflection circle, curvature radius and curvature center of the point track on the linkage rigid body are given in the case of the different contact type of move instantaneous center line and static instantaneous center line. The regularity of distribution of curvature radius and curvature center of the point track is researched. The identification methods called determination parameters and auxiliary vertical line of the diameter and direction of the inflection circle in the four bar mechanism are pointed out. A design method of the crane hoisting mechanism is discussed in the end of this paper.展开更多
Rodin and Sullivan （1987） proved Thurston＇s conjecture that a scheme based on the Circle Packing Theorem converges to the Riemann mapping, thereby proved a refreshing geometric view of the Riemann Mapping Theorem. ...Rodin and Sullivan （1987） proved Thurston＇s conjecture that a scheme based on the Circle Packing Theorem converges to the Riemann mapping, thereby proved a refreshing geometric view of the Riemann Mapping Theorem. Naturally, we consider to use the ellipses to pack the bounded simply connected domain and obtain similarly a sequence simplicial homeomorphism between the ellipse packing and the circle packing. In this paper, we prove that these simplicial homeomorphism approximate a quasiconformal mapping from the bounded simply connected domain onto the unit disk with the modulus of their complex dilatations tending to 1 almost everywhere in the domain when the ratio of the longer axis and shorter axis of the ellipse tending to ∞.展开更多
Böröczky-Lutwak-Yang-Zhang proved the log-Brunn-Minkowski inequality for two origin-symmetric convex bodies in the plane in a way that is stronger than for the classical Brunn-Minkowski inequality.In this pa...Böröczky-Lutwak-Yang-Zhang proved the log-Brunn-Minkowski inequality for two origin-symmetric convex bodies in the plane in a way that is stronger than for the classical Brunn-Minkowski inequality.In this paper,we investigate the relative positive center set of planar convex bodies.As an application of the relative positive center,we prove the log-Minkowski inequality and the log-Brunn-Minkowski inequality.展开更多
In the field of computer vision and image processing, the characteristic parameters such as center coordinates and radius of circle industrial parts often need to be measured. In this paper, three robust, accurate and...In the field of computer vision and image processing, the characteristic parameters such as center coordinates and radius of circle industrial parts often need to be measured. In this paper, three robust, accurate and reliable linear direct algorithms are presented based on the analysis and research of various algorithms in the past, and experimental resalts are given at the end.展开更多
In this paper, we present the analytical expressions for computing the minimum distance between a point and a torus, which is called the orthogonal projection point problem. If the test point is on the outside of the ...In this paper, we present the analytical expressions for computing the minimum distance between a point and a torus, which is called the orthogonal projection point problem. If the test point is on the outside of the torus and the test point is at the center axis of the torus, we present that the orthogonal projection point set is a circle perpendicular to the center axis of the torus;if not, the analytical expression for the orthogonal projection point problem is also given. Furthermore, if the test point is in the inside of the torus, we also give the corresponding analytical expression for orthogonal projection point for two cases.展开更多
By means of programs GTMPAC based- on generalized triangle method,analysis and synthesis of mechanism design in accordance with absolutely graphicalmethod( absolutely germetrical method) are developed.In this paper,we...By means of programs GTMPAC based- on generalized triangle method,analysis and synthesis of mechanism design in accordance with absolutely graphicalmethod( absolutely germetrical method) are developed.In this paper,we make aspecial study about centering- point curve and circling- point curve and couplercurves based on Ball’s points.展开更多
文摘It is illustrated that there exists an inflection circle on the linkage rigid body by the principle of relative motion. Confirmed methods of the inflection circle, curvature radius and curvature center of the point track on the linkage rigid body are given in the case of the different contact type of move instantaneous center line and static instantaneous center line. The regularity of distribution of curvature radius and curvature center of the point track is researched. The identification methods called determination parameters and auxiliary vertical line of the diameter and direction of the inflection circle in the four bar mechanism are pointed out. A design method of the crane hoisting mechanism is discussed in the end of this paper.
基金supported by the National Natural Science Foundation of China(10701084)Chongqing Natural Science Foundation (2008BB0151)
文摘Rodin and Sullivan （1987） proved Thurston＇s conjecture that a scheme based on the Circle Packing Theorem converges to the Riemann mapping, thereby proved a refreshing geometric view of the Riemann Mapping Theorem. Naturally, we consider to use the ellipses to pack the bounded simply connected domain and obtain similarly a sequence simplicial homeomorphism between the ellipse packing and the circle packing. In this paper, we prove that these simplicial homeomorphism approximate a quasiconformal mapping from the bounded simply connected domain onto the unit disk with the modulus of their complex dilatations tending to 1 almost everywhere in the domain when the ratio of the longer axis and shorter axis of the ellipse tending to ∞.
基金Supported by the Excellent Young Talents Fund Program of Higher Education Institutions of Anhui Province (gxyqZD2020022)the University Natural Science Research Project of Anhui Province (2022AH040067)+1 种基金the Fundamental Research Funds for the Central Universities (3132023202)National Natural Science Foundation of China (12001080).
文摘Böröczky-Lutwak-Yang-Zhang proved the log-Brunn-Minkowski inequality for two origin-symmetric convex bodies in the plane in a way that is stronger than for the classical Brunn-Minkowski inequality.In this paper,we investigate the relative positive center set of planar convex bodies.As an application of the relative positive center,we prove the log-Minkowski inequality and the log-Brunn-Minkowski inequality.
文摘In the field of computer vision and image processing, the characteristic parameters such as center coordinates and radius of circle industrial parts often need to be measured. In this paper, three robust, accurate and reliable linear direct algorithms are presented based on the analysis and research of various algorithms in the past, and experimental resalts are given at the end.
文摘In this paper, we present the analytical expressions for computing the minimum distance between a point and a torus, which is called the orthogonal projection point problem. If the test point is on the outside of the torus and the test point is at the center axis of the torus, we present that the orthogonal projection point set is a circle perpendicular to the center axis of the torus;if not, the analytical expression for the orthogonal projection point problem is also given. Furthermore, if the test point is in the inside of the torus, we also give the corresponding analytical expression for orthogonal projection point for two cases.
文摘By means of programs GTMPAC based- on generalized triangle method,analysis and synthesis of mechanism design in accordance with absolutely graphicalmethod( absolutely germetrical method) are developed.In this paper,we make aspecial study about centering- point curve and circling- point curve and couplercurves based on Ball’s points.
