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
In this paper, we investigate how to compute the minimum distance between a point and a parametric surface, and then to return the nearest point (foot point) on the surface as well as its corresponding parameter, whic...In this paper, we investigate how to compute the minimum distance between a point and a parametric surface, and then to return the nearest point (foot point) on the surface as well as its corresponding parameter, which is also called the point projection problem of a parametric surface. The geometric strategy algorithm (hereafter GSA) presented consists of two parts as follows. The normal curvature to a given parametric surface is used to find the corresponding foot point firstly, and then the Taylor's expansion of the parametric surface is employed to compute parameter increments and to get the iteration formula to calculate the orthogonal projection point of test point to the parametric surface. Our geometric strategy algorithm is essentially dependent on the geometric property of the normal curvature, and performs better than existing methods in two ways. Firstly, GSA converges faster than existing methods, such as the method to turn the problem into a root-finding of nonlinear system, subdividing methods, clipping methods, geometric methods (tangent vector and geometric curvature) and hybrid second-order method, etc. Specially, it converges faster than the classical Newton's iterative method. Secondly, GSA is independent of the initial iterative value, which we prove in Theorem 1. Many numerical examples confirm GSA's robustness and efficiency.展开更多
After more than a hundred years’development,public libraries have entered a rising period marked by government participation and public service-orientation in recent years.In this context and from the perspective of ...After more than a hundred years’development,public libraries have entered a rising period marked by government participation and public service-orientation in recent years.In this context and from the perspective of modern public culture service system,the overall public librarianship has some problems to be solved,such as facility layout with rigidified administration which is difficult展开更多
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.
基金This work is supported by the National Natural Science Foundation of China under Grant No.61263034the Feature Key Laboratory for Regular Institutions of Higher Education of Guizhou Province of China under Grant No.[2016]003+3 种基金the Key Laboratory of Advanced Manufacturing Technology of Ministry of Education of China with Guizhou University under Grant No.KY[2018]479the Training Center for Network Security and Big Data Application of Guizhou Minzu University under Grant No.20161113006the Shandong Provincial Natural Science Foundation of China under Grant No.ZR2016GM24the Progress Project for Young Science and Technology Scholars of Guizhou Provincial Department of Education under Grant No.KY[2016]164.
文摘In this paper, we investigate how to compute the minimum distance between a point and a parametric surface, and then to return the nearest point (foot point) on the surface as well as its corresponding parameter, which is also called the point projection problem of a parametric surface. The geometric strategy algorithm (hereafter GSA) presented consists of two parts as follows. The normal curvature to a given parametric surface is used to find the corresponding foot point firstly, and then the Taylor's expansion of the parametric surface is employed to compute parameter increments and to get the iteration formula to calculate the orthogonal projection point of test point to the parametric surface. Our geometric strategy algorithm is essentially dependent on the geometric property of the normal curvature, and performs better than existing methods in two ways. Firstly, GSA converges faster than existing methods, such as the method to turn the problem into a root-finding of nonlinear system, subdividing methods, clipping methods, geometric methods (tangent vector and geometric curvature) and hybrid second-order method, etc. Specially, it converges faster than the classical Newton's iterative method. Secondly, GSA is independent of the initial iterative value, which we prove in Theorem 1. Many numerical examples confirm GSA's robustness and efficiency.
文摘After more than a hundred years’development,public libraries have entered a rising period marked by government participation and public service-orientation in recent years.In this context and from the perspective of modern public culture service system,the overall public librarianship has some problems to be solved,such as facility layout with rigidified administration which is difficult
