Conventional soil maps contain valuable knowledge on soil–environment relationships.Such knowledge can be extracted for use when updating conventional soil maps with improved environmental data.Existing methods take ...Conventional soil maps contain valuable knowledge on soil–environment relationships.Such knowledge can be extracted for use when updating conventional soil maps with improved environmental data.Existing methods take all polygons of the same map unit on a map as a whole to extract the soil–environment relationship.Such approach ignores the difference in the environmental conditions represented by individual soil polygons of the same map unit.This paper proposes a method of mining soil–environment relationships from individual soil polygons to update conventional soil maps.The proposed method consists of three major steps.Firstly,the soil–environment relationships represented by each individual polygon on a conventional soil map are extracted in the form of frequency distribution curves for the involved environmental covariates.Secondly,for each environmental covariate,these frequency distribution curves from individual polygons of the same soil map unit are synthesized to form the overall soil–environment relationship for that soil map unit across the mapped area.And lastly,the extracted soil–environment relationships are applied to updating the conventional soil map with new,improved environmental data by adopting a soil land inference model(SoLIM)framework.This study applied the proposed method to updating a conventional soil map of the Raffelson watershed in La Crosse County,Wisconsin,United States.The result from the proposed method was compared with that from the previous method of taking all polygons within the same soil map unit on a map as a whole.Evaluation results with independent soil samples showed that the proposed method exhibited better performance and produced higher accuracy.展开更多
An algorithm for partitioning arbitrary simple polygons into a number of convex parts was presented. The concave vertices were determined first, and then they were moved by using the method connecting the concave vert...An algorithm for partitioning arbitrary simple polygons into a number of convex parts was presented. The concave vertices were determined first, and then they were moved by using the method connecting the concave vertices with the vertices of falling into its region B,so that the primary polygon could be partitioned into two subpolygons. Finally, this method was applied recursively to the subpolygons until all the concave vertices were removed. This algorithm partitions the polygon into O(l) convex parts, its time complexity is max(O(n),O(l 2)) multiplications, where n is the number of vertices of the polygon and l is the number of the concave vertices.展开更多
Using polar equations for conic sections, we research conic circumscribed n-sided polygons（n ≥ 4） deeply on the basis of papers[1-3]. We obtain a general fixed value theorem for directed areas of some triangles in ...Using polar equations for conic sections, we research conic circumscribed n-sided polygons（n ≥ 4） deeply on the basis of papers[1-3]. We obtain a general fixed value theorem for directed areas of some triangles in conic circumscribed n-sided polygons and derive as many as n（n - 3） concurrent points of three lines and some other collinear, equiareal results in conic circumscribed n-sided polygons（n ≥ 4）. So the results of papers[1-3] are unified.展开更多
Existing methods for recognizing polygons can be improved. A new concept ＂homograph＂ and then a new method for recognizing polygons based on the principle of homograph are proposed. First, five topological character...Existing methods for recognizing polygons can be improved. A new concept ＂homograph＂ and then a new method for recognizing polygons based on the principle of homograph are proposed. First, five topological characteristics and geometrical characteristics are introduced that are invariant to describe polygon under perspective transformation. Then, the new concept of homograph is defined in terms of five topological characteristics and geometrical characteristics. Based on this definition, a new algorithm is proposed for recognizing that two polygons are homograph. The topological structure is introduced to analyze homograph qualitatively and the algorithm is insensitive to noises; and the geometrical structure is introduced to analyze homograph quantitatively, thus the algorithms can show tiny differences between polygons. It can not only recognize the objects with different shapes but also distinguish between objects with same shape but with different sizes and scales. Comparing with other recognition algorithms, the algorithm presented showed apparent improvement. The effectiveness of the algorithm is demonstrated by experiments.展开更多
Computing the distance between two convex polygons is often a basic step to the algorithms of collision detection and path planning. Now, the lowest time complexity algorithm takes O(logm+logn) time to compute the min...Computing the distance between two convex polygons is often a basic step to the algorithms of collision detection and path planning. Now, the lowest time complexity algorithm takes O(logm+logn) time to compute the minimum distance between two disjoint convex polygons P and Q, where n and m are the number of the polygons’ edges respectively. This paper discusses the location relations of outer Voronoi diagrams of two disjoint convex polygons P and Q, and presents a new O(logm+logn) algo- rithm to compute the minimum distance between P and Q. The algorithm is simple and easy to implement, and does not need any preprocessing and extra data structures.展开更多
Two new recognition methods for the spatial planar POlygon using perspective invariants are presented. The corss-ratio (R c) of a vetex and the co-base area rotio (RA) of a edge in a spatial planar polygon are propose...Two new recognition methods for the spatial planar POlygon using perspective invariants are presented. The corss-ratio (R c) of a vetex and the co-base area rotio (RA) of a edge in a spatial planar polygon are proposed and used as the invariant primitive of the recognition eigenvector. The second distance error decision rule (SD EDR) estimating the relative error of RA is introduced also too. The mthods could recognize a spatial planar polygon with an arbitrary orientation through only a single perspective view. Experimental examples are gievn.展开更多
Two dimensional irregular polygons packing problem is very difficult to be solved in traditional optimal way.Simulated annealing(SA)algorithm is a stochastic optimization technique that can be used to solve packing pr...Two dimensional irregular polygons packing problem is very difficult to be solved in traditional optimal way.Simulated annealing(SA)algorithm is a stochastic optimization technique that can be used to solve packing problems.The whole process of SA is introduced firstly in this paper. An extended neighborhood searching method in SA is mainly analyzed. A general module of SA algorithm is given and used to lay out the irregular polygons. The judgment of intersection and other constrains of irregular polygons are analyzed. Then an example that was used in the paper of Stefan Jakobs is listed.Results show that this SA algorithm shortens the computation time and improves the solution.展开更多
The main purpose of this note is to investigate equiangular polygons with rational edges. When the number of edges is the power of a prime, we determine simple, necessary and sufficient conditions for the existence of...The main purpose of this note is to investigate equiangular polygons with rational edges. When the number of edges is the power of a prime, we determine simple, necessary and sufficient conditions for the existence of such polygons. As special cases of our investigations, we settle two conjectures involving arithmetic polygons.展开更多
This paper primarily focuses on solving the Heilbronn problem of convex polygons,which involves minimizing the area of a convex polygon P_(1)P_(2)···P_(n) while satisfying the condition that the areas o...This paper primarily focuses on solving the Heilbronn problem of convex polygons,which involves minimizing the area of a convex polygon P_(1)P_(2)···P_(n) while satisfying the condition that the areas of all triangles formed by consecutive vertices are equal to 1/2.The problem is reformulated as a polynomial optimization problem with a bilinear objective function and bilinear constraints.A new method is presented to verify the upper and lower bounds for the optimization problem.The upper bound is obtained by the affine regular decagon.Then Bilinear Matrix Inequalities(BMI)theory and the branch-and-bound technique are used to verify the lower bound of the problem.The paper concludes by proving that the lower bound for the area minimization problem of a convex polygon with 10 vertices is 13.076548.The relative error compared to the global optimum is 0.104%.展开更多
In Tian and Wu (2009),the present authors studied the inviscid and viscous flow past polygons with an arbitrary but even number of edges and with one apex pointing to the free stream.Here we extend the results to the ...In Tian and Wu (2009),the present authors studied the inviscid and viscous flow past polygons with an arbitrary but even number of edges and with one apex pointing to the free stream.Here we extend the results to the flow past polygons with an odd number of edges,and an arbitrary direction.Flow features such as the shape of stationary lines,stabilities of vortex pairs,1st critical Reynolds numbers,and flow patterns with separations,similar to or different from the results for even-sided polygons,are identified.展开更多
In this paper,we study the problem,of calculating the minimum collision distance between two planar convex polygons when one of them moves to another along a given direction.First,several novel concepts and properties...In this paper,we study the problem,of calculating the minimum collision distance between two planar convex polygons when one of them moves to another along a given direction.First,several novel concepts and properties are explored,then an optimal algorithm OPFIV with time complexity O(log(n+m))is developed and its correctness and optimization are proved rigorously.展开更多
Polygonal fault systems(PFS),characterized by multi-directional fault patterns within layered sequences,are well-documented features in global continental margin basins.While the geometry and formation mechanisms of P...Polygonal fault systems(PFS),characterized by multi-directional fault patterns within layered sequences,are well-documented features in global continental margin basins.While the geometry and formation mechanisms of PFS have been extensively studied in the northern South China Sea,the PFS in the Zhongjiannan Basin(western South China Sea)remain relatively unexplored,with a lack of quantitative analysis regarding their propagation.This study addresses this gap by using high-resolution three-dimensional(3D)seismic data and conducting a quantitative fault analysis to thoroughly examine the planform,cross-sectional geometry,and evolution of PFS in the northern Zhongjiannan Basin.The absence of a dominant strike direction among these polygonal faults suggests that their evolution is not controlled by anisotropic stress.Our interpretation of seismic data,constrained by the spatial relationship among PFS,gullies,and pockmarks,indicates that PFS mainly developed within the Miocene strata,with their initiation occurring during the late Miocene.Furthermore,the PFS act as key conduits connecting gullies to pockmarks in this area.The formation and development of PFS may be primarily driven by thermally triggered processes within siliceous sediments.The necessary heat source is probably associated with the abundant submarine magmatism observed in the Zhongjiannan Basin.To reconstruct the regional geological history,a four-stage evolutionary model,incorporating the formation of PFS,is presented.This research significantly improves our understanding of the regional geological evolution of the Zhongjiannan Basin,providing critical insights into the initiation and development of PFS in the western South China Sea.展开更多
We consider scattering of a time harmonic incident plane wave by a convex polygon with piecewise constant impedance boundary conditions.Standard finite or boundary element methods require the number of degrees of free...We consider scattering of a time harmonic incident plane wave by a convex polygon with piecewise constant impedance boundary conditions.Standard finite or boundary element methods require the number of degrees of freedom to grow at least linearly with respect to the frequency of the incident wave in order to maintain accuracy.Extending earlier work by Chandler-Wilde and Langdon for the sound soft problem,we propose a novel Galerkin boundary element method,with the approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh with smaller elements closer to the corners of the polygon.Theoretical analysis and numerical results suggest that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency of the incident wave.展开更多
This paper investigates the mechanical behavior of two-dimensional(2D)piezoelectric quasicrystals(PQCs)containing polygonal holes under external forces.Based on the linear elastic theory of quasicrystals(QCs),the anal...This paper investigates the mechanical behavior of two-dimensional(2D)piezoelectric quasicrystals(PQCs)containing polygonal holes under external forces.Based on the linear elastic theory of quasicrystals(QCs),the analytical solutions for the stress and displacement fields are derived with the Stroh formalism,Green's function method,and polygonal mapping functions.Numerical simulations are performed to study the effects of hole geometry and corner sharpness on the stress distribution.The results show that the polygonal hole shapes significantly influence the generalized hoop stress,with sharper corners leading to stronger stress concentration and enhanced piezoelectric coupling effects.The stress concentrations at hole corners reach their maximum values at specific sharpness parameters,depending on the polygon type.The results contribute to a deeper understanding of the defect-induced mechanical behavior in 2D PQCs,and provide theoretical guidance for their structural design and optimization.展开更多
An algorithm for Boolean operations on conic polygons is proposed. Conic polygons are polygons consisting of conic segments or bounded conics with directions. Preliminaries of Boolean operations on general polygons ar...An algorithm for Boolean operations on conic polygons is proposed. Conic polygons are polygons consisting of conic segments or bounded conics with directions. Preliminaries of Boolean operations on general polygons are presented. In our algorithm, the intersection points and the topological relationships between two conic polygons are computed. Boundaries are obtained by tracking path and selecting uncrossed boundaries following rule tables to build resulting conic polygons. We define a set of rules for the intersection, union, and subtraction operations on conic polygons. The algorithm considers degeneration cases such as homology, complement, interior, and exterior. The algorithm is also evaluated and implemented.展开更多
The problem of initial collision between convex polygons is studied in detail, and a fast algorithm for finding the embedded depth is obtained, by which the fast approximate algorithm for solving packing problems of c...The problem of initial collision between convex polygons is studied in detail, and a fast algorithm for finding the embedded depth is obtained, by which the fast approximate algorithm for solving packing problems of convex polygons in plane is constructed.展开更多
When am I ever going to use this?GEOGRAPHY The size and shape of each state in the United States is different.Analyze the shapes of the states in both groups at the right.1.Find the difference between the shapes of th...When am I ever going to use this?GEOGRAPHY The size and shape of each state in the United States is different.Analyze the shapes of the states in both groups at the right.1.Find the difference between the shapes of the states in Group 1and the shapes of the states in Group 2.2.Why do most states have boundaries that are not straight line segments?The states listed in Group 1 above are examples of polygons.A polygon is a simple,closed figure formed by three or more straight lines.A simple figure does not have lines that cross each other.You have drawn a closed figure when your pencil ends up where it started.展开更多
The Songliao Basin in northeast China is one of the largest petroliferous basins worldwide,and features the T_(2)fault system,which consists of numerous minor extensional normal faults.This study combines high-resolut...The Songliao Basin in northeast China is one of the largest petroliferous basins worldwide,and features the T_(2)fault system,which consists of numerous minor extensional normal faults.This study combines high-resolution 3D seismic datasets to detail the characteristics of the T_(2)fault system,contributing two key findings:(1)The T_(2)faults are confirmed as polygonal fault systems,characterized by closely spaced,layer-bounded faults with small throws,high dip angles,and random orientations,forming intricate polygonal networks.(2)The study reveals the influence of tectonic stresses on the fault system,showing spatial variations across different tectonic units.In depressions,T_(2)faults exhibit short lengths,small throws,high density,and multiple directions.In contrast,in inverted anticline belts,they have longer lengths,bigger throws,higher density,and concordant orientations.These variations demonstrate the impact of tectonic inversion on the development of T_(2)faults.The significance of this research lies in presenting a typical polygonal fault system developed in a deep lake succession and was superposed the influence by regional tectonic stress coeval with its development.The new insights facilitate a reevaluation of the T_(2)fault system's role in hydrocarbon migration and accumulation within the Songliao Basin.展开更多
基金supported by the National Natural Science Foundation of China (41431177 and 41422109)the Innovation Project of State Key Laboratory of Resources and Environmental Information System of China (O88RA20CYA)the Outstanding Innovation Team in Colleges and Universities in Jiangsu Province, China
文摘Conventional soil maps contain valuable knowledge on soil–environment relationships.Such knowledge can be extracted for use when updating conventional soil maps with improved environmental data.Existing methods take all polygons of the same map unit on a map as a whole to extract the soil–environment relationship.Such approach ignores the difference in the environmental conditions represented by individual soil polygons of the same map unit.This paper proposes a method of mining soil–environment relationships from individual soil polygons to update conventional soil maps.The proposed method consists of three major steps.Firstly,the soil–environment relationships represented by each individual polygon on a conventional soil map are extracted in the form of frequency distribution curves for the involved environmental covariates.Secondly,for each environmental covariate,these frequency distribution curves from individual polygons of the same soil map unit are synthesized to form the overall soil–environment relationship for that soil map unit across the mapped area.And lastly,the extracted soil–environment relationships are applied to updating the conventional soil map with new,improved environmental data by adopting a soil land inference model(SoLIM)framework.This study applied the proposed method to updating a conventional soil map of the Raffelson watershed in La Crosse County,Wisconsin,United States.The result from the proposed method was compared with that from the previous method of taking all polygons within the same soil map unit on a map as a whole.Evaluation results with independent soil samples showed that the proposed method exhibited better performance and produced higher accuracy.
文摘An algorithm for partitioning arbitrary simple polygons into a number of convex parts was presented. The concave vertices were determined first, and then they were moved by using the method connecting the concave vertices with the vertices of falling into its region B,so that the primary polygon could be partitioned into two subpolygons. Finally, this method was applied recursively to the subpolygons until all the concave vertices were removed. This algorithm partitions the polygon into O(l) convex parts, its time complexity is max(O(n),O(l 2)) multiplications, where n is the number of vertices of the polygon and l is the number of the concave vertices.
基金Foundation item： Supported by Natural Science Foundation of China（60675022）
文摘Using polar equations for conic sections, we research conic circumscribed n-sided polygons（n ≥ 4） deeply on the basis of papers[1-3]. We obtain a general fixed value theorem for directed areas of some triangles in conic circumscribed n-sided polygons and derive as many as n（n - 3） concurrent points of three lines and some other collinear, equiareal results in conic circumscribed n-sided polygons（n ≥ 4）. So the results of papers[1-3] are unified.
基金Supported by National Science Foundation(60675022)Key Laboratory of Nondestructive Test, Nanchang Institute of Aeronautical Technoloyg(ZD200629007)
文摘Existing methods for recognizing polygons can be improved. A new concept ＂homograph＂ and then a new method for recognizing polygons based on the principle of homograph are proposed. First, five topological characteristics and geometrical characteristics are introduced that are invariant to describe polygon under perspective transformation. Then, the new concept of homograph is defined in terms of five topological characteristics and geometrical characteristics. Based on this definition, a new algorithm is proposed for recognizing that two polygons are homograph. The topological structure is introduced to analyze homograph qualitatively and the algorithm is insensitive to noises; and the geometrical structure is introduced to analyze homograph quantitatively, thus the algorithms can show tiny differences between polygons. It can not only recognize the objects with different shapes but also distinguish between objects with same shape but with different sizes and scales. Comparing with other recognition algorithms, the algorithm presented showed apparent improvement. The effectiveness of the algorithm is demonstrated by experiments.
基金Project supported by the National Nature Science Foundation of China (Nos. 60473103 and 60473127) and the Natural Science Foundation of Shandong Province (No. Y2005G03), China
文摘Computing the distance between two convex polygons is often a basic step to the algorithms of collision detection and path planning. Now, the lowest time complexity algorithm takes O(logm+logn) time to compute the minimum distance between two disjoint convex polygons P and Q, where n and m are the number of the polygons’ edges respectively. This paper discusses the location relations of outer Voronoi diagrams of two disjoint convex polygons P and Q, and presents a new O(logm+logn) algo- rithm to compute the minimum distance between P and Q. The algorithm is simple and easy to implement, and does not need any preprocessing and extra data structures.
文摘Two new recognition methods for the spatial planar POlygon using perspective invariants are presented. The corss-ratio (R c) of a vetex and the co-base area rotio (RA) of a edge in a spatial planar polygon are proposed and used as the invariant primitive of the recognition eigenvector. The second distance error decision rule (SD EDR) estimating the relative error of RA is introduced also too. The mthods could recognize a spatial planar polygon with an arbitrary orientation through only a single perspective view. Experimental examples are gievn.
文摘Two dimensional irregular polygons packing problem is very difficult to be solved in traditional optimal way.Simulated annealing(SA)algorithm is a stochastic optimization technique that can be used to solve packing problems.The whole process of SA is introduced firstly in this paper. An extended neighborhood searching method in SA is mainly analyzed. A general module of SA algorithm is given and used to lay out the irregular polygons. The judgment of intersection and other constrains of irregular polygons are analyzed. Then an example that was used in the paper of Stefan Jakobs is listed.Results show that this SA algorithm shortens the computation time and improves the solution.
文摘The main purpose of this note is to investigate equiangular polygons with rational edges. When the number of edges is the power of a prime, we determine simple, necessary and sufficient conditions for the existence of such polygons. As special cases of our investigations, we settle two conjectures involving arithmetic polygons.
基金supported by the National Natural Science Foundation of China under Grant No.12171159the National Natural Science Fund of China Research Fund for International Scientists under Grant No.12350410363。
文摘This paper primarily focuses on solving the Heilbronn problem of convex polygons,which involves minimizing the area of a convex polygon P_(1)P_(2)···P_(n) while satisfying the condition that the areas of all triangles formed by consecutive vertices are equal to 1/2.The problem is reformulated as a polynomial optimization problem with a bilinear objective function and bilinear constraints.A new method is presented to verify the upper and lower bounds for the optimization problem.The upper bound is obtained by the affine regular decagon.Then Bilinear Matrix Inequalities(BMI)theory and the branch-and-bound technique are used to verify the lower bound of the problem.The paper concludes by proving that the lower bound for the area minimization problem of a convex polygon with 10 vertices is 13.076548.The relative error compared to the global optimum is 0.104%.
基金supported by the National Natural Science Foundation of China(Grant No. 10972116)
文摘In Tian and Wu (2009),the present authors studied the inviscid and viscous flow past polygons with an arbitrary but even number of edges and with one apex pointing to the free stream.Here we extend the results to the flow past polygons with an odd number of edges,and an arbitrary direction.Flow features such as the shape of stationary lines,stabilities of vortex pairs,1st critical Reynolds numbers,and flow patterns with separations,similar to or different from the results for even-sided polygons,are identified.
文摘In this paper,we study the problem,of calculating the minimum collision distance between two planar convex polygons when one of them moves to another along a given direction.First,several novel concepts and properties are explored,then an optimal algorithm OPFIV with time complexity O(log(n+m))is developed and its correctness and optimization are proved rigorously.
基金financially supported by the National Key Research and Development Program of China(No.2021YFC3100700)the National Natural Science Foundation of China(No.42376070)+1 种基金the Natural Science Foundation of Guangdong Province(No.2024A1515012371)the Rising Star Foundation of the South China Sea Institute of Oceanology(No.NHXX2019DZ0201)。
文摘Polygonal fault systems(PFS),characterized by multi-directional fault patterns within layered sequences,are well-documented features in global continental margin basins.While the geometry and formation mechanisms of PFS have been extensively studied in the northern South China Sea,the PFS in the Zhongjiannan Basin(western South China Sea)remain relatively unexplored,with a lack of quantitative analysis regarding their propagation.This study addresses this gap by using high-resolution three-dimensional(3D)seismic data and conducting a quantitative fault analysis to thoroughly examine the planform,cross-sectional geometry,and evolution of PFS in the northern Zhongjiannan Basin.The absence of a dominant strike direction among these polygonal faults suggests that their evolution is not controlled by anisotropic stress.Our interpretation of seismic data,constrained by the spatial relationship among PFS,gullies,and pockmarks,indicates that PFS mainly developed within the Miocene strata,with their initiation occurring during the late Miocene.Furthermore,the PFS act as key conduits connecting gullies to pockmarks in this area.The formation and development of PFS may be primarily driven by thermally triggered processes within siliceous sediments.The necessary heat source is probably associated with the abundant submarine magmatism observed in the Zhongjiannan Basin.To reconstruct the regional geological history,a four-stage evolutionary model,incorporating the formation of PFS,is presented.This research significantly improves our understanding of the regional geological evolution of the Zhongjiannan Basin,providing critical insights into the initiation and development of PFS in the western South China Sea.
文摘We consider scattering of a time harmonic incident plane wave by a convex polygon with piecewise constant impedance boundary conditions.Standard finite or boundary element methods require the number of degrees of freedom to grow at least linearly with respect to the frequency of the incident wave in order to maintain accuracy.Extending earlier work by Chandler-Wilde and Langdon for the sound soft problem,we propose a novel Galerkin boundary element method,with the approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh with smaller elements closer to the corners of the polygon.Theoretical analysis and numerical results suggest that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency of the incident wave.
基金Project supported by the National Natural Science Foundation of China(Nos.12272402 and12102458)the Chinese Universities Scientific Fund(No.2025TC014)the China Agricultural University Education Foundation(No.1101-240001)。
文摘This paper investigates the mechanical behavior of two-dimensional(2D)piezoelectric quasicrystals(PQCs)containing polygonal holes under external forces.Based on the linear elastic theory of quasicrystals(QCs),the analytical solutions for the stress and displacement fields are derived with the Stroh formalism,Green's function method,and polygonal mapping functions.Numerical simulations are performed to study the effects of hole geometry and corner sharpness on the stress distribution.The results show that the polygonal hole shapes significantly influence the generalized hoop stress,with sharper corners leading to stronger stress concentration and enhanced piezoelectric coupling effects.The stress concentrations at hole corners reach their maximum values at specific sharpness parameters,depending on the polygon type.The results contribute to a deeper understanding of the defect-induced mechanical behavior in 2D PQCs,and provide theoretical guidance for their structural design and optimization.
基金Supported by the National High Technology Development and Research 863 Program of China under Grant Nos.2007AA12Z216and 2007AA120502the National Natural Science Foundation of China under Grant Nos.40701134,40771171,and 40629001
文摘An algorithm for Boolean operations on conic polygons is proposed. Conic polygons are polygons consisting of conic segments or bounded conics with directions. Preliminaries of Boolean operations on general polygons are presented. In our algorithm, the intersection points and the topological relationships between two conic polygons are computed. Boundaries are obtained by tracking path and selecting uncrossed boundaries following rule tables to build resulting conic polygons. We define a set of rules for the intersection, union, and subtraction operations on conic polygons. The algorithm considers degeneration cases such as homology, complement, interior, and exterior. The algorithm is also evaluated and implemented.
文摘The problem of initial collision between convex polygons is studied in detail, and a fast algorithm for finding the embedded depth is obtained, by which the fast approximate algorithm for solving packing problems of convex polygons in plane is constructed.
文摘When am I ever going to use this?GEOGRAPHY The size and shape of each state in the United States is different.Analyze the shapes of the states in both groups at the right.1.Find the difference between the shapes of the states in Group 1and the shapes of the states in Group 2.2.Why do most states have boundaries that are not straight line segments?The states listed in Group 1 above are examples of polygons.A polygon is a simple,closed figure formed by three or more straight lines.A simple figure does not have lines that cross each other.You have drawn a closed figure when your pencil ends up where it started.
基金supported by the Open Funds for Hubei Key Laboratory of Marine Geological Resources,China University of Geosciences(No.MGR202303)the National Natural Science Foundation of China(No.41672110)。
文摘The Songliao Basin in northeast China is one of the largest petroliferous basins worldwide,and features the T_(2)fault system,which consists of numerous minor extensional normal faults.This study combines high-resolution 3D seismic datasets to detail the characteristics of the T_(2)fault system,contributing two key findings:(1)The T_(2)faults are confirmed as polygonal fault systems,characterized by closely spaced,layer-bounded faults with small throws,high dip angles,and random orientations,forming intricate polygonal networks.(2)The study reveals the influence of tectonic stresses on the fault system,showing spatial variations across different tectonic units.In depressions,T_(2)faults exhibit short lengths,small throws,high density,and multiple directions.In contrast,in inverted anticline belts,they have longer lengths,bigger throws,higher density,and concordant orientations.These variations demonstrate the impact of tectonic inversion on the development of T_(2)faults.The significance of this research lies in presenting a typical polygonal fault system developed in a deep lake succession and was superposed the influence by regional tectonic stress coeval with its development.The new insights facilitate a reevaluation of the T_(2)fault system's role in hydrocarbon migration and accumulation within the Songliao Basin.
