A new method to design a cubic Pythagorean-hodograph(PH)spline curve from any given control polygon is proposed.The key idea is to suitably choose a set of auxiliary points associated with the edges of the given contr...A new method to design a cubic Pythagorean-hodograph(PH)spline curve from any given control polygon is proposed.The key idea is to suitably choose a set of auxiliary points associated with the edges of the given control polygon to guarantee the constructed PH spline has G1 continuity or curvature continuity.The method facilitates intuitive and efficient construction of open and closed cubic PH spline curves that typically agrees closely with the same friendly interface and properties as B-splines,for example,the convex hull and variation-diminishing properties.展开更多
Voronoi diagram is founded by using computational geometry based on originaldistribution of the waypoints, and then the elements from Voronoi diagram are metamorphosed by usingthe rule for airsppce partition, and the ...Voronoi diagram is founded by using computational geometry based on originaldistribution of the waypoints, and then the elements from Voronoi diagram are metamorphosed by usingthe rule for airsppce partition, and the controller's workload is accounted in each element that ismade up of Metamorphic Voronoi polygon. Then in accordance with the rule about balance ofcontroller's workload, Simulated Annealing algorithm (SA) is used to achieve the optimization ofcombination of those elements , and the new resolution has satisfied the restriction of two rulesfor airspace partition. Therefore, the boundaries of the aggregates of these elements are theoptimal borderlines of sectors. The result of actual airspace design example validates therationality of the sector optimization method presented in this paper.展开更多
Pythagorean-hodograph（PH） curves offer computational advantages in Computer Aided Geometric Design, Computer Aided Design, Computer Graphics, Computer Numerical Control machining and similar applications. In this pa...Pythagorean-hodograph（PH） curves offer computational advantages in Computer Aided Geometric Design, Computer Aided Design, Computer Graphics, Computer Numerical Control machining and similar applications. In this paper, three methods are utilized to construct the identifications of planar regular sextic PH curves. The first exhibits purely the control polygon legs＇ constraints in the complex form. Such reconstruction of a PH sextic can be elaborated by C1 Hermite data and another one condition. The second uses polar representation in two cases. One of them can produce a family of convex sextic PH curves related with a quintic PH curve, and the other one may naturally degenerate a sextic PH curve to a quintic PH curve. In the third identification, we use some odd PH curves to construct a family of sextic PH curves with convexity-preserving property.展开更多
文摘A new method to design a cubic Pythagorean-hodograph(PH)spline curve from any given control polygon is proposed.The key idea is to suitably choose a set of auxiliary points associated with the edges of the given control polygon to guarantee the constructed PH spline has G1 continuity or curvature continuity.The method facilitates intuitive and efficient construction of open and closed cubic PH spline curves that typically agrees closely with the same friendly interface and properties as B-splines,for example,the convex hull and variation-diminishing properties.
文摘Voronoi diagram is founded by using computational geometry based on originaldistribution of the waypoints, and then the elements from Voronoi diagram are metamorphosed by usingthe rule for airsppce partition, and the controller's workload is accounted in each element that ismade up of Metamorphic Voronoi polygon. Then in accordance with the rule about balance ofcontroller's workload, Simulated Annealing algorithm (SA) is used to achieve the optimization ofcombination of those elements , and the new resolution has satisfied the restriction of two rulesfor airspace partition. Therefore, the boundaries of the aggregates of these elements are theoptimal borderlines of sectors. The result of actual airspace design example validates therationality of the sector optimization method presented in this paper.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1167106811401077+4 种基金1127106011290143)Fundamental Research of Civil Aircraft(Grant No.MJ-F-2012-04)the Program for Liaoning Excellent Talents in University(Grant No.LJQ2014010)the Fundamental Research Funds for the Central Universities(Grant No.DUT16LK38)
文摘Pythagorean-hodograph（PH） curves offer computational advantages in Computer Aided Geometric Design, Computer Aided Design, Computer Graphics, Computer Numerical Control machining and similar applications. In this paper, three methods are utilized to construct the identifications of planar regular sextic PH curves. The first exhibits purely the control polygon legs＇ constraints in the complex form. Such reconstruction of a PH sextic can be elaborated by C1 Hermite data and another one condition. The second uses polar representation in two cases. One of them can produce a family of convex sextic PH curves related with a quintic PH curve, and the other one may naturally degenerate a sextic PH curve to a quintic PH curve. In the third identification, we use some odd PH curves to construct a family of sextic PH curves with convexity-preserving property.
