Minimal surface is extensively employed in many areas. In this paper, we propose a control mesh representation of a class of minimal surfaces, called generalized helicoid minimal surfaces, which contain the right heli...Minimal surface is extensively employed in many areas. In this paper, we propose a control mesh representation of a class of minimal surfaces, called generalized helicoid minimal surfaces, which contain the right helicoid and catenoid as special examples. We firstly construct the Bézier-like basis called AHT Bézier basis in the space spanned by {1, t, sint, cost, sinht, cosht}, t∈[0,α], α∈[0,5π/2]. Then we propose the control mesh representation of the generalized helicoid using the AHT Bézier basis. This kind of representation enables generating the minimal surfaces using the de Casteljau-like algorithm in CAD/CAGD mod- elling systems.展开更多
In this paper, a process of the quadtree mesh generation is described, then a mesh control device of the tree based mesh generators is analyzed in detail. Some examples are given to demonstrate that the mesh contro...In this paper, a process of the quadtree mesh generation is described, then a mesh control device of the tree based mesh generators is analyzed in detail. Some examples are given to demonstrate that the mesh control device allows for efficient a priori and a posteriori mesh refinements.展开更多
By means of direct analysis of the connection between Loop subdivision surface and its control mesh and the computation of the basis functions, we obtain a bound on the distance between Loop subdivision surface patch ...By means of direct analysis of the connection between Loop subdivision surface and its control mesh and the computation of the basis functions, we obtain a bound on the distance between Loop subdivision surface patch and its control mesh. The bound can be used to compute the numbers of subdivision for a given tolerance. Finally, two examples are listed in this paper to demon- strate the applications of the bound.展开更多
A heightened risk for lateral ankle sprain injuries has been associated with excessive shoe-surface friction.‘Spraino’is a novel product specifically designed towards preventing friction-related lateral ankle sprain...A heightened risk for lateral ankle sprain injuries has been associated with excessive shoe-surface friction.‘Spraino’is a novel product specifically designed towards preventing friction-related lateral ankle sprains.In a recent 510-athlete randomized controlled trial,allocation to this“low-friction”shoe-patch resulted in a 53%reduction of severe ankle sprain injuries.Until now,however,a theoretical explanation linking shoe-surface friction and lateral ankle sprain injury mechanism is missing,and the extent to which Spraino reduces shoesurface friction remains unknown.Therefore,the purpose of this study was to present a theoretical link between lateral edge shoe-surface friction and the mechanism of lateral ankle sprain injuries,and ultimately establish the ability of Spraino to reduce lateral edge shoe-surface friction.In this paper,we present a theory on how ankle sprain mechanics are directly affected by the friction between shoe and surface,and why friction modifications might be a viable preventive strategy.When testing slip resistance in a modified mechanical testsetup,we detected a 63%reduction(0.83–0.31)in friction coefficient between the lateral edge of the outsole and the indoor sports floor when adding Spraino to the side of the shoe.Justified in our theory,and the previously established clinical effectiveness,this reduction in friction can mitigate both the risk and severity of lateral ankle sprain injuries.This suggests that reducing friction on the lateral edge of footwear can be an effective ankle sprain injury prevention strategy.展开更多
基金Project supported by the National Natural Science Foundation of China (No. 60473130) and the National Basic Research Program (973) of China (No. 2004CB318000)
文摘Minimal surface is extensively employed in many areas. In this paper, we propose a control mesh representation of a class of minimal surfaces, called generalized helicoid minimal surfaces, which contain the right helicoid and catenoid as special examples. We firstly construct the Bézier-like basis called AHT Bézier basis in the space spanned by {1, t, sint, cost, sinht, cosht}, t∈[0,α], α∈[0,5π/2]. Then we propose the control mesh representation of the generalized helicoid using the AHT Bézier basis. This kind of representation enables generating the minimal surfaces using the de Casteljau-like algorithm in CAD/CAGD mod- elling systems.
文摘In this paper, a process of the quadtree mesh generation is described, then a mesh control device of the tree based mesh generators is analyzed in detail. Some examples are given to demonstrate that the mesh control device allows for efficient a priori and a posteriori mesh refinements.
基金Supported by the National Natural Science Foundation of China (No.61170324)the Natural Science Foundation of Fujian Province of China (No.2010J01012)the National Defense Basic Scientific Research Program of China (No.B1420110155)
文摘By means of direct analysis of the connection between Loop subdivision surface and its control mesh and the computation of the basis functions, we obtain a bound on the distance between Loop subdivision surface patch and its control mesh. The bound can be used to compute the numbers of subdivision for a given tolerance. Finally, two examples are listed in this paper to demon- strate the applications of the bound.
基金Innovation Fund Denmark[grant number 7038-00087B].
文摘A heightened risk for lateral ankle sprain injuries has been associated with excessive shoe-surface friction.‘Spraino’is a novel product specifically designed towards preventing friction-related lateral ankle sprains.In a recent 510-athlete randomized controlled trial,allocation to this“low-friction”shoe-patch resulted in a 53%reduction of severe ankle sprain injuries.Until now,however,a theoretical explanation linking shoe-surface friction and lateral ankle sprain injury mechanism is missing,and the extent to which Spraino reduces shoesurface friction remains unknown.Therefore,the purpose of this study was to present a theoretical link between lateral edge shoe-surface friction and the mechanism of lateral ankle sprain injuries,and ultimately establish the ability of Spraino to reduce lateral edge shoe-surface friction.In this paper,we present a theory on how ankle sprain mechanics are directly affected by the friction between shoe and surface,and why friction modifications might be a viable preventive strategy.When testing slip resistance in a modified mechanical testsetup,we detected a 63%reduction(0.83–0.31)in friction coefficient between the lateral edge of the outsole and the indoor sports floor when adding Spraino to the side of the shoe.Justified in our theory,and the previously established clinical effectiveness,this reduction in friction can mitigate both the risk and severity of lateral ankle sprain injuries.This suggests that reducing friction on the lateral edge of footwear can be an effective ankle sprain injury prevention strategy.
