A family of two-order Hermite vector-interpolating subdivision schemes is proposed and its convergence and con- tinuity are analyzed. The iterative level can be estimated for given error. The sufficient conditions of ...A family of two-order Hermite vector-interpolating subdivision schemes is proposed and its convergence and con- tinuity are analyzed. The iterative level can be estimated for given error. The sufficient conditions of C2 continuity are proved. Geometric features of subdivision curves, such as line segments, cusps and inflection points, are obtained by appending some conditions to initial vectorial Hermite sequence. An algorithm is presented for generating geometric features. For an initial se- quence of two-order Hermite elements from unit circle, the numerical error of the 4th subdivided level is O(10?4).展开更多
Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and repr...Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and representative numerical model of projectile flight requires a relatively good approximation of the aerodynamics.The aerodynamic coefficients of the projectile model should be described as a series of piecewise polynomial functions of the Mach number that ideally meet the following conditions:they are continuous,differentiable at least once,and have a relatively low degree.The paper provides the steps needed to generate such piecewise polynomial functions using readily available tools,and then compares Piecewise Cubic Hermite Interpolating Polynomial(PCHIP),cubic splines,and piecewise linear functions,and their variant,as potential curve fitting methods to approximate the aerodynamics of a generic small arms projectile.A key contribution of the paper is the application of PCHIP to the approximation of projectile aerodynamics,and its evaluation against a set of criteria.Finally,the paper provides a baseline assessment of the impact of the polynomial functions on flight trajectory predictions obtained with 6-degree-of-freedom simulations of a generic projectile.展开更多
Ying Guang Shi(1995 & 1999) obtained some quadratures, which is based onthe zeros of the so-called s-orthogonal polynomials with respect to some JacobiB.Bojanov(1996) and our recent work, we give here a simple and...Ying Guang Shi(1995 & 1999) obtained some quadratures, which is based onthe zeros of the so-called s-orthogonal polynomials with respect to some JacobiB.Bojanov(1996) and our recent work, we give here a simple and unified approachto these questions of this type and obtain quadratures in terms of the divided differ-ences, which is based on an appropriate representation of the Hermite interpolatingpolynomial, of corresponding function at the zeros of the appropriate s-orthogonalpolynomial with multiplicities.展开更多
针对群组移动节点定位算法普遍基于不切实际的假设,存在普适性欠佳和精度不高的问题,提出一种基于运动参数预测的群组移动节点定位算法。该算法根据群组移动节点具有相似运动的特点,运用Hermite插值多项式预测、过滤节点运动参数。为确...针对群组移动节点定位算法普遍基于不切实际的假设,存在普适性欠佳和精度不高的问题,提出一种基于运动参数预测的群组移动节点定位算法。该算法根据群组移动节点具有相似运动的特点,运用Hermite插值多项式预测、过滤节点运动参数。为确保定位精度,应对节点移动性带来的采样区域变化,运用预测节点运动参数构建粒子有效采样区域;为节省时间开销,基于采样粒子真实分布与其极大似然估计值之间的最大K-L(Kullback-Leibler)距离确定能够满足不同采样区域的最少粒子数目;为改善算法收敛性,运用预测运动参数创建滤波公式,并选取优质粒子参与节点位置估计。在与经典算法MCL(Monte Carlo localization)法和加权最小二乘法的MATLAB对比实验中,分析了节点移动速度、自由度、K-L距离阈值、采样方格边长对定位精度的影响。结果表明,较上述算法,本算法的定位误差和时间开销较小,无须锚节点辅助,普适性较好。展开更多
文摘A family of two-order Hermite vector-interpolating subdivision schemes is proposed and its convergence and con- tinuity are analyzed. The iterative level can be estimated for given error. The sufficient conditions of C2 continuity are proved. Geometric features of subdivision curves, such as line segments, cusps and inflection points, are obtained by appending some conditions to initial vectorial Hermite sequence. An algorithm is presented for generating geometric features. For an initial se- quence of two-order Hermite elements from unit circle, the numerical error of the 4th subdivided level is O(10?4).
文摘Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and representative numerical model of projectile flight requires a relatively good approximation of the aerodynamics.The aerodynamic coefficients of the projectile model should be described as a series of piecewise polynomial functions of the Mach number that ideally meet the following conditions:they are continuous,differentiable at least once,and have a relatively low degree.The paper provides the steps needed to generate such piecewise polynomial functions using readily available tools,and then compares Piecewise Cubic Hermite Interpolating Polynomial(PCHIP),cubic splines,and piecewise linear functions,and their variant,as potential curve fitting methods to approximate the aerodynamics of a generic small arms projectile.A key contribution of the paper is the application of PCHIP to the approximation of projectile aerodynamics,and its evaluation against a set of criteria.Finally,the paper provides a baseline assessment of the impact of the polynomial functions on flight trajectory predictions obtained with 6-degree-of-freedom simulations of a generic projectile.
文摘Ying Guang Shi(1995 & 1999) obtained some quadratures, which is based onthe zeros of the so-called s-orthogonal polynomials with respect to some JacobiB.Bojanov(1996) and our recent work, we give here a simple and unified approachto these questions of this type and obtain quadratures in terms of the divided differ-ences, which is based on an appropriate representation of the Hermite interpolatingpolynomial, of corresponding function at the zeros of the appropriate s-orthogonalpolynomial with multiplicities.
文摘针对群组移动节点定位算法普遍基于不切实际的假设,存在普适性欠佳和精度不高的问题,提出一种基于运动参数预测的群组移动节点定位算法。该算法根据群组移动节点具有相似运动的特点,运用Hermite插值多项式预测、过滤节点运动参数。为确保定位精度,应对节点移动性带来的采样区域变化,运用预测节点运动参数构建粒子有效采样区域;为节省时间开销,基于采样粒子真实分布与其极大似然估计值之间的最大K-L(Kullback-Leibler)距离确定能够满足不同采样区域的最少粒子数目;为改善算法收敛性,运用预测运动参数创建滤波公式,并选取优质粒子参与节点位置估计。在与经典算法MCL(Monte Carlo localization)法和加权最小二乘法的MATLAB对比实验中,分析了节点移动速度、自由度、K-L距离阈值、采样方格边长对定位精度的影响。结果表明,较上述算法,本算法的定位误差和时间开销较小,无须锚节点辅助,普适性较好。
