查询词典 harmonics

The recursive formulas of the spherical harmonics integral between every other order are proved to be fast and stable by numerical computation.

数值试验表明，球谐函数跨次递推算法具有快速、稳定的优点。

To realize the realistic rendering of the scene in applying environment mapping to VR systems, an approach to fast calculating diffuse environment maps was proposed starting from the analysis of spherical harmonics.

为了把环境贴图应用于VR系统中，实现场景对象的真实感绘制，首先从分析球面调和函数入手，提出了漫反射环境纹理图的快速计算方法。

Keywords: Earth nutation; electro-magnetic coupling; differential rotation; generalized surface spherical harmonics; Mars

中文关键词：地球章动；电磁耦合；较差转动；广义球函数；火星

Using the properties of the harmonic function and the theories of the expansion of the spherical harmonics,the equivalence between Moritz analytical continuation and Bjerhammar s virtual spherical solution is proved according to the power series expanded form of the real number field function,the differences in meaning between the two solutions are analyzed.

利用调和函数的性质以及球谐函数展开理论，并根据实数域上函数的幂级数展开式证明了Moritz解析延拓解与Bjerhammar虚拟球面解的等价性，同时分析了两种解的内在区别。

Third, The author analyzed the shimming method of the existing magnet system and programmed it. Because the base field homogeneity of the open magnet is worse and only passive shimming is available, it is necessary to study more effective shimming algorithm. The ordinary shimming method is based on the disintegration of the magnetic field using spherical harmonics. It is so tedious that involved in large scaled non-linear equations.

再次，详细分析了现有磁体系统的匀场方法，并通过编程运算，发现在开放型磁体这一特殊情况下，由于基场均匀度差和只能使用水磁材料垫补进行匀场等原因，基于对磁场分布用球谐函数分解并消去球谐函数高次项的常规匀场方法在实现上相当繁琐，牵涉到大型非线性方程组的求解，所以必须采用更有效的匀场算法。

Based on the recovered 3D shape, the "texture image" calibrated to a standard illumination is generated by spherical harmonics ratio image and finally the illumination independent 3D face is reconstructed completely. The proposed method combines the strength of statistical deformable model to describe the shape information and the compact representations of the illumination in spherical frequency space, and handles both the pose and illumination variation simultaneously.

基于此重建的3D形状，进而通过球面谐波商图像的方法估计输入图像的光照属性并提取输入图像的光照无关的纹理信息，从而将光照无关的3D人脸完全重构出来，生成输入人脸图像在标准姿态和光照条件下的虚拟视图，用于最终的分类识别，实现了对光照和姿态问题的同时处理。

Superior at approximating high frequency lighting than spherical harmonics function,wavelets have been increasingly adopted in PRT based global light rendering algorithm.

由于小波相比球面谐波函数能够更好地表现许多高频光照细节，哈尔小波被越来越多地被应用在许多基于PRT的全局光照渲染算法中。

By means of uniform orthogonal sampling, we represent the shape signature of each model as a statistical distribution of its surface normals weighted by view-dependent depth. The distribution is further processed by spherical harmonics analysis to construct the final representation. By calculating the distance between shape descriptors of individual 3D models, a faithful similarity measurement is achieved.

算法从规一化处理后的物体形状出发，计算视点相关的深度加权的物体表面法向统计分布，并对该分布实行球面调和分析，得到深度加权法向映射特征，进而利用特征之间的距离度量任意三维模型之间的相似性。

Angular momentum: operators, commutator algebra, eigenvalues and eigenstates, spherical harmonics.

角动量：算符，对易代数，本征值和本征态，球谐函数。

Based on the research on the scattering of the Gaussian beam from single sphere, the intensity distributions of LGB beam in different propagation distance is analyzed. Without considering the relationship of scattering and phase shift, the beam coefficients is gained by the solution of scattering cross section, and the LGB is expanded in terms of the vector spherical harmonics as fundamental Gaussian beam. The scattering of the beam with orbital angular momentum from single sphere located on the propagation axis is studied.

在单体球粒子对高斯光束散射研究的基础上，分析了在自由空间不同传输距离LGB光束的光强分布情况，在不考虑散射和波束相移关系的情况下，将LGB作为入射高斯光束，通过对波束入射时的散射衰减截面求解得到波束因子，利用矢量球谐函数对入射高斯波束进行展开，从而研究了单球粒子在在轴条件下对具轨道角动量高斯波束入射的散射问题。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。