球面

GuoShouJing his ancestors in the Yuan Dynasty in China are well-known astronomer, mathematician, hydraulic engineering experts, he advanced mathematics, spherical geometry, triangulation has become highly literate, living in the home environment such郭伯of jade, from the favorite Math, especially for simpler and quicker abacus, but also aroused the interest of his research, he studies at abacus are enormous achievements, the Qing Dynasty famous mathematician Mei-ting in the "ancient Yan count slightly," Chu said plate of law, began in the early Ming郭伯jade, jade郭伯abacus at laws on the tremendous contribution to the world people have been referred to as "beads set of laws," the creators

他的先辈郭守敬是我国元代著名的天文学家、数学家、水利工程学家，他对高等数学、球面几何、三角都有很高的造诣，生活在这种家庭环境中的郭伯玉，从小就喜爱数学，尤其对简便、快捷的珠算，更引起他研究的兴趣，他在珠算研究上的成就是巨大的，清代著名数学家梅文鼎在《古算衍略》中说珠盘之法，始于明初郭伯玉，郭伯玉在珠算之法上的巨大贡献，被世人人称为"珠盘之法"的创制者

There are statistical functions as well as advanced mathematical functions like spherical harmonics.

例如，这里有许多统计函数，比方说高等数学里的球面低函数。

A 3-D face model is constructed by the imaging theory and spherical harmonics, combining with the principle of 3-D projection and PCA.

根据3-D数据的优势，利用图像成像原理和球面调和函数理论，结合3-D投影原理和PCA技术建立了一个3-D人脸模型。

Expanding the modification model in vector spherical harmonics, we obtained the absorption and scattering coefficients of the beam wave case.

将所得的修正解按矢量球面波函数展开，就球形粒子对束状波的消光系数进行推演和计算，并与平面波Mei理论和国外的实验结果进行比较，验证了修正解的正确性。

Sampling data for BRDF is analyzed with Spherical Harmonics, and then the BRDF surface could be rendered fast under environment illumination.

物体表面双向反射分布函数的采样数据利用球面调和函数系进行分析，然后可以在环境光源下作快速绘制。

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。

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。

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。

Lugalbanda was a god and shepherd king of Uruk where he was worshipped for over a thousand years.

Lugalbanda 是神和被崇拜了一千年多 Uruk古埃及喜克索王朝国王。

I am coming just now,' and went on perfuming himself with Hunut, then he came and sat.

我来只是现在，'歼灭战perfuming自己与胡努特，那麼，他来到和SAT 。