球面域

For genus zero closed surfaces,the parameter domain is sphere,so the cutting of the surface meshes in the parametrization process is avoided.

对于零亏格封闭网格曲面，以球面为参数域的参数化方法可以有效避免对网格的切割，是近年来的研究热点。

Then we re-sampling all signals defined on the surface of the original triangle mesh at the vertices of the spherical subdivision mesh and get a set of discrete geometry signals with subdivision topology which can be compressed by using spherical wavelet.

于是，在参数域内位于细分网格顶点处对定义在参数网格表面上的各种几何信号进行重采样，可得到新的具有细分结构的几何信号近似表示原始几何信号，以此满足球面细分小波对处理对象的细分结构要求，从而使得用球面细分小波对几何信号进行压缩得以实现。

An explicit mathematical representation of the exact boundary of a ball Bézier surface was given by recurring to the envelope theory of the family of bivariate surfaces in the classic differential geometry, as well as the spherical coordinates and the Cramer's rule.

根据经典微分几何中双参数曲面族的包络原理，运用球面参数坐标和Cramer法则，给出了球域Bézier曲面边界的精确数学显式表达式。

Feasible region of unit-sphere was defined by standard if angle between normals and stamping direction was less than 90°.

以冲压方向与网格法线夹角不大于90°为冲压方向可行的判据，确定在单位球面上的冲压方向可行域。

According to monotone assembly sequence planning, a decomposition process is developed to generate the assembly sequences. We infer the disassembly direction set of part by use of sphere projection and Cobstacle etc.

在建立的装配模型基础上，先通过对装配模型中零件间的装配关系做矢量分析，应用球面投影处理、投影法和C-空间障碍可以得到各零件在产品中的拆卸方向域信息。

Near-surface influence ; ground attenuation by absorption ; time-frequency-space domain ; spherical dispersion and absorption ; compensation for attenuation

近地表影响；大地吸收衰减；时频空间域；球面发散与吸收；衰减补偿

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。

The resolution kernel and the root square deviation of the inversion solution can be obtained by analyzing the spherical harmonic coefficients.

在变换后的球面域上用球谐函数来拟合速度函数，达到降低球谐系数阶数的目的。

Then, we present an efficient sampling algorithm on the unit sphere, and the generated point distribution can match the SRBF representation. We are capable of creating images with multiple measured BRDFs under global illumination.

此外，根据球面射基底函的表现形式，我们也提出一种有效的重要性采样方法，其产生出的采样分布可以合球面射基底函所描述的资分布，此方法可以在全域光源照射的环境下，有效地绘制包含多种复杂材质的场景影像。

As it can be expressed easily by argument equations, we use the conicoid as the criteria of points" classification. Based on the point"s normal and the adjacent field, corresponding to the conicoid equation such as plane, ball and cylinder, we search the points that fit the equation along the adjacent field. Using this method, we realized the automatic classification of unorganized points.The experiments using the algoritlim and criteria approved from this thesis are also carried out.

本文采用了可以比较方便地用参数方程表示的二次曲面作为数据点的分类标准，根据点的法向量以及其邻域结点的各种属性，对应于平面、球面、柱面等二次曲面，依据曲面方程的特点，从起始点开始沿邻域深度优先递归寻找符合方程的数据点，实现了散乱数据点的自动分类。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。