查询词典 polynomial expression

The equations of two classes of 3D polynomial maps that are equivariant with respect to the rotational symmetries of either a regular tetrahedron group or a regular octahedron group are strictly given, on the basis of which the properties of the general Julia sets created by these 3D polynomial maps are discussed and proved.

从理论上分析并证明了三维多项式映射满足等变的条件，精确地给出了关于正四面体群和正八面体群具有旋转不变对称性的两类三维等变映射的具体公式，在此基础上讨论并证明了三维多项式映射的广义Julia集所具有的性质。

The SEIDEL coefficients solved by wavefront fitting with Zernike annular polynomial and Zernike circular polynomial were compared.

比较对于不同遮拦比的环孔径波面采用Zernike环多项式拟合与采用Zernike圆多项式拟合求取SEIDEL系数的差别。

When the ratio of central obscuration is small, the circular polynomial with 9 terms could take place of the annular polynomial to solve the SEIDEL coefficients in some special situations.

在某些特殊情况下，对于中心遮拦很小的环孔径波面，可以采用9项Zernike圆多项式来代替环多项式进行拟合求取SEIDEL系数。

Because the free form surface expressed by discret points has difficulties in aberration correction, manufacture and test, the Zernike polynomial was adopted to express the free form surface. The performance of this system was optimized on the basis of the relationship between Zernike polynomial and Seidel aberration.

由于离散点表述的自由曲面在像差校正、加工及检测等方面存在困难，提出了采用Zernike多项式表征自由曲面的面形，并利用Zernike多项式与Seidel像差之间的关系，优化自由曲面成像系统性能。

This paper presents a new class of piecewise trigonometric polynomial curves and a weighted trigonometric polynomial curve which has simple structure and can be used to design curves.

提出了一类新的分段三角多项式曲线，给出了加权三角多项式曲线，表示式结构简单，能用于曲线设计。

This trigonometric polynomial can be used to construct open and closed curves. Moreover, the class of piecewise trigonometric polynomial curves can be accurate and flexible to express ellipse.

利用该类分段三角多项式，给出了开曲线和闭曲线的构造方法，并提出了分段三角多项式可精确、灵活地表示椭圆。

A kind of blending functions with shape parameters is constructed based on trigonometric polynomial functions. Then the method of generating trigonometric polynomial Coons patch is discussed.

给出一类含参数的三角多项式混合函数，在此基础上构造一类三角多项式混合Coons曲面片，提出带形状参数的双三次三角多项式Coons曲面片的表达式。

Experiments show that C-B spline curve, uniform B-spline with shape parameter, hyperbolic polynomial uniform B-spline with shape parameter and trigonometric polynomial uniform B-spline with shape parameter can be used to produce some frequently used free form curves in the industrial field when the shape parameter is assigned with some specific values.

通过调整形状参数来修改曲线形状是计算机辅助几何设计中一个非常活跃的研究课题，研究形状参数的变化对样条曲线形状的影响，对于增加曲线造型的灵活性是非常必要的。

Experiments show that C-B spline curve, uniform B-spline with shape parameter, hyperbolic polynomial uniform B-spline with shape parameter and trigonometric polynomial uniform B-spline with shape parameter can be used to produce some frequently used free form curves in the industrial field when the shape parameter is assigned with some specific values. This process is simpler than producing these free form curves by using controlling vertex.

实验证明，C-B样条曲线、带形状参数的均匀B样条曲线、带形状参数双曲多项式的均匀B样条曲线、带形状参数三角多项式的均匀B样条曲线都可利用形状参数的特定取值表示一些工业领域常用的自由曲线，这比起用控制顶点表示同样的自由曲线更为简单。

The polynomial function bases are used to form the approximately matching function. Moreover, the discrete values of grey image is transformed to polinomial function that are exact fit at the considered pixel locations. As a result, The mathematical operations performed such as derivation, integration, and gradient evaluation also give out the polynomial functions, therefore, the system of undetermined coefficient equations is derived to be a system of linear algebraic equations.

我们把立体匹配过程看作泛函的极小化过程，因此选用变分问题近似解法的Ritz法构造数值算法，以多项式函数为基构作匹配函数的近似解，进而又利用多项式过样值点的拟合将离散的灰度图象变换为多项式函数，因此计算中所需的求导，积分，及梯度运算的结果仍然是多项式函数，最终将待定系数方程组化为线性代数方程组。

Who? I never heard of him, Paul said, before asking teammate James Posey if he had heard of him.

赛后，科比说，他一直都是一名非常出色的射手，今天他打得很棒。

When I joined the company, I rotated around the different sections.

我加入这个公司时，轮换过几个不同的部门。