目录 收起 1 History 2 Laplace's Spherical Harmonics 2.1 Transformation of the Equation 2.2 Separate Solution of 2.3 General Solution of 3 Spherical Harmonics in Cartesian Form Definition: an orthonormal basis on the surface of a sphere ...
Introduction Spherical harmonics are solutions of Laplace's equation in three dimensions, and they are collected together as homogeneous polynomials of degree l , with in each group. The simplest spherical harmonics are the three Cartesian coordinates x, y, z , which are three homogeneous ...
} 2、三维空间的Spherical Harmonics 在三维空间下绘制SH基函数,使用的是球坐标。 下面将会引进几个函数 1 2 3 4 5 6 //计算整数的阶乘,即x!=x*(x-1)*(x-2)*...*2*1 intfactorial(int); //给定带宽l和m,计算阶乘因子K doubleevaluateK(int,int); //给定带宽l和m,以及球坐标的两个角度,计算S...
Therefore, the irradiance—or equivalently, the reflected light field from a convex Lambertian object—can be well approximated using spherical harmonics up to order 2 (a 9-term representation), i.e., as a quadratic polynomial of the Cartesian coordinates of the surface normal vector. This is ...
We introduce behavioral spherical harmonic (BSH), a novel approach to efficiently and compactly represent the directional-dependent behavior of agent. BSH is based on spherical harmonics to project the directional information of a group of multiple agent
Spherical harmonics can be thought of as signal-processing tools on the unit sphere, analogous to the Fourier series or sines and cosines on the line or circle. They can be written either as trigonometric functions of the spherical coordinates, or as simple polynomials of the Cartesian components...
The derivatives of the Earth gravitational potential are considered in the global Cartesian Earth-fixed reference frame. Spherical harmonic series are constructed for the potential derivatives of the first and second orders on the basis of a general expression of Cunningham (Celest Mech 2:207–216, ...
The Cartesian–Taylor series for an analytic function in three dimensions is rewritten as a series of solid spherical harmonics. A discussion of the distribution theory definition of singular spherical harmonics is given, which leads to a definition of spherical delta functions. An expansion of source...