This paper describes how spherical harmonics (SH) can be used to process HRTF data with the use in real-time capable auralization environments. During the generation of the SH coefficients, the optimal transformation center point is used to achieve a compact transformation. Several strategies are ...
The real and symmetric spherical harmonics form an orthonormal basis on the unit sphere (Blanco et al., 1997): (134)∫u∈S2yj(u)yj′(u)du=δjj′. We have seen that the basis of spherical harmonics {yj} breaks down most spherical continuous functions into a Fourier series expansion on ...
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 diffe...
A recurrence procedure is derived for constructing the rotation matrices between real spherical harmonics directly in terms of the elements of the original 3×3 rotation matrix without the intermediary of any parameters. The procedure furnishes a simple, efficient, and general method for the formal as...
9 RegisterLog in Sign up with one click: Facebook Twitter Google Share on Facebook spherical triangle Thesaurus Encyclopedia Wikipedia Related to spherical triangle:right spherical triangle spherical triangle n. A triangle the three sides of which are arcs of great circles. ...
Spherical harmonics are proposed as a new methodology to identify DP from head 3D models. The ideal fitted ellipsoid for each head is computed and the orthogonal distances between head and ellipsoid are obtained. Finally, the distances are modelled using spherical harmonics. Spherical harmonic ...
A triangle on the surface of a sphere formed by the intersections of three great circles (see illustration). The arcs BC, AC, and AB form the sides of the spherical triangle ABC. The lengths of these sides (a,b, andc), in angular measure, are equal to the angles BOC, COA, and AO...
先放202的手写笔记,日后再整理,感谢闫大神的无私! __EOF__
spherical harmonics are a specific set of spherical harmonics that forms an orthogonal system, first introduced by Pierre Simon de Laplace. [1] Spherical harmonics are important in many theoretical and practical applications, particularly in the computation of atomic orbital electron configurations, repres...
The first 3 orders of real spherical harmonics (l = 0, 1, 2) corresponding to a total of 9 basis functions. In these images, we show only the front of the sphere, with green denoting positive values and blue denoting negative values. Also note that these images show the real form of...