henuguyu / shbox Goto Github PK
View Code? Open in Web Editor NEWThis project forked from yxiong/shbox
A Matlab toolbox for spherical harmonics.
License: MIT License
This project forked from yxiong/shbox
A Matlab toolbox for spherical harmonics.
License: MIT License
================================================================ SHBox --- A matlab toolbox for spherical harmonics. ================================================================ Author: Ying Xiong. Created: Jul 21, 2013. Release: Jan 17, 2014 (v0.1). ================================================================ Quick start. ================================================================ >> addpath('Utils'); >> SHBoxTest; >> demoSHBox; ================================================================ Definitions. ================================================================ The inner product in spherical space is defined as / \pi / \pi <f, g> = | | f(\theta,\phi) g*(\theta,\phi) d\Omega, / \theta=0 / \phi=-pi where d\Omega = sin(\theta) d\phi d\theta. The spherical harmonic functions are defined as (2l+1) (l-m)! Y_l^m(\theta,\phi) = sqrt{---------------} P_l^m(cos(\theta)) exp(im\phi) 4 pi (l+m)! = (-1)^m sqrt{1/(2 pi)} N_l^m(cos(\theta)) exp(im\phi), where P_l^m is associated Legendre function, and N_l^m is fully normalized associated Legendre function. Therefore, we have < Y_{l1}^{m1}, Y_{l2}^{m2} > = \delta_{l1,l2} \delta_{m1,m2}. The real spherical harmonic functions are defined as / 1/sqrt(2) (Y_l^{-m} + (-1)^m Y_l^m) if m>0 Y_{l,m} = | Y_l^0 if m=0 \ 1/sqrt(2) (Y_l^m - (-1)^m Y_l^{-m}) if m<0. ================================================================ Representations. ================================================================ A spherical function f(\theta, \phi) is represented by a matrix 'F' with two (optional) coordinate lists 'lTheta' and 'lPhi', such that F(i,j) = f(lTheta(i), lPhi(j)). If not specified, 'lTheta' and 'lPhi' are by default lTheta = linspace(0, pi, size(F,1)), lPhi = linspace(-pi, pi, size(F,2)). If 'lTheta' and 'lPhi' are scalars, they will be converted to lTheta = linspace(0, pi, lTheta), lPhi = linspace(-pi, pi, lPhi). ================================================================ Features. ================================================================ * Generate real and complex spherical harmonic functions. * Visualize spherical functions. * Inner product in spherical space. * Decompose spherical function into spherical harmonic components. See 'SphericalHarmonics.pdf' for a more detailed documentation. ================================================================ Other notes. ================================================================ The 'pisa.png' file is a light probe image downloaded from http://gl.ict.usc.edu/Data/HighResProbes/ and modified (tone-mapped and resized) by Ying Xiong.
A declarative, efficient, and flexible JavaScript library for building user interfaces.
๐ Vue.js is a progressive, incrementally-adoptable JavaScript framework for building UI on the web.
TypeScript is a superset of JavaScript that compiles to clean JavaScript output.
An Open Source Machine Learning Framework for Everyone
The Web framework for perfectionists with deadlines.
A PHP framework for web artisans
Bring data to life with SVG, Canvas and HTML. ๐๐๐
JavaScript (JS) is a lightweight interpreted programming language with first-class functions.
Some thing interesting about web. New door for the world.
A server is a program made to process requests and deliver data to clients.
Machine learning is a way of modeling and interpreting data that allows a piece of software to respond intelligently.
Some thing interesting about visualization, use data art
Some thing interesting about game, make everyone happy.
We are working to build community through open source technology. NB: members must have two-factor auth.
Open source projects and samples from Microsoft.
Google โค๏ธ Open Source for everyone.
Alibaba Open Source for everyone
Data-Driven Documents codes.
China tencent open source team.