Experimental investigation on distribution of phase and magnitude of spherical harmonic coefficients

• Main Author: Aditya Bansal
• Other Authors: School of Computer Engineering
• Format: Final Year Project
• Language: English
• Published: 2012
• Subjects: DRNTU::Science::Mathematics::Analysis
• Online Access: http://hdl.handle.net/10356/48535
• Institution: Nanyang Technological University

Fourier analysis is an invaluable tool to engineers and scientists since a wide range of physical phenomena have been modeled using the classical theory of Fourier series and transforms. Spherical Harmonics for data defined on a sphere (e.g the temperature on the surface of the earth) is the natural spherical equivalent of the planar Fourier transform. The spherical harmonics form a countable orthonormal basis for square integrable functions on the sphere. Associated with each basis function is an order L, a nonnegative integer analogous to frequency. In 3D computer graphics, spherical harmonics play a special role in a wide variety of topics including indirect lighting (ambient occlusion, global illumination, pre-computed radiance transfer, etc.) and recognition of 3D shapes. This project aims to explore the distribution of the magnitude and phase of the Spherical Harmonic coefficients using the Princeton shape benchmark as the test data set. This analysis can help address issues such as the degree upto which one might need to find the Spherical Harmonic coefficients in order to represent real-world objects to a sufficient level of accuracy.