Numerical Aspects of Image Rendering using Spherical Harmonics

Image rendering is the process of creating realistic computer images from geometric models and physical laws of light and reflection. This master thesis deals mainly with the numerical intricacies of implementing an image renderer using spherical harmonics. It investigates how to calculate the reflection of light in a surface using the Phong model, and employs ray tracing to create a realistic image of a geometric model. Further, it investigates different ways of calculating the spherical harmonic


1 Introduction
1.1 Overview
2 Reflection of Light
2.1 BRDF
2.1.1 Diffuse Reflection
2.1.2 Specular Reflection
2.2 Lighting
3 Spherical Harmonics
3.1 Spherical Coordinates
3.2 Basis Functions
3.3 Properties
3.4 Triple Product Integral
3.5 Representation of BRDF
4 Least Squares Approximations of Functions defined on the Sphere
4.1 Quadrature
4.1.1 Equi-Longitudinal Grid
4.1.2 Equi-Latitudinal Grid
4.1.3 Uniform Grid
4.1.4 Zero Point Grid .
4.2 The Discrete Case
5 Implementation
5.1 Geometric Models
5.2 Ray Tracing
5.2.1 Calculating Intersections
5.2.2 Accelerated Data Structure (ADS)
5.3 Precalculations
5.3.1 Occlusion Functions
5.4 Re-Rendering
5.5 Computing the Coefficients
5.6 Transfer Matrices
5.7 Summary of Implementation Steps
6 Results
6.1 Relative Error
6.2 Error Made When Calculating the Coefficients
6.2.1 Comparison of Sampling Patterns
6.2.2 Comparison of Methods
6.3 Diagonal Dominans
6.4 Occlusion Functions
6.5 Environment Functions
6.6 Evaluating Picture Quality
6.7 Computational Speed
7 Conclusions
8 Future Work

Author: Gyllensten, Johan

Source: Linköping University

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