Local uniform error estimates for spherical basis functions interpolation

2013 ◽  
Vol 37 (9) ◽  
pp. 1364-1376
Author(s):  
Ming Li ◽  
Feilong Cao
Keyword(s):  
Error Estimates ◽  
Basis Functions ◽  
Uniform Error ◽  
Spherical Basis ◽  
Uniform Error Estimates ◽  
Spherical Basis Functions

scholarly journals $L^p$ Bernstein estimates and approximation by spherical basis functions

2009 ◽  
Vol 79 (271) ◽  
pp. 1647-1679 ◽  
Author(s):  
H. N. Mhaskar ◽  
F. J. Narcowich ◽  
J. Prestin ◽  
J. D. Ward
Keyword(s):  
Basis Functions ◽  
Spherical Basis ◽  
Spherical Basis Functions

scholarly journals Interactive Generation of Path-Traced Lightmaps

2021 ◽  
Author(s):  
◽  
Thomas Roughton
Keyword(s):  
Real Time ◽  
Low Frequency ◽  
Basis Functions ◽  
Prior Work ◽  
Path Tracing ◽  
Spherical Basis ◽  
Real Time Applications ◽  
Indirect Illumination ◽  
Progressive Rendering ◽  
Spherical Basis Functions

<p>Indirect illumination is an important part of realistic images, and accurately simulating the complex effects of indirect illumination in real-time applications has long been a challenge for the industry. One popular approach is to use offline precomputed solutions such as lightmaps (textures containing the precomputed lighting in a scene) to efficiently approximate these effects. Unfortunately, these offline solutions have historically enforced long iteration times that come at a cost to artist productivity. These solutions have additionally either supported only the low-frequency diffuse component of indirect lighting, yielding poor visual results for glossy or metallic materials, or have used overly expensive approximations.  In recent years, the state of the art lightmap precomputation pipeline has shifted to using highly vectorised path tracing, often on GPU hardware, to compute the indirect illumination effects. The use of path tracing enables progressive rendering, wherein an approximation to the full solution is found and then refined as opposed to solving for the final result in a single step. Progressive rendering through path tracing thereby helps to provide rapid iteration for artists.  This thesis describes a system that can progressively path-trace indirect illumination lightmaps on the GPU.Contributing to this system, itintroduces a new gather-based method for sample accumulation, enhances algorithms from prior work, and presents a range of encoding methods, including a novel progressive method for non-negative least-squares encoding of spherical basis functions.  In addition, it presents a novel, efficient solution for high-quality precomputed diffuse and low-frequency specular indirect illumination that extends the Ambient Dice family of spherical basis functions. This solution provides comparable or better specular reconstruction to prior work at lower runtime cost and has potential for widespread use in real-time applications.</p>

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