On the representation of operators in bases of compactly supported wavelets
SIAM Journal on Numerical Analysis
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Wavelets for computer graphics: theory and applications
Wavelets for computer graphics: theory and applications
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Interactive Design of Complex Time-Dependent Lighting
IEEE Computer Graphics and Applications
All-frequency shadows using non-linear wavelet lighting approximation
ACM SIGGRAPH 2003 Papers
Triple product wavelet integrals for all-frequency relighting
ACM SIGGRAPH 2004 Papers
A frequency analysis of light transport
ACM SIGGRAPH 2005 Papers
Wavelet importance sampling: efficiently evaluating products of complex functions
ACM SIGGRAPH 2005 Papers
Precomputed shadow fields for dynamic scenes
ACM SIGGRAPH 2005 Papers
Precomputed local radiance transfer for real-time lighting design
ACM SIGGRAPH 2005 Papers
Generalized wavelet product integral for rendering dynamic glossy objects
ACM SIGGRAPH 2006 Papers
Real-time soft shadows in dynamic scenes using spherical harmonic exponentiation
ACM SIGGRAPH 2006 Papers
The Visual Computer: International Journal of Computer Graphics
A first-order analysis of lighting, shading, and shadows
ACM Transactions on Graphics (TOG)
Fast multiresolution image operations in the wavelet domain
IEEE Transactions on Visualization and Computer Graphics
Spherical harmonic gradients for mid-range illumination
EGSR'04 Proceedings of the Fifteenth Eurographics conference on Rendering Techniques
All-frequency precomputed radiance transfer for glossy objects
EGSR'04 Proceedings of the Fifteenth Eurographics conference on Rendering Techniques
All-frequency relighting of non-diffuse objects using separable BRDF approximation
EGSR'04 Proceedings of the Fifteenth Eurographics conference on Rendering Techniques
Efficient wavelet rotation for environment map rendering
EGSR'06 Proceedings of the 17th Eurographics conference on Rendering Techniques
Precomputation-Based Rendering
Foundations and Trends® in Computer Graphics and Vision
Frequency analysis and sheared filtering for shadow light fields of complex occluders
ACM Transactions on Graphics (TOG)
Display-camera calibration using eye reflections and geometry constraints
Computer Vision and Image Understanding
The State of the Art in Interactive Global Illumination
Computer Graphics Forum
Interactive, multiresolution image-space rendering for dynamic area lighting
EGSR'10 Proceedings of the 21st Eurographics conference on Rendering
Visibility editing for all-frequency shadow design
EGSR'10 Proceedings of the 21st Eurographics conference on Rendering
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Many problems in computer graphics involve integrations of products of functions. Double- and triple-product integrals are commonly used in applications such as all-frequency relighting or importance sampling, but are limited to distant illumination. In contrast, near-field lighting from planar area lights involves an affine transform of the source radiance at different points in space. Our main contribution is a novel affine double- and triple-product integral theory; this generalization enables one of the product functions to be scaled and translated. We study the computational complexity in a number of bases, with particular attention to the common Haar wavelets. We show that while simple analytic formulae are not easily available, there is considerable sparsity that can be exploited computationally. We demonstrate a practical application to compute near-field lighting from planar area sources, that can be easily combined with most relighting algorithms. We also demonstrate initial results for wavelet importance sampling with near-field area lights, and image processing directly in the wavelet domain.