Monograph records
https://feeds.library.caltech.edu/people/Arvo-J-R/monograph.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenFri, 12 Apr 2024 23:15:12 +0000Closed-Form Expressions for Irradiance from Non-Uniform Lambertian Luminaires Part II: Polynomially-Varying Radiant Exitance
https://resolver.caltech.edu/CaltechCSTR:2000.cs-tr-00-04
Authors: {'items': [{'id': 'Chen-Min', 'name': {'family': 'Chen', 'given': 'Min'}}, {'id': 'Arvo-J-R', 'name': {'family': 'Arvo', 'given': 'James'}}]}
Year: 2001
DOI: 10.7907/Z9XG9P5B
We present new analytical techniques for computing illumination from non-uniform luminaires. The methods are based on new closed-form expressions derived by generalizing the concepts of irradiance tensor and angular moment to rational forms and an arbitrary number of directions, known as rational irradiance tensors and rational angular moments, respectively. The techniques apply to any emission, reflection or transmission distribution expressed as a polynomial over a polygonal surface, and provide a powerful mathematical tool to handle more complex BRDF's. We derive closed-form expressions for irradiance due to polygonal luminaires with polynomially varying radiant exitance, which satisfy a recurrence relation that subsumes Lambert's formula for uniform luminaires. Our formulas extend the class of available closed-form expressions for computing direct radiative transfer from planar surfaces to points, and can find many potential applications in simulating non-Lambertian illumination and scattering phenomenahttps://authors.library.caltech.edu/records/epsbd-9q996Closed-Form Expressions for Irradiance from Non-Uniform Lambertian Luminaires Part I: Linearly-Varying Radiant Exitance
https://resolver.caltech.edu/CaltechCSTR:2000.cs-tr-00-01
Authors: {'items': [{'id': 'Chen-Min', 'name': {'family': 'Chen', 'given': 'Min'}}, {'id': 'Arvo-J-R', 'name': {'family': 'Arvo', 'given': 'James'}}]}
Year: 2001
DOI: 10.7907/Z92805MQ
We present a closed-form expression for the irradiance at a point on a surface due to an arbitrary polygonal Lambertian lurninaire with linearly-varying radiant exitance. The solution consists of elementary functions and a single well-behaved special function that can be either approximated directly or computed exactly in terms of classical special functions such as Clausen's integral or the closely related dilogarithm. We first provide a general boundary integral that applies to all planar luminaires and then derive the closed-form expression that applies to arbitrary polygons, which is the result most relevant for global illumination. Our approach is to express the problem as an integral of a simple class of rational functions over regions of the sphere, and to convert the surface integral to a boundary integral using a generalization of irradiance tensors. The result extends the class of available closed-form expressions for computing direct radiative transfer from finite areas to differential areas. We provide an outline of the derivation, a detailed proof of the resulting formula, and complete pseudo-code of the resulting algorithm. Finally, we demonstrate the validity of our algorithm by comparison with Monte Carlo. While there are direct applications of this work, it is primarily of theoretical interest as it introduces much of the machinery needed to derive closed-form solutions for the general case of luminaires with radiance distributions that vary polynomially in both position and direction.https://authors.library.caltech.edu/records/n5cvt-77741