Improving radiosity solutions through the use of analytically determined form-factors
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Introduction to algorithms
On the form factor between two polygons
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Applications of irradiance tensors to the simulation of non-Lambertian phenomena
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Illumination for computer generated pictures
Communications of the ACM
A Closed-Form Solution for the Irradiance due to Linearly-Varying Luminaires
Proceedings of the Eurographics Workshop on Rendering Techniques 2000
Exact Illumination in Polygonal Environments using Vertex Tracing
Proceedings of the Eurographics Workshop on Rendering Techniques 2000
Analytic methods for simulated light transport
Analytic methods for simulated light transport
Mathematical methods for image synthesis
Mathematical methods for image synthesis
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We present a new technique for exactly computing glossy reflections and transmissions of polygonal Lambertian luminaires with linearly-varying radiant exitance. To derive the underlying closed-form expressions, we introduce a rational generalization of irradiance tensors and an associated recurrence relation. The generalized tensors allow us to integrate a useful class of rational polynomials over regions of the sphere; this class of rational polynomials can simultaneously account for the linear variation of radiant exitance across a planar luminaire and simple forms of non-Lambertian scattering. Applications include the computation of irradiance at a point, view-dependent reflections from glossy surfaces, and transmissions through glossy surfaces, where the scattering is limited to Phong distributions and the incident illumination is due to linearlyvarying luminaires. In polyhedral environments, the resulting expressions can be exactly evaluated in quadratic time (in the Phong exponent) using dynamic programming or efficiently approximated in linear time using standard numerical quadrature. To illustrate the use of generalized irradiance tensors, we present a greatly simplified derivation of a previously published closed-form expression for the irradiance due to linearly-varying luminaires, and simulate Phong-like scattering effects from such emitters. The validity of our algorithm is demonstrated by comparison with Monte Carlo.