of wavelength points, or photons) characteristic of such volume. The spectral content of the rays evolve as they travel through the media, and the absorbed energy at every finite volume is recorded. The wire frame boxes in Figure 1(a) show the finite volumes of the participating radiation media, where the dots represent a set of isotropic rays emitted from the centroid of these finite volumes. Figure 1(b) shows the wire frame of a simulated HID lamp arc tube and figures 1(c) and 1(d) show the reconstruction of the arc tube from rays from a finite volume above and below the equatorial plane of the lamp. This is a preliminary test to judge that the number of rays emitted from a finite-volume will be statistically sufficient to solve the radiation transfer equation by reconstructing the object.

Abstract A new calculation scheme is proposed for the explicitly discretized solution of the three-dimensional (3D) radiation transfer equation (RTE) for inhomogeneous atmospheres. To separate the independent variables involved in the 3D RTE approach, the spherical harmonic series expansion was used to discretize the terms, depending on the direction of the radiance, and the finite-volume method was applied to discretize the terms, depending on the spatial coordinates. A bidirectional upwind difference scheme, which is a specialized scheme for the discretization of the partial differential terms in the spherical harmonic-transformed RTE, was developed to make the equation determinate. The 3D RTE can be formulated as a simultaneous linear equation, which is expressed in the form of a vector–matrix equation with a sparse matrix. The successive overrelaxation method was applied to solve this equation. Radiative transfer calculations of the solar radiation in two-dimensional cloud models have shown that this method can properly simulate the radiation field in inhomogeneous clouds. A comparison of the results obtained using this method with those using the Monte Carlo method shows reasonable agreement for the upward flux, the total downward flux, and the intensities of radiance.

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On the structure of the continuity set of the solution to a boundary-value problem for the radiation transfer equation

Mathematical Notes ◽

10.1134/s0001434609070256 ◽

2009 ◽

Vol 86 (1-2) ◽

pp. 234-248 ◽

Cited By ~ 9

Author(s):

I. V. Prokhorov

Keyword(s):

Boundary Value Problem ◽

Transfer Equation ◽

Radiation Transfer ◽

Boundary Value ◽

Radiation Transfer Equation

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Generation of Surface Models of 3D Objects From Their Wire-Frame Models

4th Conference on Flexible Assembly Systems ◽

10.1115/detc1992-0452 ◽

1992 ◽

Author(s):

S. Gupta ◽

A. Shirkhodaie ◽

A. H. Soni

Keyword(s):

Common Vertex ◽

Surface Model ◽

Edge Information ◽

Frame Model ◽

3D Objects ◽

Wire Frame ◽

Surface Models ◽

Plane Passing ◽

Generate Surface ◽

The Wire

Abstract This paper presents an algorithm to generate surface models of 3D objects from their wire-frame models. The algorithm firstly, obtains information about edges of the object from the wire-frame model of the object and uses this edge information to generate the pairs. A pair of an object is a combination of two non-collinear edges which have a common vertex. The algorithm then determines the unique plane passing through each pair and groups the coplanar pairs together. Then it sorts each of the groups of coplanar pairs to form one or more loops of edges. Finally for each group of coplanar pairs, all the loops are combined, using a few rules, to form faces of the object. Hence a surface model of the object is generated.

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