Hemi-cube Algorithm Research Articles

Virtual Geographic Simulation of Light Distribution within Three-Dimensional Plant Canopy Models

Virtual geographic environments (VGEs) have been regarded as an important new means of simulating, analyzing, and understanding complex geological processes. Plants and light are major components of the geographic environment. Light is a critical factor that affects ecological systems. In this study, we focused on simulating light transmission and distribution within a three-dimensional plant canopy model. A progressive refinement radiosity algorithm was applied to simulate the transmission and distribution of solar light within a detailed, three-dimensional (3D) loquat (Eriobotrya japonica Lindl.) canopy model. The canopy was described in three dimensions, and each organ surface was represented by a set of triangular facets. The form factors in radiosity were calculated using a hemi-cube algorithm. We developed a module for simulating the instantaneous light distribution within a virtual canopy, which was integrated into ParaTree. We simulated the distribution of photosynthetically active radiation (PAR) within a loquat canopy, and calculated the total PAR intercepted at the whole canopy scale, as well as the mean PAR interception per unit leaf area. The ParaTree-integrated radiosity model simulates the uncollided propagation of direct solar and diffuse sky light and the light-scattering effect of foliage. The PAR captured by the whole canopy based on the radiosity is approximately 9.4% greater than that obtained using ray tracing and TURTLE methods. The latter methods do not account for the scattering among leaves in the canopy in the study, and therefore, the difference might be due to the contribution of light scattering in the foliage. The simulation result is close to Myneni’s findings, in which the light scattering within a canopy is less than 10% of the incident PAR. Our method can be employed for visualizing and analyzing the spatial distribution of light within a canopy, and for estimating the PAR interception at the organ and canopy levels. It is useful for designing plant canopy architecture (e.g., fruit trees and plants in urban greening) and planting planning.

Calculating Hierarchical Radiosity Form Factors using Programmable Graphics Hardware

We present a method for the efficient calculation of multiresolution radiosity form factors using programmable graphics hardware. Mipmapped ID textures are used to allow for highly refined patches with the mipmapping mechanism working as a hardware-accelerated oracle for the dynamic linking of patch hierarchies. The actual form factor values for unoccluded patches are then computed with the analytic differential area to polygon form factor using programmable graphics hardware. The resulting method allows for the efficient calculation of radiosity solutions with refined patch hierarchies as well as form factor values that are more accurate than those computed with the traditional hemicube algorithm.

HEMI-CUBE ALGORITHM AND ITS APPLICATION TO THERMAL ANALYSIS OF CRYSTAL GROWTH FURNACE

View factor calculation is important but difficult for complex geometries in surface radiation problems. Exact determination of view factors for a crystal growth furnace is essential in view of its high surface temperature as well as the complicated heating system. In this study a view factor calculation algorithm based on the hemi-cube algorithm is introduced and applied to a simple cylindrical crystal growth furnace. The results show good agreement with those of approximate kernel solutions. To determine the effect of furnace shapes and heat flux distributions on furnace performance, temperature profiles and heat flux distributions for a variety of furnaces are calculated, and the shape criteria for better furnaces are suggested.

Hemi-cube algorithm and its application to thermal analysis of crystal growth furnace

View factor determination is very important in thermal analysis problems with surface radiation but it is very difficult to determine view factors for complex geometries. Exact calculation of view factors for crystal growth furnace is essential due to not only its high surface temperature but the radiation shield, complicated heating system. In this study, view factor calculation algorithm is introduced and applied to cylindrical crystal growth furnace. This algorithm is based on the Hemi-Cube Algorithm and the results obtained with this algorithm show good agreements with those of analytical solution. As an application of this algorithm, temperature profiles and heating value distributions for various furnaces are calculated and the shape criteria for better furnace are suggested.

The super-plane buffer: An efficient form-factor evaluation algorithm for progressive radiosity

An efficient algorithm for form-factor evaluation is presented with curved surface geometry being accounted for. By adopting two separate plane buffers, namely the form-factor buffer and the shadow buffer, to serve the distinct purposes of form-factor evaluation and visibility determination independently, the new approach inherits most of the computational advantage of hemi-cube algorithm, while avoiding its limitations to progressive radiosity solution. With the use of form-factor buffer, the computation of form-factor from a source patch to a receiving sample point is reduced to a summation of delta form-factors defined over regularly shaped pixels and aliasing is mostly eliminated. By exploiting the spatial coherence of environment, the shadow buffer offers a simple “yes” or “no” answer to a visibility test with less computational cost. As an attempt to extend the progressive radiosity to nondiffuse environment, a specular reflection buffer is provided to facilitate the measurement of light energy transfer from the source patch to a receiving sample point via specular reflections. Theoretical analysis and experimental results demonstrate great potentials of this algorithm.

Accelerating the Hemi-Cube Algorithm for Calculating Radiation Form Factors

The calculation of form factors for the analysis of radiation heat transfer is computationally expensive when surfaces are not in full view of one another. Because of its lower time complexity, the hemi-cube method is efficient for problems with large numbers of surfaces. In this note, methods to improve the hemi-cube algorithm by taking advantage of graphics hardware and two types of geometric coherence are presented. The implementation of the methods on a computer workstation is described, and timings demonstrating speedups by factors of up to 6.7 are given. The acceleration of the calculation of form factors is not an isolated computational problem. The ability to calculate form factors very quickly can alter the overall computational methodology used to analyze radiant heat transfer, and can greatly extend the complexity of geometries that can be studied.

Acceleration techniques for progressive refinement radiosity

The progressive refinement radiosity method provides a means for computing the global illumination of an environment in time proportional to the size of the environment. Additionally, the method supplies a sequence of solutions that monotonically converge to a high-quality result, allowing it to be used for interactive applications that deliver "near real-time" updates as the computation proceeds. This paper presents two methods for accelerating the radiosity method. First, the traditional hemi-cube algorithm is modified to accelerate the expensive form-factor calculation. Second, the radiosity method is parallelized across a coarse-grain network, and the efficiency of the parallel system is discussed.

Improving radiosity solutions through the use of analytically determined form-factors

Current radiosity methods rely on the calculation of geometric factors, known as form-factors, which describe energy exchange between pairs of surfaces in the environment. The most computationally efficient method for form-factor generation is a numerical technique known as the hemi-cube algorithm. Use of the hemi-cube is based on assumptions about the geometry of the surfaces involved. First, this paper examines the types of errors and visual artifacts that result when these assumptions are violated. Second, the paper shows that these errors occur more frequently in progressive refinement radiosity than in the originally proposed full matrix radiosity solution. Next, a new analytical technique for determining form-factors that is immune to the errors of the hemi-cube algorithm is introduced. Finally, a hybrid progressive refinement method that invokes the new technique to correctly compute form-factors when hemi-cube assumptions are violated is presented.

A Ray tracing algorithm for progressive radiosity

A new method for computing form-factors within a progressive radiosity approach is presented. Previously, the progressive radiosity approach has depended on the use of the hemi-cube algorithm to determine form-factors. However, sampling problems inherent in the hemi-cube algorithm limit its usefulness for complex images. A more robust approach is described in which ray tracing is used to perform the numerical integration of the form-factor equation. The approach is tailored to provide good, approximate results for a low number of rays, while still providing a smooth continuum of increasing accuracy for higher numbers of rays. Quantitative comparisons between analytically derived form-factors and ray traced form-factors are presented.