Visualization of errors on form-factor computation

Abstract

This paper compares the form-factors obtained using the hemi-cube [3] and the Wallace's ray tracing method [13] with the exact values computed according to the analytical formula [1]. The experiments are conducted for both non-blocking and partial blocking cases. The errors obtained are then displayed using color-coded images. These pictures give strong clues to the magnitude and the sources of the errors. It is found that the errors of the hemi-cube method depend on the the aspect ratio of the source patch, the normalized distance between the source and a receiving patch, and the degree of partial blocking. Aliasing effect is observed in the pictures obtained using the ray tracing method. The seriousness depends on the number and the distribution of the sample disks. Moreover, the approximated formula of the ray tracing method may induce as much as 15% of relative errors. Guidelines for reducing errors in using the two methods are suggested.