A Method ro Colculate the Illumination due to Light from Surface Sorwce

Abstract

The method using unit sphere has been used to calculate the illumination due to a surface luminous source. In general, however, it necessitates to solve the algebraic equation with higher order and so use some computing device to get the orthogonal projection with respect to the unit sphere.In the present report, the author has proposed a convenient method and rather simplified the process to obtain the curve of orthogonal projection, Then his method has been applied to several light sources with simple forms (i. e. ellipsoid, elliptic plate, and parabolic plate). And especially the equation of the orthogonal projection curve has been obtained for the extreme point on the inner surface of toroidal light source.Leading merits of the present method are as follows.1) The process to obtain the orthogonal projection curve for the light source has been simplified, while the complicated technic to get the equation of circumscriving cone has been omitted.2) So for the light sources which have been hardly solved by the usual unit sphere method, their orthogonal projection curves have been calculated using the author's one.3) By the new method, the coordinate of the light source can be always introduced as a parameter to the equation for the orthogonal projection concerning the unit sphere. Then, the correspondence between the points on the surface of light source and its orthogonal projection curve has been made clear.