Hemispherical Projection of a Triangle

Publisher Summary Form-factor calculation is very important to obtain an accurate simulation of a real scene. The form factor is calculated analytically in terms of the area of a hemispherical projection of a planar patch. This chapter discusses the area of a hemispherical projection of a planar patch by using triangle as an example. The intensity of the receiving triangle, because of a luminous planar triangle in space is proportional to the area of the hemispherical projection of the luminous triangle. The area of the projected triangle is obtained by adding or subtracting the three areas corresponding to the three sectors formed by the three sides in their respective great ellipses. When quadrilateral patches or polygons with even more vertices are used, the number of area calculations is equal to the number of vertices.