Configuration factor & form factor with triangular subdivision -- Algorithm 3.16

Triangle 1 subtends a spherical triangle from a vertex of triangle 2. If the spherical triangle is sufficiently small to be treated as a point source, the configuration factor is a simple function of the angular size and the angle of incidence at the vertex.

a. Test for size of subtended triangle for configuration factor calculation

In lighting calculations, an area source may be treated as a point if the ratio of its maximum dimension to its distance to the illuminated surface is less than an arbitrary value e. The value of e is frequently taken to be 1/5.

Input

Sides of spherical triangle, (algorithms 5.17 & 5.18)

Maximum ratio of source dimension to distance, e

Equation

Note

b. Configuration factor

Input

Angles between surface normal of triangle 2 and directions of vertices qa, qb, qc radians (algorithm 5.13)

Area of spherical triangle, S radians (algorithm 5.17)

Equation

The configuration factor of triangle 1 at vertex 1 of triangle 2 is

Source

General theory of analytic geometry.

c. Form factor

The form factor which relates the illuminance of triangle 2 to the emittance of triangle 1 is found by determining the mean configuration factors over regular points on the receiving triangle. If the receiving triangle is small, the form factor can be found from the vertex values, as follows:

Input

Configuration factors at the vertices of triangle 2,

Equation

Source

General theory of analytic geometry.