Torrance Sparrow lighting model

The Torrance-Sparrow lighting model (sometimes also called Cook-Torrance lighting model ) is a local lighting model that is used in 3D computer graphics and is based on physical models . The surface is modeled by many small facets (mirrors), which enables the refraction ratio, roughness and shadowing to be taken into account.

The refraction ratio is calculated using the Fresnel equation , the roughness using the Beckmann probability density function / microfacet distribution .

Density function of the roughness: ${\ displaystyle D = {\ frac {e ^ {- \ lbrack {\ frac {\ tan \ beta} {m}} \ rbrack ^ {2}}} {4m ^ {2} \ cos ^ {4} \ beta }}}$

It is the angle between the surface normal and the bisector between the light incident direction and the observation direction . The size denotes the standard deviation of the slopes of the individual facets on the surface. ${\ displaystyle \ beta}$ ${\ displaystyle {\ vec {N}}}$ ${\ displaystyle {\ vec {L}}}$ ${\ displaystyle {\ vec {V}}}$ ${\ displaystyle m}$

Final formula of attenuation, Fresnel formula and roughness: . ${\ displaystyle \ rho = {\ frac {F _ {\ lambda} DG} {4 ({\ vec {N}} \ cdot {\ vec {V}}) ({\ vec {N}} \ cdot {\ vec {L}})}}}$

The Fresnel term describes how light is reflected by each of the facets, the geometric attenuation factor is used to take into account shading and covering of the facets from one another. ${\ displaystyle F _ {\ lambda}}$ ${\ displaystyle G}$

Compared to the common lighting models like the Phong model , the Torrance-Sparrow model is much closer to reality. Due to the complex calculations, however, it takes a long time, which is why this lighting is rarely used. Only the HTSG lighting model or models resulting from the complete simulation of the micro-geometry are even closer to reality with glossy surfaces.

literature

KE Torrance, EM Sparrow: Theory of off-specular reflection from roughened surfaces. Journal of the Optical Society of America A 57 (1967): 1105-1114, ISSN 1084-7529
KE Torrance, RL Cook: A Reflectance Model for Computer Graphics. ACM Transactions on Graphics 1, 1 (Jan. 1982): 7-24, ISSN 0730-0301 - A reflectance model for computer graphics . From Computer Graphics (SIGGRAPH '81 Proceedings), Vol. 15, No. 3, July 1981, pp. 301-316.