Phong reflection model
The Phong lighting model is a lighting model in 3D computer graphics that is used to calculate the lighting of objects. The model was named after its developer Bùi Tường Phong and first presented in 1975 ( Illumination for Computer Generated Pictures, June 1975).
The Phong model is suitable for the representation of smooth, plastic-like surfaces. Here, the highlight of the surface is described by the term, the parameter controls the " roughness " of the surface.
It is a fully empirical model, which is based on no physical basis. So it is not fulfilled, for example, the energy conservation law, which requires that a surface can not reflect more light than is provided by the light source. In addition, it is relatively slow to compute. There are other lighting models are physically correct or partially physically correct, such as the mud or Cook - Torrance model.
Despite its shortcomings, it is still often an essential part of many popular 3D display methods.
Formula
Simplifications of the Phong lighting model
- Light sources are punctiform
- The geometry of the surfaces except for the surface normal is ignored
- Diffuse and specular reflection is modeled only locally
- Ambient reflection is modeled globally
The composition of the reflected light
In the Phong lighting model, the reflection of light is described as a combination of of ambient, ideal diffuse and ideal specular reflection.
The individual components are described below.
Atmosphere component of the reflected light
The ambient component of the reflected light is independent of the angle of incidence of the light beam of the point light source and the viewing angle of the observer of the scene. It depends on the for all points on all surfaces constant ambient light and an empirically determined reflectance ( material constant ).
With
- Intensity of ambient light ...
- Material constant ...
Diffuse component of the reflected light
Diffuse reflection light is independent of the position of the viewer in all directions reflected ( Lambert 's law). The light intensity of the reflected light from the point light source still depends on the angle of incidence, since changes the illuminance of the surface with the incident angle. Thus, the light intensity of the diffuse component of the incident angle of the light beam of the point light source and an empirically determined reflectance ( material constant ) depends, however, from the viewpoint of the observer of the scene independently.
With
- ... Light intensity of the incident light beam, the point light source
- Empirically determined ... reflection coefficient for diffuse component of the reflection
- ... Angle between the normal vector of the surface and a unit vector in the direction of the incident light beam
Specular component of the reflected light
In specular reflection the light is reflected in a certain neighborhood of the ideal reflection direction. The light intensity of the reflected light is the angle of incidence of the light beam of the point light source from an empirically determined reflectance ( material constant ), and the surface condition and the viewing angle of the observer of the scene dependent.
With
- ... Light intensity of the incident light beam, the point light source
- Empirically determined ... reflection factor specular component of the reflection
- Angle between ... ideal reflection direction of the emergent light beam and viewing direction of the observer
- ... Constant factor to describe the surface texture ( rough less than 32, greater than 32 slick, would be a perfect mirror )
Further, a normalization factor should be used which ensures that the brightness does not decrease at high levels exponent ().
A reasonable factor is usually taken.
Thus, the following formula is used to calculate the specular reflection:
Complete formula
And here the composite formula for the Phong lighting model:
With
Multiple light sources
Are a plurality of light sources is present, initially, the respective components are calculated separately for each light source and this is then summed.