Blinn lighting model

Comparison of the Blinn and Phong models.

The Blinn lighting model (also Blinn-Phong model ) is a local lighting model in image synthesis for light reflection on surfaces. The Phong lighting model is used as the basis . By using so-called halfway vectors , the necessary calculations are accelerated without influencing the result in any noticeable way. The model was described in 1977 by James F. Blinn ( Jim Blinn ), who also developed bump mapping .

application

In practice, the Blinn lighting model is used in OpenGL , for example , because it avoids the calculation of the reflection vector. Instead, the bisector is used: ${\displaystyle H}$

${\displaystyle H={\frac {V+L}{\|V+L\|}}}$

With

• ${\displaystyle V}$... normalized vector from the point to the viewer
• ${\displaystyle L}$ ... normalized vector from the point to the point light source to be considered

With this the cosine of the angle between the normal and the bisector can be calculated: ${\displaystyle \theta '}$ ${\displaystyle N}$ ${\displaystyle H}$

${\displaystyle \cos \theta '=N\cdot H}$

The above formula is of course only valid provided that is. This cosine can now be used instead of the formula known from the Phong lighting model to calculate the specular component: ${\displaystyle \|N\|=1}$ ${\displaystyle \cos \theta }$

${\displaystyle {\begin{matrix}I_{specular}&=&I_{in}\cdot k_{specular}\cdot \cos ^{n}\theta '\\&=&I_{in}\cdot k_{specular}\cdot \left({\frac {(V+L)\cdot N}{\|(V+L)\|\cdot \|N\|}}\right)^{n}\end{matrix}}}$

With

• ${\displaystyle I_{in}}$ ... luminous intensity of the incident light beam from the point light source
• ${\displaystyle k_{specular}}$ ... empirically determined reflection factor for specular components of the reflection
• ${\displaystyle n}$ ... constant exponent to describe the surface properties (called "Shininess" in OpenGL)

Comparison with the Phong model

The angle is approximately half the size of the angle in the Phong model . (This relationship is exact when L , V and N are in one plane.) ${\displaystyle \theta '}$ ${\displaystyle \theta }$

In order to achieve results that are comparable with the Blinn model as with the Phong model, one has to choose the exponent n in the above formula four times as large as the exponent n in the Phong model.

literature

• James F. Blinn: Models of light reflection for computer synthesized pictures. In SIGGRAPH 1977 Proceedings , pp. 192-198. ACM Press, San José 1977, ISSN  0097-8930