Blinn–Phong shading model

The Blinn–Phong reflection model (also called the modified Phong reflection model) is a modification to the Phong reflection model developed by Jim Blinn.

Blinn–Phong is the default shading model used in OpenGL and Direct3D's fixed-function pipeline (before Direct3D 10 and OpenGL 3.1), and is carried out on each vertex as it passes down the graphics pipeline; pixel values between vertices are interpolated by Gouraud shading by default, rather than the more computationally-expensive Phong shading.

In Phong shading, one must continually recalculate the dot product ${\displaystyle R\cdot V}$ between a viewer (V) and the beam from a light-source (L) reflected (R) on a surface.

If, instead, one calculates a halfway vector between the viewer and light-source vectors,

we can replace ${\displaystyle R\cdot V}$ with ${\displaystyle N\cdot H}$, where ${\displaystyle N}$ is the normalized surface normal. In the above equation, ${\displaystyle L}$ and ${\displaystyle V}$ are both normalized vectors, and ${\displaystyle H}$ is a solution to the equation ${\displaystyle V=P_{H}(-L),}$ where ${\displaystyle P_{H}}$ is the Householder matrix that reflects a point in the hyperplane that contains the origin and has the normal ${\displaystyle H.}$

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