Blinn-Phong Reflectance Model

Formula

In the Blinn-Phong Reflectance Model, reflectance is defined as:

$I_T = I_A + \sum_{i=0}^l I_D + I_S$

For $l$ lights where:

$I_T$ is the total reflectance.

$I_A$ is the ambient reflectance.

$I_D$ is the diffuse reflectance for a given light.

$I_S$ is the specular reflectance for a given light.

To compute these components, we need to define a few vectors.

Vectors

All vectors used should be normalized.

$\vec N$ is the surface normal.

$\vec L$ is the light vector, pointing from the surface towards the light.

$\vec V$ is the view vector, pointing from the surface towards the viewer (camera).

$\vec H$ is the half vector, halfway between the $L$ and $V$ vectors. It can be computed by $\frac{L + V}{||L + V||}$

Note that we are not concerned with $\vec R$ , the Reflection vector, for the Blinn-Phong model.

Components

All dot products used should be clamped between $0$ and $1$ .

Ambient

$I_A = k_a$

Diffuse

$I_D = k_d * (\vec N \cdot \vec L)$

Specular

$I_S = k_s * (\vec H \cdot \vec N)^\alpha$

Implementation

$k_a$ , $k_d$ , and $k_s$ are the material properties. They should be vec3 (colors).

$\alpha$ is also a material property, sometimes called shininess or lower-case n. It is a scalar.

Don’t forget to:

Normalize all vectors
- Vectors passed from the vertex shader to the fragment shader should be normalized both before and after passing. The interpolation of two or more normalized vectors is not guaranteed to be normalized.
Clamp all dot products between $0$ and $1$

Note that the equation $\frac{L + V}{||L + V||}$ does not mean you actually need to divide by the length of $L + V$ . This is merely the notation for a normalized vector. You should simply write in GLSL:

vec3 H = normalize(L + V);