Geometry.FresnelTerm(Single,Single) Method (Microsoft.DirectX.Direct3D)

Calculates the Fresnel term.

Definition

Visual Basic	Public Shared Function FresnelTerm( _     ByVal cosTheta As Single, _     ByVal refractionIndex As Single _ ) As Single
C#	public static float FresnelTerm(     float cosTheta,     float refractionIndex );
C++	public: static float FresnelTerm(     float cosTheta,     float refractionIndex );
JScript	public static function FresnelTerm(     cosTheta : float,     refractionIndex : float ) : float;

Parameters

cosTheta	System.Single Cosine of the incident angle; must be between 0 and 1.
refractionIndex	System.Single Refraction index of a material; must be greater than 1.

Return Value

System.Single
Fresnel term for unpolarized light.

Remarks

To find the Fresnel term, use the following equation.

If F is the Fresnel term, A is the angle of incidence, and B is the angle of refraction, then

F = 0.5 * [tan2(A - B) / tan2(A + B) + sin2(A - B) / sin2(A + B)]
  = 0.5 * sin2(A - B) / sin2(A + B) * [cos2(A + B) / cos2(A - B) + 1]

Let r   = sina(A) / sin(B)      (the relative refractive index)
Let c   = cos(A)
Let g   = (r2 + c2 - 1)1/2

Then, expand using the trigonometric identities and simplifying to produce the following result.

F = 0.5 * (g + c)2 / (g - c)2 * ([c(g + c) - 1]2 / [c(g - c) + 1]2 + 1)