D3DXFresnelTerm

Calculate the Fresnel term.

FLOAT D3DXFresnelTerm(
  FLOAT CosTheta,
  FLOAT RefractionIndex
);

Parameters

CosTheta

[in] The value must be between 0 and 1.

RefractionIndex

[in] The refraction index of a material. The value must be greater than 1.

Return Values

This function returns the Fresnel term for unpolarized light. CosTheta is the cosine of the incident angle.

Remarks

To find the Fresnel term (F):

If A is 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, expanding using the trig identities and simplifying, you get:

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

Requirements

Header: Declared in D3dx9math.h.