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XMVector3Refract method

Refracts an incident 3D vector across a 3D normal vector.


XMVECTOR XMVector3Refract(
  [in] XMVECTOR Incident,
  [in] XMVECTOR Normal,
  [infloat    RefractionIndex


Incident [in]

3D incident vector to refract.

Normal [in]

3D normal vector to refract the incident vector through.

RefractionIndex [in]

Index of refraction. See remarks.

Return value

Returns the refracted incident vector. If the refraction index and the angle between the incident vector and the normal are such that the result is a total internal reflection, the function will return a vector of the form < 0.0f, 0.0f, 0.0f, undefined >.


The following pseudocode demonstrates the operation of the function:


float t = ( Incident.x * Normal.x + Incident.y * Normal.y + Incident.z * Normal.z );
float r = 1.0f - RefractionIndex * RefractionIndex * (1.0f - t * t);

if (r < 0.0f) // Total internal reflection
	Result.x = 0.0f;
	Result.y = 0.0f;
	Result.z = 0.0f;
	float s = RefractionIndex * t + sqrt(r);
	Result.x = RefractionIndex * Incident.x - s * Normal.x;
	Result.y = RefractionIndex * Incident.y - s * Normal.y;
	Result.z = RefractionIndex * Incident.z - s * Normal.z;

Result.w = undefined;

return Result;

The index of refraction is the ratio of the index of refraction of the medium containing the incident vector to the index of refraction of the medium being entered (where the index of refraction of a medium is itself the ratio of the speed of light in a vacuum to the speed of light in the medium).

Platform Requirements

Microsoft Visual Studio 2010 or Microsoft Visual Studio 2012 with the Windows SDK for Windows 8. Supported for Win32 desktop apps, Windows Store apps, and Windows Phone 8 apps.



Use DirectX.



See also

DirectXMath Library 3D Vector Geometric Functions



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