Spherical Harmonics Math

dxsdk, directxmath

Originally posted to Chuck Walbourn's Blog on MSDN, Jul 28, 2012

DirectXMath (aka XNAMath version 3) provides almost all the functionality of the original D3DXMath library with two exceptions. The first is the ‘matrix stack’ helper and the second is the ‘spherical harmonics’ math functions. The matrix stack is fairly easy to implement, but the SH math functions are another story. The original code for SH math in the D3DX utility library was written by John Snyder (MSR) and Peter-Pike Sloan (former Microsoft now at NVIDIA), and was the basis for a number of DirectX SDK samples and graphics publications as well as several ATI/AMD demos. With the removal of the SH math functionality from D3DX11 and the retirement of the D3DX library generally (see Where is the DirectX SDK?), this post provides a replacement for this functionality.

This post does not include the Precomputed Radiance Transfer (PRT) simulator that was shipped in D3DX9. You can continue to make use of that library for offline computations, and then use this post’s SH math routines for runtime usage in a modern Direct3D 11 application without any legacy D3DX dependencies.

API

The DirectXSH.h/.cpp file pair provides the SH math functions. It is based on DirectXMath and requires Visual Studio 2012 or VS 2010 with the Windows 8.0 SDK.

Note it is fairly easy to modify these files if you must use XNAMath for compatibility with Xbox 360 or VS 2008 by removing namespaces and changing from SAL2 to VS-style SAL, but that is left as an exercise to the reader.

`XMSHEvalDirection`	Evaluates the Spherical Harmonic basis functions. Equivalent to D3DXSHEvalDirection function.
`XMSHRotate`	Rotates SH vector by a rotation matrix. Equivalent to the D3DXSHRotate function.
`XMSHRotateZ`	Rotates the SH vector in the Z axis by an angle. Equivalent to the D3DXSHRotateZ function.
`XMSHAdd`	Adds two SH vectors. Equivalent to the D3DXSHAdd function.
`XMSHScale`	Scales a SH vector. Equivalent to the D3DXSHScale function.
`XMSHDot`	Computes the dot product of two SH vectors. Equivalent to the D3DXSHDot function.
`XMSHMultiply XMSHMultiply2 XMSHMultiply3 XMSHMultiply4 XMSHMultiply5 XMSHMultiply6`	Computes the product of two functions represented using SH. Equivalent to D3DXSHMultiply2, ``D3DXSHMultiply3``, ``D3DXSHMultiply4``, ``D3DXSHMultiply5``, and ``D3DXSHMultiply6``.
`XMSHEvalDirectionalLight`	Evaluates a directional light and returns spectral SH data. Equivalent to the D3DXSHEvalDirectionalLight function.
`XMSHEvalSphericalLight`	Evaluates a spherical light and returns spectral SH data. Equivalent to the D3DXEvalSphericalLight function.
`XMSHEvalConeLight`	Evaluates a light that is a cone of constant intensity and returns spectral SH data. Equivalent to the D3DXSHEvalConeLight function.
`XMSHEvalHemisphereLight`	Evaluates a light that is a linear interpolant between two colors over the sphere. Equivalent to the D3DXSHEvalHemisphereLight function.
`SHProjectCubeMap`	Projects a function represented in a cube map into spherical harmonics. Equivalent to the D3DX11SHProjectCubeMap function.

The DirectXSHD3D11.cpp module provides the function for computing the SH projection of a cubemap.

SHProjectCubeMap Projects a function represented in a cube map into spherical harmonics. Equivalent to the D3DX11SHProjectCubeMap function.

Update: The source code for this project is now available on GitHub under the MIT license.

Games for Windows and the DirectX SDK blog

Spherical Harmonics Math

API

Further Reading