Efficient irradiance normal mapping

Irradiance normal mapping is a method to combine two popular techniques, light mapping and normal mapping, and is used in games such as Half-Life 2 or Halo 3. This combination allows using low-resolution light caching on surfaces with only a few coefficients which are evaluated by normal maps to render spatial high-frequency changes in the lighting. Though there are dedicated bases for this purpose such as the Half-Life 2 basis, higher order basis functions such as quadratic Spherical Harmonics are needed for an accurate representation. However, a full spherical basis is not needed since the irradiance is stored on the surface of a scene. In order to represent the irradiance signals efficiently, we propose a novel polynomial, hemispherically orthonormal basis function set that is specifically designed to carry a directional irradiance signal on the hemisphere and which makes optimal use of the number of coefficients. To compare our results with previous work, we analyze the relations and attributes of previously proposed basis systems and show that 6 coefficients are sufficient to accurately represent an irradiance signal on the hemisphere. To create the necessary irradiance signals, we use Spherical Harmonics as an intermediate basis due to their fast filtering capabilities.