Environment maps are a widely used techniques to approximate reflections ininteractive rendering. Although environment maps make the assumption that the reflected environment is far away - thus being an approximation - they often nevertheless achieve convincing reflections. Recently environment maps have been introduced as a means to render glossy reflections. All of these methods prefilter a given environment map with either a fixed reflection model or a certain class of BRDF's(bidirectional reflectance distribution functions). Although these methods are similar,they have different strengths and weakness,which are worthwhile to discuss. In order to be able to compare these methods we present a general notation of prefiltered environment maps,which allows us to classify and contrast all the well-known prefiltering techniques.
We consider the rendering of diffuse objects under distant illumination, as specified by an environment map. Using an analytic expression for the irradiance in terms of spherical harmonic coefficients of the lighting, we show that one needs to compute and use only 9 coefficients, corresponding to the lowest-frequency modes of the illumination, in order to achieve average errors of only 1%. In other words, the irradiance is insensitive to high frequencies in the lighting, and is well approximated using only 9 parameters. In fact, we show that the irradiance can be procedurally represented simply as a quadratic polynomial in the cartesian components of the surface normal, and give explicit formulae. These observations lead to a simple and efficient procedural rendering algorithm amenable to hardware implementation, a prefiltering method up to three orders of magnitude faster than previous techniques, and new representations for lighting design and image-based rendering.
Using an analytic expression for the irradiance in terms of spherical harmonic coefficients of the lighting, we show that one needs to compute and use only 9 coefficients, corresponding to the lowest-frequency modes of the illumination, in order to achieve average errors of only 1%.
In fact, we show that the irradiance can be procedurally represented simply as a quadratic polynomial in the cartesian components of the surface normal, and give explicit formulae.
These observations lead to a simple and efficient procedural rendering algorithm amenable to hardware implementation, a prefiltering method up to three orders of magnitude faster than previous techniques, and new representations for lighting design and image-based rendering.
Lighting in most real scenes is complex, coming from a variety of sources including area lights and large continuous lighting distributions like skylight. But current graphics hardware only supports point or directional light sources. One reason is the lack of simple procedural formulas for general lighting distributions. Instead, an integration over the upper hemisphere must be done for each pixel.
We present such a simple formula for diffuse objects, i.e. for the irradiance. The key to our approach is the rapid computation of an analytic approximation to the irradiance environment map. For rendering, we demonstrate a simple procedural algorithm that runs at interactive frame rates, and is amenable to hardware implementation. No texture-mapping is required for the irradiance with our approach.
The main ingredient is the derivation of an analytic formula for the irradiance in terms of spherical harmonic coefficients of the lighting. For rendering, the key observation is that the Lambertian BRDF behaves sufficiently closely to a low-pass filter that we need consider only the first 2 orders of spherical harmonics, i.e. 9 parameters. The simple form of the first 9 spherical harmonics makes implementation straightforward.
Lighting in most real scenes is complex, coming from a variety of sources including area lights and large continuous lighting distributions like skylight. But current graphics hardware only supports point or directional light sources. One reason is the lack of simple procedural formulas for general lighting distributions. Instead, an integration over the upper hemisphere must be done for each pixel.
We present such a simple formula for diffuse objects, i.e. for the irradiance. The key to our approach is the rapid computation of an analytic approximation to the irradiance environment map. For rendering, we demonstrate a simple procedural algorithm that runs at interactive frame rates, and is amenable to hardware implementation. No texture-mapping is required for the irradiance with our approach.
The main ingredient is the derivation of an analytic formula for the irradiance in terms of spherical harmonic coefficients of the lighting. メインの要素はライティングの球面調和係数に関した放射照度のための解析的な公式の導出です。
For rendering,the key observation is that the Lambertian BRDF behaves sufficiently closely to a low-pass filter that we need consider only the first 2 orders of spherical harmonics, i.e. 9 parameters. The simple form of the first 9 spherical harmonics makes implementation straightforward.
