An Efficient Representation for Irradiance Environment Maps Ravi
- Slides: 27
An Efficient Representation for Irradiance Environment Maps Ravi Ramamoorthi Pat Hanrahan Stanford University SIGGRAPH 2001
Irradiance Environment Maps R Incident Radiance (Illumination Environment Map) N Irradiance Environment Map
Assumptions • Diffuse surfaces • Distant illumination • No shadowing, interreflection Hence, Irradiance is a function of surface normal
Diffuse Reflection Reflectance (albedo/texture) Radiosity (image intensity) = Irradiance (incoming light) × quake light map
Computing Irradiance • Classically, hemispherical integral for each pixel Incident Radiance • Lambertian surface is like low pass filter • Frequency-space analysis Irradiance
Spherical Harmonics 0 1 2. . . -2 -1 0 1 2
Spherical Harmonic Expansion Expand lighting (L), irradiance (E) in basis functions =. 67 +. 36 + …
Analytic Irradiance Formula Lambertian surface acts like low-pass filter 0 0 1 2
9 Parameter Approximation Order 0 1 term Exact image RMS error = 25 % 0 1 2 -2 -1 0 1 2
9 Parameter Approximation Order 1 4 terms Exact image RMS Error = 8% 0 1 2 -2 -1 0 1 2
9 Parameter Approximation Order 2 9 terms Exact image RMS Error = 1% For any illumination, average error < 3% [Basri Jacobs 01] 0 1 2 -2 -1 0 1 2
Computing Light Coefficients Compute 9 lighting coefficients Llm • 9 numbers instead of integrals for every pixel • Lighting coefficients are moments of lighting • Weighted sum of pixels in the environment map
Comparison Incident illumination 300 x 300 Irradiance map Texture: 256 x 256 Hemispherical Integration 2 Hrs Irradiance map Texture: 256 x 256 Spherical Harmonic Coefficients 1 sec
Rendering • We have found the SH coefficients for irradiance which is a spherical function. • Given a spherical coordinate, we want to calculate the corresponding irradiance quickly.
Rendering Irradiance approximated by quadratic polynomial 4 x 4 matrix (depends linearly on coefficients Llm) Surface Normal vector column 4 -vector
Hardware Implementation Simple procedural rendering method (no textures) • Requires only matrix-vector multiply and dot-product • In software or NVIDIA vertex programming hardware
Complex Geometry Assume no shadowing: Simply use surface normal
Lighting Design Final image sum of 3 D basis functions scaled by Llm Alter appearance by changing weights of basis functions
Results
Summary Theory • • Analytic formula for irradiance Frequency-space: Spherical Harmonics To order 2, constant, linear, quadratic polynomials 9 coefficients (up to order 2) suffice Practical Applications • Efficient computation of irradiance • Simple procedural rendering • New representation, many applications
Precomputed Radiance Transfer for Real-Time Rendering in Dynamic, Low-Frequency Lighting Environments Peter-Pike Sloan, Microsoft Research Jan Kautz, MPI Informatik John Snyder, Microsoft Research SIGGRAPH 2002
Basic idea Preprocess for alli
Precomputation Use 25 bases. . . Basis 16 Basis 17 Basis 18. . . illuminate result
Diffuse No Shadows/Inter Shadows+Inter
Glossy No Shadows/Inter Shadows+Inter • Glossy object, 50 K mesh • Runs at 3. 6/16/125 fps on 2. 2 Ghz P 4, ATI Radeon 8500
Arbitrary BRDF Anisotropic BRDFs Other BRDFs Spatially Varying
Volumes • Diffuse volume: 32 x 32 grid • Runs at 40 fps on 2. 2 Ghz P 4, ATI 8500 • Here: dynamic lighting
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