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Real-Time Rendering

Real-Time Rendering. Digital Image Synthesis Yung-Yu Chuang 01/03/2006. with slides by Ravi Ramamoorthi and Robin Green. Realistic rendering. So far, we have talked photorealistic rendering including complex materials, complex geometry and complex lighting. They are slow.

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Real-Time Rendering

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  1. Real-Time Rendering Digital Image Synthesis Yung-Yu Chuang 01/03/2006 with slides by Ravi Ramamoorthi and Robin Green

  2. Realistic rendering • So far, we have talked photorealistic rendering including complex materials, complex geometry and complex lighting. They are slow.

  3. Real-time rendering • Goal is to achieve interactive rendering with reasonable quality. It’s important in many applications such as games, visualization, computer-aided design, …

  4. Basic themes • Interactive ray-tracing • Programmable graphics hardware • Image-based rendering • Precomputation-based methods

  5. Natural illumination People perceive materials more easily under natural illumination than simplified illumination. Images courtesy Ron Dror and Ted Adelson

  6. Natural illumination Classically, rendering with natural illumination is very expensive compared to using simplified illumination directional source natural illumination

  7. Reflection maps Blinn and Newell, 1976

  8. Environment maps Miller and Hoffman, 1984

  9. HDR lighting

  10. Examples

  11. Examples

  12. Examples

  13. Complex illumination

  14. Basisfunctions • Basis Functions are pieces of signal that can be used to produce approximations to a function

  15. Basis functions • We can then use these coefficients to reconstruct an approximation to the original signal

  16. Basis functions • We can then use these coefficients to reconstruct an approximation to the original signal

  17. Orthogonal basis functions • Orthogonal Basis Functions • These are families of functions with special properties • Intuitively, it’s like functions don’t overlap each other’s footprint • A bit like the way a Fourier transform breaks a functions into component sine waves

  18. Basis functions • Transform data to a space in which we can capture the essence of the data better • Here, we use spherical harmonics, similar to Fourier transform in spherical domain

  19. Real spherical harmonics • A system of signed, orthogonal functions over the sphere • Represented in spherical coordinates by the function where l is the band and m is the index within the band

  20. Real spherical harmonics

  21. Reading SH diagrams Thisdirection + – Not thisdirection

  22. Reading SH diagrams Thisdirection + – Not thisdirection

  23. The SH functions

  24. The SH functions

  25. Spherical harmonics

  26. Spherical harmonics m 0 l 1 2 -2 -1 0 1 2

  27. SH projection • First we define a strict order for SH functions • Project a spherical function into a vector ofSH coefficients

  28. SH reconstruction • To reconstruct the approximation to a function • We truncate the infinite series of SH functions to give a low frequency approximation

  29. Examples of reconstruction

  30. An example • Take a function comprised of two area light sources • SH project them into 4 bands = 16 coefficients

  31. Low frequency light source • We reconstruct the signal • Using only these coefficients to find a low frequency approximation to the original light source

  32. SH lighting for diffuse objects • An Efficient Representation for Irradiance Environment Maps, Ravi Ramamoorthi and Pat Hanrahan, SIGGRAPH 2001 • Assumptions • Diffuse surfaces • Distant illumination • No shadowing, interreflection irradiance is a function of surface normal

  33. Diffuse reflection reflectance (albedo/texture) radiosity (image intensity) irradiance (incoming light) × = quake light map

  34. L n Irradiance environment maps Illumination Environment Map Irradiance Environment Map

  35. Spherical harmonic expansion Expand lighting (L), irradiance (E) in basis functions = .67 + .36 + …

  36. Analytic irradiance formula Lambertian surface acts like low-pass filter 0 2 0 1 cosine term

  37. m 0 l 1 2 2 -2 -1 0 1 9 parameter approximation Order 0 1 term Exact image RMS error = 25 %

  38. m 0 l 1 2 2 -2 -1 0 1 9 Parameter Approximation Order 1 4 terms Exact image RMS Error = 8%

  39. m 0 l 1 2 2 -2 -1 0 1 9 Parameter Approximation Order 2 9 terms Exact image RMS Error = 1% For any illumination, average error < 3% [Basri Jacobs 01]

  40. Comparison Irradiance map Texture: 256x256 Spherical Harmonic Coefficients 1sec Irradiance map Texture: 256x256 Hemispherical Integration 2Hrs Incident illumination 300x300

  41. Rendering Irradiance approximated by quadratic polynomial 4x4 matrix (depends linearly on coefficients Llm) Surface Normal vector column 4-vector

  42. Complex geometry Assume no shadowing: Simply use surface normal

  43. Video

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