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Appearance Models for Graphics

n. a. a. da. Appearance Models for Graphics. COMS 6998-3 Brief Overview of Reflection Models. Assignments. E-mail me name, status, Grade/PF. If you don’t do this, you won’t be on class list. [and give me e-mails now] Let me know if you don’t receive e-mail by tomorrow

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Appearance Models for Graphics

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  1. n a a da Appearance Models for Graphics COMS 6998-3 Brief Overview of Reflection Models

  2. Assignments • E-mail me name, status, Grade/PF. If you don’t do this, you won’t be on class list. [and give me e-mails now] • Let me know if you don’t receive e-mail by tomorrow • E-mail me list of papers to present (rank 4 in descending order). Must receive by Fri or you might be randomly assigned. • Next week, e-mail brief descriptions of proposed projects. Think about this when picking papers

  3. Today Appearance models • Physical/Structural (Microfacet: Torrance-Sparrow, Oren-Nayar) • Phenomenological (Koenderink van Doorn)

  4. n a a da Masking Interreflection Shadowing dA Symmetric Microfacets Brdf of grooves simple: specular/Lambertian Torrance-Sparrow: Specular Grooves. Specular direction bisects (half-angle) incident, outgoing directions Oren-Nayar: Lambertian Grooves. Analysis more complicated. Lambertian plus a correction

  5. Phenomenological BRDF model Koenderink and van Doorn • General compact representation • Domain is product of hemispheres • Same topology as unit disk, adapt basis • Zernike Polynomials

  6. Paper presentations • Torrance-Sparrow (Kshitiz) • Oren-Nayar (Aner) • Koenderink van Doorn (me, briefly)

  7. Phenomenological BRDF model Koenderink and van Doorn • General compact representation • Preserve reciprocity/isotropy if desired • Domain is product of hemispheres • Same topology as unit disk, adapt basis • Outline • Zernike Polynomials • Brdf Representation • Applications

  8. Zernike Polynomials • Optics, complete orthogonal basis on unit disk using polynomials of radius • R has terms of degree at least m. Even or odd depending on m even or odd • Orthonormal, using measure dd n-|m| even |m|n Cool Demo: http://wyant.opt-sci.arizona.edu/zernikes/zernikes.htm

  9. |m| 0 1 2 n |m|  n |m|  n 0 n-|m| must be even |m|  n n-|m| must be even 1 n-|m| must be even n-|m| must be even 2

  10. m>0:cos(m) m=0:sqrt(2) m<0:sin(m) azm= Hemispherical Zernike Basis • Measure Disk: Hemisphere: sin()dd • Set dd

  11. BRDF representation • Reciprocity: aklmn=amnkl

  12. BRDF representation • Reciprocity: aklmn=amnkl • Isotropy: Dep. only on  = |i-r| Expand as a function series of form cos(m[i-r]) • Can define new isotropic functions • Symmetry (Reciprocity): alnm= anlm

  13. BRDF Representation: Properties • First two terms in series • 5 terms to order 2,14 to order 4, 55 order 8 • Lambertian: First term only • Retroreflection: ln • Mirror Reflection: (-1)m ln • Very similar to Fourier Series alnm = l0 n0 m0 alnm = ln alnm = (-1)mln

  14. Applications • Interpolating, Smoothing BRDFs • Fitting coarse BRDFs (e.g. CURET). Authors: Order 2 often sufficient • Extrapolation • Some BRDF models can be exactly represented (Lambertian, Opik) • Others to low order after filtering/truncation • High-order terms are typically noisy

  15. Discussion/Analysis • Strong unified foundation • Spectral analysis interesting in own right • Ringing!! Must filter • Don’t handle BRDF features well • Specularity requires many terms • Theoretically superior to spherical harmonics but in practice?

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