Normal Mapping for Precomputed Radiance Transfer PeterPike Sloan

Normal Mapping for Precomputed Radiance Transfer Peter-Pike Sloan Microsoft

Inspiration • [Mc. Taggart 04] Half-Life 2 “Radiosity Normal Mapping”

Related Work • [Willmott 99] Vector irradiance formulation of radiosity (for accelerating computation) • [Tabellion 04] Lighting model similar to above (dominant light direction) • [Good 2005] “Spherical Harmonic Light Maps”

Goal • Develop lightweight techniques to decouple normal variation (ala HL 2) – From parameterized models of lighting (PRT) – For rigid objects • Non goals – Modeling “local GI” of the bumps [Sig 05] – Masking effects – Glossy materials

PRT

PRT

PRT

Bi-Scale Radiance Transfer

Bi-Scale Radiance Transfer • l : vector = source radiance spherical function • Mp : 25 x 25 transfer matrix at point p (source → transferred incident) • q(xp) : ID map (2 D → 2 D, maps RTT patch over surface) • b(x, v) : RTT (4 D → 25 D, tabulated over small spatial patch) applies macro-scale transferred radiance to meso-scale RTT

Bi-Scale Radiance Transfer • l : vector = source radiance spherical function • Mp : 25 x 25 transfer matrix at point p (source → transferred incident) • q(xp) : ID map (2 D → 2 D, maps RTT patch over surface) • b(x, v) : RTT (4 D → 25 D, tabulated over small spatial patch) applies macro-scale transferred radiance to meso-scale RTT

Bi-Scale Radiance Transfer • l : vector = source radiance spherical function • Mp : 25 x 25 transfer matrix at point p (source → transferred incident) • q(xp) : ID map (2 D → 2 D, maps RTT patch over surface) • b(x, v) : RTT (4 D → 25 D, tabulated over small spatial patch) applies macro-scale transferred radiance to meso-scale RTT

Limitations • Expensive – Stores 64 “response vectors” that are 9 -36 D (x 3 for spectral) • Parallax mapping cheaper way of getting masking – Local radiance is too much data (9 – 36 x 3) for low res textures/per-vertex • Add constraints – Just model normal variation – Diffuse only

Diffuse + Normal Maps • Quadratic SH [Ramamoorthi 2001] Distant Lighting Environment

Diffuse + Normal Maps • Quadratic SH [Ramamoorthi 2001] Distant Radiance to Transferred Incident Radiance In local frame

Diffuse + Normal Maps • Quadratic SH [Ramamoorthi 2001] Diagonal Convolution Matrix Clamped cosine kernel

Diffuse + Normal Maps • Quadratic SH [Ramamoorthi 2001] Irradiance Environment Map

Diffuse + Normal Maps • Quadratic SH [Ramamoorthi 2001] Irradiance Environment Map

Diffuse + Normal Maps • Quadratic SH [Ramamoorthi 2001] Evaluate SH basis with normal

Concerns • Lot of data at low res – 9 x. O 2 matrices (x 3 with color bleeding) – Can compress using CPCA [Sig 03] • Too much data passed from low res to high res – Irradiance emap (27 numbers, 7 interpolators) • Alternatives – Project into analytic basis – Separable approximation

Analytic Basis Project into new basis (fewer rows)

Shifted Associated Legendre Polynomials [Gautron 2005]

Half-Life 2 Basis

Comparison PRT Gold Standard HL 2 SAL

Comparison PRT Gold Standard HL 2 SAL

Normal Mapping for PRT • Use same ideas as BRDF factorization [Kautz and Mc. Cool 1999] Bi-linear basis functions over hemisphere (4 non-zero) Matrix, rows “normal directions” columns quadratic SH light Aij equals evaluating convolved light basis function “j” in normal direction “i”

Normal Mapping for PRT

Normal Mapping for PRT • Compute SVD of A Nx 9 matrix (each column is a “normal basis” texture) 9 x 9 diagonal matrix (singular values) 9 x 9 matrix

Normal Mapping for PRT • Old equation • New equation

Normal Mapping for PRT • Use first M singular values • Mx. O 2 matrix • M channel “normal direction” texture

Pixel Shader Standard. SVDPS( VS_OUT In, out float 3 rgb : COLOR ) { float 2 Normal = tex 2 D(Normal. Sampler, In. Tex. Coord); float 2 v. Tex = Normal*0. 5 + float 2(0. 5, 0. 5); float 4 v. U = tex 2 D(USampler, v. Tex); rgb. r = dot(In. c. R, v. U); rgb. g = dot(In. c. G, v. U); rgb. b = dot(In. c. B, v. U); rgb *= tex 2 D(Albedo. Sampler, In. Tex. Coord); }

Comparison

Demo

Conclusions • Lightweight form of normal mapping for PRT – Inspired by Half-Life 2 – For static objects, diffuse only • HL 2 basis and separable basis seem to be best • Experiment with CPCA more [Sig 03] • Integrate with other techniques – Parallax mapping for masking – Ambient Occlusion for local effects

Acknowledgments • Gary Mc. Taggart for HL 2 images • Shanon Drone for Models • Paul Debevec for Light Probes