A system for interactive display and rendering of BRDF models Adrià Forés Herranz Advisors: Sumanta N. Pattanaik Carles Bosch
Importance of materials
Overview Analytic models General Measured Display representation data Simulated data Fitting Render
Outline • Previous Work • Input Models • Display • Fitting • Rendering • Simulation • Conclusions and Future Work
Outline • Previous Work • Input Models Analytic • Display models General Measured Display • Fitting representation data Simulated • Rendering data Fitting Render • Simulation • Conclusions and Future Work
Outline • Previous Work • Input Models • Display • Fitting • Rendering • Simulation • Conclusions and Future Work
Previous Work • Currently there does not exist a system to work on materials • bv - a BRDF browser
Previous Work • Currently there does not exist a system to work on materials • bv - a BRDF browser
BRDF • Bidirectional reflectance function (BRDF) ‣ 4 Dimensional function ‣ Spherical coordinates
BRDF: Properties • Helmholtz reciprocity • Energy conservation • Isotropy vs Anisotropy
Input Models Analytic models General Measured Display representation data Simulated data Fitting Render
Analytic models General Measured Display representation data Analytical Models Simulated data Fitting Render • Lambertian • Phong • Lafortune • Ward • Ashikhmin • Cook-Torrance
Analytic models General Measured Display representation data Analytical Models Simulated data Fitting Render • Lambertian • Phong • Lafortune • Ward • Ashikhmin • Cook-Torrance
Analytic models General Measured Display representation data Analytical Models Simulated data Fitting Render • Lambertian • Phong • Lafortune • Ward • Ashikhmin • Cook-Torrance
Analytic models General Measured Display representation data Analytical Models Simulated data Fitting Render • Lambertian • Phong • Lafortune • Ward • Ashikhmin • Cook-Torrance
Analytic models General Measured Display representation data Analytical Models Simulated data Fitting Render • Lambertian • Phong • Lafortune • Ward • Ashikhmin • Cook-Torrance
Analytic models General Measured Display representation data Real World Materials Simulated data Fitting Render
Analytic models General Measured Display representation data Real World Materials Simulated data Fitting Render + + =
Analytic models General Measured Display representation data Measured Data Simulated data Fitting Render • Gonioreflectometer Main idea [DVGNK99] [MWL*99]
Analytic models General Measured Display representation data Measured data Simulated data Fitting Render • MERL library [MPBM03] ‣ 330 images for each material
Analytic models General Measured Display representation data Measured data Simulated data Fitting Render • MPI’s Car Paint library [GCG*05] ‣ 256 images for each material
Analytic models General Measured Display representation data Simulated Simulated data Fitting Render • Some attempts has been made [CMS87,WAT92] • Mostly in optics literature • e.g. Scatmech C++ library
Overview Analytic models General Measured Display representation data Simulated data Fitting Render
Analytic models General Measured Display representation data Display Simulated data Fitting Render • Display the BRDF shape to understand how a material reflects the incident light. • 4 Dimensional Function. ‣ Given a fixed incoming direction (2D), the result in all the outgoing directions is represented (2D). • Allow the user to change the incoming direction
Analytic models General Measured Display representation data Display Simulated data Fitting Render • Geodesic hemisphere • Vertex displacement to match the BRDF shape: ‣ BRDF evaluated per vertex, only possible with analytical models ‣ Adaptive texture-based evaluation: A texture indexed by ϴ and Φ stores the precomputed BRDF ‣ Simply by using points
Analytic models General Measured Display representation data Display - Analytic Simulated data Fitting Render
Analytic models General Measured Display representation data Display - Simulated Simulated data Fitting Render
Analytic models General Measured Display representation data Display - Measured Simulated data Fitting Render
Overview Analytic models General Measured Display representation data Simulated data Fitting Render
Analytic models General Measured Display representation data Fitting Simulated data Fitting Render • Approximate a set of data with an analytical model • Non-linear optimizer ‣ Levenberg-Marquardt • The user is able to set the initial guess values for the optimization step to see how they approximate the data
Analytic models High Computational General Measured Display representation data Simulated data Fitting Render Cost • System of equations defined by the input data ‣ e.g. a material from the MERL library defines 16384 data points • The number of parameters to optimize grow with the number of lobes used
Analytic models General Measured Display representation data Non-linear estimation Simulated data Fitting Render • Combination of linear and non-linear steps during the iterative optimization process ‣ Linear optimization for the scaling factors ‣ Non-linear optimization for the lobe parameters
Analytic models General Measured Display representation data Display Fitting Results Simulated data Fitting Render
Overview Analytic models General Measured Display representation data Simulated data Fitting Render
Analytic models General Measured Display representation data Rendering Simulated data Fitting Render • Point light • Environment light ‣ HDR Environment Map [CK07a, CK07b]
Analytic models General Measured Display representation data Rendering Simulated data Fitting Render • Point light • Environment light ‣ HDR Environment Map [CK07a, CK07b]
Analytic models General Measured Display representation data Rendering Simulated data Fitting Render • Point light • Environment light ‣ HDR Environment Map [CK07a, CK07b]
Analytic models General Measured Display representation data Point light Simulated data Fitting Render • Compute the BRDF on the fragment shader
Analytic models Lighting equation General Measured Display representation data Simulated data Fitting Render • General • Discretized
Analytic models Monte Carlo General Measured Display representation data Simulated data Fitting Render Integration
Analytic models General Measured Display representation data Importance Sampling Simulated data Fitting Render • Choose a few random samples • Selected according to the PDF
Analytic models Mipmap Filtered General Measured Display representation data Simulated data Fitting Render Samples
Analytic models Rendering a fitted General Measured Display representation data Simulated data Fitting Render material
Overview Analytic models General Measured Display representation data Simulated data Fitting Render
Analytic models General Measured Display representation data Origin of BRDFs Simulated data Fitting Render • surface interaction • subsurface interaction
Analytic models General Measured Display representation data Origin of BRDFs Simulated data Fitting Render • surface interaction • subsurface interaction
Analytic models General Measured Display representation data Origin of BRDFs Simulated data Fitting Render • surface interaction • subsurface interaction
Analytic models General Measured Display representation data Origin of BRDFs Simulated data Fitting Render • surface interaction • subsurface interaction
Analytic models General Measured Display representation data Origin of BRDFs Simulated data Fitting Render • surface interaction • subsurface interaction
Analytic models General Measured Display representation data Simulation Simulated data Fitting Render • Given a material structure, obtain its BRDF Material structure Reflected Ray Tracer BRDF shape directions Light direction • Performing this operation with different light directions the full BRDF is obtained • Light is assumed to be parallel as the simulation is done at microscopic level
Analytic Height Field Simulation models General Measured Display representation data Simulated data Fitting Render Material Structure • Relief Map
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