•1Slide 1 Lecture 19Copyright Amitabh VarshneyRadiosity• Local Lighting (OpenGL). – Captures interaction of light source and surface, but nothing else in environment.• Shadow maps– Light source gated by environment.• Ray tracing– Captures light rays striking surface from light source orfrom specular or refractive direction.• What is missing?– Light striking diffuse material from non-sources.Slide 2 Lecture 19Copyright Amitabh VarshneyDoes this matter?Is it black here?•2Slide 3 Lecture 19Copyright Amitabh Varshney(Wikipedia)Slide 4 Lecture 19Copyright Amitabh VarshneyRadiosity• Global illumination for diffuse surfaces• Models view-independent illumination• Diffuse/soft shadows, color bleeding•3Slide 5 Lecture 19Copyright Amitabh VarshneyLocal IlluminationSlide 6 Lecture 19Copyright Amitabh VarshneyRay-tracing-like Illumination•4Slide 7 Lecture 19Copyright Amitabh VarshneyRadiosity-like IlluminationSlide 8 Lecture 19Copyright Amitabh VarshneyRadiosity IlluminationImage: Lightscape Inc.•5Slide 9 Lecture 19Copyright Amitabh VarshneyRadiosity• Light energy per unit time per unit area• Based on conservation of light energy• Assumes area light sourcesSlide 10 Lecture 19Copyright Amitabh VarshneyRadiosity EquationFor every surface patch i :Bi= Ei+ iHi, where Biis the radiosity, Eiis the emissivity, iis the coefficient of reflectivity, and Hiis the incident energy per unit time per unit area for patch i .Ei= 0 for all surfaces that are not light sources•6Slide 11 Lecture 19Copyright Amitabh VarshneyModeling Light ReflectionsSlide 12 Lecture 19Copyright Amitabh VarshneyForm F actor• Fji= Fraction of light energy leaving surface j and arriving at surface i• Ai Fij= AjFji• Sum of Fijfor all j’s is 1•7Slide 13 Lecture 19Copyright Amitabh VarshneyRadiosity EquationAssuming n surface patches in the environment:Hi= j=1 to n( FjiBjAj/Ai ) = j=1 to n(FijBj) Therefore, the radiosity equation is:Bi= Ei+ iHi= Ei+ ij=1 to n(FijBj), orBi -ij=1 to n(FijBj) = EiSlide 14 Lecture 19Copyright Amitabh VarshneyRadiosity EquationAssuming n surface patches in the environment:Hi= j=1 to n(FijBj) Therefore, the radiosity equation is:Bi= Ei+ iHi= Ei+ ij=1 to n(FijBj), orBi -ij=1 to n(FijBj) = Ei•8Slide 15 Lecture 19Copyright Amitabh VarshneyRadiosity Equation1 –1F11–1F12 …–1F1n–2F2 1 –2F22 …–2F2n : : :: : :–nFn1 –nFn2 …1 –nFnnB1B2::BnE1E2::En=Fij’s are the form factors that are dependent on scene geometryand can be determined (Fii= 0 for planar polygons).Slide 16 Lecture 19Copyright Amitabh VarshneyRadiosity Equation• Directly solving the linear system of equations on the previous slide: A b = e is expensive– Gaussian Elimination method takes O(n3) time• In practice we take advantage of the structure of A (strictly diagonally dominant) to efficiently solve this system•9Slide 17 Lecture 19Copyright Amitabh VarshneyBut first ! let us see how to compute Form FactorsSlide 18 Lecture 19Copyright Amitabh VarshneyHemi-Cube Form Factors•10Slide 19 Lecture 19Copyright Amitabh VarshneyProgressive Refinement Radiosity• This approach computes an approximate solution of the system of linear equations A b = e• The basic approach is to identify the brightest patch in the environment and shoot (distribute) its energy to the other patches that can see it. • This is equivalent to computing only those rows of the form-factor matrix A that correspond to the brightest patches. • In practice, this approach results in a fast convergence to the solution without computing all the rows of ASlide 20 Lecture 19Copyright Amitabh VarshneyProgressive Refinement RadiosityInitially, Bi= Eiwhile max(Bi) > { select patch i with maximum unshot energy Bifor each patch j do{ R = jBiFijAi/AjBj= Bj+ R (unshot energy for patch j)Bj= Bj+ R (accumulated energy) Bi= 0}•11Slide 21 Lecture 19Copyright Amitabh Varshney(Wikipedia)Slide 22 Lecture 19Copyright Amitabh VarshneyRadiosity Artefacts• Light Leaks• Hemicube aliasing • Light distribution at patches, whereas vertices are used for shading• Mesh discretization (solution: adaptive meshing)• Need a separate specular pass to capture specular