10/29/2010. Rendering techniques. Global Illumination. Local Illumination methods. Today : Global Illumination Modules and Methods

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1 Rendeing techniques Compute Gaphics Lectue 10 Can be classified as Local Illumination techniques Global Illumination techniques Global Illumination 1: Ray Tacing and Radiosity Taku Komua 1 Local Illumination methods Global Illumination Consides light souces and suface popeties only. Phong Illumination, Phong shading, Gouaud Shading Using techniques like Shadow maps, shadow volume, shadow textue fo poducing shadows Vey fast Used fo eal-time applications such as 3D compute games Methods that simulate not only the diect illuminations but also the indiect illuminations Monte-Calo ay tacing Radiosity, Photon Mapping Global illuminations can handle Reflection (one object in anothe) Refaction (Snell s Law) Shadows Colou bleeding unde the same famewok Requies moe computation and is slow 4 Today : Global Illumination Modules and Methods Ray Tacing [Appel 68] Ray Tacing Radiosity 5 Ray tacing is one of the most popula methods used in 3D compute gaphics to ende an image Good at simulating specula effects Tacing the path taken by a ay of light though the scene Rays ae eflected, efacted, o absobed wheneve intesect an object Can poduce shadows 6 1

2 Sometimes the ay misses all of the objects: sometimes the ay will hit an object: 7 8 Shadow If the ay hits an object, we want to know if that point on the object is in a shadow. So, when the ay hits an object, a seconday ay, called a "shadow" ay, is shot towads the light souces Shadow(2) If this shadow ay hits anothe object befoe it hits a light souce, then the fist intesection point is in the shadow of the second object. We only apply the ambient tem fo that light souce. Othewise do the local Phong Illumination and expand the Ray Tee 9 10 Shadow (3) Fist Intesection point in the shadow of the second object Reflected Ray Also, when a ay hits an object, a eflected ay is geneated which is tested against all of the objects in the scene

3 Contibution fom the eflected ay If the eflected ay hits an object then a local illumination model is applied at the point of intesection and the esult is caied back to the fist intesection point. Tansmitted Ray If the intesected object is tanspaent, then a tansmitted ay is geneated and tested against all the objects in the scene Contibution fom the tansmitted ay As with the eflected ay, if the tansmitted ay hits an object then a local illumination model is applied at the point of intesection and the esult is caied back to the fist intesection point. Ray Tee [Whitted 80] Fie off seconday ays fom suface that ay intesects. Towads Light Souce(s) : shadow ays. L (shadow feeles) In the eflection diection : eflection ays, R In a diection dictated by Snell s Law : tansmitted ays, T N R V (Viewe diection) L θ θ T α Recusive ay tee. Reflection and Tansmission Rays spawn othe ays. Shadow ays used to check occlusion / local illumination of diffuse sufaces Bightness ecusively computed by I = Ilocal + K * R + Kt * T whee Ilocal is the colo by local illumination, R is the colo by eflection, T is the colo by tansmission, and K, Kt ae coefficients The complete set of ays is called a Ray Tee. L 1 T 1 L 3 Light Souce ay detemines colou of cuent object. Ray tee depth 1. Note only ambient shade on mio and teapot Viewpoint R 3 L 2 R 1 T 2 R

4 Ray tee depth 2. Note only ambient shade on eflection of mio and teapot. Ray tee depth 3. Note only ambient shade on eflection of mio in teapot Ray tee depth 4. Ray tee depth 5. Note ambient shade on eflection of teapot in eflection of mio in teapot Ray tee depth 6. Ray tee depth

5 When to stop? When the a ay hits a pefectly diffusive suface Fo specula suface, we can define a fixed depth I = I R = I R' = I M local local local + K R + K T + K R + K T + K R + K T t t t 25 Adaptive tee depth contol. Calculate maximum contibution of a ay to a pixels final value. Fo example, if the suface is moe diffusive, smalle influence fom the eflection ay Multiply contibution of ay s ancestos down the tee. Stop when below some theshold I = I + K I + K ( I + K ( I + K (...)))) local ( local local local In the case above, stop when K K K K... < theshold Hall, R. A. and Geenbeg D.P., "A Testbed fo Realistic Image Synthesis", IEEE Compute Gaphics and Applications, 3(8), Nov., 1983 Examples of Ray-taced images. Ray-polygon intesection. Not so easy! 1.Detemine whethe ay intesects polygon s plane. 2.Detemine whethe intesection lies within polygon. Easiest to detemine (2) with an othogaphic pojection onto the neaest axis and the 2D point-in-polygon test. Then calculate the baycentic coodinates z Ray 27 y x 28 Acceleating Ray Taces Ray Tacing is vey time-consuming because of intesection calculations Solutions: Use faste machines Use specialized hadwae, especially paallel pocessos. Use pespective pojection fo the fist ay Use a lage theshold fo adaptive depth tee contol Reduce the numbe of ays / polygon intesection check Bounding volumes Reducing Ray-Object Intesections Bounding Volumes: Enclose goups of objects in sets of hieachical bounding volumes Octee Fist test fo intesection with the bounding volume Then only if thee is an intesection, against the objects enclosed by the volume

6 Ray Tacing : Dawbacks Colou Bleeding Can we poduce soft shadows? Can we poduce bleeding effects? Can we ende caustics? Can we geneate shadows of efactive objects? Caustics Tough Cases Caustics Light focuses though a specula suface onto a diffuse suface Which diection should seconday ays be cast to detect caustic? 33 Bleeding Colo of diffuse suface eflected in anothe diffuse suface Which diection should seconday ays be cast to detect bleeding? Tacking the light souce afte hitting diffuse suface is not vey easy 34 Today : Global Illumination Modules and Methods Ray Tacing Radiosity 35 The Radiosity Method (84 -) Can poduce soft shadows, colou bleeding View independent the endeing calculation does not have to be done although the viewpoint is changed The basic method can only handle diffuse colo need to be combined with aytacing to handle specula light 6

7 The Radiosity Model The Radiosity Model(2) At each suface in a model the amount of enegy that is given off (Radiosity) is compised of the enegy that the suface emits intenally (E), plus the amount of enegy that is eflected off the suface (ρh) The amount of incident light hitting the suface can be found by summing fo all othe sufaces the amount of enegy that they contibute to this suface Fom Facto (Fij) the faction of enegy that leaves suface i and lands on suface j Between diffeential aeas, it is cosφi cosφ j dai daj π 2 The oveall fom facto between i and j is = i j i Fij 2 cosφ cosφ j dai daj π The Radiosity Matix The adiosity equation now looks like this: The deived adiosity equations fom a set of N linea equations in N unknowns. This leads nicely to a matix solution: Radiosity Steps: 1 - Geneate Model 2 - Compute Fom Factos 3 - Solve Radiosity Matix 4 Rende Only if the geomety of the model is changed must the system stat ove fom step 1. If objects ae moved, stat ove fom step 2. If the lighting o eflectance paametes of the scene ae modified the system may stat ove fom step 3. If the view paametes ae changed, the system must meely e-ende the scene (step 4). Radiosity Featues: The faces must be subdivided into small patches to educe the atifacts The computational cost fo calculating the fom factos is expensive Quadatic to the numbe of patches Solving fo Bi is also vey costly Cannot handle specula light 7

8 Recommended Reading Foley at al. Chapte 16, sections 16.11, and Intoductoy text Chapte 14 sections 14.6 and An Efficient Ray-Polygon Intesection by Didie Badouel fom Gaphics Gems I Most gaphics texts cove ecusive ay tacing. 43 8

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