11/2/2010. In the last lecture. Monte-Carlo Ray Tracing : Path Tracing. Today. Shadow ray towards the light at each vertex. Path Tracing : algorithm

Transcription

1 Comuter Grahics Global Illumination: Monte-Carlo Ray Tracing and Photon Maing Lecture 11 In the last lecture We did ray tracing and radiosity Ray tracing is good to render secular objects but cannot handle indirect diffuse reflections Radiosity can render indirect diffuse reflections but not secular reflections Both can be combined to synthesize hotorealistic images But radiosity is very slow and roblems with arallelisation 2 Taku Komura And cannot handle caustics well Today Other ractical methods to synthesize hoto-realistic images Monte-Carlo Ray Tracing Path Tracing Bidirectional Path Tracing Photon Maing Monte-Carlo Ray Tracing : Path Tracing Start from the eye When hitting a diffuse surface, ick one ray at random Otherwise, follow the ordinary raytracing rocedure Trace many aths er ixel ( er ixel) by Kajiya, SIGGRAPH Shadow ray towards the light at each vertex Cast an extra shadow ray towards the light source at each ste in ath Produce a shadow ray 5 Path Tracing : algorithm Render image using ath tracing for each ixel color = 0 For each samle ick ray in ixel color = color + trace(ray) ixel_color = color/#samles trace(ray) find nearest intersection with scene comute intersection oint and normal color = shade (oint, normal) return color Shade ( oint, normal ) color = 0 for each light source test visibility on light source if visible color=color+direct illumination color = color + trace ( a randomly reflected ray) return color 6 1

2 Path tracing : roblems Vulnerable to noise need many samles Using too few aths er ixel result in noise Difficulty rendering caustics - aths traced only from the camera side The ath needs to go through a number of secular surfaces before hitting the light Less likely to haen Examles 7 Jensen, Stanford 8 Comuting the ixel color Bidirectional Path Tracing Send aths from light source, record ath vertices Send aths from eye, record ath vertices Connect every vertex of eye ath with every vertex in light ath Lafortune & Willems, Comugrahics 93, Veach & Guibas, EGRW 94 The colour of the ixel can be comuted by the weighted sum of contributions from all aths 9 10 In what case it works better than ath tracing? Caustics Indoor scenes where indirect lighting is imortant Bidirectional methods take into account the inter-reflections at diffuse surfaces When the light sources are not easy to reach from the eye Summary for Monte Carlo Ray tracing Can simulate caustics Can simulate bleeding Requires a lot of samles er ixel

3 Today : Global Illumination Methods Monte-Carlo Ray Tracing Photon Maing Photon Maing A fast, global illumination algorithm based on Monte-Carlo method 1. Casting hotons from the light source, and 2. saving the information of reflection in the hoton ma, then 3. render the results A stochastic aroach that estimates the radiance from limited number of samles 13 htt:// Photon Maing A two ass global illumination algorithm First Pass - Photon Tracing Second Pass - Rendering Photon Tracing The rocess of emitting discrete hotons from the light sources and tracing them through the scene Photon Emission Photon Scattering A hoton s life begins at the light source. Different tyes of light sources Brighter lights emit more hotons Emitted hotons are scattered through a scene and are eventually absorbed or lost When a hoton hits a surface we can decide how much of its energy is absorbed, reflected and refracted based on the surface s material roerties 3

4 What to do when the hotons hit surfaces Attenuate the ower and reflect the hoton For arbitrary BRDFs Use Russian Roulette techniques Decide whether the hoton is reflected or not based on the robability Review : Bidirectional Reflectance Distribution Function (BRDF) The reflectance of an object can be reresented by a function of the incident and reflected angles This function is called the Bidirectional Reflectance Distribution Function (BRDF) where E is the incoming irradiance and L is the reflected radiance Arbitrary BRDF reflection Can randomly calculate a direction and scale the ower by the BRDF Russian Roulette If the surface is diffusive+secular, a Monte Carlo technique called Russian Roulette is used to robabilistically decide whether hotons are reflected, refracted or absorbed. Produce a random number between 0 and 1 Determine whether to transmit, absorb or reflect in a secular or diffusive manner, according to the value Diffuse and secular reflection If the hoton is to make a diffuse reflection, randomly determine the direction If the hoton is to make a secular reflection, reflect in the mirror direction Probability of diffuse and secular reflection, and absortion Probability of reflection can be the maximum energy in any colour band The robability of diffuse reflection is Similarly, the robability of secular reflection is 4

5 Power adjusted after reflectance The ower Pref of the reflected hoton is: Pref,sr = Pinc,r sr / Ps Pref,sg = Pinc,g sg / Ps Pref,sb = Pinc,b sb / Ps where Pinc is the ower of the incident hoton. The above equation is for secular reflection, but so the same for diffusive reflection Photon Ma When a hoton makes a diffuse bounce, the ray intersection is stored in memory 3D coordinates on the surface Colour intensity Incident direction The data structure of all the hotons is called Photon Ma The hoton data is not recorded for secular reflections Second Pass Rendering Finally, a traditional ray tracing rocedure is erformed by shooting rays from the camera At the location the ray hits the scene, a shere is created and enlarged until it includes N hotons Radiance Estimation The radiance estimate can be written by the following equation N Φ L ( x, ω) f ( x, ω, ω) r x : f : BRDF A : = 1 location the ray hits the scene ω :direction towards the camera ω :incident vector of hoton r Φ = : ower of hoton Area of the circle r πr 2 ( x, ω ) A Saving hotons: KD tree The hoton mas are classified and saved in a KD-tree KD-tree : dividing the samles at the median The median samle becomes the arent node, and the larger data set form a right child tree, the smaller data set form a left child tree Further subdivide the children trees Can efficiently find the neighbours when rendering the scene Saving hotons: Satial Hashing Produce a 3D grid Create a hash function that mas each grid to a list that saves the hotons Scan the hotons in the list to find those close to the samle oint 5

6 NN-search in the grids Decide the maximum radius of search Examine the distance between the samle oint and the hotons in the grid Gradually increase the radius, search in all the reachable grids until all the hotons are found Suitable for hardware imlementation Photon Maing on Programmable Grahics Hardware, Proceedings of the ACM SIGGRAPH/EUROGRAPHICS Conference on Grahics Hardware, , 2003 Precision The recision of the final results deends on the number of hotons emitted the number of hotons counted for calculating the radiance htt://grahics.ucsd.edu/~henrik/animation s/jensen-the_light_of_mies_small.mg By hotons and 50 samles(left), and hotons and 500 samles (right) htt://grahics.ucsd.edu/~henrik/animation s/jensen-the_light_of_mies_small.avi Summary Photon Maing A stochastic aroach that estimates the radiance from a limited number of hotons Requires less comutation comaring to ath tracing Readings Realistic Image Synthesis Using Photon Maing by Henrik Wann Jensen, AK Peters Global Illumination using Photon Mas (EGRW 96) Henrik Wann Jensen Caustics Generation by using Photon Maing, Presentation by Michael Kaiser and Christian Finger A Practical Guide to Global Illumination using Photon Mas Siggrah 2000 Course 8 htt://grahics.stanford.edu/courses/cs348b-01/course8.df 6