Assignments • New due dates – Checkpoint 7 / Code – tonight Photon Mapping • Drop code in mycourses drop box. • Renderman – Due Nov 8 th (new date) – Server up and running. – Images on Web site – Code in mycourses drop box. – DID I SAY VALUABLE PRIZES!!!! Projects Finals date • Approx 17 projects • For last day of presentations • Listing of projects now on Web • Presentation schedule • Friday, November 18 th – Presentations (20 min max) • 12:30pm – 2:30pm – Last 3 classes (week 10 + finals week) • 70-1445 – Sign up • Email me with 1 st , 2 nd , 3 rd choices • First come first served. • Times on SCHEDULE • Presentations all signed up!!! Logistics Computer Graphics as Virtual Photography • Final Report real camera photo Photographic Photography: – Introduction scene (captures processing print light) – Approach Taken – Implementation Details – Results processing – Appendix/Code • Presentation – 10-15 minutes camera Computer 3D synthetic tone model Graphics: models reproduction image • All project material due Friday, Nov 18 th (focuses simulated – No late submission lighting) • else I can’t get your grades in! 1
Two Pass Method Components of Phong Illumination • Remember the Phong Illumination Model • Specular – Dependent upon incoming and outgoing ∑ ∑ = + • + • k L ( V ) k L k L ( S N) k L ( R V) e direction a a d i i s i i i i – Mirror-like reflection ambient diffuse specular • Diffuse • Most complete local illumination – Assumes equal reflectance in all directions approximation. – BDRF is constant 1. Why a Two-Pass Global Illumination Method? Which Global Illumination Technique? • Ray Tracing – Good for specular reflections – Bad for diffuse reflections – View Dependent – Computationally intensive • Radiosity – Good for diffuse reflections – Bad for specular reflections – View independent [Cohen85] – Even more computationally intensive [Heckbert84] • A two-pass method gives us the best of both worlds (std ray tracing) Two Pass Method Two Pass Method • Four mechanisms of light transport between two • Pass 1: View independent (radiosity) surfaces • Pass 2: View dependent (ray tracing) BRDF Diffuse Specular Diffuse to Specular to to Diffuse Specular to Diffuse Specular (std radiosity) [Wallace87] 2
Two Pass Method - Preprocess Two Pass Method - Preprocess • Pass 1: Use hemi-cube radiosity method • Recall: – View independent pass – Form factors give fraction of light emitted at – Will provide diffuse reflections for all objects one patch that arrive at another patch – Already handles diffuse-to-diffuse reflections • Modification: – Basic algorithm is modified to account for – Increase form factor for patch to account for • Diffuse reflections from specular sources additional light arriving at the point via • Diffuse transmission specular reflection. • Handles curved surfaces (Wallace) – And transmission (Sillion extended to all surface types) Two Pass Method - Preprocess Two Pass Method – Preprocessing Results Like calculating reflection • Form Factor Modification For each surface, the diffuse intensity emitted by the surface has been calculated, whether light is received from diffuse or specular sources. [Wallace87] Two Pass Method - Pass Two Two Pass Method - Pass Two Diffuse-to-specular • Pass 2: Ray Tracing • Ideally, would consider incoming light from all directions that contribute to specular component. – View dependent pass • In reality, the light contributing MOST HEAVILY to – Calculation per pixel limits work specular reflection comes from direction of incident – Ray tracing already accounts for specular-to- ray. specular • This allows limiting integration to solid angle over – Must be modified to accurately account for which the weighted intensity is significant, rather than diffuse-to-specular whole hemisphere. 3
Two Pass Method - Pass Two The Reflection Frustum The Reflection Frustum • Sampling intensities arrive through reflection frustum • Light is collected from a solid angle • Incoming specularity is obtained recursively, surrounding the ray of incidence reducing resolution each level • The smaller angle, the more mirror-like (material properties) • Solid angle is approximated by point samples • Light to be considered for specular reflection is determined by a weighted average of the sampled rays [Wallace87] The Reflection Frustum Two Pass Method • Reflection frustum - example • Acts like integration with BDRF providing pre- computed importance weights • Used a 10 x 10 pixel array • Used z-buffer • Diffuse component - Gouraud shading • Anti-aliasing performed by jittered rotation of frustum • Solution similar to that used in distributed ray tracing [Wallace87] Two Pass Method - Example Two Pass Method - Summary • Rendering in Two Passes • Pass 1: Radiosity – Considers diffuse-to-diffuse reflections – Considers specular-to-diffuse reflections • Pass 2: Ray Tracing – Considers diffuse-to-specular reflections – Considers specular-to-specular reflections • The total light emitted at a point is – Diffuse component, as calculated in Pass 1, plus – Specular component, as calculated in Pass 2 Perfectly diffuse floors Floors after “polishing” [Wallace87] 4
Results Results [Wallace87] [Wallace87] Two Pass Method - Example Ray Tracing • Integrated aspects of light and object interaction that had formerly been handled by separate algorithms: – Hidden surface removal – Reflection – Refraction – Shadows Full solution Without diffuse Diffuse to diffuse added – Global specular interaction Turner Whitted [Wallace87] Ray Tracing – Avoiding Ray Traced Look Ray Tracing - Problems • Object - ray intersection • Avoiding that “ray traced look” , i.e., handle • Ray traced images are point sampled diffuse interaction – “Too sharp” (super real) – “wrong image” – Ray tracing is point sampling – Sharp shadows – Sharp Reflection/Refraction • 1 ray per pixel • Multiple reflections especially are too sharp – Assumes pixel is a single point – Aliasing – Assumes pin hole camera • Doesn’t handle major light transport functions • 1 ray for transmission & reflection – Diffuse interaction – Assumes all reflection is specular – Scattering of light – Assumes that BRDF for all incoming directions is single – Caustics out going direction • Computation time 5
The Rendering Equation Ray Tracing – Avoiding Ray Traced Look • Local vs Global Illumination Models • Problem = ε + ε + ε + ε + … – Only considering single path of light to eye for 2 3 I g g ( Rg ) g ( Rg ) g ( Rg ) each pixel. direct 1st scattering 2nd scattering 3rd scattering – Only considering rays in perfectly reflective and transmissive directions. Local illumination - only considers direct component • Some approaches Global illumination - also considers other scattered – Trace objects other than rays component – Stochastic sampling Indirect lighting Indirect Lighting • The ambient kludge – Used to approximate light in those latter term of the rendering equation expansion Classic ray tracing Using photon mapping Photon Mapping Photon Mapping - Motivation • Combines “backward”/ “reverse” ray tracing with stochastic ray tracing • Used to simulate the interaction of light with a variety transparent substances (caustics) – Glass – Water – Diffuse Inter-reflections between illuminated objects – Effects of particulate matter • Smoke • Water vapor Without With 6
Photon Mapping Photon Mapping • Pass 1 – Shoot and Store Photons • Henrik Wann Jensen 95/96 – photons are shot from the light into the scene. • Simulates the transport of individual photons – Photons are allowed to interact with objects in emitted from light sources the environment • Photons bounce off specular surfaces – Where photons fall are stored in a special data • Photons deposited on diffuse surfaces structure called a “photon map” • Photons collected by ray tracing from eye – 1000s of photons not billions • Statistical approximation based on density • http://www.ypoart.com/ Photon Mapping Photon Mapping • Shooting photons • Photon Scattering point directional square general [Jensen 2002] [Jensen 2002] Photon Map Photon Mapping • The photon • Pass 2 – Gather illumination – Use ray tracing – Direct illumination determined by ray tracing – Indirect illumination determined by stochastically sampling photon map • Placed in k-d tree for efficient access 7
Monte Carlo methods Photon Mapping - Caustics • Pattern of light focused on a surface after having • Driven by chance / randomness original light path bent by intermediate surface. • Rendering and Monte Carlo – Multiple rays per pixel • See how many reach a light – Multiple rays from light • See how many reach the eye – Photon Mapping • Goes from both sides [Jensen] Caustics Photon Mapping • Three separate photon maps – Global – photon emitted toward all objects – Caustics – specular to diffuse interactions – Volume – for volumetric effects Reflective caustics Refractive caustics Yves Poissant Photon Mapping The Light of Mies van der Rohe caustic global 2000ET 8
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