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1 Octrees Spatial Subdivision Subdivision algorithm Volume is - PDF document

Sep 30, 2022 •214 likes •293 views

Photon Mapping Combines backward/ reverse ray tracing Photon Mapping with stochastic ray tracing Used to simulate the interaction of light with a variety transparent substances (caustics) Glass Water Diffuse

  1. Photon Mapping  Combines “backward”/ “reverse” ray tracing Photon Mapping 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 Photon Mapping - Motivation Photon Mapping  Henrik Wann Jensen 95/96  Simulates the transport of individual photons emitted from light sources  Photons bounce off specular surfaces  Photons deposited on diffuse surfaces  Photons collected by ray tracing from eye  http://www.ypoart.com/ Without With Spatial Subdivision Spatial Subdivision  The collected photons will need to be  Subdivide your scene volume into hierarchical regions stored in an efficient, 3D accessible  Octrees  BSP Trees data structure  K-D Trees  Create a tree structure that indicates for each region:  if the region is empty  Spatial subdivision algorithms subdivide  the object present at that particular region  Used in the 3D space for quick and easy query.  Ray Tracing  Collision detection (animation)  Photon Mapping 1

  2. Octrees Spatial Subdivision  Subdivision algorithm  Volume is subdivided into 4 equal  Recursively subdivide volume regions.  If subregion is empty or contains a predefined #  Each iteration results in 8 subdivisions. of objects, then stop  Otherwise, further subdivide.  Continue until each subregion is empty or contains a predefined #of objects.  Use tree to represent subdivision hierarchy Octrees Oct(quad)trees  Subdivisions represented as a tree [Foley/Van Dam] [Watt/Watt,244] Octrees Oct(quad)trees  Quadtree applet  Images from http://www.flipcode.com/tutorials/tut_octrees.shtml http://njord.umiacs.umd.edu:1601/users/brab ec/quadtree/points/pointquad.html 2

  3. Octrees Octrees BSP Trees Spatial Subdivision  Binary Space Partitioning Trees (BSP  Octrees vs BSP Trees Trees)  Like Octrees but divides space into a pair of subregions  Subregions need not be equally spaced  Planes separating regions can be placed at object boundaries. [Watt/Watt,246] BSP Trees K-d Trees  BSP Trees – Each non-terminal node represents a single  K-d Tree is a BSP where dividing planes partitioning plane that divides space in two are axis aligned  K-d Tree applet http://donar.umiacs.umd.edu/quadtree/ points/kdtree.html [Watt/Watt,247 ] 3

  4. Spatial Subdivision Spatial Subdivision  Advantages  Octrees vs BSP trees  Efficient means for finding objects within your  BSP Trees are generally more balanced space than Octrees  Compact representation  BSP Traversal more efficient  Disadvantages  Preprocessing required  BSP Trees have additional storage  If scene changes, must rebuild your tree overhead as must store subdivision planes  Not foolproof  Now back to photon mapping Photon Mapping Photon Mapping  Pass 1 – Shoot and Store Photons  Shooting photons  photons are shot from the light into the scene.  Photons are allowed to interact with objects in the environment  Where photons fall are stored in a special data structure called a “photon map” point directional square general  1000s of photons not billions  Statistical approximation based on density [Jensen 2002] Photon Mapping Photon Map  Photon Scattering  The photon  Placed in k-d tree for efficient access [Jensen 2002] 4

  5. Photon Mapping Monte Carlo methods  Pass 2 – Gather illumination  Driven by chance / randomness  Use ray tracing  Rendering and Monte Carlo  Direct illumination determined by ray  Multiple rays per pixel tracing  See how many reach a light  Indirect illumination determined by  Multiple rays from light stochastically sampling photon map  See how many reach the eye  Gather photon within a volume in the required  Photon Mapping direction.  Goes from both sides Photon Mapping - Caustics Caustics  Pattern of light focused on a surface after having original light path bent by intermediate surface. Reflective caustics Refractive caustics Yves Poissant [Jensen] Photon Mapping Photon Mapping  Three separate photon maps  Global – photon emitted toward all objects  Caustics – specular to diffuse interactions  Volume – for volumetric effects caustic global 5

  6. Example Example -- Caustics [Jensen 1996] [Jensen 1996] The Light of Mies van der Rohe Photon Mapping in real time  But doesn’t this take a long time.  No, grasshopper…not with GPUs…  Let’s go to the video. 2000ET Want to learn more? Summary  Fixing ray tracing  Spawning complex structures (cones, cylinders, etc.)  Stochastic sampling (distributed ray tracing, monte carlo)  “backwards” ray tracing (Photon Mapping)  Questions 6

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