Photon Mapping Combines backward/ reverse ray tracing with - PDF document

Photon Mapping Photon Mapping  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 1

Photon Mapping - Motivation Without With 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/ 2

Spatial Subdivision  The collected photons will need to be stored in an efficient, 3D accessible data structure  Spatial subdivision algorithms subdivide the 3D space for quick and easy query. Spatial Subdivision  Subdivide your scene volume into hierarchical regions  Octrees  BSP Trees  K-D Trees  Create a tree structure that indicates for each region:  if the region is empty  the object present at that particular region  Used in  Ray Tracing  Collision detection (animation)  Photon Mapping 3

Spatial Subdivision  Subdivision algorithm  Recursively subdivide volume  If subregion is empty or contains a predefined # 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  Volume is subdivided into 4 equal regions.  Each iteration results in 8 subdivisions. 4

Octrees [Foley/Van Dam] Oct(quad)trees  Subdivisions represented as a tree [Watt/Watt,244] 5

Oct(quad)trees  Quadtree applet http://donar.umiacs.umd.edu/quadtree/ points/prquad.html Octrees  Images from http://www.flipcode.com/tutorials/tut_octrees.shtml 6

Octrees Octrees 7

BSP Trees  Binary Space Partitioning Trees (BSP 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. Spatial Subdivision  Octrees vs BSP Trees [Watt/Watt,246] 8

BSP Trees  BSP Trees – Each non-terminal node represents a single partitioning plane that divides space in two [Watt/Watt,247 ] K-d Trees  K-d Tree is a BSP where dividing planes are axis aligned  K-d Tree applet http://donar.umiacs.umd.edu/quadtree/ points/kdtree.html 9

Spatial Subdivision  Advantages  Efficient means for finding objects within your space  Compact representation  Disadvantages  Preprocessing required  If scene changes, must rebuild your tree  Not foolproof Spatial Subdivision  Octrees vs BSP trees  BSP Trees are generally more balanced than Octrees  BSP Traversal more efficient  BSP Trees have additional storage overhead as must store subdivision planes  Now back to photon mapping 10

Photon Mapping  Pass 1 – Shoot and Store 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”  1000s of photons not billions  Statistical approximation based on density Photon Mapping  Shooting photons point directional square general [Jensen 2002] 11

Photon Mapping  Photon Scattering [Jensen 2002] Photon Map  The photon  Placed in k-d tree for efficient access 12

Photon Mapping  Pass 2 – Gather illumination  Use ray tracing  Direct illumination determined by ray tracing  Indirect illumination determined by stochastically sampling photon map  Gather photon within a volume in the required direction. Monte Carlo methods  Driven by chance / randomness  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 13

Photon Mapping - Caustics  Pattern of light focused on a surface after having original light path bent by intermediate surface. [Jensen] Caustics Reflective caustics Refractive caustics Yves Poissant 14

Photon Mapping  Three separate photon maps  Global – photon emitted toward all objects  Caustics – specular to diffuse interactions  Volume – for volumetric effects Photon Mapping caustic global 15

Example [Jensen 1996] Example -- Caustics [Jensen 1996] 16

The Light of Mies van der Rohe 2000ET Photon Mapping in real time  But doesn’t this take a long time.  No, grasshopper…not with GPUs…  Let’s go to the video. 17

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 18