Lecture 15: Many Lights. CS 6620, Spring 2009 Kavita Bala Computer Science Cornell University. Many Lights

Transcription

1 Lecture 15: Many Lights CS 6620, Spring 2009 Kavita Bala Computer Science Cornell University Many Lights Most techniques work for a single light source Many light sources For environment maps For indirect illumination Treat it is a single integration domain Importance sample lights Importance sampling (with visibility) still hard problem 1

2 Ward 91 Research on many lights Shirley, Wang, Zimmerman 9 Fernandez, Bala, Greenberg 02 Donikian, Fernandez.. 06 Lightcuts 05 Shirley, Wang, Zimmerman 9 Try to avoid linear cost of evaluating lights Separate lights into Set of important lights (a small set) Set of dim lights (large set) Construct pdf using: all important lights 1 out of all the dim lights Importance sample these lights 2

3 Shirley, Wang, Zimmerman 9 Region of influence for important lights Octree cells in region of influence have light in important set However, the partitioning into important and dim sets remains hard Also, still are not taking visibility into account Lightcuts [SIGGRAPH 05, 06] Walter, Fernandez, Arbree, Bala Efficient, accurate complex illumination Environment map lighting & indirect Textured area lights & indirect Time 111s Time 98s (60x80, Anti-aliased, Glossy materials) 3

4 Scalable Scalable solution for many point lights Thousands to millions Sub-linear cost Time (secs) Standard Ward Lightcut Number of Point Lights Tableau Scene GI as many-point lights Approach: unify illumination Area lights HDR environment maps Sun & sky light Indirect illumination Convert to point lights P = L(...)dl hemisphere( indirect+ direct ) = k i I i i alllights Kitchen light: area, sun/sky, indirect

5 Convert Illumination HDR environment map Apply captured light to scene Convert to directional point lights using [Agarwal et al. 2003] Indirect Illumination Convert indirect to direct illumination using Instant Radiosity [Keller 97] Caveats: no caustics, clamping, etc. More lights = more indirect detail Lightcuts Problem Camera 5

6 Illumination Equation result = M i G i V i I i Σlights Geometric term Material term Light intensity Visibility term Currently support diffuse, phong, and Ward Illumination Equation result = M i G i V i I i Σlights Geometric term Material term Light intensity Visibility term 6

7 Illumination Equation result = M i G i V i I i Σlights Geometric term Material term Light intensity Visibility term Key Concepts Light Cluster Approximate many lights by a single brighter light (the representative light) 7

8 Key Concepts Light Cluster Light Tree Binary tree of lights and clusters Clusters Individual Lights Light Cluster Light Tree A Cut Key Concepts A set of nodes that partitions the lights into clusters 8

9 Simple Example #1 #2 #3 # Representative Light Light Tree 1 Clusters Individual Lights Three Example Cuts Three Cuts #1 #2 # #1 #3 # #1 #

10 Three Example Cuts Three Cuts #1 #2 # #1 #3 # #1 # Good Bad Bad Three Example Cuts Three Cuts #1 #2 # #1 #3 # #1 # Bad Good Bad 10

11 Three Example Cuts Three Cuts #1 #2 # #1 #3 # #1 # Good Good Good Algorithm Overview Pre-process Convert illumination to point lights Build light tree For each eye ray Choose a cut to approximate the illumination 11

12 Algorithm Overview Pre-process Convert illumination to point lights Build light tree For each eye ray Choose a cut to approximate the local illumination Cost vs. accuracy Avoid visible transition artifacts Threshold visibility ΔL L L+ΔL ΔL L = kl Weber s s law TVI functions L 12

13 Perceptual Metric Weber s Law Contrast visibility threshold is fixed percentage of signal Used 2% in our results Ensure each cluster s error < visibility threshold Transitions will not be visible Used to select cut Cluster Approximation result ~ M j G j V j I i Σlights Cluster j is the representative light 13

14 Cluster Error Bound error < M ub G ub V ub I i Σlights Cluster Bound each term Visibility <= 1 (trivial) Intensity is known Bound material and geometric terms using cluster bounding volume ub == upper bound Cut Selection Algorithm Start with coarse cut (eg, root node) Cut 1

15 Cut Selection Algorithm Select cluster with largest error bound Cut Cut Selection Algorithm Refine if error bound > 2% of total Cut 15

16 Cut Selection Algorithm Cut Cut Selection Algorithm Cut 16

17 Cut Selection Algorithm Cut Cut Selection Algorithm Repeat until cut obeys 2% threshold Cut 17

18 Lightcuts (128s) Error Reference (1096s) Error x16 Kitchen, 388K polygons, Kavita 608 Bala, Computer lights Science, (72 area Cornell sources) University Kitchen, 388K polygons, 59,672 Lights 18

19 Kitchen, shadow ray false color Combined Illumination Lightcuts 128s 608 Lights (Area lights only) Avg. 259 shadow rays / pixel Lightcuts 290s Lights (Area + Sun/sky + Indirect) Avg. 78 shadow rays / pixel (only 5 to area lights) 19

20 Avg. shadow rays per eye ray 6 (0.03%) Grand Central, 1.6M polygons, 13 6 lights, (Area+Sun/sky+Indirect) Avg. shadow rays per eye ray 17 (0.13%) Tableau, 630K polygons, lights, (EnvMap+Indirect) 20

21 Avg. shadow rays per eye ray 17 (0.003%) Bigscreen, 628K polygons, lights, (Area+Indirect) P = Problem: Many Lights and GI L(...)dl hemisphere lightsources ( indirect+ direct) P eye Many Lights + env map Indirect Illumination + sun/sky Grand Central Station Kalabsha temple 21

22 AA, Volumetric, Motion Blur, DOF aperture time volume Pixel = pixelarea hemisphere L(...) Volumetric: Fog Motion Blur Depth-of-Field eye pixel eye pixel How to scale to complexity? If you can t see it, don t compute it Kalabsha temple, Egypt 22

23 More complexity is Less visually salient More is Less Direct only (relative cost 1x) Direct+Indirect+Fog (1.8x) Direct+Indirect (1.3x) Direct+Indirect+Fog+Motion (2.2x) 23

24 Multidimensional LC[SIG 06] aperture time Pixel = Discretize full integral into 2 point sets Light points (L) Gather points (G) volume pixelarea hemisphere L(...) Light points eye Pixel t = 0.81 t = 0.3 Gather points Multidimensional problem Sum of all pairs of gather and light points Σ Pixel = S j k ji I i (j,i) GxL Gather strength Weight of ray Light intensity Time (secs) Standard Ward Lightcut Light points Number of Point Lights Gather points 2

25 Product Graph Explicit hierarchy would be too expensive Use implicit hierarchy: product graph L0 L1 L2 L3 L L6 L5 eye G0 G1 L0 L1 L2 L3 Gather tree Light tree X G2 G0 G1 Product Graph Cartesian product of two trees (gather & light) L6 L L5 L0 L1 L2 L3 L0 L L1 L6 L2 L5 L3 Light tree X = G0 G2 G2 G1 G0 G1 Gather tree Refine cut until perceptual threshold Generalize cut, representative, error bounds 25

26 Product Graph L6 L L5 L0 L1 L2 L3 Light tree X = G0 G2 L0 L L1 L6 L2 L5 L3 G2 G1 G0 G1 Gather tree Refine cut until perceptual threshold Generalize cut, representative, error bounds Summary Unified illumination handling Scalable solution for many lights Locally adaptive representation (the cut) Perceptual visibility metric Time (secs) Standard Ward Lightcut Number of Point Lights 26