Distributed Area Lighting

1. Distributed Area Lighting Joon Jae Lee Keimyung University

2. Overview • Motivation • Compact Lights • Distributed Lights

3. General Case • Light comes from all positions and from all directions • We need approximations in order to model in finite time • Choices are: • Represent lighting envt as small number of compact light sources • Model a real nature of light sources

4. Compact Lighting Model • Well known, understood • Light characterized solely by direction vector • Shadows have sharp edges • stencils, horizon maps, etc.

5. Shadowing • Cast shadows • Self shadowing

6. Motivation • Most common case • everything is a secondary reflector • and therefore a light source

7. Distributed Lighting Models • Environment Mapping • Specular—common, understood • blur somewhat for lower power • Diffuse—less commonly used • use normal instead of reflection vector • blur texture—prefilter to integrate

8. Environment map types • Cube • LonLat • Hemisphere • Paraboloid • Dual paraboloid • Spherical Harmonics • etc.

9. Hardware Environment Maps • see Debevec • Facilitated by next generation hardware

10. Model Elements Sky Color Ground Color Hemisphere Model Final Color

11. Diffuse Envt Mapped Bunny

12. Diffuse Environment Mapped Head

13. Distributed Light Model Hemisphere of possible incident light directions q Surface Normal Microfacet Normal - defines axis of hemisphere

14. Procedural Environment Maps • Generate environment maps by: • rendering into cube map • if you have cube map hardware, okay • otherwise, use other method • Rendering into other maps types is possible too • especially the the light sources

15. Procedural Hemisphere Map

16. Procedural Diffuse Maps • Hemisphere Lighting • Spherical Harmonic Lighting

17. Hemisphere Lighting • Simplest area light model • Fairly accurate model for sky/ground case • Somewhat generalizable to other profiles • Building/canyon version

18. 2-Hemisphere Model Sky Color q Ground Color

19. Area Light Shadows • Self occlusion not well represented • Representation is a scalar • At each point • Ray-trace to generate

20. Distributed Light Model Hemisphere of possible incident light directions q Microfacets Other facets can shadow this one: Occlusion

21. Approximating Occlusion • Need to determine extent of shadowing • Cast rays out from facet to see which ones intersect the object

22. Ray Cast Occlusion Model Microfacet Some rays hit this object, others miss it

23. Occlusion Representations • Can store result in various ways • Compute ratio of hits / misses • Occlusion Factor • A single scalar parameter • Should weight with cosine • Use to blend in shadow color • Sufficient for hemisphere lighting

24. Model Elements Sky Color Ground Color Object Color Sphere Model Occlusion Factor Final Color

25. Occlusion Factor Absent

26. Occlusion Factor Present

27. Occlusion Factor Absent

28. Occlusion Factor Present

29. Occlusion Factor Absent

30. Occlusion Factor Present

31. Lightwave Image

32. Hi-Res

33. Per Pixel Occlusion Factor • Estimate area based on adjacent pixels in height field • Should cast to all pixels in image • Should ray-cast bumps and pixels at the same time

34. Pixel Occlusion

35. Other Occlusion Methods • What if we need to produce sharp shadows? • e.g. to model effect of compact lights • Compute cone of visibility • = cone of unocclusion • Store as more than a scalar • put axis of cone (xyz) + cos cone angle in alpha • There are other representations • C. F. Heidrichs et al. “Ellipses”

36. Occlusion Cone Model Axis Ang Surface Normal Fit cone to horizon between hits and misses

37. Occlusion Cone Shadows • Each sample has a cone • Check to see if light ray is in it • If ( L dot Axis > cosAng ) • If so then • It is lit • Else • It is in shadow • Need not be Boolean • For softer edged shadows

38. Horizon Maps • Enable Per-Pixel shadowing • Also per-vertex for terrain engines • Representation is a set of scalar samples • 1 for each direction • Cone is ~ octahedral

39. Standard Bump Map

40. Horizon Map Shadows

41. Horizon Maps: Occlusion Cones • Horizon maps represent occlusion cones as 8-sided figures • Cone is parameterized as 8 values • N, NE, E, SE, S, SW, W, NW • Works fine for compact lights • Scalar factor works for hemispheres • What about lights in between?

42. Spherical Harmonics • Another way to parameterize information on a sphere • Analogous to Fourier Transforms, but over surface of a sphere

43. Spherical Harmonics

44. Spherical Harmonic Environment Maps • Represent environment map as set of colors for each harmonic • Very compact representation • 16 colors sufficient for diffuse • Very efficient math to use • Just multiply-adds or dot products • Simple to generate procedurally • Easy to generate from image data

45. Buddha No Shadow

46. Environment + Scalar Occlusion

47. Procedural with No Shadow

48. Procedural with Occlusion

49. Spherical Harmonic Surface Response • What about occlusion/shadow terms? • Representation is set of SH scalar weights • Store set at each point • Pixel or vertex • Ray-trace to generate • Convert to SH basis

50. Environment + Scalar Occlusion