Introduction | Crepuscular rays and Caustics

2. Introduction |Crepuscular rays and Caustics • Caustics are high intensity highlights due to convergence of light via different paths • Crepuscular rays (godrays) are formed by the in-scattering of light in dense participating media, like water • Why are godrays and caustics important? • Both phenomena present in shallow water environments • They convey the presence of a dense volume • Define the proximity and direction of surface and lighting

3. Introduction | Offline rendering • Caustics: • Bidirectional ray tracing • Particle tracing from light source (sun) • Local contribution to shading (no gathering step) • Godrays: • Ray marching - Integration of in/out-scattering functions over the line of sight in view direction. • Monte Carlo integration • Stratified sampling with constant jittering

4. Moving to Real Time | Early Approaches • Caustics • Render the caustics as an animated texture • Projective texturing • Inverse tracing of rays to a light map above water using surface vertex data • Intersect geometric light shafts (polyhedra) with receiving geometry • Godrays • Render godrays as geometry “shafts” (polyhedra) • Sample a variable density function on planes parallel to the view plane.

5. Moving to Real Time | Particle Tracing? • Generic GPU-based particle tracing: • Fully captures the effects • Unsuitable for real-time rendering (too slow) • Point-based particle tracing (splatting) • Can effectively model caustics • Replaces near-sample search (particle tracing) by point accumulation • The approach: • Considers light-space line segments • Intersects segments with Z-buffer • Accumulates point samples in frame buffer • Does not account for godrays

6. Our Method | Introduction • Specialized particle tracing • Traces particles from the light through the water surface to the underwater part of the scene • Handles both caustics and godrays • Compatible with both direct and deferred rendering schemes

7. Our Method | Overview • Render the scene (camera view)  depth buffer • Render the scene (light view)  shadow map • Create photon mask • Cast photons: • Generate coarse light-space point grid • Tesselate the grid • Cast photons and create refracted trajectories • Intersect trajectories with depth buffer  photon positions • Produce underwater godray line segments • Draw (image space splatted) photons  caustics • Draw (image space weighted) godrays • Filter caustics and godrays • Combine results Mask

8. Frame Preparation • Rendering: • The scene is normally rendered • We record the frame buffer (in FBO) • The shadow map of the “sun” light source is captured • The above steps are standard to any rendering engine • Photon (shadow) mask: • The shadow map is compared with the water level • No photons will be cast for lit points above water level (outside the water volume) • Saves on calculations • Ensures proper shadowing for floating props Depth buffer Shadow map Mask

9. Photon Tracing | Photon generation (in light space) • Render a coarse grid of points • In a geometry shader: • Tesselate grid • Generate primary ray • Produce refracted ray • Calculate intersection point between refracted ray and shadow map

10. Photon Tracing | Intersection estimation • Uses an Newton-Rhapson-like image space (shadow map) estimator • Approximates the intersection point in two iterations: Water surface intersection A B Water surface intersection Initial estimate d second estimate Water surface intersection Initial estimate projection projection d final point

11. Rendering the Caustics | Splatting • Splatting replaces the photon storage and search stage of conventional photon mapping • Photons are transformed to screen space and rendered as points • We splat the photons by perspectively varying the point primitive size: • Account for perspective foreshortening • Ensure adequate blending for photons near view plane • Avoid excessive overlap for distant photons • Points are attenuated according to distance from water surface (absorption) γ=9.2W/sr

12. Rendering the Caustics | Splatting

13. Rendering the Godrays • Godrays are rendered as line primitives in screen space • They are attenuated per fragment accounting for: • Fragment-to-eye absorption (out-scattering) • Surface-to-fragment absorption (out-scattering) • Light-to-viewing direction contribution (in-scattering) • Mie scattering is modeled by the Henyey-Greenstein phase function dfromViewer Line frags

14. Post-Filtering • In low-intensity areas (poor photon concentration), aliasing may occur • The same goes for the godrays • Both buffers are post-filtered to spread the intensity • We use a rotating-kernel joint bilateral gaussian filter • Kernel size is modulated by depth

15. Post-Filtering | Caustics Unfiltered Filtered

16. Post-Filtering | Godrays Unfiltered Filtered

17. Putting it All Together • Godrays + caustics + filtering + SSAO + shadows: 1440X850 @ 60+ fps • 800X600 @ 110+ fps

18. Thank you! The work presented in this paper is funded by the Athens University of Economics and Business Special Account for Research Grants (EP-1600-10/00-1)