(c) 2002 University of Wisconsin Last Time An introduction to global illumination We can’t solve the general case, so we look to special cases Light paths as a way of classifying rendering algorithms: L(S|D)*E Raytracing Captures LDS*E paths: Start at the eye, any number of specular bounces before ending at a diffuse surface and going to the light Can also do LSE and LE if light source is not a point 12/10/02 (c) 2002 University of Wisconsin

(c) 2002 University of Wisconsin Today A bit more on ray-tracing Bi-directional ray-tracing Radiosity Take home point: What algorithms do what sort of light paths, and what assumptions do they make 12/10/02 (c) 2002 University of Wisconsin

(c) 2002 University of Wisconsin Mapping Techniques Raytracing provides a wealth of information about the visible surface point: Position, normal, texture coordinates, illuminants, color… Raytracing also has great flexibility Every point is computed independently, so effects can easily be applied on a per-pixel basis Reflection and transmission and shadow rays can be manipulated for various effects Even the intersection point can be modified 12/10/02 (c) 2002 University of Wisconsin

(c) 2002 University of Wisconsin Bump Mapping Examples 12/10/02 (c) 2002 University of Wisconsin

(c) 2002 University of Wisconsin Displacement Mapping Bump mapping changes only the normal, not the intersection point Silhouettes will not show bumps, even though shading does Displacement mapping actually shifts the intersection point according to a map Gives bump map effects and also correct silhouettes and self shadowing, if implemented fully 12/10/02 (c) 2002 University of Wisconsin

(c) 2002 University of Wisconsin From RmanNotes http://www.cgrg.ohio-state.edu/~smay/RManNotes/index.html 12/10/02 (c) 2002 University of Wisconsin

(c) 2002 University of Wisconsin Soft Shadows Light sources that extend over an area (area light sources) should cast soft-edged shadows Some points see all the light - fully illuminated Some points see none of the light source - the umbra Some points see part of the light source - the penumbra To ray-trace area light sources, cast multiple shadow rays Each one to a different point on the light source Weigh illumination by the number that get through 12/10/02 (c) 2002 University of Wisconsin

(c) 2002 University of Wisconsin Soft Shadows Penumbra Umbra Penumbra 12/10/02 (c) 2002 University of Wisconsin

(c) 2002 University of Wisconsin Soft Shadows All shadow rays go through No shadow rays go through Some shadow rays go through 12/10/02 (c) 2002 University of Wisconsin

Ray-Tracing and Sampling Basic ray-tracing casts one ray through each pixel, sends one ray for each reflection, one ray for each point light, etc This represents a single sample for each point, and for an animation, a single sample for each frame Many important effects require more samples: Motion blur: A photograph of a moving object smears the object across the film (longer exposure, more motion blur) Depth of Field: Objects not located at the focal distance appear blurred when viewed through a real lens system Rough reflections: Reflections in a rough surface appear blurred 12/10/02 (c) 2002 University of Wisconsin

Distribution Raytracing Distribution raytracing casts more than one ray for each sample Originally called distributed raytracing, but the name’s confusing How would you sample to get motion blur? How would you sample to get rough reflections? How would you sample to get depth of field? 12/10/02 (c) 2002 University of Wisconsin

Distribution Raytracing Multiple rays for each pixel, distributed in time, gives you motion blur Object positions have to vary continuously over time Casting multiple reflection rays at a reflective surface and averaging the results gives you rough, blurry reflections Simulating multiple paths through the camera lens system gives you depth of field 12/10/02 (c) 2002 University of Wisconsin

(c) 2002 University of Wisconsin Motion Blur 12/10/02 (c) 2002 University of Wisconsin

Distribution Raytracing Depth of Field From Alan Watt, “3D Computer Graphics” 12/10/02 (c) 2002 University of Wisconsin

(c) 2002 University of Wisconsin Missing Paths Basic recursive raytracing cannot do: LS*D+E: Light bouncing off a shiny surface like a mirror and illuminating a diffuse surface LD+E: Light bouncing off one diffuse surface to illuminate others Basic problem: The raytracer doesn’t know where to send rays out of the diffuse surface to capture the incoming light Also a problem for rough specular reflection Fuzzy reflections in rough shiny objects 12/10/02 (c) 2002 University of Wisconsin

Bi-directional Raytracing Cast rays from the light sources out into the scene When a ray hits a diffuse surface, accumulate some light there Surfaces record the amount of light that hits them Store the light in texture maps Store the light in quadtrees Store the light in photon maps Cast rays from the eye out into the scene When a ray hits a diffuse surface, look up the amount of light that hit it in the light-ray phase What paths does it capture? What sort of visual effects do you see? 12/10/02 (c) 2002 University of Wisconsin

Caustics Standard raytracer: Bi-directional raytracer Diffuse table and blue ball, mirrors left, right and back, transparent red ball Bi-directional raytracer More rays in the light pass Note the LS*DS*E paths From Alan Watt, “3D Computer Graphics” 12/10/02 (c) 2002 University of Wisconsin

(c) 2002 University of Wisconsin Refraction caustic Henrik wann Jensen, http://www.gk.dtu.dk/~hwj 12/10/02 (c) 2002 University of Wisconsin

(c) 2002 University of Wisconsin Refraction caustics Henrik wann Jensen, http://www.gk.dtu.dk/~hwj 12/10/02 (c) 2002 University of Wisconsin

(c) 2002 University of Wisconsin Still Missing… LD*E paths – Diffuse-diffuse transport Formulated and solved with radiosity methods L(S|D)*E paths Solved with Monte-Carlo renderers – very very inefficient Also solvable with multi-pass methods, but also very very inefficient, and subject to aliasing An unsolved problem 12/10/02 (c) 2002 University of Wisconsin

(c) 2002 University of Wisconsin Real World LD*E Paths From Alan Watt, “3D Computer Graphics” 12/10/02 (c) 2002 University of Wisconsin

Radiosity Assumptions All surfaces are perfectly diffuse Means that is doesn’t matter which way light hits or leaves a surface Illumination is constant over a patch Can break the world up into a discrete number of pieces Problems at sharp illumination boundaries - shadows Ways around these problems, but less efficient and less able to manage scene complexity Assumptions allow us to solve for LD*E paths 12/10/02 (c) 2002 University of Wisconsin

(c) 2002 University of Wisconsin Radiosity Example Color bleeding is extreme in this example Textures are applied after solving for illumination Some meshing artifacts are visible - note the banding around the pictures on the wall From Alan Watt, “3D Computer Graphics” 12/10/02 (c) 2002 University of Wisconsin

(c) 2002 University of Wisconsin Radiosity Meshing Each patch is colored with its illumination Note the discrete nature of the solution The previous image was obtained by pushing color to vertices and then Gourand shading From Alan Watt, “3D Computer Graphics” 12/10/02 (c) 2002 University of Wisconsin