Real-Time ShadowsLast Time?ScheduleQuestions?TodayWhy are Shadows Important?Shadows as a Depth CueFor Intuition about Scene LightingShadows as the Origin of PaintingShadows and ArtSlide 11ShadowsSoft ShadowsSlide 14Shadows in Ray TracingTraditional Ray TracingRay Tracing + Soft ShadowsSlide 18Slide 19Cast Shadows on Planar SurfacesLimitations of Planar ShadowsSlide 22Texture MappingSlide 24Shadow/View DualityFake Shadows using Projective TexturesShadow mapsShadow MappingShadow Map Look UpShadow MapsLimitations of Shadow Maps1. Field of View Problem2. The Bias (Epsilon) Nightmare2. Bias (Epsilon) for Shadow Maps3. Shadow Map AliasingShadow Map FilteringPercentage Closer FilteringSlide 38Projective Texturing + Shadow MapShadows in ProductionSlide 41Slide 42Shadow VolumesSlide 44Slide 45Stencil BufferSlide 47Shadow Volumes w/ the Stencil BufferIf the Eye is in Shadow...1. Test Eye with Respect to Volumes2. Clip the Shadow Volumes3. "Z-Fail" Shadow VolumesSlide 53Optimizing Shadow VolumesLimitations of Shadow VolumesSlide 56Next Time:MIT EECS 6.837, Durand and CutlerReal-Time ShadowsMIT EECS 6.837, Durand and CutlerLast Time?•The graphics pipeline•Clipping & rasterization of polygons•Visibility — the depth buffer (z-buffer)MIT EECS 6.837, Durand and CutlerSchedule•Quiz 2: Thursday November 20th, in class(two weeks from Thursday)•Project Presentations (to staff): December 1st - 5th (~ 4 weeks) •Project Report due: Tuesday December 9th(5 weeks from today)MIT EECS 6.837, Durand and CutlerQuestions?MIT EECS 6.837, Durand and CutlerToday•Why are Shadows Important?•Shadows & Soft Shadows in Ray Tracing•Planar Shadows•Shadow Maps•Shadow VolumesMIT EECS 6.837, Durand and CutlerWhy are Shadows Important?•Depth cue•SceneLighting•Realism•Contact pointsMIT EECS 6.837, Durand and CutlerShadows as a Depth CueMIT EECS 6.837, Durand and CutlerFor Intuition about Scene Lighting•Position of the light (e.g. sundial)•Hard shadows vs. soft shadows•Colored lights•Directional light vs. point lightMIT EECS 6.837, Durand and CutlerShadows as the Origin of PaintingMIT EECS 6.837, Durand and CutlerShadows and Art•Only in Western pictures (here Caravaggio)MIT EECS 6.837, Durand and CutlerToday•Why are Shadows Important?•Shadows & Soft Shadows in Ray Tracing•Planar Shadows•Shadow Maps•Shadow VolumesMIT EECS 6.837, Durand and CutlerShadows•One shadow ray per intersection per point light sourceno shadow raysone shadow rayMIT EECS 6.837, Durand and CutlerSoft Shadows•Caused by extended light sources•Umbra –source completely occluded•Penumbra –Source partially occluded•Fully litMIT EECS 6.837, Durand and CutlerSoft Shadows•Multiple shadow rays to sample area light sourceone shadow raylots of shadow raysMIT EECS 6.837, Durand and CutlerShadows in Ray Tracing•Shoot ray from visible point to light source•If blocked, discard light contribution•Optimization?–Stop after first intersection (don’t worry about tmin)–Coherence: remember the previous occluder,and test that object firstMIT EECS 6.837, Durand and CutlerTraditional Ray TracingMIT EECS 6.837, Durand and CutlerRay Tracing + Soft ShadowsMIT EECS 6.837, Durand and CutlerQuestions?MIT EECS 6.837, Durand and CutlerToday•Why are Shadows Important?•Shadows & Soft Shadows in Ray Tracing•Planar Shadows•Shadow Maps•Shadow VolumesMIT EECS 6.837, Durand and CutlerCast Shadows on Planar Surfaces•Draw the object primitives a second time, projected to the ground planeMIT EECS 6.837, Durand and CutlerLimitations of Planar Shadows•Does not produce self-shadows, shadows cast on other objects, shadows on curved surfaces, etc.MIT EECS 6.837, Durand and CutlerToday•Why are Shadows Important?•Shadows & Soft Shadows in Ray Tracing•Planar Shadows•Shadow Maps–Texture Mapping–Shadow View Duality•Shadow VolumesMIT EECS 6.837, Durand and CutlerTexture Mapping•Don't have to represent everything with geometryMIT EECS 6.837, Durand and CutlerTexture Mapping•Like wallpapering or gift-wrapping with stretchy paper•Curved surfaces require extrastretching or cutting•More on this in a couple weeks...MIT EECS 6.837, Durand and CutlerShadow/View Duality•A point is lit if it is visible from the light source•Shadow computation similar to view computationMIT EECS 6.837, Durand and CutlerFake Shadows using Projective Textures•Separate obstacle and receiver•Compute b/w image of obstacle from light•Use image as projective texture for each receiverImage from light source BW image of obstacle Final imageFigure from Moller & Haines “Real Time Rendering”MIT EECS 6.837, Durand and CutlerShadow maps•In Renderman–(High-end production software)MIT EECS 6.837, Durand and CutlerShadow Mapping•Texture mapping with depth information•≥ 2 passes through the pipeline–Compute shadow map (depth from light source) –Render final image(check shadow map to see if points are in shadow)Figure from Foley et al. “Computer Graphics Principles and Practice”MIT EECS 6.837, Durand and CutlerShadow Map Look Up•We have a 3D point (x,y,z)WS•How do we look up the depth from the shadow map?•Use the 4x4 perspective projection matrix from the light source to get (x',y',z')LS•ShadowMap(x',y') < z'?Foley et al. “Computer Graphics Principles and Practice”(x,y,z)WS(x',y',z')LSMIT EECS 6.837, Durand and CutlerShadow Maps•Can be done in hardware•Using hardware texture mapping–Texture coordinates u,v,w generated using 4x4 matrix–Modern hardware permits tests on texture valuesMIT EECS 6.837, Durand and CutlerLimitations of Shadow Maps1. Field of View2. Bias (Epsilon)3. AliasingMIT EECS 6.837, Durand and Cutler1. Field of View Problem•What if point to shadow is outside field of view of shadow map?–Use cubical shadow map–Use only spot lights!MIT EECS 6.837, Durand and Cutler2. The Bias (Epsilon) Nightmare•For a point visible from the light sourceShadowMap(x’,y’) z’•How can we avoid erroneous self-shadowing?–Add bias (epsilon)MIT EECS 6.837, Durand and Cutler2. Bias (Epsilon) for Shadow MapsShadowMap(x’,y’) + bias < z’Choosing a good bias value can be very trickyCorrect image Not enough bias Way too much biasMIT EECS 6.837, Durand and Cutler3. Shadow Map Aliasing•Under-sampling of the shadow map•Reprojection aliasing – especially bad when the camera & light are pointing towards each otherMIT EECS 6.837, Durand and CutlerShadow Map Filtering•Should
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