Week 11 - Monday What did we talk about last time? Project 2 work - PowerPoint PPT Presentation

Week 11 - Monday

 What did we talk about last time?  Project 2 work day  Before that: environment mapping  Blinn and Newell's method  Sphere mapping  Cubic environmental mapping  Environment mapping in MonoGame

 The reflectance equation we have been studying is: ∫ = ⊗ L ( p , v ) f ( l , v ) L ( p , l ) cos θ d ω o i i i Ω  The full rendering equation is: ∫ = ⊗ − L ( p , v ) f ( l , v ) L ( r ( p , l ), l ) cos θ d ω o o i i Ω  The difference is the L o ( r ( p , l ),- l ) term which means that the incoming light to our point is the outgoing light from some other point  Unfortunately, this is all recursive (and can go on nearly forever)

 Real-time rendering uses local (non-recursive) lighting whenever possible  Global illumination causes all of our problems (unbounded object-object interaction)  Transparency  Reflections  Shadows

 We can describe a path that light L makes to the eye E using the following notation Operator Description Example Explanation Zero or more specular S * * Zero or more bounces One or more diffuse D + + One or more bounces Zero or one specular S ? ? Zero or one bounces Either a diffuse or two D | SS | Either/or specular bounces Zero or more of diffuse or ( D | S )* () Group specular

 Shadow terminology:  Occluder: object that blocks the light  Receiver: object the shadow is cast onto  Point lights cast hard shadows (regions are completely shadows or not)  Area lights cast soft shadows  Umbra is the fully shadowed part  Penumbra is the partially shadowed part

 A planar shadow occurs when an object casts a shadow on a flat surface  Projection shadows are a technique for making planar shadows:  Render the object normally  Project the entire object onto the surface  Render the object a second time with all its polygons set to black  The book gives the projection matrix for arbitrary planes

 We need to bias (offset) the plane just a little bit  Otherwise, we get z fighting and the shadows can be below the surface  Shadows can be draw larger than the plane  The stencil buffer can be used to fix this  Only opaque shadows work  Partially transparent shadows will make some parts too dark  Z -buffer and stencil buffer tricks can Hard to see example from Shogo: MAD help with this too

 Another fix for projection shadows is rendering them to a texture, then rendering the texture  Effects like blurring the texture can soften shadow  If the light source is between the occluder and the receiver, an antishadow is generated

 True soft shadows occur due to area lights  We can simulate area lights with a number of point lights  For each point light, we draw a shadow in an accumulation buffer  We use the accumulation buffer as a texture drawn on the surface  Alternatively, we can move the receiver up and down slightly and average those results  Both methods can require many passes to get good results

 You can also blur based on the amount of distance from the occluder to the receiver  It doesn't always look right if the occluder touches the receiver  Haines's method is to paint the silhouette of the hard shadow with gradients  The width is proportional to the height of the silhouette edge casting the shadow

 All you need is the appropriate matrix to flatten all the geometry of your model onto a plane Matrix shadow = Matrix.CreateShadow(Vector3.UnitY, new Plane(Vector3.UnitY, 100));  In this case, the shadow is cast from a light vector that's in positive y onto a plane with a normal that's also positive y , 100 units below the origin  All that's needed is to update the world matrix: world = world * shadow  Then draw the model with lighting off and a black color

 More on shadows  Shadow volumes  Shadow mapping  Ambient occlusion

 Start Assignment 4  Start Project 3  Keep reading Chapter 9