Computer Graphics Mirror and Shadows Taku Komura Lecture 16

Today Mirrors Shadows How to render the scene Using the stencil buffer Overview Projective shadows Shadow texture Shadow volume Shadow map Lecture 16

Planar Reflections (Flat Mirrors)‏ Basic idea: Drawing a scene with mirrors! We need to draw all the stuff around the mirror We need to draw the stuff in the mirror, reflected, without drawing over the things around the mirror Key point: You can reflect the viewpoint about the mirror to see what is seen in the mirror, or you can reflect the world about the mirror Lecture 16

Reflecting Objects If the mirror passes through the origin, and is aligned with a coordinate axis, then just negate appropriate coordinate Otherwise, transform into mirror space, reflect, transform back Wall Mirror Lecture 16

We need to use the “Stencil Buffer” The stencil buffer acts like a paint stencil - it lets some fragments through but not others It stores multi-bit values You specify two things: The test that controls which fragments get through The operations to perform on the buffer when the test passes or fails Lecture 16

Stencil Tests You give an operation, a reference value, and a mask Operations: Always let the fragment through Never let the fragment through Logical operations between the reference value and the value in the buffer: <, <=, =, !=, >, >= Lecture 16

Color Buffer, Z-Buffer Color Buffer (frame buffer)‏ The buffer in which the RGB data is saved Z-Buffer (depth buffer)‏ The depth to the object is saved Depth test can be conducted; check whether the new object is farther or closer than the depth in the buffer Only update the color buffer when the depth is smaller Lecture 16

Stencil Operations Specify three different operations Operations are: If the stencil test fails If the stencil passes but the depth test fails If the stencil passes and the depth test passes Operations are: Keep the current stencil value Zero the stencil Replace the stencil with the reference value Increment the stencil Decrement the stencil Invert the stencil (bitwise)‏ Lecture 16

Reflection Example mirror Lecture 16

Normal first, reflected area next First pass: Render the scene without the mirror For each mirror Second pass: Clear the stencil, render the mirror, setting the stencil if the depth test passes Third pass: Clear the depth buffer with the stencil active, passing things inside the mirror only Reflect the world and draw using the stencil test. Only things seen in the mirror will be drawn Combine it with the scene made during the first pass The stencil buffer after the second pass The color buffer after the second pass – the reflected scene cleared outside the stencil Lecture 16

Multiple mirrors Can manage multiple mirrors Render normal view, then do other passes for each mirror A recursive formulation exists for mirrors that see other mirrors After rendering the reflected area inside the mirror surface, render the mirrors inside the mirror surface, and so on Lecture 16

Today Mirrors Shadows How to render the scene Using the stencil buffer Overview Projective shadows Shadow texture Shadow volume Shadow map Lecture 16

Why Shadows? Shadows tell us about the relative locations and motions of objects Lecture 16

Shadows and Motion Humans conceive the motion of objects using shadows Demo movie http://gandalf.psych.umn.edu/users/kersten/kersten-lab/images/ball-in-a-box.mov Lecture 16

Facts about Shadows Shadows can be considered as areas hidden from the light source A shadow on A due to B can be found by projecting B onto A with the light as the center of projection Suggests the use of projection transformations Point lights have hard edges, and area lights have soft edges Lecture 16

Soft and hard shadows Soft shadows Hard shadows Lecture 16

Today Mirrors Shadows How to render the scene Using the stencil buffer Overview Projective shadows Shadow texture Shadow volume Lecture 16

Ground Plane Shadows L(light position)‏ Shadows cast by point light sources onto planes are an important case that is relatively easy to compute Shadows cast by objects (cars, players) onto the ground (xl,yl,zl)‏ (xp,yp,zp)‏ (xsw,ysw,zsw)‏ Lecture 16

Point Light Shadows Light source Object Floor Lecture 16

Point Light Shadows Blinn ’88 gives a matrix that works for local point light sources Takes advantage of perspective transformation (and homogeneous coordinates)‏ Lecture 16

Drawing the Shadow We now have a matrix that transforms an object into its shadow Drawing the shadow: Draw the polygon Multiply the shadow matrix into the model transformation Redraw the object in grey with blending on Tricks: Lift the shadow a little off the plane to avoid z-buffer quantization errors (can be done with extra term in matrix)‏ Lecture 16

Lifting the shadow above the surface Light Viewer Z equal with hit polygon Z-buffer quantization errors Z above hit polygon Apparent shadow too big Lecture 16

Point Light Shadows : problem shadows can only be cast onto planes and not on arbitrary objects. the resulting shadows generated have hard edges If there is a texture on the floor, grey shadows look bad If we use blending, the shadow part with multiple polygons overlapping will look darker Lecture 16

Improving Planar Projected Shadows with Stencil Only pixels tagged with the ground plane’s unique stencil value will be updated when the shadow is rendered. When a shadow is rendered, the stencil value is set to zero subsequent pixel updates will fail Lifting the shadows above the floor not necessary, stencil buffer used to avoid rendering the floor over the shadow region Lecture 16

Shadow Texture Use a shadow image as a projective texture Generate an image of the occluder from the light’s view and color it grey Project this image onto the background and render it using texture mapping Can render shadows over curved surfaces Lecture 16

Shadow Texture : Drawbacks The occluder and receiver must be specified Occluding objects cannot shadow themselves Magnification of textures Resolution must be adapted Lecture 16

Adaptive Shadow Mapping The resolution of the shadow maps is lower than that of the rendered image Many box shape artifacts Need to use shadow map of higher resolutions Changing the resolution the shadow map according to the viewpoint [Fernando et al. 2001] Lecture 16

Today Mirrors Shadows How to render the scene Using the stencil buffer Overview Projective shadows Shadow texture Shadow volume Shadow map Lecture 16

Shadow Volume In the real world, the shadow cast by an object blocking a light is a volume, not merely some two-dimensional portion of a plane. An algorithm that models shadow regions as volumes. Lecture 16

Using Shadow Volumes to Render Shadows Two stages Compute the shadow volume formed by a light source and a set of shadowing objects. Check whether the point is inside / outside the shadow volume inside  shadowed Outside  illuminated by light source Lecture 16

Lecture 16

How to decide inside or out Get the polygonal boundary representation for the shadow volume Render the scene with the lights enabled Clear the stencil buffer, and render the shadow volume Whenever a rendered fragment of the shadow volume is closer than the depth of the other objects, invert a bit in the stencil value for that pixel After rendering, if the bit is on, then it means the fragment is inside the shadow volume, so must be shadowed Otherwise outside the shadow Lecture 16

Advantage / Disadvantages of Shadow Volume It can be used on general-purpose graphics hardware Only using the stencil buffer Disadvantage Bottle neck at the rasterizer Many shadow volumes covering many pixels Lecture 16

Shadow Mapping A method using the Z-buffer Render the scene from the light source using the Z- buffer algorithm The Z-buffer contains the distance to the object shadow depth map / shadow buffer Render the scene from the view point If the rendered vertex is farther away from the value in the Z-buffer, it is in the shadow Lecture 16

Shadow Map Checking whether Va,Vb is closer to the light Lecture 16

Shadow Map Preparation Prepare a depth buffer for each light Render the scene from the light position Save the depth information in the depth buffer Rendering the scene Render the objects; when ever rendering an object, check if it is shadowed or not by transforming its coordinate into the light space After the transformation, if the depth value is larger than that in the light’s depth buffer it should be shadowed Lecture 16

Shadow Map Advantage Don’t need a stencil buffer When there are many shadows, it is faster then shadow volume Disadvantage Less accurate than the shadow volume – why? Lecture 16

Soft shadowing by multiple point light sources Model an area light source as a collection of point light sources Can be used with both planar projected shadows approach or shadow volume approach Additive blending is used to accumulate the contribution of each light. The softness of the shadow depends on an adequate number of samples. The time to render the scene increases linearly with the number of samples used to approximate an area light source. Artifacts are introduced if not enough samples are used Lecture 16

Other techniques to generate soft shadow Using convolutions - Creating a hard edged shadow texture and render it a number of times by jittering the location, and finally filtering it Lecture 16

Summary Mirrors Shadows How to render the scene Using the stencil buffer Shadows Overview Projective shadows Shadow texture Shadow volume Shadow map Lecture 16