1. Computer Graphics Mirror and Shadows
Taku Komura
Lecture 16

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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. Reflection Example
mirror
Lecture 16

10. 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

11. 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

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

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

14. Shadows and Motion Humans conceive the motion of objects using shadows
Demo movie
Lecture 16

15. 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

16. Soft and hard shadows
Soft shadows Hard shadows
Lecture 16

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

18. 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

19. Point Light Shadows
Light source
Object
Floor
Lecture 16

20. 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

21. 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

22. 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

23. 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

24. 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

25. 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

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

27. 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

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

29. 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

30. 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

31. Lecture 16

32. 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

33. 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

34. 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

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

36. 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

37. 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

38. 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

39. 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

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