Last Time
• Bump Mapping
• Multi-pass algorithms
09/18/03
CS679 - Fall 2003 - Copyright Univ. of Wisconsin
Today
• Reflections
• Shadows part 1
09/18/03
CS679 - Fall 2003 - Copyright Univ. of Wisconsin
Planar Reflections (Flat Mirrors)
• Use the stencil buffer, color buffer and depth buffer
• Basic idea:
– 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
09/18/03
CS679 - Fall 2003 - Copyright Univ. of Wisconsin
Reflecting Objects
Wall Mirror
09/18/03
• 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
CS679 - Fall 2003 - Copyright Univ. of Wisconsin
Small Problem
• Reflecting changes the apparent vertex order as seen by the
viewer
– Why is this a problem?
• Reflecting the view has the same effect, but this time it also
shifts the left-right sense in the frame buffer
– Works, just harder to understand what’s happening
09/18/03
CS679 - Fall 2003 - Copyright Univ. of Wisconsin
Rendering Reflected First
• First pass:
– Render the reflected scene without mirror, depth test on
• Second pass:
– Disable the color buffer, Enable the stencil buffer to always pass but
set the buffer, Render the mirror polygon
– Now, set the stencil test to only pass points outside the mirror
– Clear the color buffer - does not clear points inside mirror area
• Third Pass:
– Enable the color buffer again, Disable the stencil buffer
– Render the original scene, without the mirror
– Depth buffer stops from writing over things in mirror
09/18/03
CS679 - Fall 2003 - Copyright Univ. of Wisconsin
Reflection Example
The stencil buffer after the
second pass
09/18/03
The color buffer after the second
pass – the reflected scene cleared
outside the stencil
CS679 - Fall 2003 - Copyright Univ. of Wisconsin
Reflection Example
The color buffer after
the final pass
09/18/03
CS679 - Fall 2003 - Copyright Univ. of Wisconsin
Making it Faster
• Under what circumstances can you skip the second pass (the
stencil buffer pass)?
• These are examples of designing for efficient rendering
09/18/03
CS679 - Fall 2003 - Copyright Univ. of Wisconsin
Making it Faster
• Under what circumstances can you skip the second pass (the
stencil buffer pass)?
– Infinite mirror plane (effectively infinite)
– Solid object covering mirror plane
• These are examples of designing for efficient rendering
09/18/03
CS679 - Fall 2003 - Copyright Univ. of Wisconsin
Reflected Scene First (issues)
• Objects behind the mirror cause problems:
– Will appear in reflected view in front of mirror
– Solution is to use clipping plane to cut away things on wrong side of
mirror
• Curved mirrors by reflecting vertices differently
• Doesn’t do:
– Reflections of mirrors in mirrors (recursive reflections)
– Multiple mirrors in one scene (that aren’t seen in each other)
09/18/03
CS679 - Fall 2003 - Copyright Univ. of Wisconsin
Rendering Normal First
• First pass:
– Render the scene without the 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
09/18/03
CS679 - Fall 2003 - Copyright Univ. of Wisconsin
Normal First Addendum
• Same problem with objects behind mirror
– Same solution
• Can manage multiple mirrors
– Render normal view, then do other passes for each mirror
– Only works for non-overlapping mirrors (in view)
– But, could be extended with more tests and passes
• A recursive formulation exists for mirrors that see other
mirrors
09/18/03
CS679 - Fall 2003 - Copyright Univ. of Wisconsin
Frame Buffer Blending
• When a fragment gets to the frame buffer, it is blended with
the existing pixel, and the result goes in the buffer
• Blending is of the form:
R S
s
r
 Rd Dr , Gs S g  Gd Dg , Bs Sb  Bd Db , As S a  Ad Da ,
– s=source fragment, d = destination buffer, RGBA color
– In words: You get to specify how much of the fragment to take, and
how much of the destination, and you add the pieces together
• All done per-channel
09/18/03
CS679 - Fall 2003 - Copyright Univ. of Wisconsin
Blending Factors
• The default is: Srgba=(1,1,1,1), Drgba=(0,0,0,0)
– Overwrite buffer contents with incoming fragment
• You can use the colors themselves as blending functions: eg
Srgba=(Rd,Gd,Bd,Ad), Drgba=(0,0,0,0)
– What use is this?
– Hint: What if there is an image in the buffer and the source is a constant gray
image? A light map?
• Common is to use the source alpha:
– Srgba=(As,As,As,As), Drgba=(1-As,1-As,1-As,1-As)
– What does this achieve? When might you use it?
• Note that blending can simulate multi-texturing with multi-pass
09/18/03
CS679 - Fall 2003 - Copyright Univ. of Wisconsin
Accumulation Buffer
• The accumulation buffer is not available for writing directly
• It is more like a place to hold and compute on pixel data
• Operations:
– Load the contents of a color buffer into the accumulation buffer
– Accumulate the contents of a color buffer, which means multiply them by a
value then add them into the buffer
– Return the buffer contents to a color buffer (scaled by a constant)
– Add or multiply all pixel values by a given constant
• It would appear that it is too slow for games
– Lots of copying data too and fro
09/18/03
CS679 - Fall 2003 - Copyright Univ. of Wisconsin
Accum. Buffer Algorithms
• Anti-aliasing: Render multiple frames with the image plane jittered
slightly, and add them together
– Hardware now does this for you, but this would be higher quality
• Motion blur: Render multiple frames representing samples in time, and
add them together
– More like strobing the object
• Depth of field: Render multiple frames moving both the viewpoint and
the image plane in concert
– Keep a point – the focal point – fixed in the image plane while things in
front and behind appear to shift
09/18/03
CS679 - Fall 2003 - Copyright Univ. of Wisconsin
Why Shadows?
• Shadows tell us about the relative locations and motions of objects
09/18/03
CS679 - Fall 2003 - Copyright Univ. of Wisconsin
Shadows and Motion
09/18/03
CS679 - Fall 2003 - Copyright Univ. of Wisconsin
Facts about Shadows
• Shadows can be considered as areas hidden from the light
source
– Suggests the use of hidden surface algorithms
• 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
• For scenes with static lights and geometry, the shadows are
fixed
– Can pre-process such cases
– Cost is in moving lights or objects
• Point lights have hard edges, and area lights have soft edges
09/18/03
CS679 - Fall 2003 - Copyright Univ. of Wisconsin
Ground Plane Shadows
• Shadows cast by point light
sources onto planes are an
important case that is relatively
easy to compute
L(directional light)
– Shadows cast by objects (cars,
players) onto the ground
(xp,yp,zp)
• Accurate if shadows don’t
overlap
– Can be fixed, but not well
(xsw,ysw,zsw)
09/18/03
CS679 - Fall 2003 - Copyright Univ. of Wisconsin
Ground Shadow Math
• The shadow point lies on the line from the light through the
vertex:
S  P L
• The shadow is on the ground, zsw=0, so =zp/zl, giving:
xsw  x p  z p zl xl ,
ysw  y p  z p zl yl
• Matrix form:
 xsw  1
 y  0
 sw   
 0  0
  
 1  0
09/18/03
0  xl zl
1  yl z l
0
0
0
0
CS679 - Fall 2003 - Copyright Univ. of Wisconsin
0  x p 
0  y p 
0  z p 
 
1  1 
Drawing the Shadow
• We now have a matrix that transforms an object into its
shadow
• Drawing the shadow:
– Draw the ground and the object
– Multiply the shadow matrix into the model transformation
– Redraw the object in gray 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)
– Works for other planes by transforming into plane space, then
shadow, then back again
– Take care with vertex ordering for the shadow (it reverses)
09/18/03
CS679 - Fall 2003 - Copyright Univ. of Wisconsin
Point Light Shadows
• Blinn ’88 gives a matrix that works for local point light
sources
– Takes advantage of perspective transformation (and homogeneous
coordinates)
 xsw   zl
y  0
 sw   
 0  0
  
 1  0
0
 xl
zl
 yl
0
0
0
1
0  xp 



0  yp
 
0  z p 
 
zl   1 
• Game Programming Gems has an approximation that does
not use perspective matrices, Chapter 5.7
09/18/03
CS679 - Fall 2003 - Copyright Univ. of Wisconsin
Todo
• By Monday, Sept 22: Lock in Stage 1
09/18/03
CS679 - Fall 2003 - Copyright Univ. of Wisconsin