Transcript #11: Lighting - UCSD Computer Graphics Lab

#14: Ray Tracing II &
Antialiasing
CSE167: Computer Graphics
Instructor: Ronen Barzel
UCSD, Winter 2006
Outline for today
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Speeding up Ray Tracing
Antialiasing
Stochastic Ray Tracing
1
Where we are now
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Ray tracing:
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cast primary rays from eye through pixels
intersect with objects
cast rays towards lights to determine shadowing
recursively cast reflection and refraction rays
Qui ckTi me™ and a
TIFF (Uncompressed) decompressor
are needed to see this pictur e.
QuickTime™ and a
TIFF(Uncompres sed) decompressor
are needed t o see this pict ure.
Quick Time™ a nd a
TIFF ( Un compr ess ed ) de co mp res sor
ar e n eed ed to s ee this pic tur e.
2
Need for acceleration structures
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Lots of rays:
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Infeasible to test every object for intersection
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Scenes can contain millions or billions of primitives
Ray tracers need to trace millions of rays
This means zillions of potential ray-object intersections
Just looping through all objects*rays would take days
Not even counting time to do the intersection testing or illumination
Acceleration structures
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Major goal: minimize number of intersection tests
• Tests that would return false (no intersection)
• Tests that would return an intersection that’s not closest to origin
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Core approach: Hierarchical subdivision of space
• Can reduce O(N) tests to O(log(N)) tests
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(Other acceleration techniques too…
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beam tracing, cone tracing, photon maps, …)
3
Bounding Volume Hierarchies
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Enclose objects with hierarchy of simple shapes
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Same idea as for frustum culling
Test ray against outermost bounding volume
• If ray misses bounding volume, can reject entire object
• If ray intersects volume, recurse to child bounding volumes
• When reaching the leaves of the hierarchy, intersect with primitives
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Can keep track of current nearest intersection along ray
• If bounding volume is farther away that, no need to test intersection
4
Culling complex objects or groups
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If an object is big and complex, it’s possible that only parts
of it will be in view.
Or if we have groups of objects, it’s possible that entire
groups will be out of view.
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Want to be able to cull the whole group quickly
But if the group is partly in and partly out, want to be able to cull
individual objects.
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E.g. Sphere Hierarchy
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Test for intersection against outermost sphere
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E.g. Sphere Hierarchy
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Outer sphere hits: test children
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ignore child spheres that don’t intersect
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E.g. Sphere Hierarchy
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Test contents of bottom-most spheres
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(Actually, hierachy would probably go down a few more levels)
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Bounding Volume Hierarchies
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Spheres good example of the concept
Spheres not used much in practice:
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No great techniques to automatically construct a good sphere hierarchy
Spheres tend to overlap, so we would do redundant intersection tests
Other bounding volumes
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Axis-aligned bounding boxes (AABBs)
Oriented bounding boxes (OBBs)
Can be good individual models
Not great for organizing entire scenes
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Octrees
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Start by placing a cube around the entire scene
If the cube contains “too many” primitives (say, 10)
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split equally into 8 nested cubes
recursively test and possibly subdivide each of those cubes
More regular structure than the sphere tree
Provides a clear rule for subdivision and no overlap between cells
This makes it a better choice than sphere usually
But still not ideal; lots of empty cubes
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Octree
(2D illustration is a quadtree)
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KD Trees
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Place a box (not necessarily a cube) around the entire scene
If the box contains too many primitives:
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Adapts to irregular geometry
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Tighter fit than octree
Pretty good for ray tracing
Main drawback: tree can get deep
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Split into two boxes
Boxes need not be equal
Split in the x, y, or z direction, at some arbitrary position within the box
Heuristics to choose the split direction & position
Lots of time traversing the tree itself
(called “KD” because it works the same in any number of dimensions)
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KD Tree
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BSP Trees
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Binary Space Partitioning (BSP) tree
Start with all of space
If there are too many objects, split into two subspaces:
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Similar to KD tree: recursively splits space into two (unequal) parts
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choose a plane to divide the space in two
the plane can be placed anywhere and oriented any direction
heuristics to choose a good plane
recurse to children
Potential to more tightly bound objects
Harder to choose splitting plane
Harder to work with arbitrary-shaped regions
In practice, BSP trees tend to perform well for ray tracing
14
BSP Tree
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Uniform Grids
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Divide space into a uniform grid, instead of hierarchically
Use ray marching to test the cells
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Don’t need to test intersection against each grid cell
Find cell where ray enters grid
Test all objects in current cell
• If intersected an object, we’re done
• Else, move to the next cell the ray passes through
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Uniform grids can be very fast, or can be slow and a waste of memory
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Depends on distribution of objects into cells
Need to choose grid size properly
No good distribution if scene has large variation in object size and location
Uniform grids not a practical general-purpose solution
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Uniform Grid
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Ray Marching
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Hierarchical Grids
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Start with a uniform grid
If any cell has too many primitives
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subdivide that cell into a grid
subgrid can have any number of cells
recurse if needed
(Octree: a hierarchical grid limited to 2x2x2 subdivision
Hierarchical grids can perform very well
19
Acceleration Structures
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Ray tracers always use acceleration structures to make the algorithm feasible
No one “best” structure
Ongoing research into new structures and new ways of using existing structures
Considerations include:
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Memory overhead of data structure
Preprocessing time to construct data structure
Ability to optimize well, given machine architecture
For animation: Ability to update data structure as objects move
20
Outline for today
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Speeding up Ray Tracing
Antialiasing
Stochastic Ray Tracing
21
Texture Minification
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Remember texture minification
Texture mapped triangle
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Point-sample the texture?
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triangle small or far away
many texels land in a single pixel
i.e. take the texel at the center
misses lots of detail
causes “shimmering” or “buzzing”
especially noticeable of object
or view moves
Solution was to filter
Texture buzzing is an example of aliasing
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Filtering the texture is an example of antialiasing
22
Small Triangles
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Aliasing when triangles very small
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About the size of a pixel, or smaller
Scan conversion: point sampling
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Pixel color due to triangle that hits
center of pixel
Can miss triangles
Can have gaps if narrow triangle
misses pixel centers
If view or object moves, can flicker as
triangles cross pixel centers
23
Jaggies
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Aliasing when drawing a diagonal on a
square grid:
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stairstepping
AKA jaggies
Especially noticeable:
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high-contrast eges
near horizontal or near vertical
As line rotates (in 2D)
• steps change length
• corners of steps slide along the edge
• known as crawlies
24
Moiré Patterns
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Aliasing when rendering high detail
regular patterns
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can see concentric curve patterns
known as Moiré patterns
caused by interference between pattern
and pixel grid
Also in real life: hold two window
screens in front of each other
25
Strobing
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Consider 30 frame-per-second animation of a spinning propeller
If the propeller is spinning at 1 rotation per second
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If the propeller is spinning at 30 rotations per second
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each image shows propeller rotated 360 degrees
i.e. in same place as previous frame
i.e. propeller appears to stand still
If the propeller is spinning at
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each frame shows propeller rotated 12 degrees more than previous
looks OK
31 rotations per second: will appear to rotate slowly forwads
29 rotations per second: will appear to rotate slowly backwards
Example of strobing problems
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temporal aliasing
caused by point-sampling the motion in time
26
Aliasing
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These examples cover a wide range of problems…
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The image we are making is trying to represent a continuous signal
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The “true” image color is a function that varies with continuous X & Y (and time) values
For digital computation, our standard approach is to:
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… but they all result from essentially the same thing
sample the original signal at discrete points (pixel centers or texels or wherever)
Use the samples to reconstruct a new signal, that we present to the audience
Want the audience to perceive the new signal the same as the original would be
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Unfortunately, the sampling/reconstruction process causes some data to be misrepresented
Hence the term alias: some part of the signal masquerading as something else
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Often refer to instances of problems as artifacts or aliasing artifacts
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Antialiasing: trying to avoid aliasing problems. Three basic approaches:
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Modify the original data so that it won’t have properties that cause aliasing
Use more sophisticated sampling/reconstruction techniques
Clean up the artifacts after-the-fact
27
Signal Analysis
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Signal Analysis: the field that studies these problems in pure form
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Applies also to digital audio, electrical engineering, radio, …
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Artifacts are different, but the theory is the same
Includes a variety of mathematical and engineering methods for working with signals:
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Kinds of signals:
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electrical: a voltage changing over time. 1D signal: e = f(t)
audio: sound pressure changing over time. 1D signal: a = f(t)
computer graphics image: color changing over space. 2D signal: c=f(x,y)
computer graphics animation: color changing over space & time. 3D signal: c=f(x,y,t)
Examples and concepts typically shown for scalar 1D signal
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Fourier analysis, sampling theory, filter, digital signal processing (DSP), …
but they extend to more dimensions for the signal parameters
but they extend to more dimensions for the signal value
A signal:
28
Sampling
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Think of ideal image as perfect triangles in continuous (floating point) device space
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To render this image onto a regular grid of pixels:
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Then we are thinking of our image as a continuous signal
Continuous image has infinite resolution
Edges of triangles are perfect straight lines
We employ some sort of discrete sampling technique
Examine the original continuous image and sample it onto a finite resolution grid of pixels
If signal represents the red intensity of our virtual scene along some horizontal line, the
sampled version consists of a row of discreet 8 bit red values
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This is similar to what happens when a continuous analog sound signal is digitally sampled
onto a CD
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Reconstruction
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Once we have our sampled signal, we then reconstruct it
In the case of computer graphics, this reconstruction takes place as a bunch
of colored pixels on a monitor
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In the case of CD audio, the reconstruction happens in a DAC (digital to analog
converter) and then finally in the physical movements of the speaker itself
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Reconstruction Filters
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Filtering or filtration happens at the reconstruction phase:
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Some filtering due to the device, medium, and observer
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raw sample data isn’t used as is
real world isn’t discrete
Pixels of a monitor aren’t perfects squares or points of uniform color; they have some shape
and distribution over space
The human eye filters so that a grid of pixels appears to be a continuous image
In audio, the loudspeaker has physical limitations on its movement
But we also introduce more filtering to help get the right result
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In audio, digital processing or analog circuitry
In computer graphics, techniques such as bilinear or bicubic filtering
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Low Frequency Signals
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Original signal
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Point sampled at relatively
high frequency
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Reconstructed signal
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High Frequency Signals
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Original signal
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Point sampled at relatively low
frequency
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Reconstructed signal
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Regular Signals
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Original repeating signal
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Point sampled at relatively
low frequency
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Reconstructed signal
repeating at incorrect
frequency (result frequency
aliases the original
frequency)
34
Nyquist Limit
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Any signal can be considered as a sum of signals with varying frequencies
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In order to correctly reconstruct a signal whose highest frequency is x:
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That’s what an equalizer or spectrum display on an audio device shows
sampling rate must have frequency at least 2x
This is known as the Sampling Theorem
• AKA Nyquist Sampling Theorem, AKA Nyquist-Shannon Sampling Theorem
The 2x sampling frequency is known as the Nyquist frequency or Nyquist limit
Frequencies below the Nyquist limit come through OK
Frequencies above the Nyquist limit come through as lower-frequency
aliases, mixed in with the data
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Nyquist Limit
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In images, having high (spatial) frequencies means:
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having lots of detail
having sharp edges
Basic way to avoid aliasing: choose sampling rate higher than Nyquist limit
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This assumes we are doing idealized sampling and reconstruction
In practice, better to sample at least 4x
But in practice, we don’t always know the highest frequency
In fact, we might not have an upper limit!
• E.g. checkerboard pattern receding to the horizon in perspective
• Spatial frequency is infinite
• Must use antialiasing techniques
36
Aliasing Problems, summary
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Shimmering / Buzzing:
Rapid pixel color changes (flickering) caused by high detail textures or high detail
geometry. Ultimately due to point sampling of high frequency color changes at low
frequency pixel intervals
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Stairstepping / Jaggies:
Noticeable stairstep edges on high contrast edges that are nearly horizontal or
vertical. Due to point sampling of effectively infinite frequency color changes (step
gradient at edge of triangle)
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Moiré patterns:
Strange swimming patterns that show up on regular patterns. Due to sampling of
regular patterns on a regular pixel grid
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Strobing:
Incorrect or discontinuous motion in fast moving animated objects. Due to low
frequency sampling of regular motion in regular time intervals. (temporal aliasing)
37
Point Sampling
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The aliasing problems we’ve seen are due to low frequency point sampling of
high frequency information
With point sampling, we sample the original signal at precise points (pixel
centers, etc.)
Is there a better way to sample continuous signals?
38
Box Sampling
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We could also do a hypothetical box sampling of our image
In this method, each triangle contributes to the pixel color based on the area
of the triangle within the pixel
The area is equally weighted across the pixel
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Pyramid Sampling
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Alternately, we could use a weighted sampling filter such as a pyramid filter
The pyramid filter considers the area of triangles in the pixel, but weights
them according to how close they are to the center of the pixel
The pyramid base can be wider than a pixel
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neighboring values influence the pixel
minimizes abrupt changes
40
Sampling Filters
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We could potentially use any one of several different sampling filters
Common options include the point, box, pyramid, cone, and Gaussian filters
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The filters aren’t necessarily limited to cover only pixel.
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Different filters will perform differently in different situations,
Best all-around sampling filters tend to be Gaussian in shape
Commonly extend slightly outside, overlapping with the neighboring pixels.
If filter covers less than the square pixel, will have problems like point sampling
Trying to strike a balance between:
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Eliminating unwanted alias frequencies (antialiasing)
Eliminating wanted frequencies (blurring)
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Edge Antialiasing
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Pixel Coverage
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Various antialiasing algorithms exist to color the pixel based on the exact
area of the of the pixel that a triangle covers.
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But, without storing a lot of additional information per pixel, very hard (or
impossible) to properly handle case of several triangle edges in a single pixel
Impractical to make a coverage-based scheme compatible with z-buffering
Can do better if triangles are sorted back to front
Coverage approaches not generally used in practice for rendering
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Still apply to things such as font filtering
43
Supersampling
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A more popular method (although less elegant) is supersampling:
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By sampling more times per pixel:
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Raises the sampling rate
Raises the frequencies we can capture
Commonly use 16 or more samples per pixel
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Point sample the pixel at several locations
Combine the results into the final pixel color
Requires frame buffer and z-buffer to be 16 times as large
Requires potentially 16 times as much work to generate image
A brute-force approach
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But straightforward to implement
Very powerful
44
Uniform Sampling
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Divide each pixel into a uniform grid of subpixels
Sample at the center of each subpixel
Generates better quality images than single point sampling
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Filters out some higher-than-one-pixel frequency data
Nicely smooths lines and edges
But frequencies higher than Nyquist limit will still alias
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Regular high-frequency signals will have Moiré patterns
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Random Sampling
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Supersample at several randomly located points
Breaks up repeating signals
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Noise tends to be less objectionable to the viewer than jaggies or Moiré patterns
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Eliminates Moiré patterns
Instead of aliasing, frequencies greater than 1 pixel appear as noise in the image
The human eye is pretty good at filtering out noise
But suffers from potential clustering and gaps
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Result is not necessarily accurate
Too much noise.
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Jittered Sampling
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AKA stratified sampling,
Divide pixel into a grid of subpixels
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Combines the advantages of both uniform and random sampling
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Sample each subpixel at a random location
filters high frequencies
frequencies greater than subpixel sampling rate turned into noise
Commonly used
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Reconstruction filter
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Take average of all samples: box filter
Take weighted average of samples: other filters
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weight according to a box, cone, pyramid, Gaussian, etc…
Can apply weighting to uniform, random, or jittered supersamples
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little additional work
48
Weighted Distribution
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Jittered supersampling with Gaussian filtering does well
Because of the filter weights, some samples have more influence on the image than others
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But:
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e.g. with 16 samples, the 4 samples in the center can have higher total weight than the 12 others
We’re paying same computational price for samples that don’t contribute much
We’re giving as much attention to the regions that don’t contribute much
Instead, adjust the distribution
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Put more samples in the areas that contribute more highly
Get more accuracy for the same amount of work
known as Importance Sampling
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Adaptive Sampling
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More sophisticated option is to perform adaptive sampling
Start with a small number of samples
Analyze their statistical variation
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Varying amount of work per pixel
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It the colors are all similar, we accept that we have an accurate sampling
If the colors have a large variation, take more samples
continue until statistical error is within acceptable tolerance
Concentrates work where the image is “hard”
Tricky to add samples while keeping good distribution
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But possible!
Used in practice, especially in research renderers
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Semi-Jittered Sampling
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Can apply a unique jittering pattern for each pixel (fully jittered)
or re-use the pattern for all of the pixels (semi-jittered)
Both are used in practice
Semi-jittering advantages:
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potential performance advantages
can preselect a good distribution
straight edges look cleaner
Semi-jittering disadvantages:
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re-admits subtle Moiré patterns because of semi-regularity of grid
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Mipmapping & Pixel Antialiasing
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Mipmapping and other texture filtering techniques reduce texture aliasing problems
Combine mipmapping with pixel supersampling
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But it’s expensive to compute shading at every supersample
Hybrid approach:
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Choose mipmaps based on subpixel size
Gets better edge-on behavior than mipmapping alone
Assume that mipmapping and filters in procedural shaders minimize aliasing at pixel scale
Compute only a single shading sample per pixel
Still supersample the scan-conversion and z-buffer
Gives edge antialiasing of supersampling and texture filtering of mipmapping
Doesn’t require cost of full supersampling
GPU hardware often does this:
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Requires increase framebuffer/z-buffer memory
But doesn’t slow down performance much
Works pretty well
52
Motion Blur
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Looks cool in static images
Improves perceived quality of animation
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Details depend on display technology
(film vs CRT vs LCD vs. …)
Generally speaking: the eye normally
blurs moving objects
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Animation is sequence of still frames
Sequence of unblurred still frames look
strangely unnatural
• E.g. old Sinbad movies with stop-motion
monsters

QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
If objects in each frame are blurred in the
direction of motion, easier for brain to
reconstruct continuous object.
• In Dragonslayer (1981), go-motion
monster was introduced
•
•
Model moved with camera shutter open.
Noticeably better quality, even if most
people didn’t know why
• In CG special effects, motion blur always
computed
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Motion Blur
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Spatial antialiasing:
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Temporal antialiasing:
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Increase the temporal resultion and filter the results
Image blurred where there are temporally-varying parts
Brute force: supersample entire image in time
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Increase the spatial resolution and filter the results
Pixels slightly blurred where there are spatially-varying parts
For each frame of animation
Render several (say 16) images spaced over frame time
Combine them into final image
Techniques also to do this per-sample…
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Outline for today
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Speeding up Ray Tracing
Antialiasing
Stochastic Ray Tracing
55
Stochastic Ray Tracing
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Introduced in 1984 (Cook, Porter, Carpenter)
AKA distributed ray tracing AKA distribution ray tracing
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Technique for achieving various fancy effects:
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(originally called “distributed”, but now that refers to parallel processing)
Antialiasing
Motion Blur
Soft Shadows
Area Lights
Blurry Reflections
Camera Focus/Depth-of-field
…
The basic idea is to shoot more rays
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with values having an appropriate random distribution
i.e. stochastically
56
Antialiasing
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Supersampling can easily be implemented in ray tracing
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we’re creating whatever rays we want
we can create as many as we want and aim them wherever we want
can easily implement area-weighted jittered Gaussian distribution
(Jittered sampling was actually introduced to computer graphics by the 1984 Cook et
al. distributed ray tracing paper)
57
Motion Blur
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Assume we know the motion of our
objects as a function of time
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Given a value of time, we can look
up the position of each object
(At least within the current frame)
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Distribute rays in time
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Give each ray a time value
• E.g., jittered time distribution during
the “shutter open” interval
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For intersection testing, use the
object’s position at the ray’s time
Combining the ray colors:
• if the object is moving, the result is
motion blur
• if the object isn’t moving, all values
will be the same: no blur
first CG image with motion blur,
from 1984 Cook et al. paper
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
• seems like this case is a waste of
effort, but turns out OK…
58
Area Lights
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Traditional CG point light sources are unrealistic:
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Harsh lighting
Sharp highlights
Hard shadows
QuickT i me™ and a
T IFF (Uncompressed) decompressor
are needed to see this picture.
Real lights have some shape to them
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Light emitted from some area
Softens the lighting on objects
Gives shape to highlights
Creates soft shadows
•
(CG researchers talk mostly about soft shadows;
the other features are subtle but do affect lighting quality)
QuickTi me™ and a
T IFF (Uncompressed) decompressor
are needed to see thi s pi cture.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
QuickT i me™ and a
T IFF (Uncompressed) decom pressor
are needed to see this picture.
(www.imagearts.ryerson.ca)
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Area Lights
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Instead of having a single direction vector for a light source
Send rays distributed across the surface of the light
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Each contributes to the total lighting on the surface point
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Each may be blocked by an intervening object
Otherwise compute the illumination based on that ray’s direction
If all rays are blocked, won’t get any light: full shadow (umbra)
If some rays blocked, will get some light: penumbra
If no rays blocked, fully lit
Notes:
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Rays distribution should cover surface of the light evenly (though can be jittered)
Hard to create distributions for arbitrary shapes; typically use lines, disks, rectangles, etc.
Can need lots of samples to avoid noise in the penumbra or in specular highlights
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
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Glossy Reflections
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Distribute rays about the the ideal reflection direction
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Blurry surfaces will have a wider distribution (and will need more rays)
Polished surfaces will have a narrow distribution
Combine rays weighted according to BRDF (e.g. Phong)
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
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Translucency
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Like glossy reflection, but for refraction
Distribute rays about the ideal refraction direction
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
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Depth of Field
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With a camera lens, only objects at the focal distance are sharp
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Amount of blurring depends on the aperture (how wide open the shutter is)
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those closer or farther are blurred.
depth of field refers to the zone of acceptable sharpness
In CG, “depth of field” refers to rendering including lens focus/blurring effect
With a pinhole camera, there’s no blurring
With a wider aperture, blurring increases
Distribute rays across the aperture
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Can trace them through a real lens model or something simpler
For an object at the focal distance, whatever path the rays take all will reach the same spot on the object
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all rays will have same color value (specular highlights might blur slightly since they depend on eye direction)
object will be sharp
For an object outside the depth of field, the different rays will hit different spots on the object
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combining the rays will yield a blur.
QuickT i me™ and a
T IFF (Uncompressed) decom pressor
are needed to see this picture.
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
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Stochastic Ray Tracing
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Ray tracing had a big impact on computer graphics in 1980 with the
first images of accurate reflections and refractions from curved
surfaces
Distribution ray tracing had an even bigger impact in 1984, as it reaffirmed the power of the basic ray tracing technique and added a
whole bunch of sophisticated effects, all within a consistent
framework
Previously, techniques such as depth of field, motion blur, soft
shadows, etc., had only been achieved individually and by using a
variety of complex, hacky algorithms
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Stochastic Ray Tracing
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Many more rays!
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Good news: Don’t need extra primary rays per pixel
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Can combine distributions
E.g. 16 rays in 4x4 jittered supersampling pattern
Give each ray a different time and position in the aperture
OK news: Can get by with relatively few secondary rays
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16 samples for antialiasing * 16 samples for motion blur & 16 samples for
depth of field * 16 rays for glossy reflections * … ?
Exponential explosion of number of rays
For area lights or glossy reflection/refraction
16 primary rays will be combined; each can get by with only a few
secondary rays
Still, need more rays.
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Slower
Insufficient sampling leads to noise
Particularly noticeable for soft or blurry features
Techniques such as importance sampling to minimize noise
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Global illumination
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Take into account bouncing from diffuse objects
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Take into account light passing through objects
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Send secondary rays in all directions, accumulate all contributions
In practice that would take too many rays, be very noisy
Path Tracing
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Caustics
Conceptually simple extention to ray tracing:
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Every surface is a light source!
Find multi-step paths from light sources through scene to camera
Monte Carlo Integration:
• Numerical techniques to randomly choose rays/paths
• Weighting/importance sampling to minimize noise, maximize efficiency
• Photon Maps
• Optimize by storing intermediate distribution of light energy
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(Also, Radiosity computation:
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Diffuse light bouncing between all objects
Use numerical simultaneous equation solvers)
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Done
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Next class: Final project discussion
Upcoming classes: Guest lectures! Cool demos!
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