distributed ray tracing
DESCRIPTION
Distributed Ray Tracing. Anti-Aliasing. Graphics as signal processing Scene description: continuous signal Sample digital representation Reconstruction by monitor. Anti-Aliasing. Represent any function as sum of sinusoidals Sampling Spatial: multiply function by comb function - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/1.jpg)
CIS 681
Distributed Ray Tracing
![Page 2: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/2.jpg)
CIS 681
Anti-Aliasing
• Graphics as signal processing– Scene description: continuous signal– Sample– digital representation– Reconstruction by monitor
![Page 3: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/3.jpg)
CIS 681
Anti-Aliasing
• Represent any function as sum of sinusoidals• Sampling
– Spatial: multiply function by comb function– Frequency: convolve function by comb function
• Nyquist limit• Reconstruction
– Spatial: convolve with filter– Frequency: multiply by filter
![Page 4: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/4.jpg)
CIS 681
Typical anti-aliasing
• Increase sampling frequency– Doesn’t solve problem– Increases frequencies handled (Nyquist limit)
• Average values after sampling– Doesn’t address problem– Blurs bad results
![Page 5: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/5.jpg)
CIS 681
Ideal sampling and reconstruction
• Sample at greater than Nyquist frequency• Reconstruct using sinc (box) filter• Given sampling frequency, remove all frequencies
higher than Nyquist limit• Filter first, then sample
– or do both at the same time
![Page 6: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/6.jpg)
CIS 681
Illumination is Integration
Usually referred to as “Kajia’s Rendering Equation”
Outgoing intensity of reflected light at a point on a surface in a certain direction is
• The point’s emission ,• An integral over the hemisphere above the
surface of an illumination function L and a bidirectional reflectance function (BDRF).
The shading function may be too complex to compute analytically
![Page 7: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/7.jpg)
CIS 681
Distributed Ray Tracing
Anti-AliasingGlossTranslucency Soft Shadows (Penumbra)Motion BlurDepth of field
Sampling to approximate integral
![Page 8: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/8.jpg)
CIS 681
Importance Sampling
• Sample uniformly and average samples according to distribution function
OR
• Sample according to distribution function and average samples uniformly
![Page 9: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/9.jpg)
CIS 681
Monte Carlo Integration
• Determine area under the curve
• Non analytic function so can’t integrate
• Can tell if point is above or below curve
• Generate random samples• Count fraction below curve• Accurate in the limit
![Page 10: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/10.jpg)
CIS 681
Supersampling
• Multiple samples per pixel• Average together using uniform
weights (box filter)• Average together using a
pyrimid filter or a truncated Gaussian filter
![Page 11: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/11.jpg)
CIS 681
Adaptive Supersampling
• Trace rays at corner of pixels: initial area
• Trace ray (sample) at center of area
• If center is ‘different’ from corners,– Subdivide area into 4 sub-areas– Recurse on sub-areas
![Page 12: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/12.jpg)
CIS 681
Poison Distribution
• Similar to distribution of vision receptors• Random with minimum distance between samples
![Page 13: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/13.jpg)
CIS 681
Spectrum analysis of regular sampling
low frequency signal high frequency signal
Original signal
Sampling filter
Sampled signal
Ideal reconstruction filter
Reconstructed signal
![Page 14: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/14.jpg)
CIS 681
low frequency signal high frequency signal
Original signal
Sampling filter
Sampled signal
Ideal reconstruction filter
Reconstructed signal
Spectrum analysis of regular sampling
![Page 15: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/15.jpg)
CIS 681
Jittered SamplingFrequencies above Nyquist limit are converted to noise instead of incorrect patterns
![Page 16: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/16.jpg)
CIS 681
Gloss
![Page 17: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/17.jpg)
CIS 681
Gloss
• Mirror reflections calculated by tracing rays in the direction of reflection
• Gloss is calculated by distributing these rays about the mirror direction– The distribution is weighted according to the same
distribution function that determines highlights.
![Page 18: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/18.jpg)
CIS 681
Gloss
![Page 19: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/19.jpg)
CIS 681
Translucency
![Page 20: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/20.jpg)
CIS 681
Translucency
•Analogous to the problem of gloss• Distribute the secondary rays about the main direction of the transmitted rays
The distribution of transmitted rays is defined by a specular transmittance function
![Page 21: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/21.jpg)
CIS 681
Translucency
![Page 22: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/22.jpg)
CIS 681
Penumbras
![Page 23: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/23.jpg)
CIS 681
Penumbras
• Consider the light source to be an area, not a point• Trace rays to random areas on the surface of the light source• distribute rays according to areas of varying intensity of light source (if any)• Use the fraction of the light intensity equal to the fraction of rays which indicate an unobscured light source
![Page 24: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/24.jpg)
CIS 681
Penumbras
![Page 25: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/25.jpg)
CIS 681
Motion Blur
![Page 26: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/26.jpg)
CIS 681
Motion Blur
Post-process blurring can get some effects, but consider:•Two objects moving so that one always obscures the other
•Can’t render and blur objects separately
•A spinning top with texture blurred but highlights sharp•Can’t post-process blur a rendered object
•The blades of a fan creating a blurred shadow•Must consider the movement of other objects
![Page 27: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/27.jpg)
CIS 681
Temporal Jittered Sampling
time
Jitter in space
Jitter in time
![Page 28: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/28.jpg)
CIS 681
Temporal Jittered Sampling
1
2
3
4
56
7
8
9
10
11
12
13
14
15
16
![Page 29: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/29.jpg)
CIS 681
Pinhole Camera
Image plane
Perfect focus - low light
![Page 30: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/30.jpg)
CIS 681
Use of lens - more light
lens
Focal length
a = F/n
F=n = f-stop
![Page 31: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/31.jpg)
CIS 681
Use of lens - more lightImage plane Focal planelens
s d
fds
111
![Page 32: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/32.jpg)
CIS 681
Circle of ConfusionImage plane Focal plane
lens
s d
c = circle of confusion ~= 0.33mm
c
DrDf
![Page 33: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/33.jpg)
Depth of Field
![Page 34: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/34.jpg)
CIS 681
Depth of Field
Image plane Focal
plane
lens
s d
Given pixel, s, d
1. Construct ray from pixel through lens center to point p on focal plane
2. Randomly generate point q on 2D lens
3. Trace ray from q through pp
q
![Page 35: Distributed Ray Tracing](https://reader035.vdocuments.mx/reader035/viewer/2022062322/5681516c550346895dbf9be3/html5/thumbnails/35.jpg)
CIS 681
Summary
Space-time jitter subsample
Random on area light source
Random on lens
Random on refraction direction
Random on refraction direction