tiea311 tietokonegraikan perusteetusers.jyu.fi/~nieminen/tgp17/tiea311_2017_lec12.pdftiea311 -...
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TIEA311Tietokonegrafiikan perusteetkevat 2017
(“Principles of Computer Graphics” – Spring 2017)
Copyright and Fair Use Notice:
The lecture videos of this course are made available forregistered students only. Please, do not redistribute them forother purposes. Use of auxiliary copyrighted material(academic papers, industrial standards, web pages, videos,and other materials) as a part of this lecture is intended tohappen under academic ”fair use” to illustrate key points of thesubject matter. The lecturer may be contacted for take-downrequests or other copyright concerns (email:[email protected]).
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TIEA311 Tietokonegrafiikan perusteet – kevat 2017(“Principles of Computer Graphics” – Spring 2017)
Adapted from: Wojciech Matusik, and Fredo Durand : 6.837 ComputerGraphics. Fall 2012. Massachusetts Institute of Technology: MITOpenCourseWare, https://ocw.mit.edu/.
License: Creative Commons BY-NC-SA
Original license terms apply. Re-arrangement and new contentcopyright 2017 by Paavo Nieminen and Jarno Kansanaho
Frontpage of the local course version, held during Spring 2017 at theFaculty of Information technology, University of Jyvaskyla:http://users.jyu.fi/˜nieminen/tgp17/
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TIEA311 - Course Status in Jyvaskyla
I Assignment 1 discussion – now is a good time to wrap thisup, self-evaluate, and move on! There are further topicsyet to come!
I Assignment 2 discussion – how to start with Joints andJoint*’s?
(Technical things about C++ were supposed to be covered, too,but there was a technical glitch at the lecture room this time.)
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1 MIT EECS 6.837 – Matusik
MIT EECS 6.837 Computer Graphics Part 2 – Rendering
NVIDIA
Today: Intro to Rendering, Ray Casting
© NVIDIA Inc. All rights reserved. This content is excluded from our Creative Commonslicense. For more information, see http://ocw.mit.edu/help/faq-fair-use/.
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• Modeling – splines, hierarchies, transformations, meshes, etc.
• Animation
– skinning, ODEs, masses and springs
• Now we’ll to see how to generate
an image given a scene description!
4
The Story So Far
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TIEA311 - Rest of the Course in Jyvaskyla
The next slide is verbatim from the MIT OCW course. Here is thecurrent plan for the remaining part of our adapted short version:
I Ray Casting: cover fully. Ray Tracing: cover the basic idea, skipdetails → possible to continue as a “hobby project”; NOTE:teachers of “TIEA306 Ohjelmointityo” may be contactedregarding the possibility of receiving credit for hobby projects.
I Shading, texture mapping: Cover the principles up to Phongmodel and texture coordinates.
I Rasterization, z-buffering: cover basic ideasI Global Illumination, Monte Carlo techniques: skip this → could
be suitable for bachelor thesis (introductory topics) or evenmaster thesis (current state-of-the-art techniques)
I Image-based rendering: skip → defer to advanced courses (e.g.“TIES411 Konenako ja kuva-analyysi”)
I Sampling and antialiasing: mostly skip → defer theory to“TIES324 Signaalinkasittely” and techniques (possibly) to“TIES471 Reaaliaikainen renderointi”.
I Shadow techniques, Graphics Hardware → defer to TIES471.
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• Ray Casting and Ray Tracing • Intro to Global Illumination
– Monte Carlo techniques, photon mapping, etc. • Shading, texture mapping
– What makes materials look like they do? • Image-based Rendering • Sampling and antialiasing • Rasterization, z-buffering • Shadow techniques • Graphics Hardware
5
The Remainder of the Term
[Lehtinen et al. 2008] © ACM. All rights reserved. This content is excluded from our Creative Commonslicense. For more information, see http://ocw.mit.edu/help/faq-fair-use/.
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• What does rendering mean?
• Basics of ray casting
6
Today
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Scene 7
© source unknown. All rights reserved. This content is excluded from our CreativeCommons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/.
© Oscar Meruvia-Pastor, Daniel Rypl. All rights reserved. This content is excluded from our CreativeCommons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/.
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8
Scene Camera
This image is in the public domain.Source: openclipart
© source unknown. All rights reserved. This content is excluded from our CreativeCommons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/.
© Oscar Meruvia-Pastor, Daniel Rypl. All rights reserved. This content is excluded from our CreativeCommons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/.
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9
Scene
Camera Image plane
Pixels
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© Oscar Meruvia-Pastor, Daniel Rypl. All rights reserved.
This content is excluded from our Creative Commons
license. For more information, seehttp://ocw.mit.edu/help/faq-fair-use/.
This image is in the public domain.Source: openclipart
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10
Scene
Camera Image plane
Image
Pixels
Rendering = Scene to Image
© source unknown. All rights reserved. Thiscontent is excluded from our Creative
Commons license. For more information, seehttp://ocw.mit.edu/help/faq-fair-use/.
© Oscar Meruvia-Pastor, Daniel Rypl. All rights reserved.
This content is excluded from our Creative Commons
license. For more information, seehttp://ocw.mit.edu/help/faq-fair-use/.
This image is in the public domain.Source: openclipart
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11
Scene
Image
Each pixel corresponds to
one ray. We need to figure
out which scene point each
one hits.
Pixels
Rendering – Pinhole Camera
© source unknown. All rights reserved. Thiscontent is excluded from our Creative Commons license. For more information,see http://ocw.mit.edu/help/faq-fair-use/.
© Oscar Meruvia-Pastor, Daniel Rypl. All rights reserved.This content is excluded from our Creative Commonslicense. For more information, see http://ocw.mit.edu/help/faq-fair-use/.
This image is in the public domain.Source: openclipart
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12
Scene
Image
Pixels
Rendering
What’s the
color you put
in each pixel?
© source unknown. All rights reserved. Thiscontent is excluded from our Creative Commons license. For more information,see http://ocw.mit.edu/help/faq-fair-use/.
© Oscar Meruvia-Pastor, Daniel Rypl. All rights reserved.This content is excluded from our Creative Commonslicense. For more information, see http://ocw.mit.edu/help/faq-fair-use/.
This image is in the public domain.Source: openclipart
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13
Scene
Image
Pixels
Rendering
Pixel Color
Determined by
Lighting/Shading
© source unknown. All rights reserved. Thiscontent is excluded from our Creative Commons license. For more information,see http://ocw.mit.edu/help/faq-fair-use/.
© Oscar Meruvia-Pastor, Daniel Rypl. All rights reserved.This content is excluded from our Creative Commonslicense. For more information, see http://ocw.mit.edu/help/faq-fair-use/.
This image is in the public domain.Source: openclipart
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• “Rendering” refers to the entire process that produces color values for pixels, given a 3D representation of the scene
• Pixels correspond to rays; need to figure out the visible scene point along each ray – Called “hidden surface problem” in older texts – “Visibility” is a more modern term – Also, we assume (for now) a single ray per pixel
14
Rendering
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• “Rendering” refers to the entire process that produces color values for pixels
• Pixels correspond to rays; need to figure out the visible scene point along each ray – Called “hidden surface problem” in older texts – “Visibility” is a more modern term – Also, we assume (for now) a single ray per pixel
• Major algorithms: Ray casting and rasterization
• Note: We are assuming a pinhole camera (for now) 15
Rendering
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16
Questions?
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• Ray Casting Basics
• Camera and Ray Generation
• Ray-Plane Intersection
• Ray-Sphere Intersection
17
Ray Casting
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For every pixel
Construct a ray from the eye
For every object in the scene
Find intersection with the ray
Keep if closest
18
Ray Casting
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For every pixel
Construct a ray from the eye
For every object in the scene
Find intersection with the ray
Keep if closest
Shade
19
Shading
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• Surface/Scene Properties – surface normal – direction to light – viewpoint
• Material Properties – Diffuse (matte) – Specular (shiny) – …
• Light properties – Position – Intensity, ...
• Much more! 20
Shading = What Surfaces Look Like
Diffuse sphere Specular spheres
N
L V
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• Let’s think about shadows...
21
Ray Casting vs. Ray Tracing
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22
“camera rays” are rays from the
camera to the scene
?
Ray Casting vs. Ray Tracing
This image is in the public domain.Source: openclipart
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23
X
ray from light to hit point is blocked, i.e., point is in shadow
Ray Casting vs. Ray Tracing
This image is in the public domain.Source: openclipart
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• Ray casting = eye rays only, tracing = also secondary
24
X Secondary rays are used for
testing shadows, doing
reflections, refractions, etc.
We’ll do all this a little
later!
Ray Casting vs. Ray Tracing
This image is in the public domain.Source: openclipart
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Secondary Rays Indirect illumination
Shadows
Reflections Refractions
Caustics
Hen
rik W
ann
Jens
en
25 Courtesy of Henrik Wann Jensen. Used with permission.
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26
Ray Tracing
Reflections, refractions
Caustics
Reflections
© source unknown. All rights reserved. This content is excluded from our CreativeCommons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/.
Courtesy of Henrik Wann Jensen. Used with permission.
© Turner Whitted, Bell Laboratories. All rights reserved. This content isexcluded from our Creative Commons license. For more information,see http://ocw.mit.edu/help/faq-fair-use/.
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27
Questions?
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For every pixel
Construct a ray from the eye
For every object in the scene
Find intersection with the ray
Keep if closest
Shade depending on light and normal vector
28
Ray Casting
N Finding the
intersection point
and normal is the
central part of ray
casting
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• Origin – Point • Direction – Vector
– normalized is better • Parametric line
– P(t) = origin + t * direction
29
Ray Representation
origin direction
P(t)
How would you
represent a ray?
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• Origin – Point • Direction – Vector
– normalized is better • Parametric line
– P(t) = origin + t * direction
30
Ray Representation
origin direction
P(t)
Another way to put
the ray casting
problem statement:
Find smallest t > 0
such that P(t) lies
on a surface in the
scene
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• Albrecht Dürer, 16th century
31
Dürer’s Ray Casting Machine
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• Albrecht Dürer, 16th century
32
Dürer’s Ray Casting Machine
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• Ray Casting Basics
• Camera and Ray Generation
• Ray-Plane Intersection
• Ray-Sphere Intersection
33
Ray Casting
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For every pixel
Construct a ray from the eye
For every object in the scene
Find intersection with ray
Keep if closest
34
Cameras
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35
Pinhole Camera • Box with a tiny hole • Inverted image • Similar triangles
• Perfect image if hole infinitely small
• Pure geometric optics • No depth of field issue
(everything in focus)
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• From Gemma Frisius, 1545
36
Oldest Illustration
© source unknown. All rights reserved. This content is excluded from our CreativeCommons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/.
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Also Called “Camera Obscura”
Image courtesy of Wellcome Library, London. License: CC-BY-NC. This content is excluded fromour Creative Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/.
![Page 40: TIEA311 Tietokonegraikan perusteetusers.jyu.fi/~nieminen/tgp17/tiea311_2017_lec12.pdfTIEA311 - Course Status in Jyv askyl¨ a¨ I Assignment 1 discussion now is a good time to wrap](https://reader033.vdocuments.net/reader033/viewer/2022042111/5e8ca6c0ee33bf6a2a0e737c/html5/thumbnails/40.jpg)
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Camera Obscura Today
Abelardo Morell www.abelardomorell.net
Images removed due to copyright restrictions -- please seehttp://www.abelardomorell.net/photography/cameraobsc_01/cameraobsc_17.htmlhttp://www.abelardomorell.net/posts/camera-obscura/http://www.abelardomorell.net/photography/cameraobsc_49/cameraobsc_63.html for further details.
![Page 41: TIEA311 Tietokonegraikan perusteetusers.jyu.fi/~nieminen/tgp17/tiea311_2017_lec12.pdfTIEA311 - Course Status in Jyv askyl¨ a¨ I Assignment 1 discussion now is a good time to wrap](https://reader033.vdocuments.net/reader033/viewer/2022042111/5e8ca6c0ee33bf6a2a0e737c/html5/thumbnails/41.jpg)
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Camera Obscura Today
Abelardo Morell www.abelardomorell.net
Images removed due to copyright restrictions -- please seehttp://www.abelardomorell.net/photography/cameraobsc_01/cameraobsc_17.htmlhttp://www.abelardomorell.net/posts/camera-obscura/http://www.abelardomorell.net/photography/cameraobsc_49/cameraobsc_63.html for further details.
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• Eye-image pyramid (view frustum) • Note that the distance/size of image are arbitrary
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Simplified Pinhole Camera
same image
will result on
this image plane
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Camera Description?
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• Eye point e (center)
• Orthobasis u, v, w (horizontal, up, direction)
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Camera Description?
Object coordinates World coordinates View
coordinates
Image coordinates
u w
v
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Camera Description?
Object coordinates World coordinates View
coordinates
Image coordinates
u w
v
• Eye point e (center)
• Orthobasis u, v, w (horizontal, up, direction)
• Field of view angle
• Image rectangle aspect ratio
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Camera
Image plane
Image Coordinates
-1 ≤ x ≤ 1
-1 ≤ y ≤ 1
Convenient to define “normalized image coordinates” such that the x, y
coordinates run
from -1 to 1
regardless of the
dimensions and
aspect ratio of the
image rectangle.
This image is in the public domain.Source: openclipart
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field of view α right u
view direction w
image plane -1 < x < 1
x
eye point e
p
p is point on image plane at coordinate x, we want to know the direction of the ray r
r?
Ray Generation in 2D
This image is in the public domain. Source: openclipart
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field of view α
image plane -1 < x < 1
1
right u
view direction w
Ray Generation in 2D
What is the distance D to the screen so that the normalized coordinates go to 1?
This image is in the public domain. Source: openclipart
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field of view α
image plane -1 < x < 1
D
1
right u
view direction w
Ray Generation in 2D
This image is in the public domain. Source: openclipart
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field of view α right u
view direction w
image plane -1 < x < 1
x
D
r = p-e = (x*u, D*w)
eye point e
r
p
Ray Generation in 2D
This image is in the public domain. Source: openclipart
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Ray Generation in 2D
field of view α right u
view direction w
image plane -1 < x < 1
x
D
eye point e
r
p
then we just normalize r to get the ray
r = p-e = (x*u, D*w)
This image is in the public domain. Source: openclipart
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• y coordinate is treated just like x, except accounting for aspect ratio – r = (x*u, aspect*y*v, D*w) – Again, u, v, w are the basis vectors
of the view coordinate system – Aspect ratio handles non-square viewports
• Think of your 16:9 widescreen TV
• The point of the exercise with computing D was to allow us to use the [-1,1] image coordinate system regardless of field of view.
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That was 2D, 3D is just as simple
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Perspective vs. Orthographic
• Parallel projection • No foreshortening • No vanishing point
perspective orthographic
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• Ray Generation? – Origin = e + x*size*u + y*size*v – Direction is constant: w
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Orthographic Camera
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• E.g. fish eye, omnimax, parabolic
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Other Weird Cameras
CAVE Columbia University
© source unknown. All rights reserved. This content is excludedfrom our Creative Commons license. For more information, seehttp://ocw.mit.edu/help/faq-fair-use/.
© CAVE Lab, Columbia University. All rights reserved. Thiscontent is excluded from our Creative Commons license. Formore information, see http://ocw.mit.edu/help/faq-fair-use/.
![Page 56: TIEA311 Tietokonegraikan perusteetusers.jyu.fi/~nieminen/tgp17/tiea311_2017_lec12.pdfTIEA311 - Course Status in Jyv askyl¨ a¨ I Assignment 1 discussion now is a good time to wrap](https://reader033.vdocuments.net/reader033/viewer/2022042111/5e8ca6c0ee33bf6a2a0e737c/html5/thumbnails/56.jpg)
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Questions? Even Funkier
Multiperspective Imaging
Courtesy of Paul Rademacher. Used with permission.