As-Killing-As-Possible Vector Fields for Planar Deformation

http://imageshack.us/photo/my-images/534/sgamepixar1998brrip720p.jpg
CS 148, Summer 2012
Introduction to Computer Graphics and Imaging
Justin Solomon
http://www.youtube.com/watch?v=vS2fRUP8zJ8
http://upload.wikimedia.org/wikipedia/commons/3/33/Catmull-Clark_subdivision_of_a_cube.svg
2
2
~
¯(u; v) = 2uv + 3uv + 7u
Function of two
variables
Degree 2 in both
variables (total
degree ≤ 4!)
2
2
~
¯(u; v) = 2uv + 3uv + 7u
Function of two
variables
Degree 2 in both
variables (total
degree ≤ 4!)
F(u1; u2; v1; v2) = ¢ ¢ ¢
http://upload.wikimedia.org/wikipedia/commons/b/bf/B%C3%A9zier_surface_example.svg
http://graphics.stanford.edu/courses/cs348a-12-winter/Handouts/handout26.pdf
Couples u and v variables
Simple rules for better approximation
Define subdivision
rule and see what
happens.
Cut each
corner
http://www.idav.ucdavis.edu/education/CAGDNotes/Chaikins-Algorithm.pdf
Qi = Pi + t(Pi+1 ¡ Pi )
Ri = Pi + (1 ¡ t)(Pi+1 ¡ Pi )
1
2
n
3
…
http://www.idav.ucdavis.edu/education/CAGDNotes/Chaikins-Algorithm.pdf
1
2
n
3
…
http://www.idav.ucdavis.edu/education/CAGDNotes/Chaikins-Algorithm.pdf
Triangles
Quads
http://alice.loria.fr/publications/papers/2006/TOG_pgp//photo/workflow.png
Two potential representations
Triangles
Quads
http://alice.loria.fr/publications/papers/2006/TOG_pgp//photo/workflow.png
Two potential representations
Topology [tuh-pol-uh-jee]:
The study of geometric
properties that remain
invariant under certain
transformations
http://dictionary.reference.com/browse/topology?s=t
Geometry: “This vertex is at (x,y,z).”
http://upload.wikimedia.org/wikipedia/commons/f/fb/Dolphin_triangle_mesh.png
Topology:
“These vertices are connected.”
http://upload.wikimedia.org/wikipedia/commons/f/fb/Dolphin_triangle_mesh.png
Valence 6
Triangle mesh where
most vertices have
valence six.
http://ars.sciencedirect.com/content/image/1-s2.0-S1524070306000385-gr2.jpg
Triangle mesh where
most vertices have
valence six.
http://ars.sciencedirect.com/content/image/1-s2.0-S1524070306000385-gr2.jpg
Triangle mesh where
most vertices have
valence six.
http://ars.sciencedirect.com/content/image/1-s2.0-S1524070306000385-gr2.jpg
Have topology, need geometry.
1
8
1
16
3
8
3
8
1
8
New
1
16
10
16
1
16
1
16
1
16
1
16
Old
1
8
1
16
3
8
3
8
1
8
New
1
16
10
16
1
16
1
16
1
16
1
16
Old
http://www.sciencedirect.com/science/article/pii/S0010448511003095
Provable smoothness & regularity
Triangles
Quads
http://alice.loria.fr/publications/papers/2006/TOG_pgp//photo/workflow.png
Two potential representations
Quads (and other polygons)
http://alice.loria.fr/publications/papers/2006/TOG_pgp//photo/workflow.png
Topological strategy
Topological strategy
Topological strategy
Topological strategy
1. New face point = centroid of old face points
Geometric strategy
2. New edge point = average of old and new neighbors
Geometric strategy
3. Old points P of valence n:
F = av. face neighbor
R = av. midpoint neighbor
P’ = (F+2R+(n-3)P)/n
Geometric strategy
https://graphics.stanford.edu/wikis/cs148-09-summer/Assignment3Description
Bicubic b-spline surface
http://youtu.be/ltX-qUjbkdc?t=1m1s
http://graphics.uni-bielefeld.de/publications/
http://www-ui.is.s.u-tokyo.ac.jp/~takeo/research/rigid/rigid.png
CS 148, Summer 2012
Introduction to Computer Graphics and Imaging
Justin Solomon
http://stackoverflow.com/questions/236000/whats-a-turing-machine
I/O is an abstraction
I/O is an object of study
Computer Graphics
and
Interactive
Techniques
http://www.highdisplay.com/wp-content/uploads/2011/07/What-is-TFT-LCD-Monitor.jpg
Liquid crystal display (LCD)
Anisotropic
patterns
depending on
electricity,
heat, etc.
http://mrsec.wisc.edu/Edetc/courses/colorsymp/park/index.html
Twisted nematics
http://electronics.howstuffworks.com/lcd2.htm
Light
source
http://electronics.howstuffworks.com/lcd2.htm
Polarize
http://electronics.howstuffworks.com/lcd2.htm
Twist light
polarization
http://electronics.howstuffworks.com/lcd2.htm
Only twisted
light makes it
through
http://electronics.howstuffworks.com/lcd2.htm
Electrode
controls crystals
http://electronics.howstuffworks.com/lcd2.htm
http://img.diytrade.com/cdimg/597243/7515356/0/1276139831/Sell_CRT_Monitor.jpg
http://www.freepatentsonline.com/6741296-0-large.jpg
Cathode ray tube (CRT)
http://en.wikipedia.org/wiki/File:Shadow_mask_vs_aperture_grille.jpg
Have to convert
from RGB to
display pattern
http://en.wikipedia.org/wiki/File:Shadow_mask_closeup_cursor.jpg
http://en.wikipedia.org/wiki/ClearType
Subpixel antialiasing
Color fringing
http://en.wikipedia.org/wiki/ClearType
Subpixel antialiasing
Nonlinear relationship between
brightness and intensity
Nonlinear relationship between
brightness and intensity
Perceptual
Display-related
Nonlinear relationship between
brightness and intensity
Nonlinear relationship between
intensity and hardware response
displayed intensity = (maximum intensity)a°
Pixel color
displayed intensity = (maximum intensity)a°
http://www.kenluckephotography.com/portfolio/monitoradjust/files/page17_2.gif
displayed intensity = (maximum intensity)a°
ln 0:5
0:5 = a !
7 °=
ln a
°
½ µ
¶°
µ
¶°
µ
¶° ¾
0
1
255
displayed intensity 2 M
;M
;¢¢¢;M
255
255
255
Apply inverse transformation
Gamma and perceptual
differences in brightness cancel!
Visual sensors must communicate!
Discontinuous motion
with same average
velocity as implied
continuous motion.
http://darlingdarleen.blogspot.com/2008_01_01_archive.html
LCD Shutter
Digital Light Processing (DLP)
Alternate between eyes
Spinning color wheel
http://graphics.stanford.edu/courses/cs148-11-fall/lectures/displays.pdf
No black
Max black
Four
primaries!
http://en.wikipedia.org/wiki/CMYK_color_ model
Electronic ink
Different appearance, slow update rate
http://graphics.stanford.edu/courses/cs148-11-fall/lectures/displays.pdf
Events
Notify when state changes
Polling
Check for changed state
http://graphics.stanford.edu/courses/cs148-11-fall/lectures/interaction.pdf
+
Efficient
Need to track state
Need to decide on events of interest
http://graphics.stanford.edu/courses/cs148-11-fall/lectures/interaction.pdf
+
Cleanly deals with continuous state change
Could miss a state change
Considerable overhead
http://graphics.stanford.edu/courses/cs148-11-fall/lectures/interaction.pdf
Key press closes circuit;
character map used to
determine which key
(filter bounces)
http://www.headfuzz.co.uk/files/keyboard-matrix2-sch.png
http://graphics.stanford.edu/courses/cs148-11-fall/lectures/input.pdf
Digital Image Correlation
http://www.bidouille.org/hack/mousecam
http://www.blogcdn.com/www.engadget.com/media/2008/12/original-mouse-08dec03.jpg
DIY tables
Frustrated total internal
reflection, direct illumination
iPod/iPad/Perceptive
Pixel
Capacitive surface
Cheaper alternatives
Pressure
http://www.xda-developers.com/wp-content/uploads/2011/09/multitouch-gesture-on-iphone-ipad-and-ipod.jpg?139d23
http://www.talkandroid.com/wp-content/uploads/2011/09/ipad-multi-touch.jpg?3995d3
Game controller, joystick
Wii remote
Communicate with station
Accelerometers, IR sensor
http://0.tqn.com/d/compactiongames/1/0/J/A/1/gp2.jpg
https://images-na.ssl-images-amazon.com/images/G/01/videogames/detail-page/B0045FGET2.01.lg.jpg
Camera
Kinect
More later!
Already discussed!
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http://home.12move.nl/~sh290334/dbase_force/cybergrasp.jpg
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http://imageshack.us/photo/my-images/534/sgamepixar1998brrip720p.jpg
http://www-ui.is.s.u-tokyo.ac.jp/~takeo/research/rigid/rigid.png
CS 148, Summer 2012
Introduction to Computer Graphics and Imaging
Justin Solomon