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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAAAA
CS 148, Summer 2012 Introduction to Computer Graphics and Imaging
Justin Solomon
http://imageshack.us/photo/my-images/534/sgamepixar1998brrip720p.jpg
http://www.youtube.com/watch?v=vS2fRUP8zJ8
http://upload.wikimedia.org/wikipedia/commons/3/33/Catmull-Clark_subdivision_of_a_cube.svg
~̄(u; v) = 2uv+3uv2 +7u2
Function of two variables
Degree 2 in both variables (total degree ≤ 4!)
~̄(u; v) = 2uv+3uv2 +7u2
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
Couples u and v variables http://graphics.stanford.edu/courses/cs348a-12-winter/Handouts/handout26.pdf
Simple rules for better approximation
Define subdivision rule and see what
happens.
http://www.idav.ucdavis.edu/education/CAGDNotes/Chaikins-Algorithm.pdf
Cut each corner
Ri = Pi +(1¡ t)(Pi+1 ¡Pi)
Qi = Pi + t(Pi+1¡Pi)
1 2
3
…
n
http://www.idav.ucdavis.edu/education/CAGDNotes/Chaikins-Algorithm.pdf
1 2
3
…
n
http://www.idav.ucdavis.edu/education/CAGDNotes/Chaikins-Algorithm.pdf
Two potential representations http://alice.loria.fr/publications/papers/2006/TOG_pgp//photo/workflow.png
Triangles Quads
Two potential representations http://alice.loria.fr/publications/papers/2006/TOG_pgp//photo/workflow.png
Triangles Quads
Topology [tuh-pol-uh-jee]:
The study of geometric properties that remain invariant under certain transformations
http://dictionary.reference.com/browse/topology?s=t
http://upload.wikimedia.org/wikipedia/commons/f/fb/Dolphin_triangle_mesh.png
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.”
Valence 6
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
Triangle mesh where most vertices have valence six.
Have topology, need geometry.
New Old
3
8
3
8
1
8
1
8
1
16
1
16
1
16
1
16
1
16
1
16
10
16
New Old
3
8
3
8
1
8
1
8
1
16
1
16
1
16
1
16
1
16
1
16
10
16
Provable smoothness & regularity http://www.sciencedirect.com/science/article/pii/S0010448511003095
Two potential representations http://alice.loria.fr/publications/papers/2006/TOG_pgp//photo/workflow.png
Triangles Quads
http://alice.loria.fr/publications/papers/2006/TOG_pgp//photo/workflow.png
Quads (and other polygons)
Topological strategy
Topological strategy
Topological strategy
Topological strategy
Geometric 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
Bicubic b-spline surface https://graphics.stanford.edu/wikis/cs148-09-summer/Assignment3Description
http://youtu.be/ltX-qUjbkdc?t=1m1s
http://graphics.uni-bielefeld.de/publications/
TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAAAA
CS 148, Summer 2012 Introduction to Computer Graphics and Imaging
Justin Solomon
http://www-ui.is.s.u-tokyo.ac.jp/~takeo/research/rigid/rigid.png
I/O is an abstraction http://stackoverflow.com/questions/236000/whats-a-turing-machine
I/O is an object of study
Computer Graphics and
Interactive Techniques
Liquid crystal display (LCD) http://www.highdisplay.com/wp-content/uploads/2011/07/What-is-TFT-LCD-Monitor.jpg
Twisted nematics http://mrsec.wisc.edu/Edetc/courses/colorsymp/park/index.html
Anisotropic patterns
depending on electricity, heat, etc.
http://electronics.howstuffworks.com/lcd2.htm
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
Cathode ray tube (CRT)
http://img.diytrade.com/cdimg/597243/7515356/0/1276139831/Sell_CRT_Monitor.jpg http://www.freepatentsonline.com/6741296-0-large.jpg
http://en.wikipedia.org/wiki/File:Shadow_mask_vs_aperture_grille.jpg
http://en.wikipedia.org/wiki/File:Shadow_mask_closeup_cursor.jpg
Have to convert from RGB to
display pattern
Subpixel antialiasing http://en.wikipedia.org/wiki/ClearType
Subpixel antialiasing http://en.wikipedia.org/wiki/ClearType
Color fringing
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°
0:5 = a° 7! ° =ln0:5
lna
Apply inverse transformation
displayed intensity 2½M
µ0
255
¶°;M
µ1
255
¶°; ¢ ¢ ¢ ;M
µ255
255
¶°¾
Gamma and perceptual differences in brightness cancel!
Visual sensors must communicate!
http://darlingdarleen.blogspot.com/2008_01_01_archive.html
Discontinuous motion with same average velocity as implied continuous motion.
Digital Light Processing (DLP) Spinning color wheel
LCD Shutter Alternate between eyes
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
http://www.headfuzz.co.uk/files/keyboard-matrix2-sch.png http://graphics.stanford.edu/courses/cs148-11-fall/lectures/input.pdf
Key press closes circuit; character map used to determine which key (filter bounces)
http://www.bidouille.org/hack/mousecam Digital Image Correlation
http://www.blogcdn.com/www.engadget.com/media/2008/12/original-mouse-08dec03.jpg
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
DIY tables Frustrated total internal reflection, direct illumination
iPod/iPad/Perceptive Pixel Capacitive surface
Cheaper alternatives Pressure
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
Game controller, joystick Communicate with station
Wii remote Accelerometers, IR sensor
Camera More later!
Kinect Already discussed!
http://www.cyberware.com/products/scanners/lss.html http://home.12move.nl/~sh290334/dbase_force/cybergrasp.jpg
http://upload.wikimedia.org/wikipedia/commons/1/13/Rosies_ct_scan.jpg http://www.nemusiccenter.com/product_images/u/377/SM58__69613_zoom.jpg
http://onemillionlyrics.com/lyrics/scanner/rmu http://bssdigitalsound.files.wordpress.com/2008/02/midi-mk249c.jpg
TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAAAA
CS 148, Summer 2012 Introduction to Computer Graphics and Imaging
Justin Solomon
http://imageshack.us/photo/my-images/534/sgamepixar1998brrip720p.jpg http://www-ui.is.s.u-tokyo.ac.jp/~takeo/research/rigid/rigid.png