Projection & Interaction
|
|
- Alison Sanders
- 6 years ago
- Views:
Transcription
1 Projecion & Ineracion Algebra of projecion Canonical viewing volume rackball inerface ransform Hierarchies Preview of Assignmen #2 Lecure 8 Comp 236 Spring 25 Projecions Our lives are grealy simplified by he fac ha viewing ransformaions ransform he eye o he origin and he look-a direcion (opical axis) o a specified coordinae axis. his reduces he range of projecion marices. A projecion maps all 3-D coordinaes ono a desired viewing plane. hus, making our 3-D ino a 2-D image. his sor of mapping is no affine like all of he ransforms we ve discussed hus far. In fac, projecion marices do no ransform poins from our affine space back ino he same space. hey ransform poins ino somehing differen. Usually, we will use a projecion marix o reduce he dimensionally of our affine poins. hus, we should expec projecion marices o be less han full rank. 2/4/25 Lecure 9 2 Orhographic Projecion he simples form of projecion, is o simply projec all poins along lines parallel o he z-axis. his form of projecion is called orhographic or parallel. I is he ommon form of projecion used by drafs people for op, boom, and side views. he advanage of parallel projecion is ha he you can make accurae easuremens of image feaures in he wo dimensions ha remain. he isadvanage is ha he images don appear naural (i.e. hey lack perspecive oreshorening). ere is an example of an parallel rojecion of our scene. oice ha he parallel lines of he iled floor remain parallel fer orhographic projecion. Orhographic Projecion he projecion marix for orhographic projecion is very simple x y z x y z here are some problems wih his simple form, however. o begin wih he unis of he ransformed poins are sill he same as he model. his is grea for drafing, bu in our case we d like o unis ha are model-independen. his will allow us o perform a wide range of operaions using normalized coordinaes.
2 Normalized Device Coordinaes herefore we will compose our projecion wih a se of scale and a ranslaion ha maps our coordinaes in unis o normalized device coordinaes. Orhographic Projecions o NDC Here is he mapping: x y z righ 2 lef Some saniy checks: x lef x op boom 2 far 2 (righ lef ) righ lef (op boom) op boom (far ) far righ lef righ lef righ 2 lef lef righ lef righ lef x y z We also scale he z coordinae in exacly he same way (i.e. all z values beween and far are mapped from o respecively). echnically, his coordinae is no par of he projecion. Bu, we will use his value of z for oher purposes. x righ x 2 righ lef righ lef righ righ lef righ lef righ lef 2/4/25 Lecure 9 5 2/4/25 Lecure 9 6 Orhographic Projecion in OpenGL his marix is consruced by he following OpenGL call: void glorho(double lef, double righ, double boom, double op, double, double far ); And he 2-D version (anoher GL uiliy funcion): Perspecive Projecion Ariss (Donaello, Brunelleschi, Durer, and Da Vinci) during he renaissance discovered he imporance of perspecive for making images appear realisic. his oudaes mahemaicians by more han 3 years. Perspecive causes objecs er o he viewer o appear larger han he same objec would appear farher away. Anoher for inroducing homogenous coordinaes o compuer graphics was o accomplish perspecive projecions using li operaors. void gluorho2d( double lef, GLdouble righ, double boom, GLdouble op); Which is jus a call o glorho( ) wih - and far ;
3 Signs of Perspecive Noice how lines known o be parallel in image space appear o converge o a single poin when viewed in perspecive. his is an imporan aribue of lines in projecive spaces, hey always inersec a a poin. Perspecive Projecion he simples ransform for perspecive projecion is: wx wy w x y z We hen apply our rules for a projecive spaces, o find our preferred poin (he one wih a fourh componen of ) by dividing each elemen of he vecor by w. In his example projecion marix, w is simply he z componen. 2/4/25 Lecure 9 9 2/4/25 Lecure 9 Normalized Perspecive As in he orhographic case, perspecive projecion preserves he unis of -space. Once again, o simplify laer operaions we would like o specify a perspecive projecion where some specific range of -space coordinaes are mapped o a Normalized coordinae sysem. NDC Perspecive Marix his can be accomplished wih a clever composiion of ransforms wih our projecion marix. wx wy wz w righ 2 lef (righ lef ) righ lef (op boom) op 2 boom op boom far far 2 far far x y z he values of lef, righ, op, and boom are specified a he deph. Le s ry some saniy checks: (righ lef ) x lef 2 righ lef lef righ lef x z x righ x z 2 righ (righ lef ) righ lef righ lef
4 NDC Perspecive Marix his can be accomplished wih a clever composiion of ransforms wih our projecion marix. wx wy wz w righ 2 lef (righ lef ) righ lef (op boom) op 2 boom op boom far far 2 far far x y z he values of lef, righ, op, and boom are specified a he deph. Le s ry some saniy checks: 2 far far far far z far z far far ( far ) far far far z z far 2 far far ( far ) far far 2/4/25 Lecure 9 3 Perspecive in OpenGL OpenGL provides he following funcion o define perspecive ransformaions: void glfrusum(double lef, double righ, double boom, double op, double, double far); Some hink ha using glfrusum( ) is noninuiive. So OpenGL provides a uiliy funcion wih simpler, bu less general capabiliies. void gluperspecive(double verfov, double aspec, double, double far); 2/4/25 Lecure 9 4 gluperspecive() he following figure illusraes he parameers of gluperspecive(): Subsiuing he exens ino glfrusum() Simple camera-like model Can only specify symmeric frusums. Skewed Frusums here are many cases when a skewed frusum is he only way o ge he job done Sereo viewing on a single muliplexed display (non HMD) racked viewer (even for mono viewing) Fixed viewpor moving viewer lef righ far wx wy wz w verfov CO( ) 2 aspec CO( verfov 2 ) far far 2 far far x y z
5 Exercise: A rackball Inerface A common UI for manipulaing objecs Virual rackball 2 degree of freedom device However, is differenial behavior provides a inuiive roaion specificaion A Virual rackball Imagine he viewpor as floaing above, and jus ouching an acual rackball. You receive he coordinaes in screen space of he MouseDown() and MouseMove() evens. Wha is he axis of roaion? Wha is he angle of roaion? 2/4/25 Lecure 9 7 2/4/25 Lecure 9 8 Compuing he Roaion Consruc a vecor a v from he cener of roaion of he virual rackball o he poin of he MouseDown() even. Consruc a 2 nd vecor b v from he cener of roaion for a given MouseMove() even. Normalize â a v v a, and bˆ b v v, and hen compue axis â bˆ b hen find he angle Arc sin( â bˆ ) and consruc axis R Roae(angle, ) axis a v b v axis Where o Roae? Where do you inser i in rendering process so as o have he desired inerface? c& w& w& camera mod el ( ) w& c & camera 4243 V c& c& V V R mod el p& mod el p& mod el c& VR p& 23 mod el
6 he Proof is in he Code And he Display Rouine def onmousebuon(buon, sae, x, y): global oldx, oldy if (sae GLU_DOWN): oldx, oldy x, y def onmousedrag(x, y): global oldx, oldy, deph if (mode r ): v Vecor(oldX -.5*widh,.5*heigh - oldy,.5*widh).normalize() v Vecor(x -.5*widh,.5*heigh - y,.5*widh).normalize() axis v.cross(v) angle mah.asin(axis.lengh()) axis axis.normalize() glpushmarix() glloadideniy() glroaed(angle*8/mah.pi, axis.x, axis.y, axis.z) glmulmarixd(obj2wld.marix()) obj2wld.se(glgefloav(gl_modelview_marix)) glpopmarix() oldx, oldy x, y def display(): glclear(gl_color_buffer_bi GL_DEPH_BUFFER_BI) glpushmarix() glulooka(,,24,,,,,,) glpushmarix() glmulmarixd(obj2wld.marix()) drawframe(5) obj.draw() glpopmarix() drawbackdrop() glflush() glpopmarix() gluswapbuffers() Wha would happen if I ook ou hese pushes and pops? 2/4/25 Lecure 9 2 2/4/25 Lecure 9 22 ransformaion Hierarchies Many models are composed of independen moving pars Each par defined in i s own coordinae sysem Compose ransforms o posiion and orien he model pars A Simple One-chain Example Using Graphs o Model Hierarchies Model pars are nodes ransforms are edges Wha ransform is applied o he Head par o ge i ino coordinaes? 4 w& head Suppose ha you d like o roae he Neck join a he poin where i mees he Body. hen wha is he Head s ransform o space? 3 2 R head w& R 4 Base Body Neck Head w& head
7 Code Example ( s ry) Code Example (2 nd ry) public override void Draw() { glclear(gl_color_buffer_bi GL_DEPH_BUFFER_BI); glloadideniy(); glulooka(,,-6,,,,,,); // -o-camera ransform glcolor3d(,,); glroaed(-9,,, ); // -o- ransform mom.draw(lamp.base); mom.draw(lamp.body); mom.draw(lamp.neck); mom.draw(lamp.head); glflush(); } public override void Draw() { glclear(gl_color_buffer_bi GL_DEPH_BUFFER_BI); glloadideniy(); glranslaed(.,., -6.); // -o-view ransform glcolor3d(,,); glroaed(-9,,, ); // -o- ransform mom.draw(lamp.base); glranslaed(,,2.5); // -o- ransform mom.draw(lamp.body); glranslaed(2,,); // -o- ransform mom.draw(lamp.neck); glranslaed(2,,); // head-o- ransform mom.draw(lamp.head); glflush(); } 2/4/25 Lecure /4/25 Lecure 9 26 Code Example (3 rd ry) Demo public override void Draw() { glclear(gl_color_buffer_bi GL_DEPH_BUFFER_BI); glloadideniy(); glranslaed(., -2., -6.); // -o-view ransform glcolor3d(,,); glroaed(-9,,, ); // -o- ransform mom.draw(lamp.base); glranslaed(,,2.5); // -o- ransform glroaed(-3,,, ); // roae a pivo mom.draw(lamp.body); glranslaed(2,,); // -o- ransform glroaed(-5,,, ); // roae a pivo mom.draw(lamp.neck); glranslaed(2,,); // head-o- ransform glroaed(8,,, ); // roae head a pivo mom.draw(lamp.head); glflush(); }
8 Skeleon Code: Your Nex Projec Kinemaics Kinemaics describes he moions of bodies (pars) wihou considering he forces required o produce and mainain he moion. More abou geomeric CONSRAINS han PHYSICS. An ariculaed model wih pars, bu only 6 Models Here s where glpushmarix() and glpopmarix() earn heir keep Rs Rf head runk R L Ls Lf Head runk Rc Lc Rs Ls Rf R L Lf Rc Lc 2/4/25 Lecure /4/25 Lecure 9 3 Nex ime As well as Picking & Selecion
CENG 477 Introduction to Computer Graphics. Modeling Transformations
CENG 477 Inroducion o Compuer Graphics Modeling Transformaions Modeling Transformaions Model coordinaes o World coordinaes: Model coordinaes: All shapes wih heir local coordinaes and sies. world World
More informationGauss-Jordan Algorithm
Gauss-Jordan Algorihm The Gauss-Jordan algorihm is a sep by sep procedure for solving a sysem of linear equaions which may conain any number of variables and any number of equaions. The algorihm is carried
More information4.1 3D GEOMETRIC TRANSFORMATIONS
MODULE IV MCA - 3 COMPUTER GRAPHICS ADMN 29- Dep. of Compuer Science And Applicaions, SJCET, Palai 94 4. 3D GEOMETRIC TRANSFORMATIONS Mehods for geomeric ransformaions and objec modeling in hree dimensions
More informationSTEREO PLANE MATCHING TECHNIQUE
STEREO PLANE MATCHING TECHNIQUE Commission III KEY WORDS: Sereo Maching, Surface Modeling, Projecive Transformaion, Homography ABSTRACT: This paper presens a new ype of sereo maching algorihm called Sereo
More informationM y. Image Warping. Targil 7 : Image Warping. Image Warping. 2D Geometric Transformations. image filtering: change range of image g(x) = T(f(x))
Hebrew Universi Image Processing - 6 Image Warping Hebrew Universi Image Processing - 6 argil 7 : Image Warping D Geomeric ransormaions hp://www.jere-marin.com Man slides rom Seve Seiz and Aleei Eros Image
More informationNEWTON S SECOND LAW OF MOTION
Course and Secion Dae Names NEWTON S SECOND LAW OF MOTION The acceleraion of an objec is defined as he rae of change of elociy. If he elociy changes by an amoun in a ime, hen he aerage acceleraion during
More informationEECS 487: Interactive Computer Graphics
EECS 487: Ineracive Compuer Graphics Lecure 7: B-splines curves Raional Bézier and NURBS Cubic Splines A represenaion of cubic spline consiss of: four conrol poins (why four?) hese are compleely user specified
More informationCAMERA CALIBRATION BY REGISTRATION STEREO RECONSTRUCTION TO 3D MODEL
CAMERA CALIBRATION BY REGISTRATION STEREO RECONSTRUCTION TO 3D MODEL Klečka Jan Docoral Degree Programme (1), FEEC BUT E-mail: xkleck01@sud.feec.vubr.cz Supervised by: Horák Karel E-mail: horak@feec.vubr.cz
More informationSTRING DESCRIPTIONS OF DATA FOR DISPLAY*
SLAC-PUB-383 January 1968 STRING DESCRIPTIONS OF DATA FOR DISPLAY* J. E. George and W. F. Miller Compuer Science Deparmen and Sanford Linear Acceleraor Cener Sanford Universiy Sanford, California Absrac
More informationAML710 CAD LECTURE 11 SPACE CURVES. Space Curves Intrinsic properties Synthetic curves
AML7 CAD LECTURE Space Curves Inrinsic properies Synheic curves A curve which may pass hrough any region of hreedimensional space, as conrased o a plane curve which mus lie on a single plane. Space curves
More informationAnnouncements For The Logic of Boolean Connectives Truth Tables, Tautologies & Logical Truths. Outline. Introduction Truth Functions
Announcemens For 02.05.09 The Logic o Boolean Connecives Truh Tables, Tauologies & Logical Truhs 1 HW3 is due nex Tuesday William Sarr 02.05.09 William Sarr The Logic o Boolean Connecives (Phil 201.02)
More informationImplementing Ray Casting in Tetrahedral Meshes with Programmable Graphics Hardware (Technical Report)
Implemening Ray Casing in Terahedral Meshes wih Programmable Graphics Hardware (Technical Repor) Marin Kraus, Thomas Erl March 28, 2002 1 Inroducion Alhough cell-projecion, e.g., [3, 2], and resampling,
More informationProjective geometry- 2D
Projecive geomer- D Acknowledgemens Marc Pollefes: for allowing e use of is ecellen slides on is opic p://www.cs.unc.edu/~marc/mvg/ Ricard Harle and Andrew Zisserman, "Muliple View Geomer in Compuer Vision"
More informationMOTION DETECTORS GRAPH MATCHING LAB PRE-LAB QUESTIONS
NME: TE: LOK: MOTION ETETORS GRPH MTHING L PRE-L QUESTIONS 1. Read he insrucions, and answer he following quesions. Make sure you resae he quesion so I don hae o read he quesion o undersand he answer..
More informationgeometric transformations
geomeric ranformaion comuer grahic ranform 28 fabio ellacini linear algebra review marice noaion baic oeraion mari-vecor mulilicaion comuer grahic ranform 28 fabio ellacini 2 marice noaion for marice and
More informationImage warping Li Zhang CS559
Wha is an image Image arping Li Zhang S559 We can hink of an image as a funcion, f: R 2 R: f(, ) gives he inensi a posiion (, ) defined over a recangle, ih a finie range: f: [a,b][c,d] [,] f Slides solen
More informationSystems & Biomedical Engineering Department. Transformation
Sem & Biomedical Engineering Deparmen SBE 36B: Compuer Sem III Compuer Graphic Tranformaion Dr. Aman Eldeib Spring 28 Tranformaion Tranformaion i a fundamenal corner one of compuer graphic and i a cenral
More informationA METHOD OF MODELING DEFORMATION OF AN OBJECT EMPLOYING SURROUNDING VIDEO CAMERAS
A METHOD OF MODELING DEFORMATION OF AN OBJECT EMLOYING SURROUNDING IDEO CAMERAS Joo Kooi TAN, Seiji ISHIKAWA Deparmen of Mechanical and Conrol Engineering Kushu Insiue of Technolog, Japan ehelan@is.cnl.kuech.ac.jp,
More informationDigital Geometry Processing Differential Geometry
Digial Geomery Processing Differenial Geomery Moivaion Undersand he srucure of he surface Differenial Geomery Properies: smoohness, curviness, imporan direcions How o modify he surface o change hese properies
More informationCS 428: Fall Introduction to. Geometric Transformations (continued) Andrew Nealen, Rutgers, /20/2010 1
CS 428: Fall 2 Inroducion o Compuer Graphic Geomeric Tranformaion (coninued) Andrew Nealen, Ruger, 2 9/2/2 Tranlaion Tranlaion are affine ranformaion The linear par i he ideni mari The 44 mari for he ranlaion
More informationIn Proceedings of CVPR '96. Structure and Motion of Curved 3D Objects from. using these methods [12].
In Proceedings of CVPR '96 Srucure and Moion of Curved 3D Objecs from Monocular Silhouees B Vijayakumar David J Kriegman Dep of Elecrical Engineering Yale Universiy New Haven, CT 652-8267 Jean Ponce Compuer
More informationImage warping/morphing
Image arping/morphing Image arping Digial Visual Effecs Yung-Yu Chuang ih slides b Richard Szeliski, Seve Seiz, Tom Funkhouser and leei Efros Image formaion Sampling and quanizaion B Wha is an image We
More informationEffects needed for Realism. Ray Tracing. Ray Tracing: History. Outline. Foundations of Computer Graphics (Fall 2012)
Foundaions of ompuer Graphics (Fall 2012) S 184, Lecure 16: Ray Tracing hp://ins.eecs.berkeley.edu/~cs184 Effecs needed for Realism (Sof) Shadows Reflecions (Mirrors and Glossy) Transparency (Waer, Glass)
More informationRay Casting. Outline. Outline in Code
Foundaions of ompuer Graphics Online Lecure 10: Ray Tracing 2 Nus and ols amera Ray asing Ravi Ramamoorhi Ouline amera Ray asing (choose ray direcions) Ray-objec inersecions Ray-racing ransformed objecs
More information4. Minimax and planning problems
CS/ECE/ISyE 524 Inroducion o Opimizaion Spring 2017 18 4. Minima and planning problems ˆ Opimizing piecewise linear funcions ˆ Minima problems ˆ Eample: Chebyshev cener ˆ Muli-period planning problems
More informationGeometry Transformation
Geomer Transformaion Januar 26 Prof. Gar Wang Dep. of Mechanical and Manufacuring Engineering Universi of Manioba Wh geomer ransformaion? Beer undersanding of he design Communicaion wih cusomers Generaing
More informationVirtual Recovery of Excavated Archaeological Finds
Virual Recovery of Excavaed Archaeological Finds Jiang Yu ZHENG, Zhong Li ZHANG*, Norihiro ABE Kyushu Insiue of Technology, Iizuka, Fukuoka 820, Japan *Museum of he Terra-Coa Warrlors and Horses, Lin Tong,
More informationOverview. 9 - Game World: textures, skyboxes, etc. Texture Mapping. Texture Space. Vertex Texture Coordinates. Texture Mapping. Game World Backgrounds
CSc 165 Compuer Game Archiecure Overview Texure Mapping 9 - Game World: exure, kyboxe, ec. Game World Background SkyBoxe & SkyDome World Bound and Viibiliy Render Sae 2 Texure Mapping Texure Space Baic
More informationLast Time: Curves & Surfaces. Today. Questions? Limitations of Polygonal Meshes. Can We Disguise the Facets?
Las Time: Curves & Surfaces Expeced value and variance Mone-Carlo in graphics Imporance sampling Sraified sampling Pah Tracing Irradiance Cache Phoon Mapping Quesions? Today Moivaion Limiaions of Polygonal
More information3-D Object Modeling and Recognition for Telerobotic Manipulation
Research Showcase @ CMU Roboics Insiue School of Compuer Science 1995 3-D Objec Modeling and Recogniion for Teleroboic Manipulaion Andrew Johnson Parick Leger Regis Hoffman Marial Heber James Osborn Follow
More informationA Matching Algorithm for Content-Based Image Retrieval
A Maching Algorihm for Conen-Based Image Rerieval Sue J. Cho Deparmen of Compuer Science Seoul Naional Universiy Seoul, Korea Absrac Conen-based image rerieval sysem rerieves an image from a daabase using
More informationReal-Time Avatar Animation Steered by Live Body Motion
Real-Time Avaar Animaion Seered by Live Body Moion Oliver Schreer, Ralf Tanger, Peer Eiser, Peer Kauff, Bernhard Kaspar, and Roman Engler 3 Fraunhofer Insiue for Telecommunicaions/Heinrich-Herz-Insiu,
More informationQuantitative macro models feature an infinite number of periods A more realistic (?) view of time
INFINIE-HORIZON CONSUMPION-SAVINGS MODEL SEPEMBER, Inroducion BASICS Quaniaive macro models feaure an infinie number of periods A more realisic (?) view of ime Infinie number of periods A meaphor for many
More informationMotion Estimation of a Moving Range Sensor by Image Sequences and Distorted Range Data
Moion Esimaion of a Moving Range Sensor by Image Sequences and Disored Range Daa Asuhiko Banno, Kazuhide Hasegawa and Kasushi Ikeuchi Insiue of Indusrial Science Universiy of Tokyo 4-6-1 Komaba, Meguro-ku,
More informationWiley Plus. Assignment 1 is online:
Wile Plus Assignmen 1 is online: 6 problems from chapers and 3 1D and D Kinemaics Due Monda Ocober 5 Before 11 pm! Chaper II: Kinemaics In One Dimension Displacemen Speed and Veloci Acceleraion Equaions
More informationSam knows that his MP3 player has 40% of its battery life left and that the battery charges by an additional 12 percentage points every 15 minutes.
8.F Baery Charging Task Sam wans o ake his MP3 player and his video game player on a car rip. An hour before hey plan o leave, he realized ha he forgo o charge he baeries las nigh. A ha poin, he plugged
More informationUpper Body Tracking for Human-Machine Interaction with a Moving Camera
The 2009 IEEE/RSJ Inernaional Conference on Inelligen Robos and Sysems Ocober -5, 2009 S. Louis, USA Upper Body Tracking for Human-Machine Ineracion wih a Moving Camera Yi-Ru Chen, Cheng-Ming Huang, and
More informationResearch Article Auto Coloring with Enhanced Character Registration
Compuer Games Technology Volume 2008, Aricle ID 35398, 7 pages doi:0.55/2008/35398 Research Aricle Auo Coloring wih Enhanced Characer Regisraion Jie Qiu, Hock Soon Seah, Feng Tian, Quan Chen, Zhongke Wu,
More informationMARSS Reference Sheet
MARSS Reference Shee The defaul MARSS model (form="marxss") is wrien as follows: x = B x 1 + u + C c + w where w MVN( Q ) y = Z x + a + D d + v where v MVN( R ) x 1 MVN(π Λ) or x MVN(π Λ) c and d are inpus
More informationShortest Path Algorithms. Lecture I: Shortest Path Algorithms. Example. Graphs and Matrices. Setting: Dr Kieran T. Herley.
Shores Pah Algorihms Background Seing: Lecure I: Shores Pah Algorihms Dr Kieran T. Herle Deparmen of Compuer Science Universi College Cork Ocober 201 direced graph, real edge weighs Le he lengh of a pah
More informationVideo Content Description Using Fuzzy Spatio-Temporal Relations
Proceedings of he 4s Hawaii Inernaional Conference on Sysem Sciences - 008 Video Conen Descripion Using Fuzzy Spaio-Temporal Relaions rchana M. Rajurkar *, R.C. Joshi and Sananu Chaudhary 3 Dep of Compuer
More informationMotion Level-of-Detail: A Simplification Method on Crowd Scene
Moion Level-of-Deail: A Simplificaion Mehod on Crowd Scene Absrac Junghyun Ahn VR lab, EECS, KAIST ChocChoggi@vr.kais.ac.kr hp://vr.kais.ac.kr/~zhaoyue Recen echnological improvemen in characer animaion
More informationMATH Differential Equations September 15, 2008 Project 1, Fall 2008 Due: September 24, 2008
MATH 5 - Differenial Equaions Sepember 15, 8 Projec 1, Fall 8 Due: Sepember 4, 8 Lab 1.3 - Logisics Populaion Models wih Harvesing For his projec we consider lab 1.3 of Differenial Equaions pages 146 o
More informationFill in the following table for the functions shown below.
By: Carl H. Durney and Neil E. Coer Example 1 EX: Fill in he following able for he funcions shown below. he funcion is odd he funcion is even he funcion has shif-flip symmery he funcion has quarer-wave
More informationIntroduction to Data-Driven Animation: Programming with Motion Capture Jehee Lee
Inroducion o Daa-Driven Animaion: Programming wih Moion Caure Jehee Lee Seoul Naional Universiy Daa-Driven Animaion wih Moion Caure Programming wih Moion Caure Why is i difficul? Encomass a lo of heerogeneous
More informationProceeding of the 6 th International Symposium on Artificial Intelligence and Robotics & Automation in Space: i-sairas 2001, Canadian Space Agency,
Proceeding of he 6 h Inernaional Symposium on Arificial Inelligence and Roboics & Auomaion in Space: i-sairas 00, Canadian Space Agency, S-Huber, Quebec, Canada, June 8-, 00. Muli-resoluion Mapping Using
More informationCoded Caching with Multiple File Requests
Coded Caching wih Muliple File Requess Yi-Peng Wei Sennur Ulukus Deparmen of Elecrical and Compuer Engineering Universiy of Maryland College Park, MD 20742 ypwei@umd.edu ulukus@umd.edu Absrac We sudy a
More informationSpline Curves. Color Interpolation. Normal Interpolation. Last Time? Today. glshademodel (GL_SMOOTH); Adjacency Data Structures. Mesh Simplification
Las Time? Adjacency Daa Srucures Spline Curves Geomeric & opologic informaion Dynamic allocaion Efficiency of access Mesh Simplificaion edge collapse/verex spli geomorphs progressive ransmission view-dependen
More informationTraditional Rendering (Ray Tracing and Radiosity)
Tradiional Rendering (Ray Tracing and Radiosiy) CS 517 Fall 2002 Compuer Science Cornell Universiy Bidirecional Reflecance (BRDF) λ direcional diffuse specular θ uniform diffuse τ σ BRDF Bidirecional Reflecance
More informationOptics and Light. Presentation
Opics and Ligh Presenaion Opics and Ligh Wha comes o mind when you hear he words opics and ligh? Wha is an opical illusion? Opical illusions can use color, ligh and paerns o creae images ha can be
More informationImproved TLD Algorithm for Face Tracking
Absrac Improved TLD Algorihm for Face Tracking Huimin Li a, Chaojing Yu b and Jing Chen c Chongqing Universiy of Poss and Telecommunicaions, Chongqing 400065, China a li.huimin666@163.com, b 15023299065@163.com,
More informationCurves & Surfaces. Last Time? Today. Readings for Today (pick one) Limitations of Polygonal Meshes. Today. Adjacency Data Structures
Las Time? Adjacency Daa Srucures Geomeric & opologic informaion Dynamic allocaion Efficiency of access Curves & Surfaces Mesh Simplificaion edge collapse/verex spli geomorphs progressive ransmission view-dependen
More information1.4 Application Separable Equations and the Logistic Equation
1.4 Applicaion Separable Equaions and he Logisic Equaion If a separable differenial equaion is wrien in he form f ( y) dy= g( x) dx, hen is general soluion can be wrien in he form f ( y ) dy = g ( x )
More informationA NEW APPROACH FOR 3D MODELS TRANSMISSION
A NEW APPROACH FOR 3D MODELS TRANSMISSION A. Guarnieri a, F. Piroi a, M. Ponin a, A. Veore a a CIRGEO, Inerdep. Research Cener of Carography, Phoogrammery, Remoe Sensing and GIS Universiy of Padova, Agripolis
More informationLAMP: 3D Layered, Adaptive-resolution and Multiperspective Panorama - a New Scene Representation
Submission o Special Issue of CVIU on Model-based and Image-based 3D Scene Represenaion for Ineracive Visualizaion LAMP: 3D Layered, Adapive-resoluion and Muliperspecive Panorama - a New Scene Represenaion
More informationarxiv: v1 [cs.cv] 25 Apr 2017
Sudheendra Vijayanarasimhan Susanna Ricco svnaras@google.com ricco@google.com... arxiv:1704.07804v1 [cs.cv] 25 Apr 2017 SfM-Ne: Learning of Srucure and Moion from Video Cordelia Schmid Esimaed deph, camera
More informationRao-Blackwellized Particle Filtering for Probing-Based 6-DOF Localization in Robotic Assembly
MITSUBISHI ELECTRIC RESEARCH LABORATORIES hp://www.merl.com Rao-Blackwellized Paricle Filering for Probing-Based 6-DOF Localizaion in Roboic Assembly Yuichi Taguchi, Tim Marks, Haruhisa Okuda TR1-8 June
More informationOptimal Crane Scheduling
Opimal Crane Scheduling Samid Hoda, John Hooker Laife Genc Kaya, Ben Peerson Carnegie Mellon Universiy Iiro Harjunkoski ABB Corporae Research EWO - 13 November 2007 1/16 Problem Track-mouned cranes move
More informationEngineering Mathematics 2018
Engineering Mahemaics 08 SUBJET NAME : Mahemaics II SUBJET ODE : MA65 MATERIAL NAME : Par A quesions REGULATION : R03 UPDATED ON : November 06 TEXTBOOK FOR REFERENE To buy he book visi : Sri Hariganesh
More informationX-Splines : A Spline Model Designed for the End-User
X-Splines : A Spline Model Designed for he End-User Carole Blanc Chrisophe Schlic LaBRI 1 cours de la libéraion, 40 alence (France) [blancjschlic]@labri.u-bordeaux.fr Absrac his paper presens a new model
More informationSchedule. Curves & Surfaces. Questions? Last Time: Today. Limitations of Polygonal Meshes. Acceleration Data Structures.
Schedule Curves & Surfaces Sunday Ocober 5 h, * 3-5 PM *, Room TBA: Review Session for Quiz 1 Exra Office Hours on Monday (NE43 Graphics Lab) Tuesday Ocober 7 h : Quiz 1: In class 1 hand-wrien 8.5x11 shee
More informationDesign Alternatives for a Thin Lens Spatial Integrator Array
Egyp. J. Solids, Vol. (7), No. (), (004) 75 Design Alernaives for a Thin Lens Spaial Inegraor Array Hala Kamal *, Daniel V azquez and Javier Alda and E. Bernabeu Opics Deparmen. Universiy Compluense of
More informationRendering Pipeline/ OpenGL
Grading Programming Assignmens: 4% Chaper 2 2D Game: Inro o (6%) ou now 3D Transformaions modeling/animaion (11%) Basics of Compuer Graphics: Rendering pipeline (11%) Ray racing (12%) compuer graphics
More informationSection 2. Mirrors and Prism Systems
Secion 2 Mirrors and Prism Sysems 2-1 Plane Mirrors Plane mirrors are used o: Produce a deviaion Fold he opical pah Change he image pariy Each ray from he objec poin obeys he law of reflecion a he mirror
More informationREDUCTIONS BBM ALGORITHMS DEPT. OF COMPUTER ENGINEERING ERKUT ERDEM. Bird s-eye view. May. 12, Reduction.
BBM 0 - ALGORITHMS DEPT. OF COMPUTER ENGINEERING ERKUT ERDEM REDUCTIONS May., 0 Bird s-eye view Desideraa. Classify problems according o compuaional requiremens. complexiy order of growh examples linear
More informationChapter 4 Sequential Instructions
Chaper 4 Sequenial Insrucions The sequenial insrucions of FBs-PLC shown in his chaper are also lised in secion 3.. Please refer o Chaper, "PLC Ladder diagram and he Coding rules of Mnemonic insrucion",
More informationImage segmentation. Motivation. Objective. Definitions. A classification of segmentation techniques. Assumptions for thresholding
Moivaion Image segmenaion Which pixels belong o he same objec in an image/video sequence? (spaial segmenaion) Which frames belong o he same video sho? (emporal segmenaion) Which frames belong o he same
More informationRay Tracing II. Improving Raytracing Speed. Improving Computational Complexity. Raytracing Computational Complexity
Ra Tracing II Iproving Raracing Speed Copuer Graphics Ra Tracing II 2005 Fabio Pellacini 1 Copuer Graphics Ra Tracing II 2005 Fabio Pellacini 2 Raracing Copuaional Coplei ra-scene inersecion is epensive
More informationData Structures and Algorithms. The material for this lecture is drawn, in part, from The Practice of Programming (Kernighan & Pike) Chapter 2
Daa Srucures and Algorihms The maerial for his lecure is drawn, in par, from The Pracice of Programming (Kernighan & Pike) Chaper 2 1 Moivaing Quoaion Every program depends on algorihms and daa srucures,
More informationMORPHOLOGICAL SEGMENTATION OF IMAGE SEQUENCES
MORPHOLOGICAL SEGMENTATION OF IMAGE SEQUENCES B. MARCOTEGUI and F. MEYER Ecole des Mines de Paris, Cenre de Morphologie Mahémaique, 35, rue Sain-Honoré, F 77305 Fonainebleau Cedex, France Absrac. In image
More informationChapter Six Chapter Six
Chaper Si Chaper Si 0 CHAPTER SIX ConcepTess and Answers and Commens for Secion.. Which of he following graphs (a) (d) could represen an aniderivaive of he funcion shown in Figure.? Figure. (a) (b) (c)
More informationToday. Curves & Surfaces. Can We Disguise the Facets? Limitations of Polygonal Meshes. Better, but not always good enough
Today Curves & Surfaces Moivaion Limiaions of Polygonal Models Some Modeling Tools & Definiions Curves Surfaces / Paches Subdivision Surfaces Limiaions of Polygonal Meshes Can We Disguise he Faces? Planar
More informationReconstruct scene geometry from two or more calibrated images. scene point. image plane. Reconstruct scene geometry from two or more calibrated images
Sereo and Moion The Sereo Problem Reconsrc scene geomer from wo or more calibraed images scene poin focal poin image plane Sereo The Sereo Problem Reconsrc scene geomer from wo or more calibraed images
More informationMidterm Exam Announcements
Miderm Exam Noe: This was a challenging exam. CSCI 4: Principles o Programming Languages Lecure 1: Excepions Insrucor: Dan Barowy Miderm Exam Scores 18 16 14 12 10 needs improvemen 8 6 4 2 0 0-49 50-59
More informationViewing Transformation
CS38: Computer Graphics Viewing Transformation Sung-Eui Yoon ( 윤성의 ) Course URL: http://sglab.kaist.ac.kr/~sungeui/cg/ Class Objectives Know camera setup parameters Understand viewing and projection processes
More informationME 406 Assignment #1 Solutions
Assignmen#1Sol.nb 1 ME 406 Assignmen #1 Soluions PROBLEM 1 We define he funcion for Mahemaica. In[1]:= f@_d := Ep@D - 4 Sin@D (a) We use Plo o consruc he plo. In[2]:= Plo@f@D, 8, -5, 5
More informationReal time 3D face and facial feature tracking
J Real-Time Image Proc (2007) 2:35 44 DOI 10.1007/s11554-007-0032-2 ORIGINAL RESEARCH PAPER Real ime 3D face and facial feaure racking Fadi Dornaika Æ Javier Orozco Received: 23 November 2006 / Acceped:
More informationCS380: Computer Graphics Viewing Transformation. Sung-Eui Yoon ( 윤성의 ) Course URL:
CS38: Computer Graphics Viewing Transformation Sung-Eui Yoon ( 윤성의 ) Course URL: http://sglab.kaist.ac.kr/~sungeui/cg/ Class Objectives Know camera setup parameters Understand viewing and projection processes
More informationthe marginal product. Using the rule for differentiating a power function,
3 Augu 07 Chaper 3 Derivaive ha economi ue 3 Rule for differeniaion The chain rule Economi ofen work wih funcion of variable ha are hemelve funcion of oher variable For example, conider a monopoly elling
More informationImage Based Computer-Aided Manufacturing Technology
Sensors & Transducers 03 by IFSA hp://www.sensorsporal.com Image Based Compuer-Aided Manufacuring Technology Zhanqi HU Xiaoqin ZHANG Jinze LI Wei LI College of Mechanical Engineering Yanshan Universiy
More informationOcclusion-Free Hand Motion Tracking by Multiple Cameras and Particle Filtering with Prediction
58 IJCSNS Inernaional Journal of Compuer Science and Nework Securiy, VOL.6 No.10, Ocober 006 Occlusion-Free Hand Moion Tracking by Muliple Cameras and Paricle Filering wih Predicion Makoo Kao, and Gang
More informationScattering at an Interface: Normal Incidence
Course Insrucor Dr. Raymond C. Rumpf Office: A 337 Phone: (915) 747 6958 Mail: rcrumpf@uep.edu 4347 Applied lecromagneics Topic 3f Scaering a an Inerface: Normal Incidence Scaering These Normal noes Incidence
More informationVisual Perception as Bayesian Inference. David J Fleet. University of Toronto
Visual Percepion as Bayesian Inference David J Flee Universiy of Torono Basic rules of probabiliy sum rule (for muually exclusive a ): produc rule (condiioning): independence (def n ): Bayes rule: marginalizaion:
More informationStreamline Pathline Eulerian Lagrangian
Sreamline Pahline Eulerian Lagrangian Sagnaion Poin Flow V V V = + = + = + o V xi y j a V V xi y j o Pahline and Sreakline Insananeous Sreamlines Pahlines Sreaklines Maerial Derivaive Acceleraion
More informationImage Content Representation
Image Conen Represenaion Represenaion for curves and shapes regions relaionships beween regions E.G.M. Perakis Image Represenaion & Recogniion 1 Reliable Represenaion Uniqueness: mus uniquely specify an
More informationComputer representations of piecewise
Edior: Gabriel Taubin Inroducion o Geomeric Processing hrough Opimizaion Gabriel Taubin Brown Universiy Compuer represenaions o piecewise smooh suraces have become vial echnologies in areas ranging rom
More informationUX260 QUICK START GUIDE
UX260 QUICK START GUIDE Transferring Music Playing Music Blueooh Pairing Taking a Picure/ Recording a Video www.lgusa.com Geing o Know Your Phone Camera BACK SIDE Lef Sof Key Speakerphone Key Talk Key
More informationTHERMAL PHYSICS COMPUTER LAB #3 : Stability of Dry Air and Brunt-Vaisala Oscillations
THERMAL PHYSICS COMPUTER LAB #3 : Sabiliy of Dry Air and Brun-Vaisala Oscillaions Consider a parcel of dry air of volume V, emperaure T and densiy ρ. I displace he same volume V of surrounding air of emperaure
More informationNumerical Solution of ODE
Numerical Soluion of ODE Euler and Implici Euler resar; wih(deools): wih(plos): The package ploools conains more funcions for ploing, especially a funcion o draw a single line: wih(ploools): wih(linearalgebra):
More informationJorge Salvador Marques, Stereo Reconstruction
Jorge Slvdor Mrques, Sereo Reconsrucion roblem Gol: reconsruc he D she of objecs in he scene from or more imges. Jorge Slvdor Mrques, Jorge Slvdor Mrques, secil cse f f f f b model reconsrucion, b - fb,
More informationWhy not experiment with the system itself? Ways to study a system System. Application areas. Different kinds of systems
Simulaion Wha is simulaion? Simple synonym: imiaion We are ineresed in sudying a Insead of experimening wih he iself we experimen wih a model of he Experimen wih he Acual Ways o sudy a Sysem Experimen
More informationThe Roots of Lisp paul graham
The Roos of Lisp paul graham Draf, January 18, 2002. In 1960, John McCarhy published a remarkable paper in which he did for programming somehing like wha Euclid did for geomery. 1 He showed how, given
More informationVideo-Based Face Recognition Using Probabilistic Appearance Manifolds
Video-Based Face Recogniion Using Probabilisic Appearance Manifolds Kuang-Chih Lee Jeffrey Ho Ming-Hsuan Yang David Kriegman klee10@uiuc.edu jho@cs.ucsd.edu myang@honda-ri.com kriegman@cs.ucsd.edu Compuer
More informationLow-Cost WLAN based. Dr. Christian Hoene. Computer Science Department, University of Tübingen, Germany
Low-Cos WLAN based Time-of-fligh fligh Trilaeraion Precision Indoor Personnel Locaion and Tracking for Emergency Responders Third Annual Technology Workshop, Augus 5, 2008 Worceser Polyechnic Insiue, Worceser,
More informationEvaluation and Improvement of Region-based Motion Segmentation
Evaluaion and Improvemen of Region-based Moion Segmenaion Mark Ross Universiy Koblenz-Landau, Insiue of Compuaional Visualisics, Universiässraße 1, 56070 Koblenz, Germany Email: ross@uni-koblenz.de Absrac
More informationV103 TRIPLE 10-BIT LVDS TRANSMITTER FOR VIDEO. General Description. Features. Block Diagram
General Descripion The V103 LVDS display inerface ransmier is primarily designed o suppor pixel daa ransmission beween a video processing engine and a digial video display. The daa rae suppors up o SXGA+
More informationA Principled Approach to. MILP Modeling. Columbia University, August Carnegie Mellon University. Workshop on MIP. John Hooker.
Slide A Principled Approach o MILP Modeling John Hooer Carnegie Mellon Universiy Worshop on MIP Columbia Universiy, Augus 008 Proposal MILP modeling is an ar, bu i need no be unprincipled. Slide Proposal
More informationExperiments in Generalizing Geometry Theorems Stephen B. Gray
Experimens in Generalizing Geomery Theorems Sephen B. Gray. INTRODUCTION: THE PDN THEOREM Well-known advances in geomery have been made wih experimenal, or compueraided echniques. The irs was he proo o
More informationIDEF3 Process Description Capture Method
IDEF3 Process Descripion Capure Mehod IDEF3 is par of he IDEF family of mehods developmen funded by he US Air Force o provide modelling suppor for sysems engineering and enerprise inegraion 2 IDEF3 Mehod
More informationLearning in Games via Opponent Strategy Estimation and Policy Search
Learning in Games via Opponen Sraegy Esimaion and Policy Search Yavar Naddaf Deparmen of Compuer Science Universiy of Briish Columbia Vancouver, BC yavar@naddaf.name Nando de Freias (Supervisor) Deparmen
More information