Virtual Cameras & Their Matrices
|
|
- Janis Lambert
- 5 years ago
- Views:
Transcription
1 Virtual Cameras & Their Matrices J.Tumblin-Modified, highly edited SLIDES from: Ed Angel Professor Emeritus of Computer Science University of New Mexico 1
2 What is Projection? Any operation that reduces dimension (e.g., 3D to 2D) Orthographic Projection Perspective Projection
3 V U N Center of Projection (Camera Origin) Image Plane ( Splits the Universe )
4 Perspective Projection z = not allowed (what happens to points on plane z =?) Operation well-defined for all other points
5 The View Frustum
6 Vertex Stream WebGL: Vertex Position Pipeline gl.modelview gl.projection model + model view + view transformation transformation projection transformation HTML-5 Canvas divide: x/w, y/w, z/w 4D 3D The CVV clipping ViewPort transformation gl.viewport(llx, lly width,height) (in pixels) 6
7 Notes KEEP our four-dimensional homogeneous coordinates throughout all transforms by MODEL, VIEW, and PROJECTION matrix: - All are nonsingular - All default to identity matrices (CVV sets limits) Delay final perspective-divides until the end - Important for hidden-surface removal: we NEED depth information to draw pixels! - Efficient : FP division == expensive to compute E. Angel and D. Shreiner: Interactive Computer Graphics 6E Addison-Wesley 212 7
8 WebGL: Vertex Position Pipeline Wher do these matrices fit into the SceneGraph? MODEL (jointed objects) VIEW (camera-positioning) PROJECTION (lens-like) VIEWPORT (screen) group4 CVV t1 HTML-5 Canvas t group1 t2 group2 t7 group3... t3 t4 obj1 obj5 obj2 group3 8
9 WebGL: Vertex Position Pipeline RECALL: in scene graphs, Vertices & values move upwards, transform calls move downwards Project A: CVV == World drawing axes (group) CVV HTML-5 Canvas group4 t1 t group1 t2 t7 group3... t3 group2 t4 obj1 obj5 obj2 group3 9
10 WebGL: Vertex Position Pipeline RECALL: in scene graphs, Vertices & values move upwards, transform calls move downwards CVV HTML-5 Canvas Viewport Project A: CVV == World drawing axes (group) World CAM View Projection Project B: Viewport output HTML Canvas CVV output Viewport input Lens Axes CVV input Camera Axes Lens Input group4 t group1 t1 t2 group2 group3... t7 t3 t4 obj2 group3 World Coords Camera Axes 1 obj1 obj5
11 Simple Perspective Consider a simple point-perspective image with the COP at the origin, the near clipping plane at z = -1, and a 9 degree field of view determined by the planes x = z, y = z E. Angel and D. Shreiner: Interactive Computer Graphics 6E Addison-Wesley
12 Simple Perspective Consider a simple point-perspective image with the COP at the origin, the near clipping plane at z = -1, and a 9 degree field of view determined by the planes x = z, y = z E. Angel and D. Shreiner: Interactive Computer Graphics 6E Addison-Wesley
13 Orthographic Camera Simple Orthographic Projection Matrix: re-scale a rectangular volume in CAM coords to fit within the CVV gl.ortho(left,right,bottom,top,near,far) E. Angel and D. Shreiner: Interactive Computer Graphics 6E Addison-Wesley
14 Step 1: Orthogonal Matrix Two steps: - Translate the camera s frustum center to the origin T(-(left+right)/2, -(bottom+top)/2, (near+far)/2)) - Scale to have sides of length 2 (to match the CVV) S(2/(left-right),2/(top-bottom),2/(near-far)) P = ST = 2 right left 2 top bottom 2 near far right left right left top bottom top bottom far near far near 1 E. Angel and D. Shreiner: Interactive Computer Graphics 6E Addison-Wesley
15 Clipping & Display: Put it into the CVV! Keep 3D clipping simple, fixed and fast Don t form different clipping volumes for each kind of frustum, lens or camera! Instead, map them all into the CVV become orthogonal projections to screen One camera one matrix One camera type One function E. Angel and D. Shreiner: Interactive Computer Graphics 6E Addison-Wesley
16 Simple Perspective Consider a simple point-perspective image with the COP at the origin, the near clipping plane at z = -1, and a 9 degree field of view determined by the planes x = z, y = z E. Angel and D. Shreiner: Interactive Computer Graphics 6E Addison-Wesley
17 (Naïve) Perspective Matrix Simple projection matrix in homogeneous coordinates M = Trouble! matrix ignores near clipping plane, and CVV sets far plane by default to +1 E. Angel and D. Shreiner: Interactive Computer Graphics 6E Addison-Wesley
18 One Weird Trick to fix it (perfectionists hate it ) N = 1 1 α β 1 after perspective division, the point at (x, y, z, 1) becomes x = x/z y = y/z Z = -(az+b)/z Choose a and b carefully E. Angel and D. Shreiner: Interactive Computer Graphics 6E Addison-Wesley
19 Generalize to fix it: N = 1 1 α β 1 after perspective division, the point (x, y, z, 1) goes to x = x/z y = y/z Z = -(az+b)/z Could it span -1 to +1 (as x,y might)? could we fit it into the CVV? E. Angel and D. Shreiner: Interactive Computer Graphics 6E Addison-Wesley
20 Pseudo-Depth : Picking a and b If we pick a = b = near far far near 2near far near far the near plane is mapped to z = 1 the far plane is mapped to z =-1 and the sides are mapped to x = 1, y = 1 Hence the viewing frustum fills the CVV exactly! E. Angel and D. Shreiner: Interactive Computer Graphics 6E Addison-Wesley 212 2
21 Normalization Transformation distorted object projects correctly original clipping volume original object new clipping volume E. Angel and D. Shreiner: Interactive Computer Graphics 6E Addison-Wesley
22 Posing the Camera AWKWARD: Define position in WORLD coords 22
23 END E. Angel and D. Shriener: Interactive Computer Graphics 6E Addison-Wesley
24 Normalization and Hidden-Surface Removal Although our pseudo-depth may SEEM weirdly arbitrary, it ensures monotonic depth: if z 1 > z 2 in the original clipping volume, then inside the CVV we always have z 1 > z 2 Thus hidden surface removal still works fine based on CVV s z value However pseudo-depth DISTORTS distances. It compresses far-away depths, expands nearby ones; z = -(az+b) /z Tiny znear? Giant zfar? Expect coarse depth quantization! E. Angel and D. Shreiner: Interactive Computer Graphics 6E Addison-Wesley
25 Set z = Step 2: Final Projection (perspective) Equivalent to the homogeneous coordinate transformation M orth = Hence, general orthogonal projection in 4D is P = M orth ST E. Angel and D. Shreiner: Interactive Computer Graphics 6E Addison-Wesley
Course no. DIS4566 National Chiao Tung Univ, Taiwan By: I-Chen Lin, Assistant Professor
Computer Graphics 3. Viewing in 3D (b) Course no. DIS4566 National Chiao Tung Univ, Taiwan By: I-Chen Lin, Assistant Professor Textbook: E.Angel, Interactive Computer Graphics, 4 th Ed., Addison Wesley
More informationComputer Viewing. CS 537 Interactive Computer Graphics Prof. David E. Breen Department of Computer Science
Computer Viewing CS 537 Interactive Computer Graphics Prof. David E. Breen Department of Computer Science 1 Objectives Introduce the mathematics of projection Introduce OpenGL viewing functions Look at
More informationOrthogonal Projection Matrices. Angel and Shreiner: Interactive Computer Graphics 7E Addison-Wesley 2015
Orthogonal Projection Matrices 1 Objectives Derive the projection matrices used for standard orthogonal projections Introduce oblique projections Introduce projection normalization 2 Normalization Rather
More informationComputer Viewing and Projection. Overview. Computer Viewing. David Carr Fundamentals of Computer Graphics Spring 2004 Based on Slides by E.
INSTITUTIONEN FÖR SYSTEMTEKNIK LULEÅ TEKNISKA UNIVERSITET Computer Viewing and Projection David Carr Fundamentals of Computer Graphics Spring 24 Based on Slides by E. Angel Projection 1 L Overview Computer
More informationComputer Viewing. Prof. George Wolberg Dept. of Computer Science City College of New York
Computer Viewing Prof. George Wolberg Dept. of Computer Science City College of New York Objectives Introduce the mathematics of projection Introduce OpenGL viewing functions Look at alternate viewing
More informationOverview. Viewing and perspectives. Planar Geometric Projections. Classical Viewing. Classical views Computer viewing Perspective normalization
Overview Viewing and perspectives Classical views Computer viewing Perspective normalization Classical Viewing Viewing requires three basic elements One or more objects A viewer with a projection surface
More informationFundamental Types of Viewing
Viewings Fundamental Types of Viewing Perspective views finite COP (center of projection) Parallel views COP at infinity DOP (direction of projection) perspective view parallel view Classical Viewing Specific
More informationToday. Rendering pipeline. Rendering pipeline. Object vs. Image order. Rendering engine Rendering engine (jtrt) Computergrafik. Rendering pipeline
Computergrafik Today Rendering pipeline s View volumes, clipping Viewport Matthias Zwicker Universität Bern Herbst 2008 Rendering pipeline Rendering pipeline Hardware & software that draws 3D scenes on
More informationThree-Dimensional Graphics III. Guoying Zhao 1 / 67
Computer Graphics Three-Dimensional Graphics III Guoying Zhao 1 / 67 Classical Viewing Guoying Zhao 2 / 67 Objectives Introduce the classical views Compare and contrast image formation by computer with
More informationCS452/552; EE465/505. Intro to Lighting
CS452/552; EE465/505 Intro to Lighting 2-10 15 Outline! Projection Normalization! Introduction to Lighting (and Shading) Read: Angel Chapter 5., sections 5.4-5.7 Parallel Projections Chapter 6, sections
More informationIntroduction to Computer Graphics 4. Viewing in 3D
Introduction to Computer Graphics 4. Viewing in 3D National Chiao Tung Univ, Taiwan By: I-Chen Lin, Assistant Professor Textbook: E.Angel, Interactive Computer Graphics, 5 th Ed., Addison Wesley Ref: Hearn
More informationOn the Midterm Exam. Monday, 10/17 in class. Closed book and closed notes. One-side and one page cheat sheet is allowed. A calculator is allowed
On the Midterm Exam Monday, 1/17 in class Closed book and closed notes One-side and one page cheat sheet is allowed A calculator is allowed Covers the topics until the class on Wednesday, 1/12 Take-home
More informationClassical and Computer Viewing. Adapted From: Ed Angel Professor of Emeritus of Computer Science University of New Mexico
Classical and Computer Viewing Adapted From: Ed Angel Professor of Emeritus of Computer Science University of New Mexico Planar Geometric Projections Standard projections project onto a plane Projectors
More informationCS 418: Interactive Computer Graphics. Projection
CS 418: Interactive Computer Graphics Projection Eric Shaffer Based on John Hart s CS 418 Slides Hierarchical Solar System Model Without push/pop, You can t move the Earth scale to before you draw the
More informationCSE 167: Introduction to Computer Graphics Lecture #5: Projection. Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2017
CSE 167: Introduction to Computer Graphics Lecture #5: Projection Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2017 Announcements Friday: homework 1 due at 2pm Upload to TritonEd
More informationOne or more objects A viewer with a projection surface Projectors that go from the object(s) to the projection surface
Classical Viewing Viewing requires three basic elements One or more objects A viewer with a projection surface Projectors that go from the object(s) to the projection surface Classical views are based
More informationPhong Lighting & Materials. Some slides modified from: David Kabala Others from: Andries Van Damm, Brown Univ.
Phong Lighting & Materials Some slides modified from: David Kabala Others from: Andries Van Damm, Brown Univ. Lighting and Shading Lighting, or illumination, is the process of computing the intensity and
More informationOverview. By end of the week:
Overview By end of the week: - Know the basics of git - Make sure we can all compile and run a C++/ OpenGL program - Understand the OpenGL rendering pipeline - Understand how matrices are used for geometric
More informationCOMP Computer Graphics and Image Processing. a6: Projections. In part 2 of our study of Viewing, we ll look at. COMP27112 Toby Howard
Computer Graphics and Image Processing a6: Projections Tob.Howard@manchester.ac.uk Introduction In part 2 of our stud of Viewing, we ll look at The theor of geometrical planar projections Classes of projections
More informationNotes on Assignment. Notes on Assignment. Notes on Assignment. Notes on Assignment
Notes on Assignment Notes on Assignment Objects on screen - made of primitives Primitives are points, lines, polygons - watch vertex ordering The main object you need is a box When the MODELVIEW matrix
More informationEECS : Introduction to Computer Graphics Building the Virtual Camera ver. 1.4
EECS 351-1 : Introduction to Computer Graphics Building the Virtual Camera ver. 1.4 3D Transforms (cont d): 3D Transformation Types: did we really describe ALL of them? No! --All fit in a 4x4 matrix, suggesting
More informationEECS : Introduction to Computer Graphics Building the Virtual Camera ver. 1.5
EECS 351-1 : Introduction to Computer Graphics Building the Virtual Camera ver. 1.5 3D Transforms (cont d): We havent yet explored ALL of the geometric transformations available within a 4x4 matrix. --All
More informationLecture 4. Viewing, Projection and Viewport Transformations
Notes on Assignment Notes on Assignment Hw2 is dependent on hw1 so hw1 and hw2 will be graded together i.e. You have time to finish both by next monday 11:59p Email list issues - please cc: elif@cs.nyu.edu
More information1 Transformations. Chapter 1. Transformations. Department of Computer Science and Engineering 1-1
Transformations 1-1 Transformations are used within the entire viewing pipeline: Projection from world to view coordinate system View modifications: Panning Zooming Rotation 1-2 Transformations can also
More informationThree-Dimensional Viewing Hearn & Baker Chapter 7
Three-Dimensional Viewing Hearn & Baker Chapter 7 Overview 3D viewing involves some tasks that are not present in 2D viewing: Projection, Visibility checks, Lighting effects, etc. Overview First, set up
More informationChap 3 Viewing Pipeline Reading: Angel s Interactive Computer Graphics, Sixth ed. Sections 4.1~4.7
Chap 3 Viewing Pipeline Reading: Angel s Interactive Computer Graphics, Sixth ed. Sections 4.~4.7 Chap 3 View Pipeline, Comp. Graphics (U) CGGM Lab., CS Dept., NCTU Jung Hong Chuang Outline View parameters
More informationThree Main Themes of Computer Graphics
Three Main Themes of Computer Graphics Modeling How do we represent (or model) 3-D objects? How do we construct models for specific objects? Animation How do we represent the motion of objects? How do
More informationTransforms 3: Projection Christian Miller CS Fall 2011
Transforms 3: Projection Christian Miller CS 354 - Fall 2011 Eye coordinates Eye space is the coordinate system at the camera: x right, y up, z out (i.e. looking down -z) [RTR] The setup Once we ve applied
More informationCSC 305 The Graphics Pipeline-1
C. O. P. d y! "#"" (-1, -1) (1, 1) x z CSC 305 The Graphics Pipeline-1 by Brian Wyvill The University of Victoria Graphics Group Perspective Viewing Transformation l l l Tools for creating and manipulating
More informationCITSTUDENTS.IN VIEWING. Computer Graphics and Visualization. Classical and computer viewing. Viewing with a computer. Positioning of the camera
UNIT - 6 7 hrs VIEWING Classical and computer viewing Viewing with a computer Positioning of the camera Simple projections Projections in OpenGL Hiddensurface removal Interactive mesh displays Parallelprojection
More informationAnnouncement. Project 1 has been posted online and in dropbox. Due: 11:59:59 pm, Friday, October 14
Announcement Project 1 has been posted online and in dropbox Due: 11:59:59 pm, Friday, October 14 Project 1: Interactive Viewing of Two Teapots How to create a teapot? Before OpenGL 3., glutsolidteapot
More informationThe Graphics Pipeline and OpenGL I: Transformations!
! The Graphics Pipeline and OpenGL I: Transformations! Gordon Wetzstein! Stanford University! EE 267 Virtual Reality! Lecture 2! stanford.edu/class/ee267/!! Albrecht Dürer, Underweysung der Messung mit
More informationCS230 : Computer Graphics Lecture 6: Viewing Transformations. Tamar Shinar Computer Science & Engineering UC Riverside
CS230 : Computer Graphics Lecture 6: Viewing Transformations Tamar Shinar Computer Science & Engineering UC Riverside Rendering approaches 1. image-oriented foreach pixel... 2. object-oriented foreach
More informationIntroduction to Computer Graphics with WebGL
Introduction to Computer Graphics with WebGL Ed Angel Professor Emeritus of Computer Science Founding Director, Arts, Research, Technology and Science Laboratory University of New Mexico Models and Architectures
More informationCSE 167: Lecture #4: Vertex Transformation. Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2012
CSE 167: Introduction to Computer Graphics Lecture #4: Vertex Transformation Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2012 Announcements Project 2 due Friday, October 12
More informationCSE328 Fundamentals of Computer Graphics
CSE328 Fundamentals of Computer Graphics Hong Qin State University of New York at Stony Brook (Stony Brook University) Stony Brook, New York 794--44 Tel: (63)632-845; Fax: (63)632-8334 qin@cs.sunysb.edu
More informationLecture 3 Sections 2.2, 4.4. Mon, Aug 31, 2009
Model s Lecture 3 Sections 2.2, 4.4 World s Eye s Clip s s s Window s Hampden-Sydney College Mon, Aug 31, 2009 Outline Model s World s Eye s Clip s s s Window s 1 2 3 Model s World s Eye s Clip s s s Window
More informationComputer Graphics. Coordinate Systems and Change of Frames. Based on slides by Dianna Xu, Bryn Mawr College
Computer Graphics Coordinate Systems and Change of Frames Based on slides by Dianna Xu, Bryn Mawr College Linear Independence A set of vectors independent if is linearly If a set of vectors is linearly
More information3D Viewing. CS 4620 Lecture 8
3D Viewing CS 46 Lecture 8 13 Steve Marschner 1 Viewing, backward and forward So far have used the backward approach to viewing start from pixel ask what part of scene projects to pixel explicitly construct
More informationVirtual Cameras and The Transformation Pipeline
Virtual Cameras and The Transformation Pipeline Anton Gerdelan gerdela@scss.tcd.ie with content from Rachel McDonnell 13 Oct 2014 Virtual Camera We want to navigate through our scene in 3d Solution = create
More informationProjection and viewing. Computer Graphics CSE 167 Lecture 4
Projection and viewing Computer Graphics CSE 167 Lecture 4 CSE 167: Computer Graphics Review: transformation from the object (or model) coordinate frame to the camera (or eye) coordinate frame Projection
More informationCS 4204 Computer Graphics
CS 4204 Computer Graphics 3D Viewing and Projection Yong Cao Virginia Tech Objective We will develop methods to camera through scenes. We will develop mathematical tools to handle perspective projection.
More informationIntroduction to Computer Graphics with WebGL
Introduction to Computer Graphics with WebGL Ed Angel Classical Viewing Computer Graphics with WebGL Ed Angel, 204 Classical Viewing Viewing requires three basic elements - One or more objects - A viewer
More informationThe Graphics Pipeline. Interactive Computer Graphics. The Graphics Pipeline. The Graphics Pipeline. The Graphics Pipeline: Clipping
Interactive Computer Graphics The Graphics Pipeline: The Graphics Pipeline Input: - geometric model - illumination model - camera model - viewport Some slides adopted from F. Durand and B. Cutler, MIT
More informationViewing and Projection
CSCI 480 Computer Graphics Lecture 5 Viewing and Projection January 25, 2012 Jernej Barbic University of Southern California Shear Transformation Camera Positioning Simple Parallel Projections Simple Perspective
More informationDrawing in 3D (viewing, projection, and the rest of the pipeline)
Drawing in 3D (viewing, projection, and the rest of the pipeline) CS559 Spring 2017 Lecture 6 February 2, 2017 The first 4 Key Ideas 1. Work in convenient coordinate systems. Use transformations to get
More informationCSE 167: Introduction to Computer Graphics Lecture #4: Vertex Transformation
CSE 167: Introduction to Computer Graphics Lecture #4: Vertex Transformation Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2013 Announcements Project 2 due Friday, October 11
More information3D Viewing. With acknowledge to: Ed Angel. Professor of Computer Science, Electrical and Computer Engineering, and Media Arts University of New Mexico
3D Viewing With acknowledge to: Ed Angel Professor of Computer Science, Electrical and Computer Engineering, and Media Arts University of New Mexico 1 Classical Viewing Viewing plane projectors Classical
More informationCSE 167: Introduction to Computer Graphics Lecture #5: Rasterization. Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2015
CSE 167: Introduction to Computer Graphics Lecture #5: Rasterization Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2015 Announcements Project 2 due tomorrow at 2pm Grading window
More informationViewing with Computers (OpenGL)
We can now return to three-dimension?', graphics from a computer perspective. Because viewing in computer graphics is based on the synthetic-camera model, we should be able to construct any of the classical
More informationModels and Architectures. Ed Angel Professor of Computer Science, Electrical and Computer Engineering, and Media Arts University of New Mexico
Models and Architectures Ed Angel Professor of Computer Science, Electrical and Computer Engineering, and Media Arts University of New Mexico 1 Objectives Learn the basic design of a graphics system Introduce
More informationGEOMETRIC TRANSFORMATIONS AND VIEWING
GEOMETRIC TRANSFORMATIONS AND VIEWING 2D and 3D 1/44 2D TRANSFORMATIONS HOMOGENIZED Transformation Scaling Rotation Translation Matrix s x s y cosθ sinθ sinθ cosθ 1 dx 1 dy These 3 transformations are
More informationViewing and Projection
CSCI 480 Computer Graphics Lecture 5 Viewing and Projection Shear Transformation Camera Positioning Simple Parallel Projections Simple Perspective Projections [Geri s Game, Pixar, 1997] January 26, 2011
More information3D Viewing. CS 4620 Lecture Steve Marschner. Cornell CS4620 Spring 2018 Lecture 9
3D Viewing CS 46 Lecture 9 Cornell CS46 Spring 18 Lecture 9 18 Steve Marschner 1 Viewing, backward and forward So far have used the backward approach to viewing start from pixel ask what part of scene
More informationToday s Agenda. Geometry
Today s Agenda Geometry Geometry Three basic elements Points Scalars Vectors Three type of spaces (Linear) vector space: scalars and vectors Affine space: vector space + points Euclidean space: vector
More informationComputer Viewing. CITS3003 Graphics & Animation. E. Angel and D. Shreiner: Interactive Computer Graphics 6E Addison-Wesley
Computer Viewing CITS3003 Graphics & Animation E. Angel and D. Shreiner: Interactive Computer Graphics 6E Addison-Wesley 2012 1 Objectives Introduce the mathematics of projection Introduce OpenGL viewing
More informationLecture 4: 3D viewing and projections
Lecture 4: 3D viewing and projections Today s lecture Rotations around an arbitrary axis (Continuation from the last lecture) The view coordinate system Change of coordinate system (same origin) Change
More information7. 3D Viewing. Projection: why is projection necessary? CS Dept, Univ of Kentucky
7. 3D Viewing Projection: why is projection necessary? 1 7. 3D Viewing Projection: why is projection necessary? Because the display surface is 2D 2 7.1 Projections Perspective projection 3 7.1 Projections
More informationGeometry. CS 537 Interactive Computer Graphics Prof. David E. Breen Department of Computer Science
Geometry CS 537 Interactive Computer Graphics Prof. David E. Breen Department of Computer Science E. Angel and D. Shreiner: Interactive Computer Graphics 6E Addison-Wesley 2012. 1 Objectives Introduce
More informationCS4620/5620: Lecture 14 Pipeline
CS4620/5620: Lecture 14 Pipeline 1 Rasterizing triangles Summary 1! evaluation of linear functions on pixel grid 2! functions defined by parameter values at vertices 3! using extra parameters to determine
More informationIntroduction to Computer Graphics with WebGL
Introduction to Computer Graphics with WebGL Ed Angel Professor Emeritus of Computer Science Founding Director, Arts, Research, Technology and Science Laboratory University of New Mexico 1 Computer Viewing
More informationCSE 167: Lecture #5: Rasterization. Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2012
CSE 167: Introduction to Computer Graphics Lecture #5: Rasterization Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2012 Announcements Homework project #2 due this Friday, October
More informationCSE528 Computer Graphics: Theory, Algorithms, and Applications
CSE528 Computer Graphics: Theory, Algorithms, and Applications Hong Qin Stony Brook University (SUNY at Stony Brook) Stony Brook, New York 11794-2424 Tel: (631)632-845; Fax: (631)632-8334 qin@cs.stonybrook.edu
More informationDrawing in 3D (viewing, projection, and the rest of the pipeline)
Drawing in 3D (viewing, projection, and the rest of the pipeline) CS559 Spring 2016 Lecture 6 February 11, 2016 The first 4 Key Ideas 1. Work in convenient coordinate systems. Use transformations to get
More informationCOMP3421. Introduction to 3D Graphics
COMP3421 Introduction to 3D Graphics 3D coodinates Moving to 3D is simply a matter of adding an extra dimension to our points and vectors: 3D coordinates 3D coordinate systems can be left or right handed.
More informationViewing. Reading: Angel Ch.5
Viewing Reading: Angel Ch.5 What is Viewing? Viewing transform projects the 3D model to a 2D image plane 3D Objects (world frame) Model-view (camera frame) View transform (projection frame) 2D image View
More information1 OpenGL - column vectors (column-major ordering)
OpenGL - column vectors (column-major ordering) OpenGL uses column vectors and matrices are written in a column-major order. As a result, matrices are concatenated in right-to-left order, with the first
More information3.1 Viewing and Projection
Fall 2017 CSCI 420: Computer Graphics 3.1 Viewing and Projection Hao Li http://cs420.hao-li.com 1 Recall: Affine Transformations Given a point [xyz] > form homogeneous coordinates [xyz1] > The transformed
More informationDrawing in 3D (viewing, projection, and the rest of the pipeline)
Drawing in 3D (viewing, projection, and the rest of the pipeline) CS559 Fall 2016 Lecture 6/7 September 26-28 2016 The first 4 Key Ideas 1. Work in convenient coordinate systems. Use transformations to
More informationTransformations. Ed Angel Professor of Computer Science, Electrical and Computer Engineering, and Media Arts University of New Mexico
Transformations Ed Angel Professor of Computer Science, Electrical and Computer Engineering, and Media Arts University of New Mexico Angel: Interactive Computer Graphics 4E Addison-Wesley 25 1 Objectives
More informationINTRODUCTION TO COMPUTER GRAPHICS. It looks like a matrix Sort of. Viewing III. Projection in Practice. Bin Sheng 10/11/ / 52
cs337 It looks like a matrix Sort of Viewing III Projection in Practice / 52 cs337 Arbitrary 3D views Now that we have familiarity with terms we can say that these view volumes/frusta can be specified
More informationSingle View Geometry. Camera model & Orientation + Position estimation. What am I?
Single View Geometry Camera model & Orientation + Position estimation What am I? Vanishing point Mapping from 3D to 2D Point & Line Goal: Point Homogeneous coordinates represent coordinates in 2 dimensions
More informationCS488. Implementation of projections. Luc RENAMBOT
CS488 Implementation of projections Luc RENAMBOT 1 3D Graphics Convert a set of polygons in a 3D world into an image on a 2D screen After theoretical view Implementation 2 Transformations P(X,Y,Z) Modeling
More informationCOMP3421. Introduction to 3D Graphics
COMP3421 Introduction to 3D Graphics 3D coodinates Moving to 3D is simply a matter of adding an extra dimension to our points and vectors: 3D coordinates 3D coordinate systems can be left or right handed.
More informationProf. Feng Liu. Fall /19/2016
Prof. Feng Liu Fall 26 http://www.cs.pdx.edu/~fliu/courses/cs447/ /9/26 Last time More 2D Transformations Homogeneous Coordinates 3D Transformations The Viewing Pipeline 2 Today Perspective projection
More informationPerspective transformations
Perspective transformations Transformation pipeline Modelview: model (position objects) + view (position the camera) Projection: map viewing volume to a standard cube Perspective division: project D to
More informationProjection: Mapping 3-D to 2-D. Orthographic Projection. The Canonical Camera Configuration. Perspective Projection
Projection: Mapping 3-D to 2-D Our scene models are in 3-D space and images are 2-D so we need some wa of projecting 3-D to 2-D The fundamental approach: planar projection first, we define a plane in 3-D
More informationViewing and Projection
15-462 Computer Graphics I Lecture 5 Viewing and Projection Shear Transformation Camera Positioning Simple Parallel Projections Simple Perspective Projections [Angel, Ch. 5.2-5.4] January 30, 2003 [Red
More informationViewing and Projection Transformations
Viewing and Projection Transformations Projective Rendering Pipeline OCS WCS VCS modeling transformation viewing transformation OCS - object coordinate system WCS - world coordinate system VCS - viewing
More informationViewing and Projection
Viewing and Projection Sheelagh Carpendale Camera metaphor. choose camera position 2. set up and organie objects 3. choose a lens 4. take the picture View Volumes what gets into the scene perspective view
More informationComputer Vision Projective Geometry and Calibration. Pinhole cameras
Computer Vision Projective Geometry and Calibration Professor Hager http://www.cs.jhu.edu/~hager Jason Corso http://www.cs.jhu.edu/~jcorso. Pinhole cameras Abstract camera model - box with a small hole
More informationComputer Graphics. Chapter 10 Three-Dimensional Viewing
Computer Graphics Chapter 10 Three-Dimensional Viewing Chapter 10 Three-Dimensional Viewing Part I. Overview of 3D Viewing Concept 3D Viewing Pipeline vs. OpenGL Pipeline 3D Viewing-Coordinate Parameters
More informationChapter 4-3D Camera & Optimizations, Rasterization
Chapter 4-3D Camera & Optimizations, Rasterization Classical Viewing Taxonomy 3D Camera Model Optimizations for the Camera How to Deal with Occlusion Rasterization Clipping Drawing lines Filling areas
More informationRasterization Overview
Rendering Overview The process of generating an image given a virtual camera objects light sources Various techniques rasterization (topic of this course) raytracing (topic of the course Advanced Computer
More informationViewing/Projections IV. Week 4, Fri Feb 1
Universit of British Columbia CPSC 314 Computer Graphics Jan-Apr 2008 Tamara Munzner Viewing/Projections IV Week 4, Fri Feb 1 http://www.ugrad.cs.ubc.ca/~cs314/vjan2008 News extra TA office hours in lab
More informationModels and The Viewing Pipeline. Jian Huang CS456
Models and The Viewing Pipeline Jian Huang CS456 Vertex coordinates list, polygon table and (maybe) edge table Auxiliary: Per vertex normal Neighborhood information, arranged with regard to vertices and
More informationModels and Architectures
Models and Architectures Objectives Learn the basic design of a graphics system Introduce graphics pipeline architecture Examine software components for an interactive graphics system 1 Image Formation
More informationThe Graphics Pipeline and OpenGL I: Transformations!
! The Graphics Pipeline and OpenGL I: Transformations! Gordon Wetzstein! Stanford University! EE 267 Virtual Reality! Lecture 2! stanford.edu/class/ee267/!! Logistics Update! all homework submissions:
More informationFachhochschule Regensburg, Germany, February 15, 2017
s Operations Fachhochschule Regensburg, Germany, February 15, 2017 s Motivating Example s Operations To take a photograph of a scene: Set up your tripod and point camera at the scene (Viewing ) Position
More information3D Graphics for Game Programming (J. Han) Chapter II Vertex Processing
Chapter II Vertex Processing Rendering Pipeline Main stages in the pipeline The vertex processing stage operates on every input vertex stored in the vertex buffer and performs various operations such as
More informationSingle View Geometry. Camera model & Orientation + Position estimation. What am I?
Single View Geometry Camera model & Orientation + Position estimation What am I? Vanishing points & line http://www.wetcanvas.com/ http://pennpaint.blogspot.com/ http://www.joshuanava.biz/perspective/in-other-words-the-observer-simply-points-in-thesame-direction-as-the-lines-in-order-to-find-their-vanishing-point.html
More information5.8.3 Oblique Projections
278 Chapter 5 Viewing y (, y, ) ( p, y p, p ) Figure 537 Oblique projection P = 2 left right 0 0 left+right left right 0 2 top bottom 0 top+bottom top bottom far+near far near 0 0 far near 2 0 0 0 1 Because
More information3D Viewing Episode 2
3D Viewing Episode 2 1 Positioning and Orienting the Camera Recall that our projection calculations, whether orthographic or frustum/perspective, were made with the camera at (0, 0, 0) looking down the
More informationComputer Viewing Computer Graphics I, Fall 2008
Computer Viewing 1 Objectives Introduce mathematics of projection Introduce OpenGL viewing functions Look at alternate viewing APIs 2 Computer Viewing Three aspects of viewing process All implemented in
More informationGeometry: Outline. Projections. Orthographic Perspective
Geometry: Cameras Outline Setting up the camera Projections Orthographic Perspective 1 Controlling the camera Default OpenGL camera: At (0, 0, 0) T in world coordinates looking in Z direction with up vector
More information3D Viewing. Introduction to Computer Graphics Torsten Möller. Machiraju/Zhang/Möller
3D Viewing Introduction to Computer Graphics Torsten Möller Machiraju/Zhang/Möller Reading Chapter 4 of Angel Chapter 13 of Hughes, van Dam, Chapter 7 of Shirley+Marschner Machiraju/Zhang/Möller 2 Objectives
More informationGraphics 2009/2010, period 1. Lecture 6: perspective projection
Graphics 2009/2010, period 1 Lecture 6 Perspective projection Orthographic vs. perspective projection Introduction Projecting from arbitrary camera positions Orthographic projection and the canonical view
More informationPipeline Operations. CS 4620 Lecture Steve Marschner. Cornell CS4620 Spring 2018 Lecture 11
Pipeline Operations CS 4620 Lecture 11 1 Pipeline you are here APPLICATION COMMAND STREAM 3D transformations; shading VERTEX PROCESSING TRANSFORMED GEOMETRY conversion of primitives to pixels RASTERIZATION
More informationToday. Parity. General Polygons? Non-Zero Winding Rule. Winding Numbers. CS559 Lecture 11 Polygons, Transformations
CS559 Lecture Polygons, Transformations These are course notes (not used as slides) Written by Mike Gleicher, Oct. 005 With some slides adapted from the notes of Stephen Chenney Final version (after class)
More informationProjection Lecture Series
Projection 25.353 Lecture Series Prof. Gary Wang Department of Mechanical and Manufacturing Engineering The University of Manitoba Overview Coordinate Systems Local Coordinate System (LCS) World Coordinate
More information