Classical and Computer Viewing. Adapted From: Ed Angel Professor of Emeritus of Computer Science University of New Mexico

Size: px
Start display at page:

Download "Classical and Computer Viewing. Adapted From: Ed Angel Professor of Emeritus of Computer Science University of New Mexico"

Transcription

1 Classical and Computer Viewing Adapted From: Ed Angel Professor of Emeritus of Computer Science University of New Mexico

2 Planar Geometric Projections Standard projections project onto a plane Projectors are lines that either converge at a center of projection are parallel Such projections preserve lines but not necessarily angles Nonplanar projections are needed for applications such as map construction 1

3 Classical Projections 2

4 Taxonomy of Planar Projections planar geometric projections parallel perspective multiview axonometric orthographic 1 point 2 point 3 point oblique isometric dimetric trimetric

5 Parallel Projection 4

6 Orthographic Projection Projectors are orthogonal to projection surface 5

7 Multiview Orthographic Projection Projection plane parallel to principal face Usually form front, top, side views (6 possible) isometric (not multiview orthographic view) front top side 6

8

9 Axonometric Projections Object rotated along one or more principal axes classify by how many angles of a corner of a projected cube are the same none: trimetric two: dimetric three: isometric θ 1 θ 3 θ 2 8

10 Types of Axonometric Projections two! none! three! 9

11 Oblique Projection Arbitrary relationship between projectors and projection plane 1 0

12 Examples 1 1

13 Perspective Projection Projectors coverge at center of projection 1 2

14 Vanishing Points Parallel lines (not parallel to the projection plane) on the object converge at a single point in the projection (the vanishing point) Drawing simple perspectives by hand uses these vanishing point(s) vanishing point 1 3

15 Three-Point Perspective No principal direction parallel to projection plane Three vanishing points for cube 1 4

16 Two-Point Perspective On principal direction parallel to projection plane Two vanishing points for cube 1 5

17 One-Point Perspective One principal face parallel to projection plane One vanishing point for cube 1 6

18 Computer Viewing There are three aspects of the viewing process, all of which are implemented in the pipeline, Positioning the camera Setting the model-view matrix Selecting a lens Setting the projection matrix (ortho vs. persp) Clipping Setting the view volume 1 7

19 The Default OpenGL Camera (if you don t specify one) In OpenGL, initially the object and camera frames are the same Default model-view matrix is an identity The camera is located at origin and points in the negative z direction Default projection type is Orthographic OpenGL also specifies a default view volume that is a cube with sides of length 2 centered at the origin Default projection matrix is an identity 1 8

20 Default Projection Default projection is orthogonal clipped out 2 z=0 1 9

21 The LookAt Function The GLU library contained the function glulookat (deprecated) to form the required modelview matrix through a simple interface Replaced by LookAt() in mat.h 3D position mat4 mv = LookAt(vec4 eye, vec4 at, vec4 up); 3D position 3D Vector 20

22 LookAt LookAt(eye, at, up) 2 1

23 OpenGL Orthogonal Viewing Ortho(left,right,bottom,top,near,far) near and far measured from camera 2 2

24 OpenGL Perspective: Frustum frustum(left,right,bottom,top,near,far) near and far are distances from cam and should always be positive!!! 2 3

25 Using Field of View With Frustum it is often difficult to get the desired view perspective(fovy, aspect, near, far) often provides a better interface front plane aspect = w/h 2 4

26 Using the Model View Matrix In 3D graphics, the model-view matrix is used to Position the camera Build the scene The projection matrix is used to define the view volume and to select a camera lens Although these matrices are no longer part of the OpenGL state, you will create them in your application and pass them to shaders to be applied 2 5

27 3D_ViewingDemo

One or more objects A viewer with a projection surface Projectors that go from the object(s) to the projection surface

One 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 information

3D Viewing. CMPT 361 Introduction to Computer Graphics Torsten Möller. Machiraju/Zhang/Möller

3D Viewing. CMPT 361 Introduction to Computer Graphics Torsten Möller. Machiraju/Zhang/Möller 3D Viewing CMPT 361 Introduction to Computer Graphics Torsten Möller Reading Chapter 4 of Angel Chapter 6 of Foley, van Dam, 2 Objectives What kind of camera we use? (pinhole) What projections make sense

More information

3D Viewing. Introduction to Computer Graphics Torsten Möller. Machiraju/Zhang/Möller

3D 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 information

Overview. Viewing and perspectives. Planar Geometric Projections. Classical Viewing. Classical views Computer viewing Perspective normalization

Overview. 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 information

3D 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 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 information

Announcement. 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 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 information

Three-Dimensional Graphics III. Guoying Zhao 1 / 67

Three-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 information

Computer 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 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 information

Introduction to Computer Graphics 4. Viewing in 3D

Introduction 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 information

Introduction to Computer Graphics with WebGL

Introduction 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 information

Building Models. Angel and Shreiner: Interactive Computer Graphics 7E Addison-Wesley 2015

Building Models. Angel and Shreiner: Interactive Computer Graphics 7E Addison-Wesley 2015 Building Models 1 Objectives Introduce simple data structures for building polygonal models Vertex lists Edge lists 2 Representing a Mesh Consider a mesh v 5 v 6 e e e 3 v 9 8 8 v e 4 1 e 11 e v v 7 7

More information

Computer 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 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 information

CS452/552; EE465/505. Models & Viewing

CS452/552; EE465/505. Models & Viewing CS452/552; EE465/505 Models & Viewing 2-03 15 Outline! Building Polygonal Models Vertex lists; gl.drawarrays( ) Edge lists: gl.drawelements( )! Viewing Classical Viewing Read: Viewing in Web3D Angel, Section

More information

Introduction to Computer Graphics with WebGL

Introduction 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 information

Building Models. CS 537 Interactive Computer Graphics Prof. David E. Breen Department of Computer Science

Building Models. CS 537 Interactive Computer Graphics Prof. David E. Breen Department of Computer Science Building Models CS 537 Interactive Computer Graphics Prof. David E. Breen Department of Computer Science 1 Objectives Introduce simple data structures for building polygonal models - Vertex lists - Edge

More information

Announcements. Submitting Programs Upload source and executable(s) (Windows or Mac) to digital dropbox on Blackboard

Announcements. Submitting Programs Upload source and executable(s) (Windows or Mac) to digital dropbox on Blackboard Now Playing: Vertex Processing: Viewing Coulibaly Amadou & Mariam from Dimanche a Bamako Released August 2, 2005 Rick Skarbez, Instructor COMP 575 September 27, 2007 Announcements Programming Assignment

More information

Computer Graphics. Jeng-Sheng Yeh 葉正聖 Ming Chuan University (modified from Bing-Yu Chen s slides)

Computer Graphics. Jeng-Sheng Yeh 葉正聖 Ming Chuan University (modified from Bing-Yu Chen s slides) Computer Graphics Jeng-Sheng Yeh 葉正聖 Ming Chuan Universit (modified from Bing-Yu Chen s slides) Viewing in 3D 3D Viewing Process Specification of an Arbitrar 3D View Orthographic Parallel Projection Perspective

More information

CITSTUDENTS.IN VIEWING. Computer Graphics and Visualization. Classical and computer viewing. Viewing with a computer. Positioning of the camera

CITSTUDENTS.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 information

Computer Graphics. Bing-Yu Chen National Taiwan University The University of Tokyo

Computer Graphics. Bing-Yu Chen National Taiwan University The University of Tokyo Computer Graphics Bing-Yu Chen National Taiwan Universit The Universit of Toko Viewing in 3D 3D Viewing Process Classical Viewing and Projections 3D Snthetic Camera Model Parallel Projection Perspective

More information

2D and 3D Viewing Basics

2D and 3D Viewing Basics CS10101001 2D and 3D Viewing Basics Junqiao Zhao 赵君峤 Department of Computer Science and Technology College of Electronics and Information Engineering Tongji University Viewing Analog to the physical viewing

More information

Computer Viewing Computer Graphics I, Fall 2008

Computer 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 information

Computer 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 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 information

Viewing with Computers (OpenGL)

Viewing 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 information

COMP Computer Graphics and Image Processing. a6: Projections. In part 2 of our study of Viewing, we ll look at. COMP27112 Toby Howard

COMP 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 information

Chapter 5. Projections and Rendering

Chapter 5. Projections and Rendering Chapter 5 Projections and Rendering Topics: Perspective Projections The rendering pipeline In order to view manipulate and view a graphics object we must find ways of storing it a computer-compatible way.

More information

Overview of Projections: From a 3D world to a 2D screen.

Overview of Projections: From a 3D world to a 2D screen. Overview of Projections: From a 3D world to a 2D screen. Lecturer: Dr Dan Cornford d.cornford@aston.ac.uk http://wiki.aston.ac.uk/dancornford CS2150, Computer Graphics, Aston University, Birmingham, UK

More information

Viewing and Projection Transformations

Viewing 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 information

3D Polygon Rendering. Many applications use rendering of 3D polygons with direct illumination

3D Polygon Rendering. Many applications use rendering of 3D polygons with direct illumination Rendering Pipeline 3D Polygon Rendering Many applications use rendering of 3D polygons with direct illumination 3D Polygon Rendering What steps are necessary to utilize spatial coherence while drawing

More information

Computer Graphics. P05 Viewing in 3D. Part 1. Aleksandra Pizurica Ghent University

Computer Graphics. P05 Viewing in 3D. Part 1. Aleksandra Pizurica Ghent University Computer Graphics P05 Viewing in 3D Part 1 Aleksandra Pizurica Ghent University Telecommunications and Information Processing Image Processing and Interpretation Group Viewing in 3D: context Create views

More information

Viewing. Cliff Lindsay, Ph.D. WPI

Viewing. Cliff Lindsay, Ph.D. WPI Viewing Cliff Lindsa, Ph.D. WPI Building Virtual Camera Pipeline l Used To View Virtual Scene l First Half of Rendering Pipeline Related To Camera l Takes Geometr From ApplicaHon To RasteriaHon Stages

More information

Three-Dimensional Viewing Hearn & Baker Chapter 7

Three-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 information

Chapter 8 Three-Dimensional Viewing Operations

Chapter 8 Three-Dimensional Viewing Operations Projections Chapter 8 Three-Dimensional Viewing Operations Figure 8.1 Classification of planar geometric projections Figure 8.2 Planar projection Figure 8.3 Parallel-oblique projection Figure 8.4 Orthographic

More information

Fundamental Types of Viewing

Fundamental 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 information

Lecture 4: Viewing. Topics:

Lecture 4: Viewing. Topics: Lecture 4: Viewing Topics: 1. Classical viewing 2. Positioning the camera 3. Perspective and orthogonal projections 4. Perspective and orthogonal projections in OpenGL 5. Perspective and orthogonal projection

More information

Chapter 5-3D Camera & Optimizations, Rasterization

Chapter 5-3D Camera & Optimizations, Rasterization Chapter 5-3D Camera Optimizations, Rasterization Classical Viewing Taxonomy 3D Camera Model Optimizations for the Camera How to Deal with Occlusion Rasterization Clipping Drawing lines Filling areas Based

More information

Viewing. Reading: Angel Ch.5

Viewing. 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 information

Overview. By end of the week:

Overview. 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 information

Chap 7, 2008 Spring Yeong Gil Shin

Chap 7, 2008 Spring Yeong Gil Shin Three-Dimensional i Viewingi Chap 7, 28 Spring Yeong Gil Shin Viewing i Pipeline H d fi i d? How to define a window? How to project onto the window? Rendering "Create a picture (in a synthetic camera)

More information

Geometry: Outline. Projections. Orthographic Perspective

Geometry: 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 information

CS452/552; EE465/505. Intro to Lighting

CS452/552; 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 information

Computer Viewing and Projection. Overview. Computer Viewing. David Carr Fundamentals of Computer Graphics Spring 2004 Based on Slides by E.

Computer 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 information

CSC 470 Computer Graphics. Three Dimensional Viewing

CSC 470 Computer Graphics. Three Dimensional Viewing CSC 470 Computer Graphics Three Dimensional Viewing 1 Today s Lecture Three Dimensional Viewing Developing a Camera Fly through a scene Mathematics of Projections Producing Stereo Views 2 Introduction

More information

CS354 Computer Graphics Viewing and Modeling

CS354 Computer Graphics Viewing and Modeling Slide Credit: Donald S. Fussell CS354 Computer Graphics Viewing and Modeling Qixing Huang February 21th 2018 Computer Viewing There are three aspects of the viewing process, all of which are implemented

More information

CS452/552; EE465/505. Review & Examples

CS452/552; EE465/505. Review & Examples CS452/552; EE465/505 Review & Examples 2-05 15 Outline Review and Examples:! Shaders, Buffers & Binding! Example: Draw 3 Triangles Vertex lists; gl.drawarrays( ) Edge lists: gl.drawelements( )! Example:

More information

GEOMETRIC TRANSFORMATIONS AND VIEWING

GEOMETRIC 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 information

Chap 7, 2009 Spring Yeong Gil Shin

Chap 7, 2009 Spring Yeong Gil Shin Three-Dimensional i Viewingi Chap 7, 29 Spring Yeong Gil Shin Viewing i Pipeline H d fi i d? How to define a window? How to project onto the window? Rendering "Create a picture (in a snthetic camera) Specification

More information

Viewing/Projections IV. Week 4, Fri Feb 1

Viewing/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 information

CS 432 Interactive Computer Graphics

CS 432 Interactive Computer Graphics CS 432 Interactive Computer Graphics Lecture 4 3D Viewing Matt Burlick - Drexel University - CS 432 1 Reading Angel Chapters 3-4 Red Book Chapter 5, Appendix E Matt Burlick - Drexel University - CS 432

More information

Virtual Cameras and The Transformation Pipeline

Virtual 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 information

QUESTION BANK 10CS65 : COMPUTER GRAPHICS AND VISUALIZATION

QUESTION BANK 10CS65 : COMPUTER GRAPHICS AND VISUALIZATION QUESTION BANK 10CS65 : COMPUTER GRAPHICS AND VISUALIZATION INTRODUCTION OBJECTIVE: This chapter deals the applications of computer graphics and overview of graphics systems and imaging. UNIT I 1 With clear

More information

Viewing Transformation

Viewing Transformation Viewing and Projection Transformations Projective Rendering Pipeline OCS WCS VCS modeling transformation Mm.odd viewing transformation Mview OCS - object coordinate system WCS - world coordinate system

More information

CSC 470 Computer Graphics

CSC 470 Computer Graphics CSC 47 Computer Graphics Three Dimensional Viewing Today s Lecture Three Dimensional Viewing Developing a Camera Fly through a scene Mathematics of Producing Stereo Views 1 2 Introduction We have already

More information

Today. Rendering pipeline. Rendering pipeline. Object vs. Image order. Rendering engine Rendering engine (jtrt) Computergrafik. Rendering pipeline

Today. 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 information

Introduction to Computer Graphics with WebGL

Introduction 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 information

Chapter 4-3D Camera & Optimizations, Rasterization

Chapter 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 information

Computer Graphics 7: Viewing in 3-D

Computer Graphics 7: Viewing in 3-D Computer Graphics 7: Viewing in 3-D In today s lecture we are going to have a look at: Transformations in 3-D How do transformations in 3-D work? Contents 3-D homogeneous coordinates and matrix based transformations

More information

CS 418: Interactive Computer Graphics. Projection

CS 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 information

Computer Graphics. Chapter 10 Three-Dimensional Viewing

Computer 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 information

Virtual Cameras & Their Matrices

Virtual Cameras & Their Matrices Virtual Cameras & Their Matrices J.Tumblin-Modified, highly edited SLIDES from: Ed Angel Professor Emeritus of Computer Science University of New Mexico 1 What is Projection? Any operation that reduces

More information

Lecture 4. Viewing, Projection and Viewport Transformations

Lecture 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 information

Notes on Assignment. Notes on Assignment. Notes on Assignment. Notes on Assignment

Notes 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 information

CSE528 Computer Graphics: Theory, Algorithms, and Applications

CSE528 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 information

CS230 : 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 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 information

Projection Lecture Series

Projection 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

Chap 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 4.1~4.7 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 information

CS 4204 Computer Graphics

CS 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 information

So we have been talking about 3D viewing, the transformations pertaining to 3D viewing. Today we will continue on it. (Refer Slide Time: 1:15)

So we have been talking about 3D viewing, the transformations pertaining to 3D viewing. Today we will continue on it. (Refer Slide Time: 1:15) Introduction to Computer Graphics Dr. Prem Kalra Department of Computer Science and Engineering Indian Institute of Technology, Delhi Lecture - 8 3D Viewing So we have been talking about 3D viewing, the

More information

Lecture 3 Sections 2.2, 4.4. Mon, Aug 31, 2009

Lecture 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 information

Viewing and Projection

Viewing 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 information

CGT520 Transformations

CGT520 Transformations CGT520 Transformations Bedrich Benes, Ph.D. Purdue University Department of Computer Graphics GLM A concise library for transforms and OpenGL mathematics All overloaded, predefined, optimized glm (OpenGL

More information

Realtime 3D Computer Graphics & Virtual Reality. Viewing

Realtime 3D Computer Graphics & Virtual Reality. Viewing Realtime 3D Computer Graphics & Virtual Realit Viewing Transformation Pol. Per Verte Pipeline CPU DL Piel Teture Raster Frag FB v e r t e object ee clip normalied device Modelview Matri Projection Matri

More information

Computer Graphics. Ch 6. 3D Viewing

Computer Graphics. Ch 6. 3D Viewing Computer Graphics Ch 6. 3D Viewing 3D Viewing Basic do you see this image as flat? 12 lines 3D Coordinate System 3D homogeneous coordinates: p = [x y z w] T Our textbook and OpenGL use a RIGHT-HANDED system

More information

Models and The Viewing Pipeline. Jian Huang CS456

Models 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 information

Computer Graphics Chapter 7 Three-Dimensional Viewing Viewing

Computer Graphics Chapter 7 Three-Dimensional Viewing Viewing Computer Graphics Chapter 7 Three-Dimensional Viewing Outline Overview of Three-Dimensional Viewing Concepts The Three-Dimensional Viewing Pipeline Three-Dimensional Viewing-Coorinate Parameters Transformation

More information

5.8.3 Oblique Projections

5.8.3 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 information

CSE328 Fundamentals of Computer Graphics

CSE328 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 information

Three Main Themes of Computer Graphics

Three 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 information

MAE : Lecture #12 - Projection and Perspective. Lecture Overview:

MAE : Lecture #12 - Projection and Perspective. Lecture Overview: Lecture Overview: Miscellaneous Motivation Projection - basics Means for projecting images: Orthographic viewing - basics Perspective viewing - basics The mathematics of projection Vanishing points Numerical

More information

7. 3D Viewing. Projection: why is projection necessary? CS Dept, Univ of Kentucky

7. 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 information

The Viewing Pipeline adaptation of Paul Bunn & Kerryn Hugo s notes

The Viewing Pipeline adaptation of Paul Bunn & Kerryn Hugo s notes The Viewing Pipeline adaptation of Paul Bunn & Kerryn Hugo s notes What is it? The viewing pipeline is the procession of operations that are applied to the OpenGL matrices, in order to create a 2D representation

More information

Models 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 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 information

Computer Graphics (CS 543) Lecture 6a: Viewing & Camera Control. Prof Emmanuel Agu. Computer Science Dept. Worcester Polytechnic Institute (WPI)

Computer Graphics (CS 543) Lecture 6a: Viewing & Camera Control. Prof Emmanuel Agu. Computer Science Dept. Worcester Polytechnic Institute (WPI) Computer Graphics (CS 543) Lecture 6a: Viewing & Camera Control Prof Emmanuel Agu Computer Science Dept. Worcester Polytechnic Institute (WPI) 3D Viewing? Specify a view volume Objects inside view volume

More information

Orthogonal Projection Matrices. Angel and Shreiner: Interactive Computer Graphics 7E Addison-Wesley 2015

Orthogonal 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 information

On 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, 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 information

Transforms 3: Projection Christian Miller CS Fall 2011

Transforms 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 information

Viewing. Announcements. A Note About Transformations. Orthographic and Perspective Projection Implementation Vanishing Points

Viewing. Announcements. A Note About Transformations. Orthographic and Perspective Projection Implementation Vanishing Points Viewing Announcements. A Note About Transformations. Orthographic and Perspective Projection Implementation Vanishing Points Viewing Announcements. A Note About Transformations. Orthographic and Perspective

More information

Viewing and Projection

Viewing 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 information

SE Mock Online Retest 2-CG * Required

SE Mock Online Retest 2-CG * Required SE Mock Online Retest 2-CG * Required 1. Email address * 2. Name Of Student * 3. Roll No * 4. Password * Untitled Section 5. 10. A transformation that slants the shape of objects is called the? shear transformation

More information

CSE 167: Lecture #4: Vertex Transformation. Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2012

CSE 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 information

3.1 Viewing and Projection

3.1 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 information

Virtual Environments

Virtual Environments ELG 524 Virtual Environments Jean-Christian Delannoy viewing in 3D world coordinates / geometric modeling culling lighting virtualized reality collision detection collision response interactive forces

More information

COMP30019 Graphics and Interaction Perspective Geometry

COMP30019 Graphics and Interaction Perspective Geometry COMP30019 Graphics and Interaction Perspective Geometry Department of Computing and Information Systems The Lecture outline Introduction to perspective geometry Perspective Geometry Virtual camera Centre

More information

Overview. By end of the week:

Overview. 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 information

CSE528 Computer Graphics: Theory, Algorithms, and Applications

CSE528 Computer Graphics: Theory, Algorithms, and Applications CSE528 Computer Graphics: Theor, Algorithms, and Applications Hong Qin State Universit of New York at Ston Brook (Ston Brook Universit) Ston Brook, New York 794--44 Tel: (63)632-845; Fa: (63)632-8334 qin@cs.sunsb.edu

More information

Computer Graphics Viewing

Computer Graphics Viewing Computer Graphics Viewing What Are Projections? Our 3-D scenes are all specified in 3-D world coordinates To display these we need to generate a 2-D image - project objects onto a picture plane Picture

More information

Viewing in 3D (Chapt. 6 in FVD, Chapt. 12 in Hearn & Baker)

Viewing in 3D (Chapt. 6 in FVD, Chapt. 12 in Hearn & Baker) Viewing in 3D (Chapt. 6 in FVD, Chapt. 2 in Hearn & Baker) Viewing in 3D s. 2D 2D 2D world Camera world 2D 3D Transformation Pipe-Line Modeling transformation world Bod Sstem Viewing transformation Front-

More information

CS Computer Graphics: Transformations & The Synthetic Camera

CS Computer Graphics: Transformations & The Synthetic Camera CS 543 - Computer Graphics: Transformations The Snthetic Camera b Robert W. Lindeman gogo@wpi.edu (with help from Emmanuel Agu ;-) Introduction to Transformations A transformation changes an objects Size

More information

1 Transformations. Chapter 1. Transformations. Department of Computer Science and Engineering 1-1

1 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 information

Lecture 4: 3D viewing and projections

Lecture 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 information

Introduction to Computer Graphics with WebGL

Introduction 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 WebGL Transformations

More information