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


 Ethel Spencer
 2 years ago
 Views:
Transcription
1 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 is changed it applies to all vertices of the object that is drawn next Notes on Assignment Extensions  4 days before (Thu by midnight) not guaranteed Ask questions IN CLASS. Notes on Assignment Hierarchical Design + stacks Camera motion  will be covered today All matrices are 4x43d points + 1 homogeneous coordinate Use gl/glu/glut commands for debugging
2 OpenGL Pipeline Lecture 4 Viewing, Projection and Viewport s Model = position of objects View = position and aim camera p(x,y,z) 3D Object Coordinates Modeling 3D World Coordinates Viewing Projection WindowtoViewport p (x,y ) List of s 3D Camera Coordinates 2D Screen Coordinates 2D Image Coordinates Done last week Make the monitor a free moving video camera perspective, parallel screen coords to viewport resolution 2005, Denis Zorin Coordinate systems z x Eye coordinates x z World coordinates World coordinates  fixed initial coord system; everything is defined with respect to it Eye coordinates  coordinate system attached to the camera; in this system camera looks down negative Zaxis
3 Positioning the camera Modeling transformation: reshape the object, orient the object, position the object with respect to the world coordinate system Viewing transformation: transform world coordinates to eye coordinates Translate camera by (tx,tz) z zw w0 xw Viewing transformation is the inverse of the camera positioning transformation Viewing transformation should be rigid: rotation + translation tz tx x e z e x Steps to get the right transform: first, orient the camera correctly, then translate it 2005, Denis Zorin Initial Configuration Initial Configuration z zw z zw w0 w0 xw xw xe xe ze x ze x
4 Viewing = z x e Translate object by (tx,tz) z e tx tz z w w0 x x w x w = xw  tx z w = zw  tz Lookat positioning Find the viewing transform given the eye (camera) position, point to look at, and the up vector Need to specify two transforms: rotation and translation. translation is easy natural rotation: define implicitly using a point at which we want to look and a vector indicating the vertical in the image (up vector) can easily convert the eye point to the direction vector of the camera axis; can assume up vector perpendicular to view vector 2005, Denis Zorin OpenGL Viewing glmatrixmode(gl_modelview); Lookat Positioning Convert eye point to the direction vector of camera glloadidentity(); position camera is aimed at glulookat(cx,cy,cx,lx,ly,lz,ux,uy,uz) Eye coords Eye ( Camera ) Coordinates Up Direction
5 Lookat Positioning Convert eye point to the direction vector of camera Assume up vector to be perpendicular to dir vec Eye coords Lookat Positioning Convert eye point to the direction vector of camera Assume up vector to be perpendicular to dir vec This gives you a pair of perpendicular vectors Eye coords Lookat positioning Problem: given two pairs of perpendicular unit vectors, find the transformation mapping the first pair into the second 2005, Denis Zorin 2005, Denis Zorin Eye coords World coords Lookat positioning Determine rotation first, looking how coord vectors change:,,
6 Lookat positioning Recall the matrix for translation: Now we have the camera positioning matrix, To get the viewing transform, invert: ' For rotation the inverse is the transpose ' 2005, Denis Zorin 2005, Denis Zorin Implementation Notes for the Viewing Text Positioning the camera in OpenGL imagine that the camera is an object and write a sequence of rotations and translations positioning it change each transformation in the sequence to the opposite reverse the sequence Camera positioning is done in the code before modeling transformations OpenGL does not distinguish between viewing and modeling transformation and joins them into the modelview matrix Lookat viewing transformation p(x,y,z) 3D Object Coordinates Modeling 3D World Coordinates Viewing 3D Camera Coordinates '' ' ( ' ' ' ( ' ( ' ) ) Projection WindowtoViewport p (x,y ) 2D Screen Coordinates 2D Image Coordinates 2005, Denis Zorin
7 OpenGL Pipeline Projection s glmatrixmode(gl_projection); glloadidentity(); Orthographic Projection Perspective Projection Map viewing volume to cube [1,1]x[1,1]x[1,1] Projection s Think of this as selecting the lens Describe the viewing volume How an object is projected onto the screen Which objects or portions of objects are get clipped Orthographic Projection viewing volume  rectangular parallelepiped(=box) translating camera doesn t change size but may change visibility no foreshortening  less realistic default in opengl  cube centered at (0,0,0), side = 2 but useful in architecture and cad where actual angles and sizes important
8 Orthographic Projection Viewing frustum Volume in space that will be visible in the image is the aspect ratio of the image width/height y z glortho(left, right, bottom, top, near, far); gluortho2d(left, right, bottom, top); 2005, Denis Zorin glfrustum(left, right, bottom, top, near, far); Perspective Projection Farther the object is from camera, the smaller it appears in image. ==> Realism Translating camera may change size of objects Not good for measurements. Achieved by specifying the volume as a frustum (truncated pyramid, with apex at camera) Perspective Projection gluperspective(fovy,aspect,near far); (in degrees) symmetric in x and y
9 Projection transformation Behind the Scenes Maps the viewing frustum into a standard cube extending from 1 to 1 in each coordinate (normalized device coordinates) Space to plane projection In eye coordinate system z y v Image plane projecting to the plane z = 1 3 steps: a.k.a canonical view volume '() '() 2005, Denis Zorin 2005, Denis Zorin orthogonal projection 3 steps: perspective transformation 2005, Denis Zorin Projection transformation Behind the Scenes change the matrix of projection to keep z: result is a parallelepiped translate: parallelepiped centered at 0 scale in all directions: cube of of size 2 centered at 0 Space to plane projection In eye coordinate system '() z y Image plane v '() projecting to the plane z = , Denis Zorin 2005, Denis Zorin
10 Projection transformation '() change so that we keep z: the homogeneous result corresponds to the last component increases monotonically with z z y viewing frustum eye position Cross section at x=0 zaxis 2005, Denis Zorin Projection transformation maps the frustum to an axisaligned parallelepiped 1/ 1/ z Points (0,yi,zi,1) Plot of (zi,yi) already centered in (x,y), center in zdirection and scale: ' ( ' Multiply each point by projection transformation to get 2005, Denis Zorin
11 Points (0,yi,zi,1) Plot of (zi,yi) S = 1 r tan(α/2) tan(α/2) ( 1 f 1 n ) = Multiply each point by projection transformation to get Points (0, yi,1,zi) mult each point by S Plot of (1/zi, yi/zi) already centered in (x,y), center in zdirection and scale: ' ( 2005, Denis Zorin = mult each point by T ' Projection transformation Combined matrix, mapping frustum to a cube: ' ' ( To get normalized image plane coordinates (valid range [1,1] both), just drop z in the result and convert from homogeneous to regular. To get pixel coordinates, translate Perspective by 1, Division and scale x and y (Viewport transformation) 2005, Denis Zorin
12 Remember the Pipeline: Remember the Pipeline: homogenize then discard z component p x p y p z p z p x /p z p y /p z p z /p z 1 p x/p z p y /p z 1 = normalized image plane coordinates ([1,1] in x and y) Clipping Removal or modification of primitives based on whether they fall within a viewing volume. Done against Canonical View Volume. Why? Parameter free. Only values you need to know for clipping volume are 1 and 1 Aligned with coordinate axes  inside outside trivial (and efficient  no need for dot products) p(x,y,z) Modeling Viewing Projection WindowtoViewport p (x,y ) 3D Object Coordinates 3D World Coordinates 3D Camera Coordinates 2D Screen Coordinates 2D Image Coordinates
13 OpenGL Pipeline map square [1,1]x[1,1] to image Viewport Idea is to transform [1,1]x[1,1] to [0,w]x[0,h] Behind the scenes Translate by (1,1) Scale x by w and y by x y 1 1 w Viewport Refers to size of image you see on screen Defines the rectangular region of the window where the image is drawn OpenGL: glviewport(x, y, width, height); Default  entire window: (0,0, w,h) Lower left corner Viewport Aspect Ratio Issues
14 Visibility Objects close to the camera occlude those that are further away. Should be the case in the final image that we draw Default  latest drawn object covers older ones Another option: Visibility Sort objects in the scene from farthest to closest : Painters Algorithm not practical adding/removing objects in the scene in the front? back? not very efficient need to compute distances from eye draw pixels that will be covered sorting  usually BSP Trees One option: Visibility ObjectSpace Approach For all pairs of polygons compare against each other choose from display/no display/partial display For each polygon compare against n1 others Visibility Objects that are closer to the camera occlude the objects that are further away All objects are made of planar polygons A polygon typically projects 1 to 1 idea: project polygons in turn ; for each pixel, record distance to the projected polygon when writing pixels, replace the old color with the new one only if the new distance to camera for this pixel is less then the recorded one 2005, Denis Zorin
15 Zbuffering idea Z buffer Problem: need to compare distances for each projected point Solution: convert all points to a coordinate system in which (x,y) are image plane coords and the distance to the image plane increases when the z coordinate increases decreases In OpenGL, this is done by the projection matrix Red text refers to the negative z case What are z values? Z values are obtained by applying the projection transform, that is, mapping the viewing volume frustum to the standard cube. Z value increases with th distance to the camera. Remember the discarded z values Z values for each pixel are computed for each pixel covered by a polygon during using perspective linear interpolation division? of z values at vertices. Typical Z buffer size: 24 bits (same as RGB combined). 2005, Denis Zorin 2005, Denis Zorin Z buffer Z buffer Assumptions: each pixel has storage for a zvalue, in addition to RGB all objects are scanconvertible (typically are polygons, lines or points) Algorithm: initilize zbuf to maximal value for each object for each pixel (i,j) obtained by scan conversion if znew(i,j) < zbuf(i,j) if znew(i,j) > zbuf(i,j) zbuf(i,j) = znew(i,j) ; write pixel(i,j) What are z values? Z values are obtained by applying the projection transform, that is, mapping the viewing volume frustum to the standard cube. Z value increases with th distance to the camera. decreases Z values for each pixel are computed for each pixel covered by a polygon using linear interpolation of z values at vertices. Typical Z buffer size: 24 bits (same as RGB combined). 2005, Denis Zorin 2005, Denis Zorin
16 Pros Z Buffer  brief analysis simple to implement(hw/sw) loops over polygons compatible with pipeline architectures Cons Large amount of memory Often waste of rendering resources for obscured objects Z Buffer  OpenGL Notes Depth Buffer glutinitdisplaymode(glut_depth... ); glenable(gl_depth_test); glclear( GL_DEPTH_BUFFER_BIT... );
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 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 informationGraphics pipeline and transformations. Composition of transformations
Graphics pipeline and transformations Composition of transformations Order matters! ( rotation * translation translation * rotation) Composition of transformations = matrix multiplication: if T is a rotation
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 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 HampdenSydney 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 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 79444 Tel: (63)632845; Fax: (63)6328334 qin@cs.sunysb.edu
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 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 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 117942424 Tel: (631)632845; Fax: (631)6328334 qin@cs.stonybrook.edu
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 informationComputer Graphics. Chapter 10 ThreeDimensional Viewing
Computer Graphics Chapter 10 ThreeDimensional Viewing Chapter 10 ThreeDimensional Viewing Part I. Overview of 3D Viewing Concept 3D Viewing Pipeline vs. OpenGL Pipeline 3D ViewingCoordinate Parameters
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 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 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 informationViewing with Computers (OpenGL)
We can now return to threedimension?', graphics from a computer perspective. Because viewing in computer graphics is based on the syntheticcamera model, we should be able to construct any of the classical
More informationOpenGL Transformations
OpenGL Transformations R. J. Renka Department of Computer Science & Engineering University of North Texas 02/18/2014 Introduction The most essential aspect of OpenGL is the vertex pipeline described in
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 informationThe 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 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 informationGetting Started. Overview (1): Getting Started (1): Getting Started (2): Getting Started (3): COSC 4431/5331 Computer Graphics.
Overview (1): Getting Started Setting up OpenGL/GLUT on Windows/Visual Studio COSC 4431/5331 Computer Graphics Thursday January 22, 2004 Overview Introduction Camera analogy Matrix operations and OpenGL
More informationCMSC427 Transformations II: Viewing. Credit: some slides from Dr. Zwicker
CMSC427 Transformations II: Viewing Credit: some slides from Dr. Zwicker What next? GIVEN THE TOOLS OF The standard rigid and affine transformations Their representation with matrices and homogeneous coordinates
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 informationGame Architecture. 2/19/16: Rasterization
Game Architecture 2/19/16: Rasterization Viewing To render a scene, need to know Where am I and What am I looking at The view transform is the matrix that does this Maps a standard view space into world
More informationThreeDimensional Viewing Hearn & Baker Chapter 7
ThreeDimensional 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 information1 OpenGL  column vectors (columnmajor ordering)
OpenGL  column vectors (columnmajor ordering) OpenGL uses column vectors and matrices are written in a columnmajor order. As a result, matrices are concatenated in righttoleft order, with the first
More informationLecture 5: Viewing. CSE Computer Graphics (Fall 2010)
Lecture 5: Viewing CSE 40166 Computer Graphics (Fall 2010) Review: from 3D world to 2D pixels 1. Transformations are represented by matrix multiplication. o Modeling o Viewing o Projection 2. Clipping
More informationCSE 690: GPGPU. Lecture 2: Understanding the Fabric  Intro to Graphics. Klaus Mueller Stony Brook University Computer Science Department
CSE 690: GPGPU Lecture 2: Understanding the Fabric  Intro to Graphics Klaus Mueller Stony Brook University Computer Science Department Klaus Mueller, Stony Brook 2005 1 Surface Graphics Objects are explicitely
More informationINTRODUCTION TO COMPUTER GRAPHICS. cs123. It looks like a matrix Sort of. Viewing III. Projection in Practice 1 / 52
It looks like a matrix Sort of Viewing III Projection in Practice 1 / 52 Arbitrary 3D views } view volumes/frusta spec d by placement and shape } Placement: } Position (a point) } look and up vectors }
More informationProjection: Mapping 3D to 2D. Orthographic Projection. The Canonical Camera Configuration. Perspective Projection
Projection: Mapping 3D to 2D Our scene models are in 3D space and images are 2D so we need some wa of projecting 3D to 2D The fundamental approach: planar projection first, we define a plane in 3D
More informationAnnouncements. 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 informationComputer Graphics 7: Viewing in 3D
Computer Graphics 7: Viewing in 3D In today s lecture we are going to have a look at: Transformations in 3D How do transformations in 3D work? Contents 3D homogeneous coordinates and matrix based transformations
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 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 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 informationSurface Graphics. 200 polys 1,000 polys 15,000 polys. an empty foot.  a mesh of spline patches:
Surface Graphics Objects are explicitely defined by a surface or boundary representation (explicit inside vs outside) This boundary representation can be given by:  a mesh of polygons: 200 polys 1,000
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 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 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) Modelview (camera frame) View transform (projection frame) 2D image View
More informationRendering. Converting a 3D scene to a 2D image. Camera. Light. Rendering. View Plane
Rendering Pipeline Rendering Converting a 3D scene to a 2D image Rendering Light Camera 3D Model View Plane Rendering Converting a 3D scene to a 2D image Basic rendering tasks: Modeling: creating the world
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 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 informationCS451Realtime Rendering Pipeline
1 CS451Realtime Rendering Pipeline JYHMING LIEN DEPARTMENT OF COMPUTER SCIENCE GEORGE MASON UNIVERSITY Based on Tomas AkenineMöller s lecture note You say that you render a 3D 2 scene, but what does
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 information3D 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 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 2628 2016 The first 4 Key Ideas 1. Work in convenient coordinate systems. Use transformations to
More informationOverview 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 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. imageoriented foreach pixel... 2. objectoriented foreach
More information3.1 Viewing and Projection
Fall 2017 CSCI 420: Computer Graphics 3.1 Viewing and Projection Hao Li http://cs420.haoli.com 1 Recall: Affine Transformations Given a point [xyz] > form homogeneous coordinates [xyz1] > The transformed
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 information3D 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 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 COMPSCI 464. Image Credits: Encarta and
Viewing COMPSCI 464 Image Credits: Encarta and http://www.sackville.ednet.ns.ca/art/grade/drawing/perspective4.html Graphics Pipeline Graphics hardware employs a sequence of coordinate systems The location
More information3D computer graphics: geometric modeling of objects in the computer and rendering them
SE313: Computer Graphics and Visual Programming Computer Graphics Notes Gazihan Alankus, Spring 2012 Computer Graphics 3D computer graphics: geometric modeling of objects in the computer and rendering
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 informationViewing. Part II (The Synthetic Camera) CS123 INTRODUCTION TO COMPUTER GRAPHICS. Andries van Dam 10/10/2017 1/31
Viewing Part II (The Synthetic Camera) Brownie camera courtesy of http://www.geh.org/fm/brownie2/htmlsrc/me13000034_ful.html 1/31 The Camera and the Scene } What does a camera do? } Takes in a 3D scene
More informationCSE 167: Introduction to Computer Graphics Lecture #9: Visibility. Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2018
CSE 167: Introduction to Computer Graphics Lecture #9: Visibility Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2018 Announcements Midterm Scores are on TritonEd Exams to be
More informationCSE452 Computer Graphics
CSE45 Computer Graphics Lecture 8: Computer Projection CSE45 Lecture 8: Computer Projection 1 Review In the last lecture We set up a Virtual Camera Position Orientation Clipping planes Viewing angles Orthographic/Perspective
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 informationComputer 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 informationVisibility: Z Buffering
University of British Columbia CPSC 414 Computer Graphics Visibility: Z Buffering Week 1, Mon 3 Nov 23 Tamara Munzner 1 Poll how far are people on project 2? preferences for Plan A: status quo P2 stays
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 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 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 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 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 informationAdvanced Computer Graphics (CS & SE )
Advanced Computer Graphics (CS & SE 233.420) Topics Covered Picking Pipeline Viewing and Transformations Rendering Modes OpenGL can render in one of three modes selected by glrendermode(mode) GL_RENDER
More informationFor each question, indicate whether the statement is true or false by circling T or F, respectively.
True/False For each question, indicate whether the statement is true or false by circling T or F, respectively. 1. (T/F) Rasterization occurs before vertex transformation in the graphics pipeline. 2. (T/F)
More information3D Graphics Pipeline II Clipping. Instructor Stephen J. Guy
3D Graphics Pipeline II Clipping Instructor Stephen J. Guy 3D Rendering Pipeline (for direct illumination) 3D Geometric Primitives 3D Model Primitives Modeling Transformation 3D World Coordinates Lighting
More informationViewing and Projection
15462 Computer Graphics I Lecture 5 Viewing and Projection Shear Transformation Camera Positioning Simple Parallel Projections Simple Perspective Projections [Angel, Ch. 5.25.4] January 30, 2003 [Red
More informationCOMP3421. Introduction to 3D Graphics
COMP3421 Introduction to 3D Graphics 3D coordinates 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 informationCSCI 4620/8626. The 2D Viewing Pipeline
CSCI 4620/8626 Computer Graphics TwoDimensional Viewing (Chapter 8) Last update: 2016033 The 2D Viewing Pipeline Given a 2D scene, we select the part of it that we wish to see (render, display) using
More informationCS184 : Foundations of Computer Graphics Professor David Forsyth Final Examination
CS184 : Foundations of Computer Graphics Professor David Forsyth Final Examination (Total: 100 marks) Figure 1: A perspective view of a polyhedron on an infinite plane. Cameras and Perspective Rendering
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 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 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 informationI N T R O D U C T I O N T O C O M P U T E R G R A P H I C S
3D Viewing: the Synthetic Camera Programmer s reference model for specifying 3D view projection parameters to the computer General synthetic camera (e.g., PHIGS Camera, Computer Graphics: Principles and
More informationHidden surface removal. Computer Graphics
Lecture Hidden Surface Removal and Rasterization Taku Komura Hidden surface removal Drawing polygonal faces on screen consumes CPU cycles Illumination We cannot see every surface in scene We don t want
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 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 informationCS 130 Final. Fall 2015
CS 130 Final Fall 2015 Name Student ID Signature You may not ask any questions during the test. If you believe that there is something wrong with a question, write down what you think the question is trying
More informationCS184 : Foundations of Computer Graphics Professor David Forsyth Final Examination (Total: 100 marks)
CS184 : Foundations of Computer Graphics Professor David Forsyth Final Examination (Total: 100 marks) Cameras and Perspective Figure 1: A perspective view of a polyhedron on an infinite plane. Rendering
More informationCS Computer Graphics: Hidden Surface Removal
CS 543  Computer Graphics: Hidden Surface Removal by Robert W. Lindeman gogo@wpi.edu (with help from Emmanuel Agu ;) Hidden Surface Removal Drawing polygonal faces on screen consumes CPU cycles We cannot
More informationFigure 1. Lecture 1: Three Dimensional graphics: Projections and Transformations
Lecture 1: Three Dimensional graphics: Projections and Transformations Device Independence We will start with a brief discussion of two dimensional drawing primitives. At the lowest level of an operating
More informationCS 112 The Rendering Pipeline. Slide 1
CS 112 The Rendering Pipeline Slide 1 Rendering Pipeline n Input 3D Object/Scene Representation n Output An image of the input object/scene n Stages (for POLYGON pipeline) n Model view Transformation n
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 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 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 informationPage 1. AreaSubdivision Algorithms zbuffer Algorithm List Priority Algorithms BSP (Binary Space Partitioning Tree) Scanline Algorithms
Visible Surface Determination Visibility Culling AreaSubdivision Algorithms zbuffer Algorithm List Priority Algorithms BSP (Binary Space Partitioning Tree) Scanline Algorithms Divideandconquer strategy:
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 informationCOMP 175 COMPUTER GRAPHICS. Ray Casting. COMP 175: Computer Graphics April 26, Erik Anderson 09 Ray Casting
Ray Casting COMP 175: Computer Graphics April 26, 2018 1/41 Admin } Assignment 4 posted } Picking new partners today for rest of the assignments } Demo in the works } Mac demo may require a new dylib I
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 informationClass of Algorithms. Visible Surface Determination. Back Face Culling Test. Back Face Culling: Object Space v. Back Face Culling: Object Space.
Utah School of Computing Spring 13 Class of Algorithms Lecture Set Visible Surface Determination CS56 Computer Graphics From Rich Riesenfeld Spring 13 Object (Model) Space Algorithms Work in the model
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 informationThreeDimensional Graphics III. Guoying Zhao 1 / 67
Computer Graphics ThreeDimensional 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 information1 Transformations. Chapter 1. Transformations. Department of Computer Science and Engineering 11
Transformations 11 Transformations are used within the entire viewing pipeline: Projection from world to view coordinate system View modifications: Panning Zooming Rotation 12 Transformations can also
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 information2D 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 informationOpenGL: Open Graphics Library. Introduction to OpenGL Part II. How do I render a geometric primitive? What is OpenGL
OpenGL: Open Graphics Library Introduction to OpenGL Part II CS 35150 Graphics API ( Application Programming Interface) Software library Layer between programmer and graphics hardware (and other software
More informationRecall: Indexing into Cube Map
Recall: Indexing into Cube Map Compute R = 2(N V)NV Object at origin Use largest magnitude component of R to determine face of cube Other 2 components give texture coordinates V R Cube Map Layout Example
More information