Computer Graphics. Basic 3D Programming. Contents

Size: px
Start display at page:

Download "Computer Graphics. Basic 3D Programming. Contents"

Transcription

1 Computer Graphics Basic 3D Programming September 21, 2005 Sun-Jeong Kim 1 Contents Cameras and objects Perspective projections Orthographic projections Viewing a cube Locating the camera Building objects Hidden surface removal Rotating a color cube Exercise Sun-Jeong Kim 2

2 Cameras and Objects (1/3) Projection synthetic camera model projectors, center of projection, projection plane Sun-Jeong Kim 3 Cameras and Objects (2/3) Projection plane moved in front of the camera Sun-Jeong Kim 4

3 Cameras and Objects (3/3) View frustum degree of freedom six parameters truncated pyramid clipping volume Sun-Jeong Kim 5 Perspective Projections General viewing projection plane anywhere in front of the camera void glfrustum(gldouble left, GLdouble right, GLdouble bottom, GLdouble top, GLdouble near, GLdouble far) Sun-Jeong Kim 6

4 Orthographic Projections (1/2) Direction of projection simple camera view frustum a right parallelepiped y x void glortho(gldouble left, GLdouble right, GLdouble bottom, GLdouble top, GLdouble near, GLdouble far) z Sun-Jeong Kim 7 Orthographic Projections (2/2) Sun-Jeong Kim 8

5 Viewing a Cube (1/3) GLUT Library glut.h (include), glut32.lib (lib), glut32.dll (system32) void glutwirecube(gldouble size) void glutsoildcube(gldouble size) Sun-Jeong Kim 9 Viewing a Cube (2/3) Sun-Jeong Kim 10

6 Viewing a Cube (3/3) Sun-Jeong Kim 11 Result Viewing a Cube Sun-Jeong Kim 12

7 Locating Camera (1/2) Setting position and orient of the camera within the world coordinate system eye point, at point, up vector void glulookat(gldouble eyex, GLdouble eyey, GLdouble eyez, GLdouble atx, GLdouble aty, GLdouble atz, GLdouble upx, GLdouble upy, GLdouble upz) Sun-Jeong Kim 13 Locating Camera (2/2) Sun-Jeong Kim 14

8 Result Locating Camera Sun-Jeong Kim 15 Building Objects (1/5) Using arrays typedef Glfloat point3[3]; point3 vertices[8][3] = { { -1, -1, 1 }, { -1, 1, 1 }, { 1, 1, 1 }, { 1, -1, 1 }, { -1, -1, -1 }, { -1, 1, -1 }, { 1, 1, -1 }, { 1, -1, -1 } }; GLfloat colors[8][3] = { { 0, 0, 1 }, { 0, 1, 1 }, { 1, 1, 1 }, { 1, 0, 1 }, { 0, 0, 0 }, { 0, 1, 0 }, { 1, 1, 0 }, { 1, 0, 0 } }; Quad(0, 3, 2, 1); Quad(1, 2, 6, 5); Quad(2, 3, 7, 6); Quad(3, 0, 4, 7); Quad(4, 5, 6, 7); Quad(5, 4, 0, 1); Sun-Jeong Kim 16

9 Building Objects (2/5) Sun-Jeong Kim 17 Building Objects (3/5) Sun-Jeong Kim 18

10 Building Objects (4/5) Sun-Jeong Kim 19 Result Building Objects (1) Sun-Jeong Kim 20

11 Building Objects (5/5) Sun-Jeong Kim 21 Result Building Objects (2) Sun-Jeong Kim 22

12 Note Display List (1/2) Immediate mode: standard in OpenGL primitives are no longer in the system after passing through the OpenGL pipeline when redrawing the screen, we have to regenerate the primitives time consuming Retained mode display lists in OpenGL collections of primitives and other information can be stored avoiding costly regeneration problem Sun-Jeong Kim 23 Note Display List (2/2) Steps creating a new display list void glnewlist(gluint name, GLenum mode); void glendlist(); mode: GL_COMPILE, GL_COMPILE_AND_EXECUTE executing a display list void glcalllist(gluint name); deleting a display list display list cannot be changed!! void gldeletelists(gluint first, GLsizei number); Sun-Jeong Kim 24

13 Hidden Surface Removal (1/2) Z-Buffer Algorithm depth buffer extra storage to store depth information Sun-Jeong Kim 25 Hidden Surface Removal (2/2) Sun-Jeong Kim 26

14 Rotating a Cube Sun-Jeong Kim 27 Result Rotating a Cube Sun-Jeong Kim 28

15 Exercise Rotate a cube in the reverse direction when the left button of a mouse is clicked Change the axis of the rotation when the following keys are pressed: x or X : the x-axis rotation y or Y : the y-axis rotation z or Z : the z-axis rotation Sun-Jeong Kim 29

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

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

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

Transformations (Rotations with Quaternions) October 24, 2005

Transformations (Rotations with Quaternions) October 24, 2005 Computer Graphics Transformations (Rotations with Quaternions) October 4, 5 Virtual Trackball (/3) Using the mouse position to control rotation about two axes Supporting continuous rotations of objects

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

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

Describe the Orthographic and Perspective projections. How do we combine together transform matrices?

Describe the Orthographic and Perspective projections. How do we combine together transform matrices? Aims and objectives By the end of the lecture you will be able to Work with multiple transform matrices Describe the viewing process in OpenGL Design and build a camera control APIs Describe the Orthographic

More information

CSC Graphics Programming. Budditha Hettige Department of Statistics and Computer Science

CSC Graphics Programming. Budditha Hettige Department of Statistics and Computer Science CSC 307 1.0 Graphics Programming Department of Statistics and Computer Science Graphics Programming OpenGL 3D Drawing 2 3D Graphics Projections Getting 3D to 2D 3D scene 2D image 3 Projections Orthographic

More information

OpenGL Transformations

OpenGL 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 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

3D Graphics for Game Programming (J. Han) Chapter II Vertex Processing

3D 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 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

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

Getting Started. Overview (1): Getting Started (1): Getting Started (2): Getting Started (3): COSC 4431/5331 Computer Graphics.

Getting 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 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

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

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

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

Advanced Computer Graphics (CS & SE )

Advanced 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 information

1 (Practice 1) Introduction to OpenGL

1 (Practice 1) Introduction to OpenGL 1 (Practice 1) Introduction to OpenGL This first practical is intended to get you used to OpenGL command. It is mostly a copy/paste work. Try to do it smartly by tweaking and messing around with parameters,

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

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

COMP3421. Introduction to 3D Graphics

COMP3421. 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 information

Precept 2 Aleksey Boyko February 18, 2011

Precept 2 Aleksey Boyko February 18, 2011 Precept 2 Aleksey Boyko February 18, 2011 Getting started Initialization Drawing Transformations Cameras Animation Input Keyboard Mouse Joystick? Textures Lights Programmable pipeline elements (shaders)

More information

COMP3421. Introduction to 3D Graphics

COMP3421. 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 information

MORE OPENGL. Pramook Khungurn CS 4621, Fall 2011

MORE OPENGL. Pramook Khungurn CS 4621, Fall 2011 MORE OPENGL Pramook Khungurn CS 4621, Fall 2011 SETTING UP THE CAMERA Recall: OpenGL Vertex Transformations Coordinates specified by glvertex are transformed. End result: window coordinates (in pixels)

More information

Viewing Transformation

Viewing Transformation CS38: Computer Graphics Viewing Transformation Sung-Eui Yoon ( 윤성의 ) Course URL: http://sglab.kaist.ac.kr/~sungeui/cg/ Class Objectives Know camera setup parameters Understand viewing and projection processes

More information

COMP Computer Graphics and Image Processing. 5: Viewing 1: The camera. In part 1 of our study of Viewing, we ll look at ˆʹ U ˆ ʹ F ˆʹ S

COMP Computer Graphics and Image Processing. 5: Viewing 1: The camera. In part 1 of our study of Viewing, we ll look at ˆʹ U ˆ ʹ F ˆʹ S COMP27112 Û ˆF Ŝ Computer Graphics and Image Processing ˆʹ U ˆ ʹ F C E 5: iewing 1: The camera ˆʹ S Toby.Howard@manchester.ac.uk 1 Introduction In part 1 of our study of iewing, we ll look at iewing in

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

// double buffering and RGB glutinitdisplaymode(glut_double GLUT_RGBA); // your own initializations

// double buffering and RGB glutinitdisplaymode(glut_double GLUT_RGBA); // your own initializations #include int main(int argc, char** argv) { glutinit(&argc, argv); Typical OpenGL/GLUT Main Program // GLUT, GLU, and OpenGL defs // program arguments // initialize glut and gl // double buffering

More information

COMP3421. Introduction to 3D Graphics

COMP3421. 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 information

Spring 2013, CS 112 Programming Assignment 2 Submission Due: April 26, 2013

Spring 2013, CS 112 Programming Assignment 2 Submission Due: April 26, 2013 Spring 2013, CS 112 Programming Assignment 2 Submission Due: April 26, 2013 PROJECT GOAL: Write a restricted OpenGL library. The goal of the project is to compute all the transformation matrices with your

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

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

COMS 4160: Problems on Transformations and OpenGL

COMS 4160: Problems on Transformations and OpenGL COMS 410: Problems on Transformations and OpenGL Ravi Ramamoorthi 1. Write the homogeneous 4x4 matrices for the following transforms: Translate by +5 units in the X direction Rotate by 30 degrees about

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

Models and Architectures

Models 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 information

Graphics and Visualization

Graphics and Visualization International University Bremen Spring Semester 2006 Recap Representing graphic objects by homogenous points and vectors Using affine transforms to modify objects Using projections to display objects

More information

Wire-Frame 3D Graphics Accelerator IP Core. C Library Specification

Wire-Frame 3D Graphics Accelerator IP Core. C Library Specification Wire-Frame 3D Graphics Accelerator IP Core C Library Specification Kenji Ishimaru 1 / 29 Revision History Rev. Date Author Description 1.0 2015/09/30 Kenji Ishimaru First release

More information

Rasterization Overview

Rasterization 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 information

Getting Started. 1 st Week, Sun-Jeong Kim. Computer Graphics Applications

Getting Started. 1 st Week, Sun-Jeong Kim. Computer Graphics Applications OpenGL Programming Getting Started 1 st Week, 2008 Sun-Jeong Kim Visual Studio 2005 Windows Programming 2 Visual C++ Win32 Application New Project 3 Empty project Application Settings 4 Solution Prac01

More information

CS380: Computer Graphics Viewing Transformation. Sung-Eui Yoon ( 윤성의 ) Course URL:

CS380: Computer Graphics Viewing Transformation. Sung-Eui Yoon ( 윤성의 ) Course URL: CS38: Computer Graphics Viewing Transformation Sung-Eui Yoon ( 윤성의 ) Course URL: http://sglab.kaist.ac.kr/~sungeui/cg/ Class Objectives Know camera setup parameters Understand viewing and projection processes

More information

CS559: Computer Graphics. Lecture 12: OpenGL Transformation Li Zhang Spring 2008

CS559: Computer Graphics. Lecture 12: OpenGL Transformation Li Zhang Spring 2008 CS559: Computer Graphics Lecture 2: OpenGL Transformation Li Zhang Spring 28 Today Transformation in OpenGL Reading Chapter 3 Last time Primitive Details glpolygonmode(glenum face, GLenum mode); face:

More information

Computer Graphics (Basic OpenGL)

Computer Graphics (Basic OpenGL) Computer Graphics (Basic OpenGL) Thilo Kielmann Fall 2008 Vrije Universiteit, Amsterdam kielmann@cs.vu.nl http://www.cs.vu.nl/ graphics/ Computer Graphics (Basic OpenGL, Input and Interaction), ((57))

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

Lecture 9 Sections 2.6, 5.1, 5.2. Wed, Sep 16, 2009

Lecture 9 Sections 2.6, 5.1, 5.2. Wed, Sep 16, 2009 Lecture 9 Sections 2.6, 5.1, 5.2 Hampden-Sydney College Wed, Sep 16, 2009 Outline 1 2 3 4 5 6 Controlling 7 Definition () A frustum is a truncated pyramid. Definition ( ) The view frustum is the region

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

Introduction to OpenGL Transformations, Viewing and Lighting. Ali Bigdelou

Introduction to OpenGL Transformations, Viewing and Lighting. Ali Bigdelou Introduction to OpenGL Transformations, Viewing and Lighting Ali Bigdelou Modeling From Points to Polygonal Objects Vertices (points) are positioned in the virtual 3D scene Connect points to form polygons

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

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

Lecture 5: Viewing. CSE Computer Graphics (Fall 2010)

Lecture 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 information

Viewing and Modeling

Viewing and Modeling Viewing and Modeling Computer Science Department The Universit of Texas at Austin A Simplified Graphics ipeline Application Vertex batching & assembl Triangle assembl Triangle clipping NDC to window space

More information

The View Frustum. Lecture 9 Sections 2.6, 5.1, 5.2. Robb T. Koether. Hampden-Sydney College. Wed, Sep 14, 2011

The View Frustum. Lecture 9 Sections 2.6, 5.1, 5.2. Robb T. Koether. Hampden-Sydney College. Wed, Sep 14, 2011 The View Frustum Lecture 9 Sections 2.6, 5.1, 5.2 Robb T. Koether Hampden-Sydney College Wed, Sep 14, 2011 Robb T. Koether (Hampden-Sydney College) The View Frustum Wed, Sep 14, 2011 1 / 36 Outline 1 The

More information

Introduction to OpenGL

Introduction to OpenGL Introduction to OpenGL Tutorial 1: Create a window and draw a 2D square Introduction: The aim of the first tutorial is to introduce you to the magic world of graphics based on the OpenGL and GLUT APIs.

More information

OpenGL. 1 OpenGL OpenGL 1.2 3D. (euske) 1. Client-Server Model OpenGL

OpenGL. 1 OpenGL OpenGL 1.2 3D. (euske) 1. Client-Server Model OpenGL OpenGL (euske) 1 OpenGL - 1.1 OpenGL 1. Client-Server Model 2. 3. 1.2 3D OpenGL (Depth-Buffer Algorithm Z-Buffer Algorithm) (polygon ) ( rendering) Client-Server Model X Window System ( GL ) GL (Indy O

More information

CS 381 Computer Graphics, Fall 2008 Midterm Exam Solutions. The Midterm Exam was given in class on Thursday, October 23, 2008.

CS 381 Computer Graphics, Fall 2008 Midterm Exam Solutions. The Midterm Exam was given in class on Thursday, October 23, 2008. CS 381 Computer Graphics, Fall 2008 Midterm Exam Solutions The Midterm Exam was given in class on Thursday, October 23, 2008. 1. [4 pts] Drawing Where? Your instructor says that objects should always be

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

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

15. Clipping. Projection Transformation. Projection Matrix. Perspective Division

15. Clipping. Projection Transformation. Projection Matrix. Perspective Division 15. Clipping Procedures for eliminating all parts of primitives outside of the specified view volume are referred to as clipping algorithms or simply clipping This takes place as part of the Projection

More information

Computer graphics MN1

Computer graphics MN1 Computer graphics MN1 http://www.opengl.org Todays lecture What is OpenGL? How do I use it? Rendering pipeline Points, vertices, lines,, polygons Matrices and transformations Lighting and shading Code

More information

CIS 636 Interactive Computer Graphics CIS 736 Computer Graphics Spring 2011

CIS 636 Interactive Computer Graphics CIS 736 Computer Graphics Spring 2011 CIS 636 Interactive Computer Graphics CIS 736 Computer Graphics Spring 2011 Lab 1a of 7 OpenGL Setup and Basics Fri 28 Jan 2011 Part 1a (#1 5) due: Thu 03 Feb 2011 (before midnight) The purpose of this

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

Transformation, Input and Interaction. Hanyang University

Transformation, Input and Interaction. Hanyang University Transformation, Input and Interaction Hanyang University Transformation, projection, viewing Pipeline of transformations Standard sequence of transforms Cornell CS4620 Fall 2008 Lecture 8 3 2008 Steve

More information

CSE4030 Introduction to Computer Graphics

CSE4030 Introduction to Computer Graphics CSE4030 Introduction to Computer Graphics Dongguk University Jeong-Mo Hong Timetable 00:00~00:10 Introduction (English) 00:10~00:50 Topic 1 (English) 00:50~00:60 Q&A (English, Korean) 01:00~01:40 Topic

More information

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

Computer Graphics. Lecture 04 3D Projection and Visualization. Edirlei Soares de Lima.

Computer Graphics. Lecture 04 3D Projection and Visualization. Edirlei Soares de Lima. Computer Graphics Lecture 4 3D Projection and Visualization Edirlei Soares de Lima Projection and Visualization An important use of geometric transformations in computer

More information

Viewing transformations. 2004, Denis Zorin

Viewing transformations. 2004, Denis Zorin Viewing transformations OpenGL transformation pipeline Four main stages: Modelview: object coords to eye coords p eye = Mp obj (x obj,y obj,z obj,w obj ) (x eye,y eye,z eye,w eye ) in eye coordinates,

More information

Classical 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 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 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

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

Lecture 4 of 41. Lab 1a: OpenGL Basics

Lecture 4 of 41. Lab 1a: OpenGL Basics Lab 1a: OpenGL Basics William H. Hsu Department of Computing and Information Sciences, KSU KSOL course pages: http://snipurl.com/1y5gc Course web site: http://www.kddresearch.org/courses/cis636 Instructor

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

CS 381 Computer Graphics, Fall 2012 Midterm Exam Solutions. The Midterm Exam was given in class on Tuesday, October 16, 2012.

CS 381 Computer Graphics, Fall 2012 Midterm Exam Solutions. The Midterm Exam was given in class on Tuesday, October 16, 2012. CS 381 Computer Graphics, Fall 2012 Midterm Exam Solutions The Midterm Exam was given in class on Tuesday, October 16, 2012. 1. [7 pts] Synthetic-Camera Model. Describe the Synthetic-Camera Model : how

More information

Chapter 3 - Basic Mathematics for 3D Computer Graphics

Chapter 3 - Basic Mathematics for 3D Computer Graphics Chapter 3 - Basic Mathematics for 3D Computer Graphics Three-Dimensional Geometric Transformations Affine Transformations and Homogeneous Coordinates OpenGL Matrix Logic Translation Add a vector t Geometrical

More information

Blue colour text questions Black colour text sample answers Red colour text further explanation or references for the sample answers

Blue colour text questions Black colour text sample answers Red colour text further explanation or references for the sample answers Blue colour text questions Black colour text sample answers Red colour text further explanation or references for the sample answers Question 1. a) (5 marks) Explain the OpenGL synthetic camera model,

More information

Introduction to OpenGL Week 1

Introduction to OpenGL Week 1 CS 432/680 INTERACTIVE COMPUTER GRAPHICS Introduction to OpenGL Week 1 David Breen Department of Computer Science Drexel University Based on material from Ed Angel, University of New Mexico Objectives

More information

Objectives. Image Formation Revisited. Physical Approaches. The Programmer s Interface. Practical Approach. Introduction to OpenGL Week 1

Objectives. Image Formation Revisited. Physical Approaches. The Programmer s Interface. Practical Approach. Introduction to OpenGL Week 1 CS 432/680 INTERACTIVE COMPUTER GRAPHICS Introduction to OpenGL Week 1 David Breen Department of Computer Science Drexel University Objectives Learn the basic design of a graphics system Introduce graphics

More information

Android and OpenGL. Android Smartphone Programming. Matthias Keil. University of Freiburg

Android and OpenGL. Android Smartphone Programming. Matthias Keil. University of Freiburg Android and OpenGL Android Smartphone Programming Matthias Keil Institute for Computer Science Faculty of Engineering 1. Februar 2016 Outline 1 OpenGL Introduction 2 Displaying Graphics 3 Interaction 4

More information

Perspective transformations

Perspective 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 information

Lecture 4 Advanced Computer Graphics (CS & SE )

Lecture 4 Advanced Computer Graphics (CS & SE ) Lecture 4 Advanced Computer Graphics (CS & SE 233.420) Topics Covered Animation Matrices Viewing Lighting Animating Interactive Programs Consider planet.c Want to animate rotating the Earth around the

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

Clipping and Scan Conversion

Clipping and Scan Conversion 15-462 Computer Graphics I Lecture 14 Clipping and Scan Conversion Line Clipping Polygon Clipping Clipping in Three Dimensions Scan Conversion (Rasterization) [Angel 7.3-7.6, 7.8-7.9] March 19, 2002 Frank

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

CIS 441/541: Introduction to Computer Graphics Lecture 14: OpenGL Basics

CIS 441/541: Introduction to Computer Graphics Lecture 14: OpenGL Basics CIS 441/541: Introduction to Computer Graphics Lecture 14: OpenGL Basics Oct. 26th, 2016 Hank Childs, University of Oregon Announcements OH Hank: Weds 1-2, Thursday 11-12 Dan: Weds 4-530, Thursday 930-11

More information

CSE452 Computer Graphics

CSE452 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 information

Image Rendering. Rendering can be divided into three sub-problems. Image Formation The hidden surface problem visibility determination steps

Image Rendering. Rendering can be divided into three sub-problems. Image Formation The hidden surface problem visibility determination steps Image Rendering Rendering can be divided into three sub-problems Image Formation The hidden surface problem visibility determination steps Illumination Direct illumination Indirect illumination Shading

More information

Computer Graphics. Bing-Yu Chen National Taiwan University

Computer Graphics. Bing-Yu Chen National Taiwan University Computer Graphics Bing-Yu Chen National Taiwan University Introduction to OpenGL General OpenGL Introduction An Example OpenGL Program Drawing with OpenGL Transformations Animation and Depth Buffering

More information

Rendering. Part 1 An introduction to OpenGL

Rendering. Part 1 An introduction to OpenGL Rendering Part 1 An introduction to OpenGL Olivier Gourmel VORTEX Team IRIT University of Toulouse gourmel@irit.fr Image synthesis The Graphics Processing Unit (GPU): A highly parallel architecture specialized

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

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

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

Cameras (and eye) Ideal Pinhole. Real Pinhole. Real + lens. Depth of field

Cameras (and eye) Ideal Pinhole. Real Pinhole. Real + lens. Depth of field Cameras (and eye) Ideal Pinhole Real Pinhole Real + lens Depth of field 1 Z-buffer How do we draw objects? Polygon Based Fast Raytracing Ray/Object intersections Slow Copyright Pixar 2 Raytracing for each

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

CS 4204 Computer Graphics

CS 4204 Computer Graphics CS 4204 Computer Graphics GLUT (Continue) More Interactions Yong Cao Virginia Tech References: Interactive Computer Graphics, Fourth Edition, Ed Angle Orthographical Projection Synthetic camera model View

More information

Early History of APIs. PHIGS and X. SGI and GL. Programming with OpenGL Part 1: Background. Objectives

Early History of APIs. PHIGS and X. SGI and GL. Programming with OpenGL Part 1: Background. Objectives Programming with OpenGL Part 1: Background Early History of APIs Objectives Development of the OpenGL API OpenGL Architecture - OpenGL as a state machine Functions - Types -Formats Simple program IFIPS

More information

Visualizing Molecular Dynamics

Visualizing Molecular Dynamics Visualizing Molecular Dynamics Aiichiro Nakano Collaboratory for Advanced Computing & Simulations Department of Computer Science Department of Physics & Astronomy Department of Chemical Engineering & Materials

More information

3D Tree Generator. 3D Fractal Tree Generator. Konstantinos Seventekidis DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF IOANNINA

3D Tree Generator. 3D Fractal Tree Generator. Konstantinos Seventekidis DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF IOANNINA 3D Tree Generator 3D Fractal Tree Generator Konstantinos Seventekidis Graphical Grammars DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF IOANNINA Contents: 1. Introduction to the problem 2. How to install

More information

CSC Graphics Programming. Budditha Hettige Department of Statistics and Computer Science

CSC Graphics Programming. Budditha Hettige Department of Statistics and Computer Science CSC 307 1.0 Graphics Programming Department of Statistics and Computer Science Graphics Programming 2 Common Uses for Computer Graphics Applications for real-time 3D graphics range from interactive games

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