# CSE 167: Introduction to Computer Graphics Lecture #4: Vertex Transformation

Size: px
Start display at page:

Transcription

1 CSE 167: Introduction to Computer Graphics Lecture #4: Vertex Transformation Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2013

2 Announcements Project 2 due Friday, October 11 Compare on-line homework scores to your notes and let us know if they do not match To get graded early, please see course assistants during office hours New: Friday grading with two sign-up boards in labs 260 and 270 Changes to office hours in lab: see course web page 2

3 Lecture Overview View Volumes Vertex Transformation Rendering Pipeline Culling 3

4 View Volumes View volume = 3D volume seen by camera Orthographic view volume Camera coordinates Perspective view volume Camera coordinates World coordinates World coordinates 4

5 Projection Matrix Camera coordinates Projection matrix Canonical view volume Viewport transformation 5 Image space (pixel coordinates)

6 Orthographic View Volume Specified by 6 parameters: Right, left, top, bottom, near, far Or, if symmetrical: Width, height, near, far 6

7 Orthographic Projection Matrix In OpenGL: glortho(left, right, bottom, top, near, far) 7 2 right + left 0 0 right left right left 2 top + bottom 0 0 P ortho (right,left,top,bottom,near, far) = top bottom top bottom 2 far + near 0 0 far near far near width P ortho (width,height,near, far) = height No equivalent in OpenGL 2 far + near 0 0 far near far near

8 Perspective View Volume General view volume Camera coordinates Defined by 6 parameters, in camera coordinates Left, right, top, bottom boundaries Near, far clipping planes Clipping planes to avoid numerical problems Divide by zero Low precision for distant objects Usually symmetric, i.e., left=-right, top=-bottom 8

9 Perspective View Volume Symmetrical view volume y y=top FOV -z z=-near Only 4 parameters Vertical field of view (FOV) Image aspect ratio (width/height) Near, far clipping planes z=-far aspect ratio= tan(fov / 2) = top near right left top bottom = right top 9

10 Perspective Projection Matrix General view frustum with 6 parameters Camera coordinates In OpenGL: glfrustum(left, right, bottom, top, near, far) 10

11 Perspective Projection Matrix Symmetrical view frustum with field of view, aspect ratio, near and far clip planes Camera coordinates y y=top FOV z=-near -z z=-far aspect tan(fov / 2) P persp (FOV,aspect,near, far) = tan(fov / 2) near + far 0 0 near far In OpenGL: gluperspective(fov, aspect, near, far) 11 2 near far near far

12 Canonical View Volume Goal: create projection matrix so that User defined view volume is transformed into canonical view volume: cube [-1,1]x[-1,1]x[-1,1] Multiplying corner vertices of view volume by projection matrix and performing homogeneous divide yields corners of canonical view volume Perspective and orthographic projection are treated the same way Canonical view volume is last stage in which coordinates are in 3D Next step is projection to 2D frame buffer 12

13 Viewport Transformation After applying projection matrix, scene points are in normalized viewing coordinates Per definition within range [-1..1] x [-1..1] x [-1..1] Next is projection from 3D to 2D (not reversible) Normalized viewing coordinates can be mapped to image (=pixel=frame buffer) coordinates Range depends on window (view port) size: [x0 x1] x [y0 y1] Scale and translation required: 13 D( x 0, x 1, y 0, y 1 )= ( x 1 x 0 ) x 0 + x 1 0 ( y 1 y 0 ) 2 0 y 0 + y ( ) 2 ( ) 2

14 Lecture Overview View Volumes Vertex Transformation Rendering Pipeline Culling 14

15 Complete Vertex Transformation Mapping a 3D point in object coordinates to pixel coordinates: Object space M: Object-to-world matrix C: camera matrix P: projection matrix D: viewport matrix 15

16 Complete Vertex Transformation Mapping a 3D point in object coordinates to pixel coordinates: Object space World space M: Object-to-world matrix C: camera matrix P: projection matrix D: viewport matrix 16

17 Complete Vertex Transformation Mapping a 3D point in object coordinates to pixel coordinates: M: Object-to-world matrix C: camera matrix P: projection matrix D: viewport matrix Object space World space Camera space 17

18 Complete Vertex Transformation Mapping a 3D point in object coordinates to pixel coordinates: M: Object-to-world matrix C: camera matrix P: projection matrix D: viewport matrix Object space World space Camera space Canonical view volume 18

19 Complete Vertex Transformation Mapping a 3D point in object coordinates to pixel coordinates: Image space M: Object-to-world matrix C: camera matrix P: projection matrix D: viewport matrix Object space World space Camera space Canonical view volume 19

20 Complete Vertex Transformation Mapping a 3D point in object coordinates to pixel coordinates: Pixel coordinates: M: Object-to-world matrix C: camera matrix P: projection matrix D: viewport matrix 20

21 The Complete Vertex Transformation Object Coordinates Model Matrix World Coordinates Camera Matrix Camera Coordinates Canonical View Volume Coordinates Window Coordinates Projection Matrix Viewport Matrix 21

22 Complete Vertex Transformation in OpenGL Mapping a 3D point in object coordinates to pixel coordinates: OpenGL GL_MODELVIEW matrix M: Object-to-world matrix C: camera matrix P: projection matrix D: viewport matrix OpenGL GL_PROJECTION matrix 22

23 Complete Vertex Transformation in OpenGL GL_MODELVIEW, C -1 M Defined by the programmer. Think of the ModelView matrix as where you stand with the camera and the direction you point it. GL_PROJECTION, P Utility routines to set it by specifying view volume: glfrustum(), glperspective(), glortho() Think of the projection matrix as describing the attributes of your camera, such as field of view, focal length, etc. Viewport, D Specify implicitly via glviewport() No direct access with equivalent to GL_MODELVIEW or GL_PROJECTION 23

24 Lecture Overview View Volumes Vertex Transformation Rendering Pipeline Culling 24

25 Rendering Pipeline Scene data Rendering pipeline Hardware and software which draws 3D scenes on the screen Consists of several stages Simplified version here Most operations performed by specialized hardware (GPU) Access to hardware through low-level 3D API (OpenGL, DirectX) All scene data flows through the pipeline at least once for each frame 25 Image

26 Rendering Pipeline Scene data Modeling and viewing transformation Shading Textures, lights, etc. Geometry Vertices and how they are connected Triangles, lines, points, triangle strips Attributes such as color Projection 26 Rasterization, visibility Image Specified in object coordinates Processed by the rendering pipeline one-by-one

27 Rendering Pipeline Scene data Modeling and viewing transformation Shading Projection Transform object to camera coordinates Specified by GL_MODELVIEW matrix in OpenGL User computes GL_MODELVIEW matrix as discussed Rasterization, visibility MODELVIEW matrix 27 Image

28 Rendering Pipeline Scene data Modeling and viewing transformation Shading Look up light sources Compute color for each vertex Projection Rasterization, visibility 28 Image

29 Rendering Pipeline Scene data Modeling and viewing transformation Shading Projection Rasterization, visibility Project 3D vertices to 2D image positions GL_PROJECTION matrix 29 Image

30 Rendering Pipeline Scene data Modeling and viewing transformation Shading Projection Draw primitives (triangles, lines, etc.) Determine what is visible Rasterization, visibility 30 Image

31 Rendering Pipeline Scene data Modeling and viewing transformation Shading Projection Rasterization, visibility 31 Image Pixel colors

32 Rendering Engine Scene data Rendering pipeline Rendering Engine: Additional software layer encapsulating low-level API Higher level functionality than OpenGL Platform independent Layered software architecture common in industry Game engines Graphics middleware 32 Image

33 Lecture Overview View Volumes Vertex Transformation Rendering Pipeline Culling 33

34 Culling Goal: Discard geometry that does not need to be drawn to speed up rendering Types of culling: View frustum culling Occlusion culling Small object culling Backface culling Degenerate culling 34

35 View Frustum Culling Triangles outside of view frustum are off-screen Done on canonical view volume Images: SGI OpenGL Optimizer Programmer's Guide 35

36 Videos Rendering Optimisations - Frustum Culling View Frustum Culling Demo 36

37 Bounding Box How to cull objects consisting of may polygons? Cull bounding box Rectangular box, parallel to object space coordinate planes Box is smallest box containing the entire object 37 Image: SGI OpenGL Optimizer Programmer's Guide

38 Occlusion Culling Geometry hidden behind occluder cannot be seen Many complex algorithms exist to identify occluded geometry Images: SGI OpenGL Optimizer Programmer's Guide 38

39 Video Umbra 3 Occlusion Culling explained 39

40 Small Object Culling Object projects to less than a specified size Cull objects whose screen-space bounding box is less than a threshold number of pixels 40

41 Backface Culling Consider triangles as one-sided, i.e., only visible from the front Closed objects If the back of the triangle is facing the camera, it is not visible Gain efficiency by not drawing it (culling) Roughly 50% of triangles in a scene are back facing 41

42 Backface Culling Convention: Triangle is front facing if vertices are ordered counterclockwise p2 p1 p0 p0 Front-facing OpenGL allows one- or two-sided triangles One-sided triangles: glenable(gl_cull_face); glcullface(gl_back) Two-sided triangles (no backface culling): gldisable(gl_cull_face) p1 Back-facing p2 42

43 Backface Culling Compute triangle normal after projection (homogeneous division) Third component of n negative: front-facing, otherwise back-facing Remember: projection matrix is such that homogeneous division flips sign of third component 43

44 Degenerate Culling Degenerate triangle has no area Vertices lie in a straight line Vertices at the exact same place Normal n=0 Source: Computer Methods in Applied Mechanics and Engineering, Volume 194, Issues

45 Rendering Pipeline Primitives Modeling and Viewing Transformation Shading Projection Scan conversion, visibility Culling, Clipping Discard geometry that will not be visible 45 Image

### 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

### CSE 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

### CSE 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

### CSE 167: Introduction to Computer Graphics Lecture #10: View Frustum Culling

CSE 167: Introduction to Computer Graphics Lecture #10: View Frustum Culling Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2015 Announcements Project 4 due tomorrow Project

### 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

### CSE 167: Introduction to Computer Graphics Lecture #11: Visibility Culling

CSE 167: Introduction to Computer Graphics Lecture #11: Visibility Culling Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2017 Announcements Project 3 due Monday Nov 13 th at

### Culling. Computer Graphics CSE 167 Lecture 12

Culling Computer Graphics CSE 167 Lecture 12 CSE 167: Computer graphics Culling Definition: selecting from a large quantity In computer graphics: selecting primitives (or batches of primitives) that are

### CSE 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

### CMSC427 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

### CSE 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

### Projection 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

### 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

### 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

### 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

### Clipping & Culling. Lecture 11 Spring Trivial Rejection Outcode Clipping Plane-at-a-time Clipping Backface Culling

Clipping & Culling Trivial Rejection Outcode Clipping Plane-at-a-time Clipping Backface Culling Lecture 11 Spring 2015 What is Clipping? Clipping is a procedure for spatially partitioning geometric primitives,

### 3D 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

### Rendering. 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

### CS4620/5620: 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

### 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

### Projection: Mapping 3-D to 2-D. Orthographic Projection. The Canonical Camera Configuration. Perspective Projection

Projection: Mapping 3-D to 2-D Our scene models are in 3-D space and images are 2-D so we need some wa of projecting 3-D to 2-D The fundamental approach: planar projection first, we define a plane in 3-D

### 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

### 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

### Rendering Objects. Need to transform all geometry then

Intro to OpenGL Rendering Objects Object has internal geometry (Model) Object relative to other objects (World) Object relative to camera (View) Object relative to screen (Projection) Need to transform

### CSE 167: Lecture #8: Lighting. Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2011

CSE 167: Introduction to Computer Graphics Lecture #8: Lighting Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2011 Announcements Homework project #4 due Friday, October 28 Introduction:

### Game 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

### OpenGL: 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 351-50 Graphics API ( Application Programming Interface) Software library Layer between programmer and graphics hardware (and other software

### CSE 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

### Viewing 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

### CS451Real-time Rendering Pipeline

1 CS451Real-time Rendering Pipeline JYH-MING LIEN DEPARTMENT OF COMPUTER SCIENCE GEORGE MASON UNIVERSITY Based on Tomas Akenine-Möller s lecture note You say that you render a 3D 2 scene, but what does

### 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

### Prof. 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

### Motivation. Culling Don t draw what you can t see! What can t we see? Low-level Culling

Motivation Culling Don t draw what you can t see! Thomas Larsson Mälardalen University April 7, 2016 Image correctness Rendering speed One day we will have enough processing power!? Goals of real-time

### CS 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

### Pipeline 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

### Visibility: 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

### Surface 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

### CS 591B Lecture 9: The OpenGL Rendering Pipeline

CS 591B Lecture 9: The OpenGL Rendering Pipeline 3D Polygon Rendering Many applications use rendering of 3D polygons with direct illumination Spring 2007 Rui Wang 3D Polygon Rendering Many applications

### 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

### CS 4731/543: Computer Graphics Lecture 5 (Part I): Projection. Emmanuel Agu

CS 4731/543: Computer Graphics Lecture 5 (Part I): Projection Emmanuel Agu 3D Viewing and View Volume Recall: 3D viewing set up Projection Transformation View volume can have different shapes (different

### Pipeline Operations. CS 4620 Lecture 14

Pipeline Operations CS 4620 Lecture 14 2014 Steve Marschner 1 Pipeline you are here APPLICATION COMMAND STREAM 3D transformations; shading VERTEX PROCESSING TRANSFORMED GEOMETRY conversion of primitives

### 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

### CSE 167: Introduction to Computer Graphics Lecture #3: Projection. Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2013

CSE 167: Introduction to Computer Graphics Lecture #3: Projection Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2013 Announcements Project 1 due tomorrow (Friday), presentation

### VISIBILITY & CULLING. Don t draw what you can t see. Thomas Larsson, Afshin Ameri DVA338, Spring 2018, MDH

VISIBILITY & CULLING Don t draw what you can t see. Thomas Larsson, Afshin Ameri DVA338, Spring 2018, MDH Visibility Visibility Given a set of 3D objects, which surfaces are visible from a specific point

### To Do. Demo (Projection Tutorial) Motivation. What we ve seen so far. Outline. Foundations of Computer Graphics (Fall 2012) CS 184, Lecture 5: Viewing

Foundations of Computer Graphics (Fall 0) CS 84, Lecture 5: Viewing http://inst.eecs.berkele.edu/~cs84 To Do Questions/concerns about assignment? Remember it is due Sep. Ask me or TAs re problems Motivation

### CSE 167: Introduction to Computer Graphics Lecture #3: Projection. Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2016

CSE 167: Introduction to Computer Graphics Lecture #3: Projection Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2016 Announcements Next Monday: homework discussion Next Friday:

### The 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

### CSE 167: Introduction to Computer Graphics Lecture #5: Visibility, OpenGL

CSE 167: Introduction to Computer Graphics Lecture #5: Visibility, OpenGL Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2016 Announcements Tomorrow: assignment 1 due Grading

### CSE 167: Introduction to Computer Graphics Lecture #8: Textures. Jürgen P. Schulze, Ph.D. University of California, San Diego Spring Quarter 2016

CSE 167: Introduction to Computer Graphics Lecture #8: Textures Jürgen P. Schulze, Ph.D. University of California, San Diego Spring Quarter 2016 Announcements Project 2 due this Friday Midterm next Tuesday

### To Do. Motivation. Demo (Projection Tutorial) What we ve seen so far. Computer Graphics. Summary: The Whole Viewing Pipeline

Computer Graphics CSE 67 [Win 9], Lecture 5: Viewing Ravi Ramamoorthi http://viscomp.ucsd.edu/classes/cse67/wi9 To Do Questions/concerns about assignment? Remember it is due tomorrow! (Jan 6). Ask me or

### 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.

### 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

### 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

### Projection Matrix Tricks. Eric Lengyel

Projection Matrix Tricks Eric Lengyel Outline Projection Matrix Internals Infinite Projection Matrix Depth Modification Oblique Near Clipping Plane Slides available at http://www.terathon.com www.terathon.com/

### CS 543: Computer Graphics. Projection

CS 543: Computer Graphics Projection Robert W. Lindeman Associate Professor Interactive Media & Game Development Department of Computer Science Worcester Poltechnic Institute gogo@wpi.edu with lots of

### 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

### CSE 167: Introduction to Computer Graphics. Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2013

CSE 167: Introduction to Computer Graphics Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2013 Today Course organization Course overview 2 Course Staff Instructor Jürgen Schulze,

### E.Order of Operations

Appendix E E.Order of Operations This book describes all the performed between initial specification of vertices and final writing of fragments into the framebuffer. The chapters of this book are arranged

### 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

### Motivation. What we ve seen so far. Demo (Projection Tutorial) Outline. Projections. Foundations of Computer Graphics

Foundations of Computer Graphics Online Lecture 5: Viewing Orthographic Projection Ravi Ramamoorthi Motivation We have seen transforms (between coord sstems) But all that is in 3D We still need to make

### Exercise Max. Points Total 90

University of California San Diego Department of Computer Science CSE167: Introduction to Computer Graphics Fall Quarter 2014 Midterm Examination #1 Thursday, October 30 th, 2014 Instructor: Dr. Jürgen

### The Rendering Pipeline (1)

The Rendering Pipeline (1) Alessandro Martinelli alessandro.martinelli@unipv.it 30 settembre 2014 The Rendering Pipeline (1) Rendering Architecture First Rendering Pipeline Second Pipeline: Illumination

### 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

### CS 428: Fall Introduction to. Viewing and projective transformations. Andrew Nealen, Rutgers, /23/2009 1

CS 428: Fall 29 Introduction to Computer Graphics Viewing and projective transformations Andrew Nealen, Rutgers, 29 9/23/29 Modeling and viewing transformations Canonical viewing volume Viewport transformation

### CSE 167: Introduction to Computer Graphics Lecture #6: Lights. Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2014

CSE 167: Introduction to Computer Graphics Lecture #6: Lights Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2014 Announcements Project 2 due Friday, Oct. 24 th Midterm Exam

### CS 130 Exam I. Fall 2015

S 3 Exam I Fall 25 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

### 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

### CSE 167: Lecture #17: Procedural Modeling. Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2011

CSE 167: Introduction to Computer Graphics Lecture #17: Procedural Modeling Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2011 Announcements Important dates: Final project outline

### 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

### The 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:

### Computer Graphics with OpenGL ES (J. Han) Chapter VII Rasterizer

Chapter VII Rasterizer Rasterizer The vertex shader passes the clip-space vertices to the rasterizer, which performs the following: Clipping Perspective division Back-face culling Viewport transform Scan

### CSE 167: Lecture 11: Textures 2. Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2011

CSE 167: Introduction to Computer Graphics Lecture 11: Textures 2 Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2011 Announcements Homework assignment #5 due Friday, Nov 4,

### Pipeline Operations. CS 4620 Lecture 10

Pipeline Operations CS 4620 Lecture 10 2008 Steve Marschner 1 Hidden surface elimination Goal is to figure out which color to make the pixels based on what s in front of what. Hidden surface elimination

### Transformation Pipeline

Transformation Pipeline Local (Object) Space Modeling World Space Clip Space Projection Eye Space Viewing Perspective divide NDC space Normalized l d Device Coordinatesd Viewport mapping Screen space Coordinate

### Hidden 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

### Overview. Pipeline implementation I. Overview. Required Tasks. Preliminaries Clipping. Hidden Surface removal

Overview Pipeline implementation I Preliminaries Clipping Line clipping Hidden Surface removal Overview At end of the geometric pipeline, vertices have been assembled into primitives Must clip out primitives

### CSE 167: Introduction to Computer Graphics Lecture #7: Textures. Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2018

CSE 167: Introduction to Computer Graphics Lecture #7: Textures Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2018 Announcements Project 2 due this Friday at 2pm Grading in

### 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

### Fondamenti di Grafica 3D The Rasterization Pipeline.

Fondamenti di Grafica 3D The Rasterization Pipeline paolo.cignoni@isti.cnr.it http://vcg.isti.cnr.it/~cignoni Ray Casting vs. GPUs for Triangles Ray Casting For each pixel (ray) For each triangle Does

### 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

### CS 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

### CSE 167: Introduction to Computer Graphics Lecture #3: Coordinate Systems

CSE 167: Introduction to Computer Graphics Lecture #3: Coordinate Systems Jürgen P. Schulze, Ph.D. University of California, San Diego Spring Quarter 2015 Announcements Project 2 due Friday at 1pm Homework

### RASTERISED RENDERING

DH2323 DGI16 INTRODUCTION TO COMPUTER GRAPHICS AND INTERACTION RASTERISED RENDERING Christopher Peters HPCViz, KTH Royal Institute of Technology, Sweden chpeters@kth.se http://kth.academia.edu/christopheredwardpeters

### Lecture 2. Shaders, GLSL and GPGPU

Lecture 2 Shaders, GLSL and GPGPU Is it interesting to do GPU computing with graphics APIs today? Lecture overview Why care about shaders for computing? Shaders for graphics GLSL Computing with shaders

### 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.

### Graphics Programming

Graphics Programming 3 rd Week, 2011 OpenGL API (1) API (application programming interface) Interface between an application program and a graphics system Application Program OpenGL API Graphics Library

### CSE 167: Introduction to Computer Graphics. Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2016

CSE 167: Introduction to Computer Graphics Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2016 Today Course organization Course overview 2 Course Staff Instructor Jürgen Schulze,

### CSE 167: Introduction to Computer Graphics Lecture #7: Lights. Jürgen P. Schulze, Ph.D. University of California, San Diego Spring Quarter 2015

CSE 167: Introduction to Computer Graphics Lecture #7: Lights Jürgen P. Schulze, Ph.D. University of California, San Diego Spring Quarter 2015 Announcements Thursday in-class: Midterm Can include material

### 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.

### 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

### The Rasterization Pipeline

Lecture 5: The Rasterization Pipeline (and its implementation on GPUs) Computer Graphics CMU 15-462/15-662, Fall 2015 What you know how to do (at this point in the course) y y z x (w, h) z x Position objects

### 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

### CSE 167: Introduction to Computer Graphics Lecture #4: Coordinate Systems

CSE 167: Introduction to Computer Graphics Lecture #4: Coordinate Systems Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2017 Announcements Friday: homework 1 due at 2pm Upload

### CS602 Midterm Subjective Solved with Reference By WELL WISHER (Aqua Leo)

CS602 Midterm Subjective Solved with Reference By WELL WISHER (Aqua Leo) www.vucybarien.com Question No: 1 What are the two focusing methods in CRT? Explain briefly. Page no : 26 1. Electrostatic focusing

### Shadow Algorithms. CSE 781 Winter Han-Wei Shen

Shadow Algorithms CSE 781 Winter 2010 Han-Wei Shen Why Shadows? Makes 3D Graphics more believable Provides additional cues for the shapes and relative positions of objects in 3D What is shadow? Shadow:

### Evening s Goals. Mathematical Transformations. Discuss the mathematical transformations that are utilized for computer graphics

Evening s Goals Discuss the mathematical transformations that are utilized for computer graphics projection viewing modeling Describe aspect ratio and its importance Provide a motivation for homogenous

### CSE 167: Introduction to Computer Graphics Lecture #9: Textures. Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2013

CSE 167: Introduction to Computer Graphics Lecture #9: Textures Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2013 Announcements Added Tuesday office hours for Krishna: 11am-12

### 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