# The graphics pipeline. Pipeline and Rasterization. Primitives. Pipeline

Size: px
Start display at page:

Transcription

1 The graphics pipeline Pipeline and Rasterization CS4620 Lecture 9 The standard approach to object-order graphics Many versions exist software, e.g. Pixar s REYES architecture many options for quality and flexibility hardware, e.g. graphics cards in PCs amazing performance: millions of triangles per frame We ll focus on an abstract version of hardware pipeline Pipeline because of the many stages very parallelizable leads to remarkable performance of graphics cards (many times the flops of the CPU at ~1/5 the clock speed) 1 2 Pipeline you are here 3D transformations; shading conversion of primitives to pixels blending, compositing, shading user sees this APPLICATION COMMAND STREAM VERTEX PROCESSING TRANSFORMED GEOMETRY RASTERIZATION FRAGMENTS FRAGMENT PROCESSING FRAMEBUFFER IMAGE DISPLAY Primitives Points Line segments and chains of connected line segments Triangles And that s all! Curves? Approximate them with chains of line segments Polygons? Break them up into triangles Curved regions? Approximate them with triangles Trend has been toward minimal primitives simple, uniform, repetitive: good for parallelism 3 4

2 Rasterization First job: enumerate the pixels covered by a primitive simple, aliased definition: pixels whose centers fall inside Second job: interpolate values across the primitive e.g. colors computed at vertices e.g. normals at vertices will see applications later on Rasterizing lines Define line as a rectangle Specify by two endpoints Ideal image: black inside, white outside 5 6 Rasterizing lines Define line as a rectangle Specify by two endpoints Ideal image: black inside, white outside Point sampling Approximate rectangle by drawing all pixels whose centers fall within the line Problem: sometimes turns on adjacent pixels 6 7

3 Point sampling Approximate rectangle by drawing all pixels whose centers fall within the line Problem: sometimes turns on adjacent pixels Point sampling in action 7 8 Bresenham lines (midpoint alg.) Point sampling unit width rectangle leads to uneven line width Define line width parallel to pixel grid That is, turn on the single nearest pixel in each column Note that 45º lines are now thinner Bresenham lines (midpoint alg.) Point sampling unit width rectangle leads to uneven line width Define line width parallel to pixel grid That is, turn on the single nearest pixel in each column Note that 45º lines are now thinner 9 9

4 Bresenham lines (midpoint alg.) Point sampling unit width rectangle leads to uneven line width Define line width parallel to pixel grid That is, turn on the single nearest pixel in each column Note that 45º lines are now thinner Midpoint algorithm in action 9 10 Algorithms for drawing lines Optimizing line drawing line equation: y = b + m x Simple algorithm: evaluate line equation per column W.l.o.g. x 0 < x 1 ; 0! m! 1 for x = ceil(x0) to floor(x1) y = b + m*x output(x, round(y)) y = x Multiplying and rounding is slow At each pixel the only options are E and NE d = m(x + 1) + b y d > 0.5 decides between E and NE 11 12

5 Optimizing line drawing d = m(x + 1) + b y Only need to update d for integer steps in x and y Do that with addition Known as DDA (digital differential analyzer) Midpoint line algorithm x = ceil(x0) y = round(m*x + b) d = m*(x + 1) + b y while x < floor(x1) if d > 0.5 y += 1 d = 1 x += 1 d += m output(x, y) Linear interpolation Linear interpolation We often attach attributes to vertices e.g. computed diffuse color of a hair being drawn using lines want color to vary smoothly along a chain of line segments Recall basic definition 1D: f(x) = (1!) y 0 + " y 1 where! = (x x 0 ) / (x 1 x 0 ) In the 2D case of a line segment, alpha is just the fraction of the distance from (x 0, y 0 ) to (x 1, y 1 ) Pixels are not exactly on the line Define 2D function by projection on line this is linear in 2D therefore can use DDA to interpolate 15 16

6 Linear interpolation Pixels are not exactly on the line Define 2D function by projection on line this is linear in 2D therefore can use DDA to interpolate Linear interpolation Pixels are not exactly on the line Define 2D function by projection on line this is linear in 2D therefore can use DDA to interpolate Alternate interpretation Alternate interpretation We are updating d and! as we step from pixel to pixel d tells us how far from the line we are! tells us how far along the line we are So d and! are coordinates in a coordinate system oriented to the line View loop as visiting all pixels the line passes through Interpolate d and! for each pixel Only output frag. if pixel is in band This makes linear interpolation the primary operation 17 18

7 Pixel-walk line rasterization x = ceil(x0) y = round(m*x + b) d = m*x + b y while x < floor(x1) if d > 0.5 y += 1; d = 1; else x += 1; d += m; if 0.5 < d! 0.5 output(x, y) Rasterizing triangles The most common case in most applications with good antialiasing can be the only case some systems render a line as two skinny triangles Triangle represented by three vertices Simple way to think of algorithm follows the pixel-walk interpretation of line rasterization walk from pixel to pixel over (at least) the polygon s area evaluate linear functions as you go use those functions to decide which pixels are inside Rasterizing triangles Rasterizing triangles Input: three 2D points (the triangle s vertices in pixel space) (x 0, y 0 ); (x 1, y 1 ); (x 2, y 2 ) parameter values at each vertex q 00,, q 0n ; q 10,, q 1n ; q 20,, q 2n Output: a list of fragments, each with the integer pixel coordinates (x, y) interpolated parameter values q 0,, q n Summary 1" evaluation of linear functions on pixel grid 2" functions defined by parameter values at vertices 3" using extra parameters to determine fragment set 21 22

8 Incremental linear evaluation A linear (affine, really) function on the plane is: Linear functions are efficient to evaluate on a grid: Incremental linear evaluation lineval(xl, xh, yl, yh, cx, cy, ck) { // setup qrow = cx*xl + cy*yl + ck; // traversal for y = yl to yh { qpix = qrow; for x = xl to xh { output(x, y, qpix); qpix += cx; qrow += cy; c x =.005; c y =.005; c k = 0 (image size 100x100) 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 fragment set Defining parameter functions To interpolate parameters across a triangle we need to find the c x, c y, and c k that define the (unique) linear function that matches the given values at all 3 vertices this is 3 constraints on 3 unknown coefficients: (each states that the function agrees with the given value at one vertex) leading to a 3x3 matrix equation for the coefficients: (singular iff triangle is degenerate) 25 26

9 Defining parameter functions Defining parameter functions More efficient version: shift origin to (x 0, y 0 ) q(x, y) = c x (x x 0 ) + c y (y y 0 ) + q 0 q(x 1, y 1 ) = c x (x 1 x 0 ) + c y (y 1 y 0 ) + q 0 = q 1 q(x 2, y 2 ) = c x (x 2 x 0 ) + c y (y 2 y 0 ) + q 0 = q 2 now this is a 2x2 linear system (since q 0 falls out): solve using Cramer s rule (see Shirley): lininterp(xl, xh, yl, yh, x0, y0, q0, x1, y1, q1, x2, y2, q2) { // setup det = (x1-x0)*(y2-y0) - (x2-x0)*(y1-y0); cx = ((q1-q0)*(y2-y0) - (q2-q0)*(y1-y0)) / det; cy = ((q2-q0)*(x1-x0) - (q1-q0)*(x2-x0)) / det; qrow = cx*(xl-x0) + cy*(yl-y0) + q0; // traversal (same as before) for y = yl to yh { qpix = qrow; for x = xl to xh { output(x, y, qpix); qpix += cx; qrow += cy; q = 0 q = 1 q = Interpolating several parameters Rasterizing triangles lininterp(xl, xh, yl, yh, n, x0, y0, q0[], x1, y1, q1[], x2, y2, q2[]) { // setup for k = 0 to n-1 // compute cx[k], cy[k], qrow[k] // from q0[k], q1[k], q2[k] // traversal for y = yl to yh { for k = 1 to n, qpix[k] = qrow[k]; for x = xl to xh { output(x, y, qpix); for k = 1 to n, qpix[k] += cx[k]; for k = 1 to n, qrow[k] += cy[k]; Summary 1" evaluation of linear functions on pixel grid 2" functions defined by parameter values at vertices 3" using extra parameters to determine fragment set 29 30

10 Clipping to the triangle Interpolate three barycentric coordinates across the plane each barycentric coord is 1 at one vert. and 0 at the other two Output fragments only when all three are > 0. Barycentric coordinates A coordinate system for triangles algebraic viewpoint: geometric viewpoint (areas): Triangle interior test: [Shirley 2000] Barycentric coordinates A coordinate system for triangles geometric viewpoint: distances Barycentric coordinates Linear viewpoint: basis for the plane linear viewpoint: basis of edges in this view, the triangle interior test is just [Shirley 2000] 33 34

11 Walking edge equations We need to update values of the three edge equations with single-pixel steps in x and y Edge equation already in form of dot product components of vector are the increments Pixel-walk (Pineda) rasterization Conservatively visit a superset of the pixels you want Interpolate linear functions Use those functions to determine when to emit a fragment Rasterizing triangles Exercise caution with rounding and arbitrary decisions need to visit these pixels once but it s important not to visit them twice! Clipping Rasterizer tends to assume triangles are on screen particularly problematic to have triangles crossing the plane z = 0 After projection, before perspective divide clip against the planes x, y, z = 1, 1 (6 planes) primitive operation: clip triangle against axis-aligned plane 37 38

12 Clipping a triangle against a plane 4 cases, based on sidedness of vertices all in (keep) all out (discard) one in, two out (one clipped triangle) two in, one out (two clipped triangles) 39

### Pipeline and Rasterization. COMP770 Fall 2011

Pipeline and Rasterization COMP770 Fall 2011 1 The graphics pipeline The standard approach to object-order graphics Many versions exist software, e.g. Pixar s REYES architecture many options for quality

### Rasterization. CS4620 Lecture 13

Rasterization CS4620 Lecture 13 2014 Steve Marschner 1 The graphics pipeline The standard approach to object-order graphics Many versions exist software, e.g. Pixar s REYES architecture many options for

### Rasterization. CS 4620 Lecture Kavita Bala w/ prior instructor Steve Marschner. Cornell CS4620 Fall 2015 Lecture 16

Rasterization CS 4620 Lecture 16 1 Announcements A3 due on Thu Will send mail about grading once finalized 2 Pipeline overview you are here APPLICATION COMMAND STREAM 3D transformations; shading VERTEX

### Surface shading: lights and rasterization. Computer Graphics CSE 167 Lecture 6

Surface shading: lights and rasterization Computer Graphics CSE 167 Lecture 6 CSE 167: Computer Graphics Surface shading Materials Lights Rasterization 2 Scene data Rendering pipeline Modeling and viewing

### Rasterization. CS4620/5620: Lecture 12. Announcements. Turn in HW 1. PPA 1 out. Friday lecture. History of graphics PPA 1 in 4621.

CS4620/5620: Lecture 12 Rasterization 1 Announcements Turn in HW 1 PPA 1 out Friday lecture History of graphics PPA 1 in 4621 2 The graphics pipeline The standard approach to object-order graphics Many

### Rasterization. COMP 575/770 Spring 2013

Rasterization COMP 575/770 Spring 2013 The Rasterization Pipeline you are here APPLICATION COMMAND STREAM 3D transformations; shading VERTEX PROCESSING TRANSFORMED GEOMETRY conversion of primitives to

### Rasterization. Computer Graphics Fabio Pellacini and Steve Marschner

Rasterization 1 Approaches to rendering Rasterization: project each object onto image real-time rendering and GPUs foreach object in scene: foreach pixel in image: if object affects pixel: do_something()

### 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

### Graphics Pipeline 2D Geometric Transformations

Graphics Pipeline 2D Geometric Transformations CS 4620 Lecture 8 1 Plane projection in drawing Albrecht Dürer 2 Plane projection in drawing source unknown 3 Rasterizing triangles Summary 1 evaluation of

### graphics pipeline computer graphics graphics pipeline 2009 fabio pellacini 1

graphics pipeline computer graphics graphics pipeline 2009 fabio pellacini 1 graphics pipeline sequence of operations to generate an image using object-order processing primitives processed one-at-a-time

### graphics pipeline computer graphics graphics pipeline 2009 fabio pellacini 1

graphics pipeline computer graphics graphics pipeline 2009 fabio pellacini 1 graphics pipeline sequence of operations to generate an image using object-order processing primitives processed one-at-a-time

### Rasterization, or What is glbegin(gl_lines) really doing?

Rasterization, or What is glbegin(gl_lines) really doing? Course web page: http://goo.gl/eb3aa February 23, 2012 Lecture 4 Outline Rasterizing lines DDA/parametric algorithm Midpoint/Bresenham s algorithm

### CS Rasterization. Junqiao Zhao 赵君峤

CS10101001 Rasterization Junqiao Zhao 赵君峤 Department of Computer Science and Technology College of Electronics and Information Engineering Tongji University Vector Graphics Algebraic equations describe

### 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

### CS 4731: Computer Graphics Lecture 21: Raster Graphics: Drawing Lines. Emmanuel Agu

CS 4731: Computer Graphics Lecture 21: Raster Graphics: Drawing Lines Emmanuel Agu 2D Graphics Pipeline Clipping Object World Coordinates Applying world window Object subset window to viewport mapping

### Rasterization: Geometric Primitives

Rasterization: Geometric Primitives Outline Rasterizing lines Rasterizing polygons 1 Rasterization: What is it? How to go from real numbers of geometric primitives vertices to integer coordinates of pixels

### Rendering approaches. 1.image-oriented. 2.object-oriented. foreach pixel... 3D rendering pipeline. foreach object...

Rendering approaches 1.image-oriented foreach pixel... 2.object-oriented foreach object... geometry 3D rendering pipeline image 3D graphics pipeline Vertices Vertex processor Clipper and primitive assembler

### Computer Graphics. - Rasterization - Philipp Slusallek

Computer Graphics - Rasterization - Philipp Slusallek Rasterization Definition Given some geometry (point, 2D line, circle, triangle, polygon, ), specify which pixels of a raster display each primitive

### Einführung in Visual Computing

Einführung in Visual Computing 186.822 Rasterization Werner Purgathofer Rasterization in the Rendering Pipeline scene objects in object space transformed vertices in clip space scene in normalized device

### Line Drawing. Foundations of Computer Graphics Torsten Möller

Line Drawing Foundations of Computer Graphics Torsten Möller Rendering Pipeline Hardware Modelling Transform Visibility Illumination + Shading Perception, Interaction Color Texture/ Realism Reading Angel

### From Vertices to Fragments: Rasterization. Reading Assignment: Chapter 7. Special memory where pixel colors are stored.

From Vertices to Fragments: Rasterization Reading Assignment: Chapter 7 Frame Buffer Special memory where pixel colors are stored. System Bus CPU Main Memory Graphics Card -- Graphics Processing Unit (GPU)

### From Ver(ces to Fragments: Rasteriza(on

From Ver(ces to Fragments: Rasteriza(on From Ver(ces to Fragments 3D vertices vertex shader rasterizer fragment shader final pixels 2D screen fragments l determine fragments to be covered l interpolate

### Line Drawing Week 6, Lecture 9

CS 536 Computer Graphics Line Drawing Week 6, Lecture 9 David Breen, William Regli and axim Peysakhov Department of Computer Science Drexel University Outline Line drawing Digital differential analyzer

### CS 543: Computer Graphics. Rasterization

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

### OpenGL Graphics System. 2D Graphics Primitives. Drawing 2D Graphics Primitives. 2D Graphics Primitives. Mathematical 2D Primitives.

D Graphics Primitives Eye sees Displays - CRT/LCD Frame buffer - Addressable pixel array (D) Graphics processor s main function is to map application model (D) by projection on to D primitives: points,

### Line Drawing. Introduction to Computer Graphics Torsten Möller / Mike Phillips. Machiraju/Zhang/Möller

Line Drawing Introduction to Computer Graphics Torsten Möller / Mike Phillips Rendering Pipeline Hardware Modelling Transform Visibility Illumination + Shading Perception, Color Interaction Texture/ Realism

### CS452/552; EE465/505. Clipping & Scan Conversion

CS452/552; EE465/505 Clipping & Scan Conversion 3-31 15 Outline! From Geometry to Pixels: Overview Clipping (continued) Scan conversion Read: Angel, Chapter 8, 8.1-8.9 Project#1 due: this week Lab4 due:

### 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

### Lets assume each object has a defined colour. Hence our illumination model is looks unrealistic.

Shading Models There are two main types of rendering that we cover, polygon rendering ray tracing Polygon rendering is used to apply illumination models to polygons, whereas ray tracing applies to arbitrary

### 2D rendering takes a photo of the 2D scene with a virtual camera that selects an axis aligned rectangle from the scene. The photograph is placed into

2D rendering takes a photo of the 2D scene with a virtual camera that selects an axis aligned rectangle from the scene. The photograph is placed into the viewport of the current application window. A pixel

### 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

### Realtime 3D Computer Graphics Virtual Reality

Realtime 3D Computer Graphics Virtual Reality From Vertices to Fragments Overview Overall goal recapitulation: Input: World description, e.g., set of vertices and states for objects, attributes, camera,

### FROM VERTICES TO FRAGMENTS. Lecture 5 Comp3080 Computer Graphics HKBU

FROM VERTICES TO FRAGMENTS Lecture 5 Comp3080 Computer Graphics HKBU OBJECTIVES Introduce basic implementation strategies Clipping Scan conversion OCTOBER 9, 2011 2 OVERVIEW At end of the geometric pipeline,

### Renderer Implementation: Basics and Clipping. Overview. Preliminaries. David Carr Virtual Environments, Fundamentals Spring 2005

INSTITUTIONEN FÖR SYSTEMTEKNIK LULEÅ TEKNISKA UNIVERSITET Renderer Implementation: Basics and Clipping David Carr Virtual Environments, Fundamentals Spring 2005 Feb-28-05 SMM009, Basics and Clipping 1

### 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

### Pipeline implementation II

Pipeline implementation II Overview Line Drawing Algorithms DDA Bresenham Filling polygons Antialiasing Rasterization Rasterization (scan conversion) Determine which pixels that are inside primitive specified

### Computer Graphics (CS 543) Lecture 10: Rasterization and Antialiasing

Computer Graphics (CS 543) Lecture 10: Rasterization and Antialiasing Prof Emmanuel Agu Computer Science Dept. Worcester Polytechnic Institute (WPI) Recall: Rasterization Rasterization (scan conversion)

### Scan Conversion. Drawing Lines Drawing Circles

Scan Conversion Drawing Lines Drawing Circles 1 How to Draw This? 2 Start From Simple How to draw a line: y(x) = mx + b? 3 Scan Conversion, a.k.a. Rasterization Ideal Picture Raster Representation Scan

### Implementation III. Ed Angel Professor of Computer Science, Electrical and Computer Engineering, and Media Arts University of New Mexico

Implementation III Ed Angel Professor of Computer Science, Electrical and Computer Engineering, and Media Arts University of New Mexico Objectives Survey Line Drawing Algorithms - DDA - Bresenham 2 Rasterization

### Rasterization and Graphics Hardware. Not just about fancy 3D! Rendering/Rasterization. The simplest case: Points. When do we care?

Where does a picture come from? Rasterization and Graphics Hardware CS559 Course Notes Not for Projection November 2007, Mike Gleicher Result: image (raster) Input 2D/3D model of the world Rendering term

### Drawing Fast The Graphics Pipeline

Drawing Fast The Graphics Pipeline CS559 Spring 2016 Lecture 10 February 25, 2016 1. Put a 3D primitive in the World Modeling Get triangles 2. Figure out what color it should be Do ligh/ng 3. Position

### Tópicos de Computação Gráfica Topics in Computer Graphics 10509: Doutoramento em Engenharia Informática. Chap. 2 Rasterization.

Tópicos de Computação Gráfica Topics in Computer Graphics 10509: Doutoramento em Engenharia Informática Chap. 2 Rasterization Rasterization Outline : Raster display technology. Basic concepts: pixel, resolution,

### Computer Graphics Prof. Sukhendu Das Dept. of Computer Science and Engineering Indian Institute of Technology, Madras Lecture - 14

Computer Graphics Prof. Sukhendu Das Dept. of Computer Science and Engineering Indian Institute of Technology, Madras Lecture - 14 Scan Converting Lines, Circles and Ellipses Hello everybody, welcome again

### COMP371 COMPUTER GRAPHICS

COMP371 COMPUTER GRAPHICS LECTURE 14 RASTERIZATION 1 Lecture Overview Review of last class Line Scan conversion Polygon Scan conversion Antialiasing 2 Rasterization The raster display is a matrix of picture

### Chapter 8: Implementation- Clipping and Rasterization

Chapter 8: Implementation- Clipping and Rasterization Clipping Fundamentals Cohen-Sutherland Parametric Polygons Circles and Curves Text Basic Concepts: The purpose of clipping is to remove objects or

### The Graphics Pipeline

The Graphics Pipeline Ray Tracing: Why Slow? Basic ray tracing: 1 ray/pixel Ray Tracing: Why Slow? Basic ray tracing: 1 ray/pixel But you really want shadows, reflections, global illumination, antialiasing

### Topic #1: Rasterization (Scan Conversion)

Topic #1: Rasterization (Scan Conversion) We will generally model objects with geometric primitives points, lines, and polygons For display, we need to convert them to pixels for points it s obvious but

### CS 4620 Final Exam. (a) Is a circle C 0 continuous?

CS 4620 Final Exam Wednesday 9, December 2009 2 1 2 hours Prof. Doug James Explain your reasoning for full credit. You are permitted a double-sided sheet of notes. Calculators are allowed but unnecessary.

### Math background. 2D Geometric Transformations. Implicit representations. Explicit representations. Read: CS 4620 Lecture 6

Math background 2D Geometric Transformations CS 4620 Lecture 6 Read: Chapter 2: Miscellaneous Math Chapter 5: Linear Algebra Notation for sets, functions, mappings Linear transformations Matrices Matrix-vector

### - Rasterization. Geometry. Scan Conversion. Rasterization

Computer Graphics - The graphics pipeline - Geometry Modelview Geometry Processing Lighting Perspective Clipping Scan Conversion Texturing Fragment Tests Blending Framebuffer Fragment Processing - So far,

### CHAPTER 1 Graphics Systems and Models 3

?????? 1 CHAPTER 1 Graphics Systems and Models 3 1.1 Applications of Computer Graphics 4 1.1.1 Display of Information............. 4 1.1.2 Design.................... 5 1.1.3 Simulation and Animation...........

### CS230 : Computer Graphics Lecture 4. Tamar Shinar Computer Science & Engineering UC Riverside

CS230 : Computer Graphics Lecture 4 Tamar Shinar Computer Science & Engineering UC Riverside Shadows Shadows for each pixel do compute viewing ray if ( ray hits an object with t in [0, inf] ) then compute

### Intro to OpenGL II. Don Fussell Computer Science Department The University of Texas at Austin

Intro to OpenGL II Don Fussell Computer Science Department The University of Texas at Austin University of Texas at Austin CS354 - Computer Graphics Don Fussell Where are we? Last lecture, we started the

### Institutionen för systemteknik

Code: Day: Lokal: M7002E 19 March E1026 Institutionen för systemteknik Examination in: M7002E, Computer Graphics and Virtual Environments Number of sections: 7 Max. score: 100 (normally 60 is required

### 0. Introduction: What is Computer Graphics? 1. Basics of scan conversion (line drawing) 2. Representing 2D curves

CSC 418/2504: Computer Graphics Course web site (includes course information sheet): http://www.dgp.toronto.edu/~elf Instructor: Eugene Fiume Office: BA 5266 Phone: 416 978 5472 (not a reliable way) Email:

### Topics. From vertices to fragments

Topics From vertices to fragments From Vertices to Fragments Assign a color to every pixel Pass every object through the system Required tasks: Modeling Geometric processing Rasterization Fragment processing

### 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

### Real-Time Graphics Architecture

Real-Time Graphics Architecture Kurt Akeley Pat Hanrahan http://www.graphics.stanford.edu/courses/cs448a-01-fall Rasterization Outline Fundamentals Examples Special topics (Depth-buffer, cracks and holes,

### Drawing Fast The Graphics Pipeline

Drawing Fast The Graphics Pipeline CS559 Fall 2016 Lectures 10 & 11 October 10th & 12th, 2016 1. Put a 3D primitive in the World Modeling 2. Figure out what color it should be 3. Position relative to the

### Rendering. A simple X program to illustrate rendering

Rendering A simple X program to illustrate rendering The programs in this directory provide a simple x based application for us to develop some graphics routines. Please notice the following: All points

### Introduction to Visualization and Computer Graphics

Introduction to Visualization and Computer Graphics DH2320, Fall 2015 Prof. Dr. Tino Weinkauf Introduction to Visualization and Computer Graphics Visibility Shading 3D Rendering Geometric Model Color Perspective

### Announcements. Midterms graded back at the end of class Help session on Assignment 3 for last ~20 minutes of class. Computer Graphics

Announcements Midterms graded back at the end of class Help session on Assignment 3 for last ~20 minutes of class 1 Scan Conversion Overview of Rendering Scan Conversion Drawing Lines Drawing Polygons

### Computer Graphics Fundamentals. Jon Macey

Computer Graphics Fundamentals Jon Macey jmacey@bournemouth.ac.uk http://nccastaff.bournemouth.ac.uk/jmacey/ 1 1 What is CG Fundamentals Looking at how Images (and Animations) are actually produced in

### CS 130 Exam I. Fall 2015

CS 130 Exam I 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

### UNIT -8 IMPLEMENTATION

UNIT -8 IMPLEMENTATION 1. Discuss the Bresenham s rasterization algorithm. How is it advantageous when compared to other existing methods? Describe. (Jun2012) 10M Ans: Consider drawing a line on a raster

### CPSC / Scan Conversion

CPSC 599.64 / 601.64 Computer Screens: Raster Displays pixel rasters (usually) square pixels in rectangular raster evenly cover the image problem no such things such as lines, circles, etc. scan conversion

### COMP30019 Graphics and Interaction Scan Converting Polygons and Lines

COMP30019 Graphics and Interaction Scan Converting Polygons and Lines Department of Computer Science and Software Engineering The Lecture outline Introduction Scan conversion Scan-line algorithm Edge coherence

### Department of Computer Sciences Graphics Fall 2003 (Lecture 2) Pixels

Pixels Pixel: Intensity or color sample. Raster Image: Rectangular grid of pixels. Rasterization: Conversion of a primitive s geometric representation into A set of pixels. An intensity or color for each

### Computer Graphics : Bresenham Line Drawing Algorithm, Circle Drawing & Polygon Filling

Computer Graphics : Bresenham Line Drawing Algorithm, Circle Drawing & Polygon Filling Downloaded from :www.comp.dit.ie/bmacnamee/materials/graphics/006- Contents In today s lecture we ll have a loo at:

### Drawing Fast The Graphics Pipeline

Drawing Fast The Graphics Pipeline CS559 Fall 2015 Lecture 9 October 1, 2015 What I was going to say last time How are the ideas we ve learned about implemented in hardware so they are fast. Important:

### Fall CSCI 420: Computer Graphics. 7.1 Rasterization. Hao Li.

Fall 2015 CSCI 420: Computer Graphics 7.1 Rasterization Hao Li http://cs420.hao-li.com 1 Rendering Pipeline 2 Outline Scan Conversion for Lines Scan Conversion for Polygons Antialiasing 3 Rasterization

### 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

### Triangle Rasterization

Triangle Rasterization Computer Graphics COMP 770 (236) Spring 2007 Instructor: Brandon Lloyd 2/07/07 1 From last time Lines and planes Culling View frustum culling Back-face culling Occlusion culling

### A New Line Drawing Algorithm Based on Sample Rate Conversion

A New Line Drawing Algorithm Based on Sample Rate Conversion c 2002, C. Bond. All rights reserved. February 5, 2002 1 Overview In this paper, a new method for drawing straight lines suitable for use on

### Computer Graphics Geometry and Transform

! Computer Graphics 2014! 5. Geometry and Transform Hongxin Zhang State Key Lab of CAD&CG, Zhejiang University 2014-10-11! Today outline Triangle rasterization Basic vector algebra ~ geometry! Antialiasing

### CSCI 4620/8626. Coordinate Reference Frames

CSCI 4620/8626 Computer Graphics Graphics Output Primitives Last update: 2014-02-03 Coordinate Reference Frames To describe a picture, the world-coordinate reference frame (2D or 3D) must be selected.

### Scan Converting Lines

Scan Conversion 1 Scan Converting Lines Line Drawing Draw a line on a raster screen between two points What s wrong with the statement of the problem? it doesn t say anything about which points are allowed

### Output Primitives. Dr. S.M. Malaek. Assistant: M. Younesi

Output Primitives Dr. S.M. Malaek Assistant: M. Younesi Output Primitives Output Primitives: Basic geometric structures (points, straight line segment, circles and other conic sections, quadric surfaces,

### For this assignment, you are to implement three line drawers and a polygon drawer.

SFU CMPT 361 Computer Graphics Fall 2017 Assignment 1 Assignment due Thursday, September 28, by 11:59 pm. For this assignment, you are to implement three line drawers and a polygon drawer. These rendering

Last Time? The Traditional Graphics Pipeline Participating Media Measuring BRDFs 3D Digitizing & Scattering BSSRDFs Monte Carlo Simulation Dipole Approximation Today Ray Casting / Tracing Advantages? Ray

### Last class. A vertex (w x, w y, w z, w) - clipping is in the - windowing and viewport normalized view volume if: - scan conversion/ rasterization

Lecture 6 Last class Last lecture (clip coordinates): A vertex (w x, w y, w z, w) - clipping is in the - windowing and viewport normalized view volume if: - scan conversion/ rasterization normalized view

### Spring 2009 Prof. Hyesoon Kim

Spring 2009 Prof. Hyesoon Kim Application Geometry Rasterizer CPU Each stage cane be also pipelined The slowest of the pipeline stage determines the rendering speed. Frames per second (fps) Executes on

### Raster Scan Displays. Framebuffer (Black and White)

Raster Scan Displays Beam of electrons deflected onto a phosphor coated screen Phosphors emit light when excited by the electrons Phosphor brightness decays -- need to refresh the display Phosphors make

### Graphics (Output) Primitives. Chapters 3 & 4

Graphics (Output) Primitives Chapters 3 & 4 Graphic Output and Input Pipeline Scan conversion converts primitives such as lines, circles, etc. into pixel values geometric description a finite scene area

### CS 4300 Computer Graphics. Prof. Harriet Fell Fall 2012 Lecture 5 September 13, 2012

CS 4300 Computer Graphics Prof. Harriet Fell Fall 2012 Lecture 5 September 13, 2012 1 Today s Topics Vectors review Shirley et al. 2.4 Rasters Shirley et al. 3.0-3.2.1 Rasterizing Lines Shirley et al.

### CS559: Computer Graphics. Lecture 12: Antialiasing & Visibility Li Zhang Spring 2008

CS559: Computer Graphics Lecture 12: Antialiasing & Visibility Li Zhang Spring 2008 Antialising Today Hidden Surface Removal Reading: Shirley ch 3.7 8 OpenGL ch 1 Last time A 2 (x 0 y 0 ) (x 1 y 1 ) P

### Computer Graphics and GPGPU Programming

Computer Graphics and GPGPU Programming Donato D Ambrosio Department of Mathematics and Computer Science and Center of Excellence for High Performace Computing Cubo 22B, University of Calabria, Rende 87036,

### CSCI 420 Computer Graphics Lecture 14. Rasterization. Scan Conversion Antialiasing [Angel Ch. 6] Jernej Barbic University of Southern California

CSCI 420 Computer Graphics Lecture 14 Rasterization Scan Conversion Antialiasing [Angel Ch. 6] Jernej Barbic University of Southern California 1 Rasterization (scan conversion) Final step in pipeline:

Last Time? The Traditional Graphics Pipeline Reading for Today A Practical Model for Subsurface Light Transport, Jensen, Marschner, Levoy, & Hanrahan, SIGGRAPH 2001 Participating Media Measuring BRDFs

### 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

### Last Time: Acceleration Data Structures for Ray Tracing. Schedule. Today. Shadows & Light Sources. Shadows

Last Time: Acceleration Data Structures for Ray Tracing Modeling Transformations Illumination (Shading) Viewing Transformation (Perspective / Orthographic) Clipping Projection (to Screen Space) Scan Conversion

### 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

### Rendering. A simple X program to illustrate rendering

Rendering A simple X program to illustrate rendering The programs in this directory provide a simple x based application for us to develop some graphics routines. Please notice the following: All points

### 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

### Real-Time Graphics Architecture

Real-Time Graphics Architecture Kurt Akeley Pat Hanrahan http://www.graphics.stanford.edu/courses/cs448a-01-fall Geometry Outline Vertex and primitive operations System examples emphasis on clipping Primitive

Final Projects Proposals due Thursday 4/8 Proposed project summary At least 3 related papers (read & summarized) Description of series of test cases Timeline & initial task assignment The Traditional Graphics

### 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

### 1 Introduction to Graphics

1 1.1 Raster Displays The screen is represented by a 2D array of locations called pixels. Zooming in on an image made up of pixels The convention in these notes will follow that of OpenGL, placing the