Last time? Rasterization. Scan Conversion (Rasterization) High-level concepts for Visibility / Display. Today
|
|
- Rachel Bell
- 5 years ago
- Views:
Transcription
1 Last time? Rasterization MIT EECS Frédo Durand and Barb Cutler MIT EECS 6.837, Cutler and Durand Point and segment Clipping Planes as homogenous vectors (duality) In homogeneous coordinates before division Outcodes for efficient rejection Notion of conveity Polygon clipping via walking Line rasterization, incremental computation MIT EECS 6.837, Cutler and Durand 2 High-level concepts for Linearity Homogeneous coordinates Conveity Discrete vs. continuous Incremental computation Trying things on simple eamples Scan Conversion (Rasterization) Modeling Transformations Illumination (Shading) Viewing Transformation (Perspective / Orthographic) Clipping Projection (to Screen Space) Scan Conversion (Rasterization) Rasterizes objects into piels Interpolate values as we go (color, depth, etc.) Visibility / Display MIT EECS 6.837, Cutler and Durand 3 MIT EECS 6.837, Cutler and Durand 4 Visibility / Display Modeling Transformations Illumination (Shading) Viewing Transformation (Perspective / Orthographic) Clipping Projection (to Screen Space) Scan Conversion (Rasterization) Visibility / Display Each piel remembers the closest object (depth buffer) Almost every step in the graphics pipeline involves a change of coordinate system. Transformations are central to understanding 3D computer graphics. MIT EECS 6.837, Cutler and Durand 5 Today Line scan-conversion Polygon scan conversion smart back to brute force Visibility MIT EECS 6.837, Cutler and Durand 6
2 Scan Converting 2D Line Segments Given: Segment endpoints (integers, y; 2, y2) Identify: Set of piels (, y) to display for segment (2, y2) Line Rasterization Requirements Transform continuous primitive into discrete samples Uniform thickness & brightness Continuous appearance No gaps (2, y2) Accuracy Speed (, y) (, y) MIT EECS 6.837, Cutler and Durand 7 MIT EECS 6.837, Cutler and Durand 8 Algorithm Design Choices Assume: m = dy/d, < m < Eactly one piel per column fewer disconnected, more too thick (2, y2) Naive Line Rasterization Algorithm Simply compute y as a function of Conceptually: move vertical scan line from to 2 What is the epression of y as function of? Set piel (, round (y())) (2, y2) y = y + ( y2 y) 2 = y + m( ) (, y) y (, y) dy m = d MIT EECS 6.837, Cutler and Durand 9 MIT EECS 6.837, Cutler and Durand Efficiency Computing y value is epensive y = y + m( ) Observe: y += m at each step (m = dy/d) y(+) y() (2, y2) y(+) m y() + (, y) + MIT EECS 6.837, Cutler and Durand Bresenham's Algorithm (DDA) Select piel vertically closest to line segment intuitive, efficient, piel center always within.5 vertically Same answer as naive approach MIT EECS 6.837, Cutler and Durand 2 2
3 Bresenham's Algorithm (DDA) Observation: If we're at piel P ( p, y p ), the net piel must be either E ( p +, y p ) or NE ( p +, y p +) Why? Bresenham Step Which piel to choose: E or NE? Choose E if segment passes below or through middle point M Choose NE if segment passes above M NE E NE M E NE M E MIT EECS 6.837, Cutler and Durand 3 MIT EECS 6.837, Cutler and Durand 4 Bresenham Step Use decision function D to identify points underlying line L: F> p D(, y) = y-m-b F= M positive above L F< zero on L negative below L D(p,p y ) = vertical distance from point to line MIT EECS 6.837, Cutler and Durand 5 Bresenham's Algorithm (DDA) Decision Function: D(, y) = y-m-b Initialize: error term e = D(,y) On each iteration: update : ' = + update e: e' = e + m if (e.5): y' = y (choose piel E) if (e >.5): y' = y + (choose piel NE) e' = e - MIT EECS 6.837, Cutler and Durand 6 e e Summary of Bresenham initialize, y, e for ( = ; 2; ++) plot (,y) update, y, e NE E Line Rasterization We will use it for ray-casting acceleration March a ray through a grid Generalize to handle all eight octants using symmetry Can be modified to use only integer arithmetic MIT EECS 6.837, Cutler and Durand 7 MIT EECS 6.837, Cutler and Durand 8 3
4 Line Rasterization vs. Grid Marching Questions? Line Rasterization: Best discrete approimation of the line Ray Acceleration: Must eamine every cell the line touches MIT EECS 6.837, Cutler and Durand 9 MIT EECS 6.837, Cutler and Durand 2 Circle Rasterization Generate piels for 2nd octant only Slope progresses from Analog of Bresenham Segment Algorithm MIT EECS 6.837, Cutler and Durand 2 Circle Rasterization Decision Function: D(, y) = 2 + y 2 R 2 Initialize: error term e = D(,y) R On each iteration: update : ' = + update e: e' = e if (e.5): y' = y (choose piel E) if (e <.5): y' = y - (choose piel SE), e' = e + MIT EECS 6.837, Cutler and Durand 22 Philosophically Discrete differential analyzer (DDA): Perform incremental computation Work on derivative rather than function Gain one order for polynomial Line becomes constant derivative Circle becomes linear derivative Questions? MIT EECS 6.837, Cutler and Durand 23 MIT EECS 6.837, Cutler and Durand 24 4
5 Antialiased Line Rasterization Use gray scales to avoid jaggies Will be studied later in the course Today Line scan-conversion Polygon scan conversion smart back to brute force aliased antialiased MIT EECS 6.837, Cutler and Durand 25 Visibility MIT EECS 6.837, Cutler and Durand 26 2D Scan Conversion Geometric primitive 2D: point, line, polygon, circle... 3D: point, line, polyhedron, sphere... Primitives are continuous; screen is discrete 2D Scan Conversion Solution: compute discrete approimation Scan Conversion: algorithms for efficient generation of the samples comprising this approimation MIT EECS 6.837, Cutler and Durand 27 MIT EECS 6.837, Cutler and Durand 28 Brute force solution for triangles For each piel Compute line equations at piel center clip against the triangle Problem? Brute force solution for triangles For each piel Compute line equations at piel center clip against the triangle Problem? If the triangle is small, a lot of useless computation MIT EECS 6.837, Cutler and Durand 29 MIT EECS 6.837, Cutler and Durand 3 5
6 Brute force solution for triangles Improvement: Compute only for the screen bounding bo of the triangle How do we get such a bounding bo? Xmin, Xma, Ymin, Yma of the triangle vertices Can we do better? Kind of! We compute the line equation for many useless piels What could we do? MIT EECS 6.837, Cutler and Durand 3 MIT EECS 6.837, Cutler and Durand 32 Use line rasterization Compute the boundary piels Scan-line Rasterization Compute the boundary piels Fill the spans Shirley page 55 Shirley page 55 MIT EECS 6.837, Cutler and Durand 33 MIT EECS 6.837, Cutler and Durand 34 Scan-line Rasterization Requires some initial setup to prepare Today Line scan-conversion Polygon scan conversion smart Shirley page 55 back to brute force Visibility MIT EECS 6.837, Cutler and Durand 35 MIT EECS 6.837, Cutler and Durand 36 6
7 For modern graphics cards Triangles are usually very small Setup cost are becoming more troublesome Clipping is annoying Brute force is tractable Modern rasterization ComputeProjection Compute bbo, clip bbo to screen limits For all piels in bbo Compute line equations If all line equations> //piel [,y] in triangle Framebuffer[,y]=triangleColor MIT EECS 6.837, Cutler and Durand 37 MIT EECS 6.837, Cutler and Durand 38 Modern rasterization ComputeProjection Compute bbo, clip bbo to screen limits For all piels in bbo Compute line equations If all line equations> //piel [,y] in triangle Framebuffer[,y]=triangleColor Note that Bbo clipping is trivial Can we do better? ComputeProjection Compute bbo, clip bbo to screen limits For all piels in bbo Compute line equations If all line equations> //piel [,y] in triangle Framebuffer[,y]=triangleColor MIT EECS 6.837, Cutler and Durand 39 MIT EECS 6.837, Cutler and Durand 4 Can we do better? ComputeProjection Compute bbo, clip bbo to screen limits For all piels in bbo Compute line equations a+by+c If all line equations> //piel [,y] in triangle Framebuffer[,y]=triangleColor We don t need to recompute line equation from scratch MIT EECS 6.837, Cutler and Durand 4 Can we do better? ComputeProjection Compute bbo, clip bbo to screen limits Setup line eq compute a i d, b i dy for the 3 lines Initialize line eq, values for bbo corner L i =a i +b i y+c i For all scanline y in bbo For 3 lines, update Li For all in bbo Increment line equations: Li+=ad If all Li> //piel [,y] in triangle Framebuffer[,y]=triangleColor We save one multiplication per piel MIT EECS 6.837, Cutler and Durand 42 7
8 Adding Gouraud shading Interpolate colors of the 3 vertices Linear interpolation Adding Gouraud shading Interpolate colors of the 3 vertices Linear interpolation, e.g. for R channel: R=a R +b R y+c R Such that R[,y]=R; R[, y]=r; R[2,y2]=R2 Same as a plane equation in (,y,r) MIT EECS 6.837, Cutler and Durand 43 MIT EECS 6.837, Cutler and Durand 44 Adding Gouraud shading Interpolate colors ComputeProjection Compute bbo, clip bbo to screen limits Setup line eq Setup color equation For all piels in bbo Increment line equations Increment color equation If all Li> //piel [,y] in triangle Framebuffer[,y]=interpolatedColor Adding Gouraud shading Interpolate colors of the 3 vertices Other solution: use barycentric coordinates R=αR + β R + γ R 2 Such that P =α P + β P + γ P 2 P MIT EECS 6.837, Cutler and Durand 45 MIT EECS 6.837, Cutler and Durand 46 In the modern hardware Edge eq. in homogeneous coordinates [, y, w] Tiles to add a mid-level granularity Early rejection of tiles Memory access coherence Ref Henry Fuchs, Jack Goldfeather, Jeff Hultquist, Susan Spach, John Austin, Frederick Brooks, Jr., John Eyles and John Poulton, Fast Spheres, Shadows, Tetures, Transparencies, and Image Enhancements in Piel-Planes, Proceedings of SIGGRAPH 85 (San Francisco, CA, July 22 26, 985). In Computer Graphics, v9n3 (July 985), ACM SIGGRAPH, New York, NY, 985. Juan Pineda, A Parallel Algorithm for Polygon Rasterization, Proceedings of SIGGRAPH 88 (Atlanta, GA, August 5, 988). In Computer Graphics, v22n4 (August 988), ACM SIGGRAPH, New York, NY, 988. Figure 7: Image from the spinning teapot performance test. Triangle Scan Conversion using 2D Homogeneous Coordinates, Marc Olano Trey Greer MIT EECS 6.837, Cutler and Durand 47 MIT EECS 6.837, Cutler and Durand 48 8
9 Take-home message The appropriate algorithm depends on Balance between various resources (CPU, memory, bandwidth) The input (size of triangles, etc.) Smart algorithms often have initial preprocess Assess whether it is worth it To save time, identify redundant computation Put outside the loop and interpolate if needed Questions? MIT EECS 6.837, Cutler and Durand 49 MIT EECS 6.837, Cutler and Durand 5 Today Line scan-conversion Polygon scan conversion Visibility How do we know which parts are visible/in front? smart back to brute force Visibility MIT EECS 6.837, Cutler and Durand 5 MIT EECS 6.837, Cutler and Durand 52 Ray Casting Maintain intersection with closest object Painter s algorithm Draw back-to-front How do we sort objects? Can we always sort objects? MIT EECS 6.837, Cutler and Durand 53 MIT EECS 6.837, Cutler and Durand 54 9
10 Painter s algorithm Painter s algorithm Draw back-to-front How do we sort objects? Can we always sort objects? No, there can be cycles Requires to split polygons A A B C B Old solution for hidden-surface removal Good because ordering is useful for other operations (transparency, antialiasing) But Ordering is tough Cycles Must be done by CPU Hardly used now But some sort of partial ordering is sometimes useful Usuall front-to-back To make sure foreground is rendered first For transparency MIT EECS 6.837, Cutler and Durand 55 MIT EECS 6.837, Cutler and Durand 56 Visibility In ray casting, use intersection with closest t Now we have swapped the loops (piel, object) How do we do? Z buffer In addition to frame buffer (R, G, B) Store distance to camera (z-buffer) Piel is updated only if new z is closer than z-buffer value MIT EECS 6.837, Cutler and Durand 57 MIT EECS 6.837, Cutler and Durand 58 Z-buffer pseudo code Works for hard cases! Compute Projection, color at vertices Setup line equations Compute bbo, clip bbo to screen limits For all piels in bbo Increment line equations Compute curentz Increment currentcolor If all line equations> //piel [,y] in triangle If currentz<zbuffer[,y] //piel is visible Framebuffer[,y]=currentColor zbuffer[,y]=currentz A B C MIT EECS 6.837, Cutler and Durand 59 MIT EECS 6.837, Cutler and Durand 6
11 What eactly do we store Floating point distance Can we interpolate z in screen space? i.e. does z vary linearly in screen space? z image Z interpolation X =/z Hyperbolic variation Z cannot be linearly interpolated z image z z MIT EECS 6.837, Cutler and Durand 6 MIT EECS 6.837, Cutler and Durand 62 Simple Perspective Projection Project all points along the z ais to the z = d plane, eyepoint at the origin Yet another Perspective Projection Change the z component Compute d/z Can be linearly interpolated homogenize homogenize * d / z y * d / z d = y z z / d = /d y z MIT EECS 6.837, Cutler and Durand 63 * d / z y * d / z d/z = y z / d = /d y z MIT EECS 6.837, Cutler and Durand 64 Advantages of /z Can be interpolated linearly in screen space Puts more precision for close objects Useful when using integers more precision where perceptible Integer z-buffer Use /z to have more precision in the foreground Set a near and far plane /z values linearly encoded between /near and /far Careful, test direction is reversed far near MIT EECS 6.837, Cutler and Durand 65 MIT EECS 6.837, Cutler and Durand 66
12 Integer Z-buffer pseudo code Compute Projection, color at vertices Setup line equations, depth equation Compute bbo, clip bbo to screen limits For all piels in bbo Increment line equations Increment curent_ovz Increment currentcolor If all line equations> //piel [,y] in triangle If current_ovz>ovzbuffer[,y]//piel is visible Framebuffer[,y]=currentColor ovzbuffer[,y]=currentovz MIT EECS 6.837, Cutler and Durand 67 Gouraud interpolation Gouraud: interpolate color linearly in screen space Is it correct? [R, z G, B] image [R, z G, B] MIT EECS 6.837, Cutler and Durand 68 Gouraud interpolation Questions? Gouraud: interpolate color linearly in screen space Not correct. We should use hyperbolic interpolation But quite costly (division) However, can now be done on modern hardware image [R, z G, B] [R, z G, B] MIT EECS 6.837, Cutler and Durand 69 MIT EECS 6.837, Cutler and Durand 7 The infamous half piel I refuse to teach it, but it s an annoying issue you should know about Do a line drawing of a rectangle from [top, right] to [bottom,left] Do we actually draw the columns/rows of piels? The infamous half piel Displace by half a piel so that top, right, bottom, left are in the middle of piels Just change the viewport transform MIT EECS 6.837, Cutler and Durand 7 MIT EECS 6.837, Cutler and Durand 72 2
13 The Graphics Pipeline Modern Graphics Hardware Modeling Transformations Illumination (Shading) Viewing Transformation (Perspective / Orthographic) Clipping Projection (to Screen Space) Scan Conversion (Rasterization) Visibility / Display MIT EECS 6.837, Cutler and Durand 73 MIT EECS 6.837, Cutler and Durand 74 Graphics Hardware High performance through Parallelism Specialization No data dependency Efficient pre-fetching G task parallelism R T F D data parallelism MIT EECS 6.837, Cutler and Durand 75 G R T F D G R T F D G R T F D Programmable Graphics Hardware G P R T F P D Geometry and piel (fragment) stage become programmable Elaborate appearance More and more general-purpose computation (GPU hacking) MIT EECS 6.837, Cutler and Durand 76 Modern Graphics Hardware About 4-6 geometry units About 6 fragment units Deep pipeline (~8 stages) Tiling (about 44) Early z-rejection if entire tile is occluded Piels rasterized by quads (22 piels) Allows for derivatives Very efficient teture pre-fetching And smart memory layout MIT EECS 6.837, Cutler and Durand 77 Current GPUs Programmable geometry and fragment stages 6 million vertices/second, 6 billion teels/second In the range of tera operations/second Floating point operations only Very little cache MIT EECS 6.837, Cutler and Durand 78 3
14 Computational Requirements Questions? [Akeley, Hanrahan] MIT EECS 6.837, Cutler and Durand 79 MIT EECS 6.837, Cutler and Durand 8 Net Week: Ray Casting Acceleration MIT EECS 6.837, Cutler and Durand 8 4
Final projects. Rasterization. The Graphics Pipeline. Illumination (Shading) (Lighting) Viewing Transformation. Rest of semester. This week, with TAs
Rasterization MIT EECS 6.837 Frédo Durand and Barb Cutler MIT EECS 6.837, Cutler and Durand Final projects Rest of semester Weekly meetings with TAs Office hours on appointment This week, with TAs Refine
More informationRasterization. MIT EECS Frédo Durand and Barb Cutler. MIT EECS 6.837, Cutler and Durand 1
Rasterization MIT EECS 6.837 Frédo Durand and Barb Cutler MIT EECS 6.837, Cutler and Durand 1 Final projects Rest of semester Weekly meetings with TAs Office hours on appointment This week, with TAs Refine
More informationThe Traditional Graphics Pipeline
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
More informationFrom 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)
More informationThe Traditional Graphics Pipeline
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
More informationThe Traditional Graphics 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
More informationgraphics 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
More informationgraphics 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
More informationCSE 167: Lecture #5: Rasterization. Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2012
CSE 167: Introduction to Computer Graphics Lecture #5: Rasterization Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2012 Announcements Homework project #2 due this Friday, October
More informationCS 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
More informationGraphics Pipeline & Rasterization. CS-C3100 Fall 2017 Lehtinen
Graphics Pipeline & Rasterization 1 How Do We Render Interactively? Use graphics hardware, via OpenGL or DirectX OpenGL is multi-platform, DirectX is MS only OpenGL rendering Very basic! Our ray tracer
More informationFrom 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
More informationFondamenti 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
More informationChapter 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
More informationEinführung 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
More informationCS4620/5620: Lecture 14 Pipeline
CS4620/5620: Lecture 14 Pipeline 1 Rasterizing triangles Summary 1! evaluation of linear functions on pixel grid 2! functions defined by parameter values at vertices 3! using extra parameters to determine
More informationPipeline 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
More informationCS452/552; 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:
More informationFROM 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,
More informationCSE 167: Introduction to Computer Graphics Lecture #5: Rasterization. Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2015
CSE 167: Introduction to Computer Graphics Lecture #5: Rasterization Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2015 Announcements Project 2 due tomorrow at 2pm Grading window
More informationLine 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
More informationClipping 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 informationLine 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
More informationFall 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
More informationTopic #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
More informationComputer Graphics 7 - Rasterisation
Computer Graphics 7 - Rasterisation Tom Thorne Slides courtesy of Taku Komura www.inf.ed.ac.uk/teaching/courses/cg Overview Line rasterisation Polygon rasterisation Mean value coordinates Decomposing polygons
More informationTopics. 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
More informationPipeline Operations. CS 4620 Lecture Steve Marschner. Cornell CS4620 Spring 2018 Lecture 11
Pipeline Operations CS 4620 Lecture 11 1 Pipeline you are here APPLICATION COMMAND STREAM 3D transformations; shading VERTEX PROCESSING TRANSFORMED GEOMETRY conversion of primitives to pixels RASTERIZATION
More informationReal-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,
More informationRendering. Converting a 3D scene to a 2D image. Camera. Light. Rendering. View Plane
Rendering Pipeline Rendering Converting a 3D scene to a 2D image Rendering Light Camera 3D Model View Plane Rendering Converting a 3D scene to a 2D image Basic rendering tasks: Modeling: creating the world
More informationComputer 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
More informationPipeline 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
More informationCS 130 Final. Fall 2015
CS 130 Final Fall 2015 Name Student ID Signature You may not ask any questions during the test. If you believe that there is something wrong with a question, write down what you think the question is trying
More informationCOMP371 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
More informationRasterization. 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
More informationRaster Displays and Scan Conversion. Computer Graphics, CSCD18 Fall 2008 Instructor: Leonid Sigal
Raster Displays and Scan Conversion Computer Graphics, CSCD18 Fall 28 Instructor: Leonid Sigal Rater Displays Screen is represented by 2D array of locations called piels y Rater Displays Screen is represented
More informationCHAPTER 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...........
More informationAnnouncements. 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
More informationCOMP30019 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
More informationComputing Visibility. Backface Culling for General Visibility. One More Trick with Planes. BSP Trees Ray Casting Depth Buffering Quiz
Computing Visibility BSP Trees Ray Casting Depth Buffering Quiz Power of Plane Equations We ve gotten a lot of mileage out of one simple equation. Basis for D outcode-clipping Basis for plane-at-a-time
More informationLast 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
More informationRasterization: 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
More informationCSCI 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:
More informationScan 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
More informationRealtime 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,
More informationRasterization. Rasterization (scan conversion) Digital Differential Analyzer (DDA) Rasterizing a line. Digital Differential Analyzer (DDA)
CSCI 420 Computer Graphics Lecture 14 Rasterization Jernej Barbic University of Southern California Scan Conversion Antialiasing [Angel Ch. 6] Rasterization (scan conversion) Final step in pipeline: rasterization
More informationTriangle 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
More informationRasterization 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
More informationRay tracing. Computer Graphics COMP 770 (236) Spring Instructor: Brandon Lloyd 3/19/07 1
Ray tracing Computer Graphics COMP 770 (236) Spring 2007 Instructor: Brandon Lloyd 3/19/07 1 From last time Hidden surface removal Painter s algorithm Clipping algorithms Area subdivision BSP trees Z-Buffer
More informationLast Time. Reading for Today: Graphics Pipeline. Clipping. Rasterization
Last Time Modeling Transformations Illumination (Shading) Real-Time Shadows Viewing Transformation (Perspective / Orthographic) Clipping Projection (to Screen Space) Scan Conversion (Rasterization) Visibility
More informationOpenGL 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,
More informationPipeline 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
More informationIntroduction Rasterization Z-buffering Shading. Graphics 2012/2013, 4th quarter. Lecture 09: graphics pipeline (rasterization and shading)
Lecture 9 Graphics pipeline (rasterization and shading) Graphics pipeline - part 1 (recap) Perspective projection by matrix multiplication: x pixel y pixel z canonical 1 x = M vpm per M cam y z 1 This
More informationVisible-Surface Detection Methods. Chapter? Intro. to Computer Graphics Spring 2008, Y. G. Shin
Visible-Surface Detection Methods Chapter? Intro. to Computer Graphics Spring 2008, Y. G. Shin The Visibility Problem [Problem Statement] GIVEN: a set of 3-D surfaces, a projection from 3-D to 2-D screen,
More informationCS559: 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
More informationFor Intuition about Scene Lighting. Today. Limitations of Planar Shadows. Cast Shadows on Planar Surfaces. Shadow/View Duality.
Last Time Modeling Transformations Illumination (Shading) Real-Time Shadows Viewing Transformation (Perspective / Orthographic) Clipping Projection (to Screen Space) Graphics Pipeline Clipping Rasterization
More informationComputer Graphics. Bing-Yu Chen National Taiwan University
Computer Graphics Bing-Yu Chen National Taiwan University Visible-Surface Determination Back-Face Culling The Depth-Sort Algorithm Binary Space-Partitioning Trees The z-buffer Algorithm Scan-Line Algorithm
More informationProf. Feng Liu. Fall /25/2018
Prof. Feng Liu Fall 08 http://www.cs.pd.edu/~fliu/courses/cs7/ 0/5/08 Last time Clipping Toda Rasterization In-class Mid-term November Close-book eam Notes on page of A or Letter size paper Where We Stand
More informationGraphics Output Primitives
Important Graphics Output Primitives Graphics Output Primitives in 2D polgons, circles, ellipses & other curves piel arra operations in 3D triangles & other polgons Werner Purgathofer / Computergraphik
More informationRenderer 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
More informationCS 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
More informationCS 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
More informationCS 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
More informationComputer 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
More informationHidden surface removal. Computer Graphics
Lecture Hidden Surface Removal and Rasterization Taku Komura Hidden surface removal Drawing polygonal faces on screen consumes CPU cycles Illumination We cannot see every surface in scene We don t want
More informationOverview. 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
More informationRasterization, 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
More informationDrawing 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
More informationLast Time. Why are Shadows Important? Today. Graphics Pipeline. Clipping. Rasterization. Why are Shadows Important?
Last Time Modeling Transformations Illumination (Shading) Real-Time Shadows Viewing Transformation (Perspective / Orthographic) Clipping Projection (to Screen Space) Graphics Pipeline Clipping Rasterization
More informationCSE528 Computer Graphics: Theory, Algorithms, and Applications
CSE528 Computer Graphics: Theory, Algorithms, and Applications Hong Qin State University of New York at Stony Brook (Stony Brook University) Stony Brook, New York 11794--4400 Tel: (631)632-8450; Fax: (631)632-8334
More informationLogistics. CS 586/480 Computer Graphics II. Questions from Last Week? Slide Credits
CS 586/480 Computer Graphics II Dr. David Breen Matheson 408 Thursday 6PM Æ 8:50PM Presentation 4 10/28/04 Logistics Read research paper and prepare summary and question P. Hanrahan, "Ray Tracing Algebraic
More informationLast 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
More informationComputer 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,
More informationImplementation 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
More information0. 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:
More information2D 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
More informationGraphics (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
More informationLast Time. Correct Transparent Shadow. Does Ray Tracing Simulate Physics? Does Ray Tracing Simulate Physics? Refraction and the Lifeguard Problem
Graphics Pipeline: Projective Last Time Shadows cast ra to light stop after first intersection Reflection & Refraction compute direction of recursive ra Recursive Ra Tracing maimum number of bounces OR
More informationDisplay Technologies: CRTs Raster Displays
Rasterization Display Technologies: CRTs Raster Displays Raster: A rectangular array of points or dots Pixel: One dot or picture element of the raster Scanline: A row of pixels Rasterize: find the set
More informationTexture Mapping II. Light maps Environment Maps Projective Textures Bump Maps Displacement Maps Solid Textures Mipmaps Shadows 1. 7.
Texture Mapping II Light maps Environment Maps Projective Textures Bump Maps Displacement Maps Solid Textures Mipmaps Shadows 1 Light Maps Simulates the effect of a local light source + = Can be pre-computed
More informationReal-Time Graphics Architecture
Real-Time Graphics Architecture Lecture 5: Rasterization Kurt Akeley Pat Hanrahan http://graphics.stanford.edu/cs448-07-spring/ Rasterization Outline Fundamentals System examples Special topics (Depth-buffer,
More informationAdvanced Ray Tracing
Advanced Ray Tracing Thanks to Fredo Durand and Barb Cutler The Ray Tree Ni surface normal Ri reflected ray Li shadow ray Ti transmitted (refracted) ray 51 MIT EECS 6.837, Cutler and Durand 1 Ray Tree
More informationGraphics and Interaction Rendering pipeline & object modelling
433-324 Graphics and Interaction Rendering pipeline & object modelling Department of Computer Science and Software Engineering The Lecture outline Introduction to Modelling Polygonal geometry The rendering
More informationScanline Rendering 2 1/42
Scanline Rendering 2 1/42 Review 1. Set up a Camera the viewing frustum has near and far clipping planes 2. Create some Geometry made out of triangles 3. Place the geometry in the scene using Transforms
More informationHidden Surfaces II. Week 9, Mon Mar 15
University of British Columbia CPSC 314 Computer Graphics Jan-Apr 2010 Tamara Munzner Hidden Surfaces II Week 9, Mon Mar 15 http://www.ugrad.cs.ubc.ca/~cs314/vjan2010 ews yes, I'm granting the request
More informationPipeline 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
More informationComputer 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:
More informationS U N G - E U I YO O N, K A I S T R E N D E R I N G F R E E LY A VA I L A B L E O N T H E I N T E R N E T
S U N G - E U I YO O N, K A I S T R E N D E R I N G F R E E LY A VA I L A B L E O N T H E I N T E R N E T Copyright 2018 Sung-eui Yoon, KAIST freely available on the internet http://sglab.kaist.ac.kr/~sungeui/render
More informationIn today s lecture we ll have a look at: A simple technique The mid-point circle algorithm
Drawing Circles In today s lecture we ll have a look at: Circle drawing algorithms A simple technique The mid-point circle algorithm Polygon fill algorithms Summary raster drawing algorithms A Simple Circle
More informationCS451Real-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
More informationVisibility: Z Buffering
University of British Columbia CPSC 414 Computer Graphics Visibility: Z Buffering Week 1, Mon 3 Nov 23 Tamara Munzner 1 Poll how far are people on project 2? preferences for Plan A: status quo P2 stays
More informationIntroduction 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
More informationSpring 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
More informationUNIT -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
More informationReal-Time Rendering (Echtzeitgraphik) Michael Wimmer
Real-Time Rendering (Echtzeitgraphik) Michael Wimmer wimmer@cg.tuwien.ac.at Walking down the graphics pipeline Application Geometry Rasterizer What for? Understanding the rendering pipeline is the key
More informationDepartment 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
More informationReal-Time Shadows. Last Time? Textures can Alias. Schedule. Questions? Quiz 1: Tuesday October 26 th, in class (1 week from today!
Last Time? Real-Time Shadows Perspective-Correct Interpolation Texture Coordinates Procedural Solid Textures Other Mapping Bump Displacement Environment Lighting Textures can Alias Aliasing is the under-sampling
More informationReal-Time Shadows. Computer Graphics. MIT EECS Durand 1
Real-Time Shadows Computer Graphics MIT EECS 6.837 Durand 1 Why are Shadows Important? Depth cue Scene Lighting Realism Contact points 2 Shadows as a Depth Cue source unknown. All rights reserved. This
More informationCEng 477 Introduction to Computer Graphics Fall 2007
Visible Surface Detection CEng 477 Introduction to Computer Graphics Fall 2007 Visible Surface Detection Visible surface detection or hidden surface removal. Realistic scenes: closer objects occludes the
More informationIdentifying those parts of a scene that are visible from a chosen viewing position, and only process (scan convert) those parts
Visible Surface Detection Identifying those parts of a scene that are visible from a chosen viewing position, and only process (scan convert) those parts Two approaches: 1. Object space methods 2. Image
More information