CG (2): Tessellation Algorithms
|
|
|
- Laureen Gregory
- 6 years ago
- Views:
Transcription
1 CG (2): Tessellation Algorithms Alessandro Martinelli 18 November 2013 CG (2): Tessellation Algorithms Computational Geometry Linear Interpolation and Structures Tessellation Algorithms Tessellation Basicis Fixed Tessellation 1 Dimensional Tessellation Square [0,1]x[0,1] Baricentric Coordinates Esempi Curves and Surfaces Computer Graphics
2 Concetto di Tassellazione CG (2): Tessellation Algorithms Computational Geometry Linear Interpolation and Structures Tessellation Algorithms Tessellation Basics Fixed Tessellation 1 Dimensional Tessellation Square [0,1]x[0,1] Baricentric Coordinates Esempi Curves and Surfaces A. Martinelli Tassellazione 18/11/ / 12
3 Concetto di Tassellazione Tessellation Basics Tessellation Tessellation is the process subdividing a geometry into small tessels Tessels and Graphics They are always related to primitives. When we should use them A. Martinelli Tassellazione 18/11/ / 12
4 Concetto di Tassellazione Tessellation Basics Tessellation Tessellation is the process subdividing a geometry into small tessels Tessels are littler or smaller geometries than the starting one. Tessels and Graphics They are always related to primitives. When we should use them A. Martinelli Tassellazione 18/11/ / 12
5 Concetto di Tassellazione Tessellation Basics Tessellation Tessellation is the process subdividing a geometry into small tessels Tessels are littler or smaller geometries than the starting one. Usually they are Convex Elements (lines, triangles, etc.) Tessels and Graphics They are always related to primitives. When we should use them A. Martinelli Tassellazione 18/11/ / 12
6 Concetto di Tassellazione Tessellation Basics Tessellation Tessellation is the process subdividing a geometry into small tessels Tessels are littler or smaller geometries than the starting one. Usually they are Convex Elements (lines, triangles, etc.) Tessels and Graphics They are always related to primitives. Line, Line Strip When we should use them A. Martinelli Tassellazione 18/11/ / 12
7 Concetto di Tassellazione Tessellation Basics Tessellation Tessellation is the process subdividing a geometry into small tessels Tessels are littler or smaller geometries than the starting one. Usually they are Convex Elements (lines, triangles, etc.) Tessels and Graphics They are always related to primitives. Line, Line Strip Triangle Triangle Strip When we should use them A. Martinelli Tassellazione 18/11/ / 12
8 Concetto di Tassellazione Tessellation Basics Tessellation Tessellation is the process subdividing a geometry into small tessels Tessels are littler or smaller geometries than the starting one. Usually they are Convex Elements (lines, triangles, etc.) Tessels and Graphics They are always related to primitives. Line, Line Strip Triangle Triangle Strip When we should use them Sampling of non linear geometries (Curves, Surfaces) A. Martinelli Tassellazione 18/11/ / 12
9 Concetto di Tassellazione Tessellation Basics Tessellation Tessellation is the process subdividing a geometry into small tessels Tessels are littler or smaller geometries than the starting one. Usually they are Convex Elements (lines, triangles, etc.) Tessels and Graphics They are always related to primitives. Line, Line Strip Triangle Triangle Strip When we should use them Sampling of non linear geometries (Curves, Surfaces) Sampling of non linear properties (Illumination Model) A. Martinelli Tassellazione 18/11/ / 12
10 Concetto di Tassellazione Tessellation Basics Tessellation Tessellation is the process subdividing a geometry into small tessels Tessels are littler or smaller geometries than the starting one. Usually they are Convex Elements (lines, triangles, etc.) Tessels and Graphics They are always related to primitives. Line, Line Strip Triangle Triangle Strip When we should use them Sampling of non linear geometries (Curves, Surfaces) Sampling of non linear properties (Illumination Model) Few tessellation algorithms can be used in a wide set of situations A. Martinelli Tassellazione 18/11/ / 12
11 CG (2): Tessellation Algorithms Computational Geometry Linear Interpolation and Structures Tessellation Algorithms Tessellation Basics Fixed Tessellation 1 Dimensional Tessellation Square [0,1]x[0,1] Baricentric Coordinates Esempi Curves and Surfaces A. Martinelli Tassellazione 18/11/ / 12
12 Fixed Tessellation Fixel tessellation subdivide a geometry into smaller geometries all having the same shape. A. Martinelli Tassellazione 18/11/ / 12
13 Fixed Tessellation Fixel tessellation subdivide a geometry into smaller geometries all having the same shape. It is related to the concept of fixed step sampling 3 important cases: Tessellation of : t [0,1] Tessellation of: (s,t) [0,1]x[0,1] Tessellation of the Domain D of baricentric coordinates. A. Martinelli Tassellazione 18/11/ / 12
14 Fixed Tessellation Fixel tessellation subdivide a geometry into smaller geometries all having the same shape. It is related to the concept of fixed step sampling 3 important cases: Tessellation of : t [0,1] Tessellation of: (s,t) [0,1]x[0,1] Tessellation of the Domain D of baricentric coordinates. All this cases stay for Parametric Domains which can be used with different interpolation schemas. A. Martinelli Tassellazione 18/11/ / 12
15 1D Fixes Tessellation Applications Curves Trajectories t = 0 step t = 1 N: steps number float step=1.0f/n; glbegin(gl LINE STRIP); for(int i=0;i N;i++){ x=x(i*step); y=y(i*step); z=z(i*step); glvertex3f(x,y,z); } glend(); t P(t) = [ r cos(2πi step) r sin(2πi step) ] A. Martinelli Tassellazione 18/11/ / 12
16 Fixed Tessellation: Square [0, 1]x[0, 1] (1/2) Applicazioni Texturing Bilinear Interpolation, Tensor-Product Surfaces (prossimamente..) A. Martinelli Tassellazione 18/11/ / 12
17 Fixed Tessellation: Square [0, 1]x[0, 1] (1/2) Applicazioni Texturing Bilinear Interpolation, Tensor-Product Surfaces (prossimamente..) 2 Times strips subdivision strips rendering A. Martinelli Tassellazione 18/11/ / 12
18 Fixed Tessellation: Square [0, 1]x[0, 1] (1/2) Applicazioni Texturing Bilinear Interpolation, Tensor-Product Surfaces (prossimamente..) 2 Times strips subdivision strips rendering strip subdivision N: steps number float step=1.0f/n; for(int i=0;i < N;i++){ v i =i*step; v i+1 =v i +step; code drawing a strip [v i,v i+1 ] } v (1,1) v i+1 i u A. Martinelli Tassellazione 18/11/ / 12
19 Fixed Tessellation: Square [0, 1]x[0, 1] (2/2) A. Martinelli Tassellazione 18/11/ / 12
20 Fixed Tessellation: Square [0, 1]x[0, 1] (2/2) Drawing a strip v glbegin(gl TRIANGLE STRIP); for(int j=0;j N;j++){ u j =j*step; glvertex3f(getx(u j,v i ),gety(u j,v i ),getz(u j,v i )); glvertex3f(getx(u j,v i+1 ),gety(u j,v i+1 ),getz(u j,v i+1 )); } glend(); (1,1) Triangle Strips u A. Martinelli Tassellazione 18/11/ / 12
21 Fixed Tessellation: Square [0, 1]x[0, 1] (2/2) Drawing a strip v glbegin(gl TRIANGLE STRIP); for(int j=0;j N;j++){ u j =j*step; glvertex3f(getx(u j,v i ),gety(u j,v i ),getz(u j,v i )); glvertex3f(getx(u j,v i+1 ),gety(u j,v i+1 ),getz(u j,v i+1 )); } glend(); (1,1) Triangle Strips u All Together float step=1.0f/n; for(int i=0;i < N;i++){ v i = i step; v i+1 = v i +step; glbegin(gl TRIANGLE STRIP); Number of triangles on for(int j=0;j N;j++){ a strip: 2 N u j =j*step; Number of strips: N glvertex3f(getx(u j,v i ),gety(u j,v i ),getz(u j,v i )); Total Triangles: 2N 2 glvertex3f(getx(u j,v i+1 ),gety(u j,v i+1 ),getz(u j,v i+1 )); } glend(); A. Martinelli Tassellazione 18/11/ / 12
22 Fixed Tessellation: Baricentric Coordinates (1/2) Applications Phong Shading Approximation Baricentric Coordinates Surfaces line Bezier-Triangles Displacement Mapping and similar techniques A. Martinelli Tassellazione 18/11/ / 12
23 Fixed Tessellation: Baricentric Coordinates (1/2) Applications Phong Shading Approximation Baricentric Coordinates Surfaces line Bezier-Triangles Displacement Mapping and similar techniques 2 Times strips subdivision strips drawing A. Martinelli Tassellazione 18/11/ / 12
24 Fixed Tessellation: Baricentric Coordinates (1/2) Applications Phong Shading Approximation Baricentric Coordinates Surfaces line Bezier-Triangles Displacement Mapping and similar techniques 2 Times strips subdivision strips drawing strip subdivision N: steps number float step=1.0f/n; for(int i=0;i < N;i++){ v i =i*step; v i+1 =v i +step; code drawing a strip [v i,v i+1 ] } (u,v,w) = (0,1,0) v i+1 v i A. Martinelli Tassellazione 18/11/ / 12
25 Fixed Tessellation: Baricentric Coordinates (2/2) Drawing a Strip glbegin(gl TRIANGLE STRIP); for(int j=0;j < N i;j++){ u j =j*step; w = 1 v i u j ; glvertex3f(getx(u j,v i,w),gety(u j,v i,w),getz(u j,v i,w)); w = 1 v i+1 u j ; glvertex3f(getx(u j,v i+1,w),gety(u j,v i+1,w),getz(u j,v i+1,w)); } glvertex3f(getx(1 v i,v i,0),gety(1 v i,v i,0),getz(1 v i,v i,0)); glend(); A. Martinelli Tassellazione 18/11/ / 12
26 Fixed Tessellation: Baricentric Coordinates (2/2) Drawing a Strip glbegin(gl TRIANGLE STRIP); for(int j=0;j < N i;j++){ u j =j*step; w = 1 v i u j ; glvertex3f(getx(u j,v i,w),gety(u j,v i,w),getz(u j,v i,w)); w = 1 v i+1 u j ; glvertex3f(getx(u j,v i+1,w),gety(u j,v i+1,w),getz(u j,v i+1,w)); } glvertex3f(getx(1 v i,v i,0),gety(1 v i,v i,0),getz(1 v i,v i,0)); glend(); (u,v,w) = (0,1,0) N i 1 Number of Triangles on a Strip: 2 (N i 1)+1 Number of Strips: N Number of Triangles: N 2 isolato v i+1 v i (1,0,0) (0,0,1) A. Martinelli Tassellazione 18/11/ / 12
27 Examples Examples: Rendering a Curve A Good Number of Steps N depends upon the curvature of curve being drawn Examples Example: tassellazione.esempio0 A. Martinelli Tassellazione 18/11/ / 12
28 Examples Examples: Approximating Phong-Shading on Triangles Examples Example: tassellazione.esempio2 A. Martinelli Tassellazione 18/11/ / 12
Information Coding / Computer Graphics, ISY, LiTH. Splines
28(69) Splines Originally a drafting tool to create a smooth curve In computer graphics: a curve built from sections, each described by a 2nd or 3rd degree polynomial. Very common in non-real-time graphics,
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
Computer Graphics CS 543 Lecture 13a Curves, Tesselation/Geometry Shaders & Level of Detail
Computer Graphics CS 54 Lecture 1a Curves, Tesselation/Geometry Shaders & Level of Detail Prof Emmanuel Agu Computer Science Dept. Worcester Polytechnic Institute (WPI) So Far Dealt with straight lines
Module Contact: Dr Stephen Laycock, CMP Copyright of the University of East Anglia Version 1
UNIVERSITY OF EAST ANGLIA School of Computing Sciences Main Series PG Examination 2013-14 COMPUTER GAMES DEVELOPMENT CMPSME27 Time allowed: 2 hours Answer any THREE questions. (40 marks each) Notes are
2D Spline Curves. CS 4620 Lecture 18
2D Spline Curves CS 4620 Lecture 18 2014 Steve Marschner 1 Motivation: smoothness In many applications we need smooth shapes that is, without discontinuities So far we can make things with corners (lines,
CS-184: Computer Graphics
CS-184: Computer Graphics Lecture #12: Curves and Surfaces Prof. James O Brien University of California, Berkeley V2007-F-12-1.0 Today General curve and surface representations Splines and other polynomial
Computergrafik. Matthias Zwicker Universität Bern Herbst 2016
Computergrafik Matthias Zwicker Universität Bern Herbst 2016 Today Curves NURBS Surfaces Parametric surfaces Bilinear patch Bicubic Bézier patch Advanced surface modeling 2 Piecewise Bézier curves Each
Shading. Introduction to Computer Graphics Torsten Möller. Machiraju/Zhang/Möller/Fuhrmann
Shading Introduction to Computer Graphics Torsten Möller Machiraju/Zhang/Möller/Fuhrmann Reading Chapter 5.5 - Angel Chapter 6.3 - Hughes, van Dam, et al Machiraju/Zhang/Möller/Fuhrmann 2 Shading Illumination
CS Object Representation. Aditi Majumder, CS 112 Slide 1
CS 112 - Object Representation Aditi Majumder, CS 112 Slide 1 What is Graphics? Modeling Computer representation of the 3D world Analysis For efficient rendering For catering the model to different applications..
Computergrafik. Matthias Zwicker. Herbst 2010
Computergrafik Matthias Zwicker Universität Bern Herbst 2010 Today Curves NURBS Surfaces Parametric surfaces Bilinear patch Bicubic Bézier patch Advanced surface modeling Piecewise Bézier curves Each segment
Shape modeling Modeling technique Shape representation! 3D Graphics Modeling Techniques
D Graphics http://chamilo2.grenet.fr/inp/courses/ensimag4mmgd6/ Shape Modeling technique Shape representation! Part : Basic techniques. Projective rendering pipeline 2. Procedural Modeling techniques Shape
CS 4620 Midterm, March 21, 2017
CS 460 Midterm, March 1, 017 This 90-minute exam has 4 questions worth a total of 100 points. Use the back of the pages if you need more space. Academic Integrity is expected of all students of Cornell
Introduction to Computer Graphics
Introduction to Computer Graphics 2016 Spring National Cheng Kung University Instructors: Min-Chun Hu 胡敏君 Shih-Chin Weng 翁士欽 ( 西基電腦動畫 ) Data Representation Curves and Surfaces Limitations of Polygons Inherently
Homework #2. Hidden Surfaces, Projections, Shading and Texture, Ray Tracing, and Parametric Curves
Computer Graphics Instructor: Brian Curless CSE 457 Spring 2013 Homework #2 Hidden Surfaces, Projections, Shading and Texture, Ray Tracing, and Parametric Curves Assigned: Sunday, May 12 th Due: Thursday,
Computer Graphics Curves and Surfaces. Matthias Teschner
Computer Graphics Curves and Surfaces Matthias Teschner Outline Introduction Polynomial curves Bézier curves Matrix notation Curve subdivision Differential curve properties Piecewise polynomial curves
Modeling. Simulating the Everyday World
Modeling Simulating the Everyday World Three broad areas: Modeling (Geometric) = Shape Animation = Motion/Behavior Rendering = Appearance Page 1 Geometric Modeling 1. How to represent 3d shapes Polygonal
Direct Rendering. Direct Rendering Goals
May 2, 2005 Goals General Goals Small memory footprint Fast rendering High-quality results identical to those of Saffron V1 using distance-based anti-aliasing and alignment zones Goals Specific Goals Avoid
CMSC427 Final Practice v2 Fall 2017
CMSC427 Final Practice v2 Fall 2017 This is to represent the flow of the final and give you an idea of relative weighting. No promises that knowing this will predict how you ll do on the final. Some questions
2D Drawing Primitives
THE SIERPINSKI GASKET We use as a sample problem the drawing of the Sierpinski gasket an interesting shape that has a long history and is of interest in areas such as fractal geometry. The Sierpinski gasket
COMP30019 Graphics and Interaction Rendering pipeline & object modelling
COMP30019 Graphics and Interaction Rendering pipeline & object modelling Department of Computer Science and Software Engineering The Lecture outline Introduction to Modelling Polygonal geometry The rendering
Lecture outline. COMP30019 Graphics and Interaction Rendering pipeline & object modelling. Introduction to modelling
Lecture outline COMP30019 Graphics and Interaction Rendering pipeline & object modelling Department of Computer Science and Software Engineering The Introduction to Modelling Polygonal geometry The rendering
Graphics 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
Advanced Computer Graphics
Advanced Computer Graphics Lecture 2: Modeling (1): Polygon Meshes Bernhard Jung TU-BAF, Summer 2007 Overview Computer Graphics Icon: Utah teapot Polygon Meshes Subdivision Polygon Mesh Optimization high-level:
Rendering Curves and Surfaces. Ed Angel Professor of Computer Science, Electrical and Computer Engineering, and Media Arts University of New Mexico
Rendering Curves and Surfaces Ed Angel Professor of Computer Science, Electrical and Computer Engineering, and Media Arts University of New Mexico Objectives Introduce methods to draw curves - Approximate
Parametric description
Examples: surface of revolution Vase Torus Parametric description Parameterization for a subdivision curve Modeling Polygonal meshes Graphics I Faces Face based objects: Polygonal meshes OpenGL is based
Computer Graphics I Lecture 11
15-462 Computer Graphics I Lecture 11 Midterm Review Assignment 3 Movie Midterm Review Midterm Preview February 26, 2002 Frank Pfenning Carnegie Mellon University http://www.cs.cmu.edu/~fp/courses/graphics/
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...........
Computer Graphics 1. Chapter 2 (May 19th, 2011, 2-4pm): 3D Modeling. LMU München Medieninformatik Andreas Butz Computergraphik 1 SS2011
Computer Graphics 1 Chapter 2 (May 19th, 2011, 2-4pm): 3D Modeling 1 The 3D rendering pipeline (our version for this class) 3D models in model coordinates 3D models in world coordinates 2D Polygons in
03 Vector Graphics. Multimedia Systems. 2D and 3D Graphics, Transformations
Multimedia Systems 03 Vector Graphics 2D and 3D Graphics, Transformations Imran Ihsan Assistant Professor, Department of Computer Science Air University, Islamabad, Pakistan www.imranihsan.com Lectures
Mathematical Tools in Computer Graphics with C# Implementations Table of Contents
Mathematical Tools in Computer Graphics with C# Implementations by Hardy Alexandre, Willi-Hans Steeb, World Scientific Publishing Company, Incorporated, 2008 Table of Contents List of Figures Notation
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
CS 465 Program 4: Modeller
CS 465 Program 4: Modeller out: 30 October 2004 due: 16 November 2004 1 Introduction In this assignment you will work on a simple 3D modelling system that uses simple primitives and curved surfaces organized
How do we draw a picture?
1 How do we draw a picture? Define geometry. Now what? We can draw the edges of the faces. Wireframe. We can only draw the edges of faces that are visible. We can fill in the faces. Giving each object
CSE 167: Lecture #8: GLSL. Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2012
CSE 167: Introduction to Computer Graphics Lecture #8: GLSL Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2012 Announcements Homework project #4 due Friday, November 2 nd Introduction:
Today s Agenda. Basic design of a graphics system. Introduction to OpenGL
Today s Agenda Basic design of a graphics system Introduction to OpenGL Image Compositing Compositing one image over another is most common choice can think of each image drawn on a transparent plastic
Homework #2. Shading, Projections, Texture Mapping, Ray Tracing, and Bezier Curves
Computer Graphics Instructor: Brian Curless CSEP 557 Autumn 2016 Homework #2 Shading, Projections, Texture Mapping, Ray Tracing, and Bezier Curves Assigned: Wednesday, Nov 16 th Due: Wednesday, Nov 30
What is visualization? Why is it important?
What is visualization? Why is it important? What does visualization do? What is the difference between scientific data and information data Cycle of Visualization Storage De noising/filtering Down sampling
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
(SSOL) Simple Shape Oriented Language
(SSOL) Simple Shape Oriented Language Madeleine Tipp Jeevan Farias Daniel Mesko mrt2148 jtf2126 dpm2153 Description: SSOL is a programming language that simplifies the process of drawing shapes to SVG
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
Scalar Field Visualization I
Scalar Field Visualization I What is a Scalar Field? The approximation of certain scalar function in space f(x,y,z). Image source: blimpyb.com f What is a Scalar Field? The approximation of certain scalar
Spline Notes. Marc Olano University of Maryland, Baltimore County. February 20, 2004
Spline Notes Marc Olano University of Maryland, Baltimore County February, 4 Introduction I. Modeled after drafting tool A. Thin strip of wood or metal B. Control smooth curved path by running between
CS 4620 Program 3: Pipeline
CS 4620 Program 3: Pipeline out: Wednesday 14 October 2009 due: Friday 30 October 2009 1 Introduction In this assignment, you will implement several types of shading in a simple software graphics pipeline.
From curves to surfaces. Parametric surfaces and solid modeling. Extrusions. Surfaces of revolution. So far have discussed spline curves in 2D
From curves to surfaces Parametric surfaces and solid modeling CS 465 Lecture 12 2007 Doug James & Steve Marschner 1 So far have discussed spline curves in 2D it turns out that this already provides of
Dgp _ lecture 2. Curves
Dgp _ lecture 2 Curves Questions? This lecture will be asking questions about curves, their Relationship to surfaces, and how they are used and controlled. Topics of discussion will be: Free form Curves
Free-Form Deformation and Other Deformation Techniques
Free-Form Deformation and Other Deformation Techniques Deformation Deformation Basic Definition Deformation: A transformation/mapping of the positions of every particle in the original object to those
Scene Graphs. COMP 575/770 Fall 2010
Scene Graphs COMP 575/770 Fall 2010 1 Data structures with transforms Representing a drawing ( scene ) List of objects Transform for each object can use minimal primitives: ellipse is transformed circle
Data Representation in Visualisation
Data Representation in Visualisation Visualisation Lecture 4 Taku Komura Institute for Perception, Action & Behaviour School of Informatics Taku Komura Data Representation 1 Data Representation We have
Direct Rendering of Trimmed NURBS Surfaces
Direct Rendering of Trimmed NURBS Surfaces Hardware Graphics Pipeline 2/ 81 Hardware Graphics Pipeline GPU Video Memory CPU Vertex Processor Raster Unit Fragment Processor Render Target Screen Extended
Design, Computation and Computer Controlled Devices
4.212 Design Fabrication Design, Computation and Computer Controlled Devices Prof. Larry Sass Department of Architecture and Planning MIT LECTURE #4 [1] Designing with Paper [2] Surface Representation
Outline. The de Casteljau Algorithm. Properties of Piecewise Linear Interpolations. Recall: Linear Interpolation
CS 430/585 Computer Graphics I Curve Drawing Algorithms Week 4, Lecture 8 David Breen, William Regli and Maxim Peysakhov Geometric and Intelligent Computing Laboratory Department of Computer Science Drexel
Outline. Properties of Piecewise Linear Interpolations. The de Casteljau Algorithm. Recall: Linear Interpolation
CS 430/585 Computer Graphics I Curve Drawing Algorithms Week 4, Lecture 8 David Breen, William Regli and Maxim Peysakhov Geometric and Intelligent Computing Laboratory Department of Computer Science Drexel
Textures. Texture coordinates. Introduce one more component to geometry
Texturing & Blending Prof. Aaron Lanterman (Based on slides by Prof. Hsien-Hsin Sean Lee) School of Electrical and Computer Engineering Georgia Institute of Technology Textures Rendering tiny triangles
TSBK03 Screen-Space Ambient Occlusion
TSBK03 Screen-Space Ambient Occlusion Joakim Gebart, Jimmy Liikala December 15, 2013 Contents 1 Abstract 1 2 History 2 2.1 Crysis method..................................... 2 3 Chosen method 2 3.1 Algorithm
Computer Graphics. Instructor: Oren Kapah. Office Hours: T.B.A.
Computer Graphics Instructor: Oren Kapah (orenkapahbiu@gmail.com) Office Hours: T.B.A. The CG-IDC slides for this course were created by Toky & Hagit Hel-Or 1 CG-IDC 2 Exercise and Homework The exercise
Fall CSCI 420: Computer Graphics. 4.2 Splines. Hao Li.
Fall 2014 CSCI 420: Computer Graphics 4.2 Splines Hao Li http://cs420.hao-li.com 1 Roller coaster Next programming assignment involves creating a 3D roller coaster animation We must model the 3D curve
Design considerations
Curves Design considerations local control of shape design each segment independently smoothness and continuity ability to evaluate derivatives stability small change in input leads to small change in
Curved PN Triangles. Alex Vlachos Jörg Peters
1 Curved PN Triangles Alex Vlachos AVlachos@ati.com Jörg Peters jorg@cise.ufl.edu Outline 2 Motivation Constraints Surface Properties Performance Demo Quick Demo 3 Constraints 4 Software Developers Must
Curves and Curved Surfaces. Adapted by FFL from CSE167: Computer Graphics Instructor: Ronen Barzel UCSD, Winter 2006
Curves and Curved Surfaces Adapted by FFL from CSE167: Computer Graphics Instructor: Ronen Barzel UCSD, Winter 2006 Outline for today Summary of Bézier curves Piecewise-cubic curves, B-splines Surface
D3D11 Tessellation. Sarah Tariq NVIDIA
D3D11 Tessellation Sarah Tariq NVIDIA Outline» Motivation» Tessellation Pipeline Introduction» PN Triangles» Code» Tessellation Shaders Details» Silhouette Refinement with PN triangles Motivation Kenneth
Review of Tuesday. ECS 175 Chapter 3: Object Representation
Review of Tuesday We have learnt how to rasterize lines and fill polygons Colors (and other attributes) are specified at vertices Interpolation required to fill polygon with attributes 26 Review of Tuesday
CS130 : Computer Graphics Curves. Tamar Shinar Computer Science & Engineering UC Riverside
CS130 : Computer Graphics Curves Tamar Shinar Computer Science & Engineering UC Riverside Design considerations local control of shape design each segment independently smoothness and continuity ability
3D Graphics and OpenGl. First Steps
3D Graphics and OpenGl First Steps Rendering of 3D Graphics Objects defined in (virtual/mathematical) 3D space. Rendering of 3D Graphics Objects defined in (virtual/mathematical) 3D space. We see surfaces
Texture Mapping and Special Effects
Texture Mapping and Special Effects February 23 rd 26 th 2007 MAE 410-574, Virtual Reality Applications and Research Instructor: Govindarajan Srimathveeravalli HW#5 Due March 2 nd Implement the complete
Surface Modeling. Polygon Tables. Types: Generating models: Polygon Surfaces. Polygon surfaces Curved surfaces Volumes. Interactive Procedural
Surface Modeling Types: Polygon surfaces Curved surfaces Volumes Generating models: Interactive Procedural Polygon Tables We specify a polygon surface with a set of vertex coordinates and associated attribute
We can use square dot paper to draw each view (top, front, and sides) of the three dimensional objects:
Unit Eight Geometry Name: 8.1 Sketching Views of Objects When a photo of an object is not available, the object may be drawn on triangular dot paper. This is called isometric paper. Isometric means equal
Animation & Rendering
7M836 Animation & Rendering Introduction, color, raster graphics, modeling, transformations Arjan Kok, Kees Huizing, Huub van de Wetering h.v.d.wetering@tue.nl 1 Purpose Understand 3D computer graphics
SRM INSTITUTE OF SCIENCE AND TECHNOLOGY
SRM INSTITUTE OF SCIENCE AND TECHNOLOGY DEPARTMENT OF INFORMATION TECHNOLOGY QUESTION BANK SUB.NAME: COMPUTER GRAPHICS SUB.CODE: IT307 CLASS : III/IT UNIT-1 2-marks 1. What is the various applications
Level of Details in Computer Rendering
Level of Details in Computer Rendering Ariel Shamir Overview 1. Photo realism vs. Non photo realism (NPR) 2. Objects representations 3. Level of details Photo Realism Vs. Non Pixar Demonstrations Sketching,
2D Spline Curves. CS 4620 Lecture 13
2D Spline Curves CS 4620 Lecture 13 2008 Steve Marschner 1 Motivation: smoothness In many applications we need smooth shapes [Boeing] that is, without discontinuities So far we can make things with corners
Parametric Curves. University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell
Parametric Curves University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell Parametric Representations 3 basic representation strategies: Explicit: y = mx + b Implicit: ax + by + c
CS559 Computer Graphics Fall 2015
CS559 Computer Graphics Fall 2015 Practice Final Exam Time: 2 hrs 1. [XX Y Y % = ZZ%] MULTIPLE CHOICE SECTION. Circle or underline the correct answer (or answers). You do not need to provide a justification
Review. Stephen J. Guy
Review Stephen J. Guy Overview Pixar short Review last class Review course Area of Graphics Image Processing Rendering Modeling Animation Misc Area of Graphics Image Processing Rendering Modeling Animation
Geometry Regents Lomac Date 3/17 due 3/18 3D: Area and Dissection 9.1R. A point has no measure because a point represents a
Geometry Regents Lomac 2015-2016 Date 3/17 due 3/18 3D: Area and Dissection Name Per LO: I can define area, find area, and explain dissection it relates to area and volume. DO NOW On the back of this packet
The Essentials of CAGD
The Essentials of CAGD Chapter 6: Bézier Patches Gerald Farin & Dianne Hansford CRC Press, Taylor & Francis Group, An A K Peters Book www.farinhansford.com/books/essentials-cagd c 2 Farin & Hansford The
Chapter IV Fragment Processing and Output Merging. 3D Graphics for Game Programming
Chapter IV Fragment Processing and Output Merging Fragment Processing The per-fragment attributes may include a normal vector, a set of texture coordinates, a set of color values, a depth, etc. Using these
CSE 167: Introduction to Computer Graphics Lecture #11: Bezier Curves. Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2016
CSE 167: Introduction to Computer Graphics Lecture #11: Bezier Curves Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2016 Announcements Project 3 due tomorrow Midterm 2 next
Lecture 25: Bezier Subdivision. And he took unto him all these, and divided them in the midst, and laid each piece one against another: Genesis 15:10
Lecture 25: Bezier Subdivision And he took unto him all these, and divided them in the midst, and laid each piece one against another: Genesis 15:10 1. Divide and Conquer If we are going to build useful
Lecture 4: Geometry Processing. Kayvon Fatahalian CMU : Graphics and Imaging Architectures (Fall 2011)
Lecture 4: Processing Kayvon Fatahalian CMU 15-869: Graphics and Imaging Architectures (Fall 2011) Today Key per-primitive operations (clipping, culling) Various slides credit John Owens, Kurt Akeley,
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
Technical Report. Removing polar rendering artifacts in subdivision surfaces. Ursula H. Augsdörfer, Neil A. Dodgson, Malcolm A. Sabin.
Technical Report UCAM-CL-TR-689 ISSN 1476-2986 Number 689 Computer Laboratory Removing polar rendering artifacts in subdivision surfaces Ursula H. Augsdörfer, Neil A. Dodgson, Malcolm A. Sabin June 2007
A DIVIDE AND CONQUER METHOD FOR CURVE DRAWING
ECS 78 Course Notes A DIVIDE AND CONQUER METHOD FOR CURVE DRAWING Kenneth I. Joy Institute for Data Analysis and Visualization Department of Computer Science University of California, Davis Overview In
Transformation Hierarchies. CS 4620 Lecture 5
Transformation Hierarchies CS 4620 Lecture 5 2013 Steve Marschner 1 Data structures with transforms Representing a drawing ( scene ) List of objects Transform for each object can use minimal primitives:
Spring 2012 Final. CS184 - Foundations of Computer Graphics. University of California at Berkeley
Spring 2012 Final CS184 - Foundations of Computer Graphics University of California at Berkeley Write your name HERE: Write your login HERE: Closed book. You may not use any notes or printed/electronic
Motivation MGB Agenda. Compression. Scalability. Scalability. Motivation. Tessellation Basics. DX11 Tessellation Pipeline
MGB 005 Agenda Motivation Tessellation Basics DX Tessellation Pipeline Instanced Tessellation Instanced Tessellation in DX0 Displacement Mapping Content Creation Compression Motivation Save memory and
Spline Surfaces, Subdivision Surfaces
CS-C3100 Computer Graphics Spline Surfaces, Subdivision Surfaces vectorportal.com Trivia Assignment 1 due this Sunday! Feedback on the starter code, difficulty, etc., much appreciated Put in your README
Approximate Catmull-Clark Patches. Scott Schaefer Charles Loop
Approximate Catmull-Clark Patches Scott Schaefer Charles Loop Approximate Catmull-Clark Patches Scott Schaefer Charles Loop Catmull-Clark Surface ACC-Patches Polygon Models Prevalent in game industry Very
Until now we have worked with flat entities such as lines and flat polygons. Fit well with graphics hardware Mathematically simple
Curves and surfaces Escaping Flatland Until now we have worked with flat entities such as lines and flat polygons Fit well with graphics hardware Mathematically simple But the world is not composed of
Notes on Computer Graphics and OpenGL. Thomas Strathmann
Notes on Computer Graphics and OpenGL Thomas Strathmann February 2, 2011 Preface The purpose of this document is to server as a sort of logbook in which I put down all the interesting math and assorted
B x. Interoperability Chart Version 2011 LEGEND. Perfect compatibility. Data (Converted) compatibility. Emulated (Bake) compatibility.
Interoperability Chart Version 2011 LEGEND Perfect compatibility Data passed from a source application is recognized by the destination application, yielding identical results. Data (Converted) compatibility
CS337 INTRODUCTION TO COMPUTER GRAPHICS. Describing Shapes. Constructing Objects in Computer Graphics. Bin Sheng Representing Shape 9/20/16 1/15
Describing Shapes Constructing Objects in Computer Graphics 1/15 2D Object Definition (1/3) Lines and polylines: Polylines: lines drawn between ordered points A closed polyline is a polygon, a simple polygon
ECE 600, Dr. Farag, Summer 09
ECE 6 Summer29 Course Supplements. Lecture 4 Curves and Surfaces Aly A. Farag University of Louisville Acknowledgements: Help with these slides were provided by Shireen Elhabian A smile is a curve that
Tamy Boubekeur & Christophe Schlick
Graphics Hardware (2005) M. Meissner, B.- O. Schneider (Editors) Generic Mesh Refinement on GPU Tamy Boubekeur & Christophe Schlick LaBRI INRIA CNRS University of Bordeaux, France Abstract Many recent
Graphics Hardware and Display Devices
Graphics Hardware and Display Devices CSE328 Lectures Graphics/Visualization Hardware Many graphics/visualization algorithms can be implemented efficiently and inexpensively in hardware Facilitates interactive
Parametric Curves. University of Texas at Austin CS384G - Computer Graphics
Parametric Curves University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell Parametric Representations 3 basic representation strategies: Explicit: y = mx + b Implicit: ax + by + c
Announcements. Written Assignment 2 is out see the web page. Computer Graphics
Announcements Written Assignment 2 is out see the web page 1 Texture and other Mappings Shadows Texture Mapping Bump Mapping Displacement Mapping Environment Mapping Watt Chapter 8 COMPUTER GRAPHICS 15-462
Computer Graphics I. Assignment 3
UNIVERSITÄT DES SAARLANDES Dr.-Ing. Hendrik P.A. Lensch Max Planck Institut Informatik Art Tevs (tevs@mpi-inf.mpg.de) Boris Ajdin (bajdin@mpi-inf.mpg.de) Matthias Hullin (hullin@mpi-inf.mpg.de) 12. November
Curves. Computer Graphics CSE 167 Lecture 11
Curves Computer Graphics CSE 167 Lecture 11 CSE 167: Computer graphics Polynomial Curves Polynomial functions Bézier Curves Drawing Bézier curves Piecewise Bézier curves Based on slides courtesy of Jurgen
CS-184: Computer Graphics. Today
CS-84: Computer Graphics Lecture #5: Curves and Surfaces Prof. James O Brien University of California, Berkeley V25F-5-. Today General curve and surface representations Splines and other polynomial bases
Lecture overview. Visualisatie BMT. Fundamental algorithms. Visualization pipeline. Structural classification - 1. Structural classification - 2
Visualisatie BMT Fundamental algorithms Arjan Kok a.j.f.kok@tue.nl Lecture overview Classification of algorithms Scalar algorithms Vector algorithms Tensor algorithms Modeling algorithms 1 2 Visualization