Chapter 10: Graphics MATLAB for Scientist and Engineers Using Symbolic Toolbox.

Slides:



Advertisements
Similar presentations
MATLAB – A Computational Methods By Rohit Khokher Department of Computer Science, Sharda University, Greater Noida, India MATLAB – A Computational Methods.
Advertisements

Curves Jim Van Verth Essential Math for Games Animation Problem: want to replay stored set of transformations  Generated by.
This terms course Last term we both worked on learning 2 things –Processing –The concepts of graphics etc. This term will focus more on the basic concepts.
2D Plots 1 ENGR 1181 MATLAB 12.
Chapter 11: Symbolic Computing for Calculus
Parameterizing a Geometry using the COMSOL Moving Mesh Feature
Animation Following “Advanced Animation and Rendering Techniques” (chapter 15+16) By Agata Przybyszewska.
MATLAB Presented By: Nathalie Tacconi Presented By: Nathalie Tacconi Originally Prepared By: Sheridan Saint-Michel Originally Prepared By: Sheridan Saint-Michel.
Computer graphics & visualization Key frame Interpolation.
Math for CSLecture 11 Mathematical Methods for Computer Science Lecture 1.
Outline 1- Quick Introduction to MATLAB 2- PDE Toolbox 3- BVP
3D Rendering with JOGL Introduction to Java OpenGL Graphic Library By Ricardo Veguilla
DEPARTMENT OF MATHEMATI CS [ YEAR OF ESTABLISHMENT – 1997 ] DEPARTMENT OF MATHEMATICS, CVRCE.
TIME 2014 Technology in Mathematics Education July 1 st - 5 th 2014, Krems, Austria.
Curve Modeling Bézier Curves
CMPS1371 Introduction to Computing for Engineers NUMERICAL METHODS.
Introduction to MATLAB for Engineers Third Edition William J. Palm III Chapter 11 MuPAD PowerPoint to accompany Copyright © The McGraw-Hill Companies,
Eriq Muhammad Adams J. | Informatics University of Brawijaya.
Basic Graphics Concepts Day One CSCI 440. Terminology object - the thing being modeled image - view of object(s) on the screen frame buffer - memory that.
Chapter Create Design Ms. Robin. You will learn: To create a design and identify the coordinates used to make the design. Identify the coordinates.
11/19/02 (c) 2002, University of Wisconsin, CS 559 Last Time Many, many modeling techniques –Polygon meshes –Parametric instancing –Hierarchical modeling.
A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Spline curves 1/23 Curves and Surfaces.
Chapter 3: Formatting MuPAD Documents MATLAB for Scientist and Engineers Using Symbolic Toolbox.
Regression analysis Control of built engineering objects, comparing to the plan Surveying observations – position of points Linear regression Regression.
PDE Toolbox The Partial Differential Equation Toolbox is a Matlab based collection of tools for solving Partial Differential Equations (PDEs) on a two-dimensional.
1 Computer Programming (ECGD2102 ) Using MATLAB Instructor: Eng. Eman Al.Swaity Lecture (1): Introduction.
Chapter 9: MuPAD Programming II Procedures MATLAB for Scientist and Engineers Using Symbolic Toolbox.
Tutorial 1 Introducing Adobe Flash CS3 Professional
Chapter 2: First Steps in MuPAD MATLAB for Scientist and Engineers Using Symbolic Toolbox.
Digital Media Dr. Jim Rowan ITEC Vector Graphics Elegant way to construct digital images that –have a compact representation –are scalable –are.
University of Texas at Austin CS384G - Computer Graphics Fall 2008 Don Fussell Parametric surfaces.
110/27/ :47 Graphics II Animation Introduction and Motion Control Session 6.
Plenoptic Modeling: An Image-Based Rendering System Leonard McMillan & Gary Bishop SIGGRAPH 1995 presented by Dave Edwards 10/12/2000.
Digital Media Dr. Jim Rowan ITEC So far… We have compared bitmapped graphics and vector graphics We have discussed bitmapped images, some file formats.
Chapter 1: Brief Overview of MATLAB MATLAB for Scientist and Engineers Using Symbolic Toolbox.
A Few Things about Graphics Jian Huang Computer Science University of Tennessee.
© TMC Computer School HC20203 VRML HIGHER DIPLOMA IN COMPUTING Chapter 2 – Basic VRML.
Review on Graphics Basics. Outline Polygon rendering pipeline Affine transformations Projective transformations Lighting and shading From vertices to.
UW EXTENSION CERTIFICATE PROGRAM IN GAME DEVELOPMENT 2 ND QUARTER: ADVANCED GRAPHICS Math Review.
Subject Name: Computer Graphics Subject Code: Textbook: “Computer Graphics”, C Version By Hearn and Baker Credits: 6 1.
Recap Cubic Spline Interpolation Multidimensional Interpolation Curve Fitting Linear Regression Polynomial Regression The Polyval Function The Interactive.
Trajectory Generation
Curves: ch 4 of McConnell General problem with constructing curves: how to create curves that are “smooth” CAD problem Curves could be composed of segments.
CS 551/651 Advanced Graphics Technical Background.
CISC 110 Day 3 Introduction to Computer Graphics.
CSCE 441: Keyframe Animation/Smooth Curves (Cont.) Jinxiang Chai.
CSCE 441: Keyframe Animation/Smooth Curves (Cont.) Jinxiang Chai.
Recap Functions with No input OR No output Determining The Number of Input and Output Arguments Local Variables Global Variables Creating ToolBox of Functions.
GORT: Specifications Leon Kania – Haipin Cua – Thoren McDole – Chang Huang.
Rendering Bezier Curves (1) Evaluate the curve at a fixed set of parameter values and join the points with straight lines Advantage: Very simple Disadvantages:
MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure 5.1 Simple Plot of Time.
MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure 13.1 Interpolation between.
EEE 242 Computer Tools for Electrical Engineering
Graphics Programming. Graphics Functions We can think of the graphics system as a black box whose inputs are function calls from an application program;
Computer Graphics CC416 Lecture 04: Bresenham Line Algorithm & Mid-point circle algorithm Dr. Manal Helal – Fall 2014.
COMPUTER GRAPHICS AND LINEAR ALGEBRA AN INTRODUCTION.
Introduction to Parametric Curve and Surface Modeling.
Reading and Writing Image Files
Spatcial Description & Transformation
Constructing Objects in Computer Graphics
UW Extension Certificate Program in Game Development 2nd quarter: Advanced Graphics Animation.
Lecture 25.
CHAPTER 3 NUMERICAL METHODS.
Dr. Jim Rowan ITEC 2110 Wednesday, September 12
Lecture 25: Exploring data
Two-Dimensional Plots
INTRODUCTION TO BASIC MATLAB
© University of Wisconsin, CS559 Spring 2004
Introduction to Parametric Curve and Surface Modeling
Presentation transcript:

Chapter 10: Graphics MATLAB for Scientist and Engineers Using Symbolic Toolbox

You are going to Review the basics of plotting simple 2-D/3-D graphs and animations Create graphs with different attributes Generate advanced animated graphs with timing control Handle cameras for static and animated 3-D graphs 2

Introduction Graphics – Tool for exploring math objects MuPAD: Easy 2-D, 3-D and animated graphs Interactive graph attributes editor Plot library does it all 3

2-D Simple Function Graphs Simple function graph with range 4

2-D Multiple Function Graphs Multiple plots wo/wt legend 5

2-D Graphs – Matrix Eigenvalues Max. Eigenvalues of a Matrix 6

2-D Piecewise Graphs Piecewise functions 7

2-D Function Graphs with Y Range Y range control 8

2-D Simple Animations Additional animation parameter 9

2-D Multiple Function Animations Additional animation parameter 10 Default No. of Frames = 50

Attributes of 2D Graphs Mesh Control

Attributes Control Details Grid, Ticks and Header 12

Specifying Viewing Box Y Range of Viewing Box 13

Specifying Viewing Box (cont.) Semi-automatic control of Y Range 14

3-D Function Graphs 15

3-D Function Graphs (cont.) Generated 3-D Graphs 16

Submesh for Smoother Surface Submesh 17 Without Submesh With Submesh

3-D Animations 18 Default No. of Frames = 50 Animation Parameter Flying Carpet

Advanced 2-D Graphs Several objects with different attributes in a single graph 19 Plot primitives

Anatomy of Complex 2D Graph Function and its tangential line at a point 20 plot::Point2d plot::Line2d plot::Function2d

Advanced 2-D Animation Line and point are animated. 21

Moving Tangential Line Function and its tangential line at a moving point 22

Example: Interpolated Curve Original curve and its sampled points Interpolated points using cubic spline Both curves and sampled points 23

Compare the Curves Original curve, sampled points and interpolated curve 24

Example: Cycloids A cycloid is the curve that you get when following a point fixed to a wheel rolling along a straight line. We visualize this construction by an animation in which we use the x coordinate of the hub as the animation parameter. The wheel is realized as a circle. There are 3 points fixed to the wheel: a green point on the rim, a blue point inside the wheel and a red point outside the wheel: 25 source code can be found in 'ch10_graphics_demo.mn'

Example: ODE Vector Field We wish to visualize the solution of the ordinary differential equation (ODE) y′(x) = −y(x)3 + cos(x) with the initial condition y(0) = 0. The solution shall be drawn together with the vector field ⃗ v(x, y) = (1,−y3 + cos(x)) associated with this ODE (along the solution curve, the vectors of this field are tangents of the curve). 26 source code can be found in 'ch10_graphics_demo.mn'

Example: Surface by Rotated Curve Create an interpolated curve from a series of data points. Rotate the curve to get the corresponding surface. 27 source code can be found in 'ch10_graphics_demo.mn'

RGB Colors 28 Opacity

Simple Animation 29

Animation: Arc 30

Animation Parameters Animation parameters are for each objects. 31

Animation Parameter - Global Animation parameter serves as a global var. 32

Time Synchronization 33

Integration and Area 34 source code can be found in 'ch10_graphics_demo.mn'

Transformations Translate, rotate and scale a group of graph objects. 35

Animated Rotation 36

Using Camera 37

Animated Camera Camera trajectory Lorenz attractor 38 source code can be found in 'ch10_graphics_demo.mn'

Key Takeaways Now, you are able to plot 2-D and 3-D graphs using different objects and attributes, generate 2-D and 3-D animations with different objects and attributes, and to control colors and cameras for your graphs. 39

Notes 40