3D Graphics Module Ramesh Srigiriraju. Abstract Project Areas: 3D Graphics, Modular design Purpose: to test data schemes for 3D rotatons Four different.

Slides:



Advertisements
Similar presentations
Picture Manipulation The manipulation of (already created) pictures. May be applied to vector graphics or bitmaps. We will consider bitmaps and introduce.
Advertisements

Matlab Experiment of Holliday Junction Kenny and Ryan.
Maths for Computer Graphics
1 Markov Chains Tom Finke. 2 Overview Outline of presentation The Markov chain model –Description and solution of simplest chain –Study of steady state.
CS 376 Introduction to Computer Graphics 02 / 09 / 2007 Instructor: Michael Eckmann.
Introduction to MATLAB MECH 300H Spring Starting of MATLAB.
Module 6 Matrices & Applications Chapter 26 Matrices and Applications I.
Matrix Definition A Matrix is an ordered set of numbers, variables or parameters. An example of a matrix can be represented by: The matrix is an ordered.
Fundamentals of matrices
Introduction to Matlab Jianguo Wang CSSCR September 2009.
Whiteboardmaths.com © 2011 All rights reserved
CS32310 MATRICES 1. Vector vs Matrix transformation formulae Geometric reasoning allowed us to derive vector expressions for the various transformation.
Little Linear Algebra Contents: Linear vector spaces Matrices Special Matrices Matrix & vector Norms.
Martin Ellison University of Warwick and CEPR Bank of England, December 2005 Introduction to MATLAB.
3D Graphics Module Ramesh Srigiriraju. Abstract Project Areas: 3D Graphics, Modular design Purpose: to test data schemes for 3D rotatons Four different.
EXCEL Introduction to EXCEL EXCEL Formulas. History of the Spreadsheet  VisiCalc designed by Dan Bricklin and Robert Frankston in 1979 for the Apple.
Timing Trials An investigation arising out of the Assignment CS32310 – Nov 2013 H Holstein 1.
Mathematics for Computer Graphics. Lecture Summary Matrices  Some fundamental operations Vectors  Some fundamental operations Geometric Primitives:
4.4 & 4.5 Notes Remember: Identity Matrices: If the product of two matrices equal the identity matrix then they are inverses.
Different Types of Fields to Describe the Earth. Anisotropy, heterogeneity SEM of shale (Josh et al., 2012)
Adjoint matrix Yes! The array of algebraic complements!
Working with Spreadsheets A spreadsheet is a worksheet that resembles a table and is used for organizing numbers. An electronic spreadsheet file can contain.
Matrices NamingCalculatorApplication. Making & Naming a Matrix Matrix A.
Introduction to Matlab T.E. Ochsner Getting Started with Matlab etting-started-with-matlab.html
What is MATLAB? MATLAB is one of a number of commercially available, sophisticated mathematical computation tools. Others include Maple Mathematica MathCad.
Vectors and Matrices In MATLAB a vector can be defined as row vector or as a column vector. A vector of length n can be visualized as matrix of size 1xn.
Binding UI Components to Data. Adding UI Components to the Page You can create components on a page by: Dragging a component from the Component Palette.
Parallelization of the Classic Gram-Schmidt QR-Factorization
Overview of Course Java Review 1. This Course Covers, using Java Abstract data types Design, what you want them to do (OOD) Techniques, used in implementation.
Class Opener:. Identifying Matrices Student Check:
4.8 Rank Rank enables one to relate matrices to vectors, and vice versa. Definition Let A be an m  n matrix. The rows of A may be viewed as row vectors.
Rotation matrices 1 Constructing rotation matricesEigenvectors and eigenvalues 0 x y.
State Space Control of a Magnetic Suspension System Margaret Glavin Supervisor: Prof. Gerard Hurley.
Lecture 20: Choosing the Right Tool for the Job. What is MATLAB? MATLAB is one of a number of commercially available, sophisticated mathematical computation.
Cramer’s Rule for Matrices You can use properties of matrix determinants for a variety of applications. Today: – Solving 3 variable systems of equations.
3D Graphics Module Ramesh Srigiriraju. Abstract Project Areas: 3D Graphics, Modular design Purpose: to test data schemes for 3D rotatons Four different.
A (VERY) SHORT INTRODUCTION TO MATLAB J.A. MARR George Mason University School of Physics, Astronomy and Computational Sciences.
Honors Geometry.  We learned how to set up a polygon / vertex matrix  We learned how to add matrices  We learned how to multiply matrices.
Composite 3D Transformations. Example of Composite 3D Transformations Try to transform the line segments P 1 P 2 and P 1 P 3 from their start position.
Math 252: Math Modeling Eli Goldwyn Introduction to MATLAB.
Matrix Multiplication The Introduction. Look at the matrix sizes.
Table of Contents Matrices - Definition and Notation A matrix is a rectangular array of numbers. Consider the following matrix: Matrix B has 3 rows and.
Jacobian Implementation Ryan Keedy 5 / 23 / 2012.
Notes Over 4.2 Finding the Product of Two Matrices Find the product. If it is not defined, state the reason. To multiply matrices, the number of columns.
MATLAB (Matrix Algebra laboratory), distributed by The MathWorks, is a technical computing environment for high performance numeric computation and.
Chapter 1 Computing Tools Variables, Scalars, and Arrays Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
THREE COLUMN (Click to edit) Introduction or Abstract Type in or past your text (Click to edit) Materials and Methods Type in or past your text (Click.
Introduction to R Chris Free. Introduction to R Free! Superior (if not comparable) to commercial alternatives Available on all platforms Not just for.
Matlab Workshop Getting Started.
CPT450 – Computer Graphics
Umm Al-Qura University
Matrix Arithmetic Prepared by Vince Zaccone
13.4 Product of Two Matrices
Matrices and Data Holt Algebra 2.
COMPOUND ANGLE FORMULAE: sin(A + B)
Chapter 5 Markov Analysis
Use of Mathematics using Technology (Maltlab)
SLOPE = = = The SLOPE of a line is There are four types of slopes
Angle between two vectors
Introduction To Slope.
A graphing calculator is required for some problems or parts of problems 2000.
Applications of Matrices
Marvellous Motion Episode 2 Jump and Run 1.
Matrices and Data Holt Algebra 2.
COMPOUND ANGLE FORMULAE: sin(A + B)
COMPOUND ANGLE FORMULAE: sin(A + B)
3.6 Multiply Matrices.
A square matrix is a matrix with the same number of columns as rows.
Matrix A matrix is a rectangular arrangement of numbers in rows and columns Each number in a matrix is called an Element. The dimensions of a matrix are.
Matrix Multiplication Sec. 4.2
Presentation transcript:

3D Graphics Module Ramesh Srigiriraju

Abstract Project Areas: 3D Graphics, Modular design Purpose: to test data schemes for 3D rotatons Four different test cases for data storage Graphing calculator program to perform tests

Abstract 1) Matrix expression tree, recalculate each time, column vectors 2) Matrix expression tree, recalculates, row vectors 3) Matrix expression tree, row vectors, calculate only once 4) Hard-coded formulas, calculate only once

Introduction Will be put on student Intranet, so it requires modular design Matrices used for rotations & stretches A=[[cos(a) -sin(a)] [sin(a) cos(a)]] Matrix above rotates graphs by an angle a

Introduction Current programs in this area: Maple MatLab Mathematica Other programs built-in to calculators

Development & Construction Programs written in Java All programs run on 1.2 Ghz processor No other processes running, except for IDE 10 million trials b/c of outliers First million ignored so steady state can be reached

Development & Construction Matrix editor module used to test matrix trees Calculator module used to test binary expression trees Graphing module used to test data storage scheme

Results & Conclusion Scheme 1: 2685 ns Scheme 2: 2513 ns Scheme 3: 2592 ns Scheme 4: 2440 ns Hard-coding sped up program Row vectors had impact on speed

Results & Conclusion 40 million data points 240 MB of data collected Graphing module made Can rotate graphs while viewing Future plans: Z- Buffer alg.