Vector storage and access; algorithms in GIS. This is lecture 6

 To view this video please enable JavaScript, and consider upgrading to a web browser that supports HTML5 video
Save this PDF as:

Size: px
Start display at page:

Download "Vector storage and access; algorithms in GIS. This is lecture 6"

Transcription

1 Vector storage and access; algorithms in GIS This is lecture 6

2 Vector data storage and access Vectors are built from points, line and areas. (x,y) Surface: (x,y,z)

3

4 Vector data access Access to vector data requires some ingenuity. In the past, pointers to a sequential list were used to indicate the relationships between basic vector units (points, lines and areas). Problems with access time especially when points out of sequence.

5 Database indexing Database indexing introduced to speed up data access. Indexing speeds up queries by keeping track of information. It organizes the data in sequential order.. Search time shifts from linear to logarithmic time.

6 note that. means etc.

7 Indexes Index field: contains the value of the indexing field (in sorted order). Pointer field: contains the addresses of disk blocks that have the index value Speed up performance of other fields too but at the expense of the extra space required for the index itself.

8 Problem with indices They can get really big, and take up almost as much space as the information they point to. Search time can be further decreased by allowing the index to be indexed (recursive index). This is the principle behind the multi-level index. The B Tree is a multi-level index.

9

10 B-tree as a multi-level index Example: We have a set of data records that are indexed using integers. Each index field has a pointer to a record that is indexed. Each node of the B-tree contains a list of index fields (with pointers to the data) interleaved. The value of the index field for all descendants is within the range set by the index fields of the ancestor node. Here, we have a range of 3 for each pointer. The fan-order of our B-tree is 4. (see previous slide)

11 A search begins at the root node and a route is traced to one of the descendants or the bottom of the tree, whichever comes first. If the bottom is reached, a message to that effect is returned. If a node runs of spaces for pointers (3 per node in this case), the B-tree is restructured.

12 Properties of B-trees 1. They are balanced because branches remain equal length as the tree grows. 2. Insertion and deletion can be calculated in terms of time complexity using a logarithmic function. 3. Each node is guaranteed to be roughly half-full at all stages of the tree s evolution.

13 R-tree index R-trees group objects using a rectangular approximation of their location (minimum bounding rectangle). Indexes points, lines or areas. Can be used for vector and true object data models. The MBR is assigned a parameter for maximum expansion.

14

15 R-tree index. Note applicability to GIS from a spatial perspective.

16 Other uses for MBR.

17 Object storage Every object in a GIS is not defined individually. That would be a painstaking task. Groups of like objects are organized into classes. Each class and sub-classes have attributes which apply to the entire group. In addition, operations or methods that describe possible pertinent actions, can be be defined with reference to the class. Attributes and procedures are bequethed through a hierarchical system of inheritance.

18

19 What is an algorithm? The specification of the computational processes used to perform an operation (in GIS). We write algorithms in text initially or using flowcharts and later encode them. They are encoded in high-level languages and later translated into machine instructions by a compiler.

20 What is a flowchart/cartographic model? A flowchart is a graphic representation of the algorithm. It shows the flow of processing from the beginning to the end of the solution.

21

22 Rules for flowcharting 1. All boxes in the chart are connected with arrows (not plain lines) 2. Each flowchart symbol has a data entry point on top of its symbol with no other entry points. 3. The exit point for data is always on the bottom except for decisions symbols. Decision symbols have two exit points - on either side or on the bottom and one side. 4. The flow of data is generally from top to bottom.

23 5. Connectors are used to connect breaks in the flowchart, like from one page to another or from the bottom of one page to the top of another. They generally look like this: O 6. Subroutines have their own flowcharts, independent of the main one. All flowcharts start with a Terminal symbol. They also end with one.

24 Algorithms in IDRISI Algorithms are expressed as cartographic models in IDRISI. IDRISI cartographic modelling is designed to help plan and structure analysis, but also serves the purpose of documentation. Documentation is an important, but underexecuted step in programming.

25 Squares are used for file names; triangles for vector files; raster files by rectangles; values files are ovals; and tabular data (like excel data) is represented by a page with the corner turned down.

26 Geometric algorithms Used for many operations in GIS. They often have to deal with special cases What looks like a trivial problem is often more complex Classic case of point in polygon procedure. Easy for humans to see the solution.

27

28 Polygon painting Scan conversion is used to display lines on a CRT or LCD monitor. Electron beam scans the lines of the screen, and is turned off when it encounters the edge of lines. Parity is used to keep track of inside/outside of polygon position in current beam. Every time the beam crosses the boundary of a polygon, its on-off switch toggles (binary system)

29

30 Representational algorithms GIS is conducted primarily in Euclidean space, but fails to fulfill assumptions of continuity associated with Real numbers that populate Euclidean space. Problem of discretization. There are algorithms that circumvent problems of discretization. Example: intersection not at a point on the grid. What do we do?

31 Can t add the point to the poin tset because it is not a domain grid point.

32

33

34

35

36 Simple vector algorithms for analysis Distance from a point to a line. In GIS, we always mean the minimum distance between two entities when we talk about distance.

37 Suppose that the point p is given by the coordinate pair (X,Y); the line l is described as {(x,y) ax + by + c = 0} (this is a formal definition and peripheral to this explanation) then the distance from p to l is given by the formula: distance (p,l) = ax + by + c / a 2 + b 2 the distance is, in effect, the distance from p to l measured by the length of the line segment through p and orthogonal to l.

38

39

40 Polygon to polygon distance Distance between polygons can be calculated as the distance between their closest points. But usually, the distance between polygons is determined by distance from their centroids. Need to know how to calculate a centroid.

41

42 The centroid is easily calculated: Just add all the X values of vertices and then all the Y vertices in the coverage and divide each by the number of (x,y) points. Often centroids are weighted or moved to the center of gravity of the variable rather than the area.

43 Distance between centroids. What we are actually concerned with is how to calculate the distance between centroids. The distance between centroids then becomes the distance between the two centroid points.

R-trees. R-Trees: A Dynamic Index Structure For Spatial Searching. R-Tree. Invariants

R-Trees: A Dynamic Index Structure For Spatial Searching A. Guttman R-trees Generalization of B+-trees to higher dimensions Disk-based index structure Occupancy guarantee Multiple search paths Insertions

Computational Geometry. Lecture 1: Introduction and Convex Hulls

Lecture 1: Introduction and convex hulls 1 Geometry: points, lines,... Plane (two-dimensional), R 2 Space (three-dimensional), R 3 Space (higher-dimensional), R d A point in the plane, 3-dimensional space,

Data Warehousing und Data Mining

Data Warehousing und Data Mining Multidimensionale Indexstrukturen Ulf Leser Wissensmanagement in der Bioinformatik Content of this Lecture Multidimensional Indexing Grid-Files Kd-trees Ulf Leser: Data

Spatial Partitioning and Indexing Responsible persons: Claudia Dolci, Dante Salvini, Michael Schrattner, Robert Weibel

Geographic Information Technology Training Alliance (GITTA) presents: Spatial Partitioning and Indexing Responsible persons: Claudia Dolci, Dante Salvini, Michael Schrattner, Robert Weibel Content 1.

Big Data and Scripting. Part 4: Memory Hierarchies

1, Big Data and Scripting Part 4: Memory Hierarchies 2, Model and Definitions memory size: M machine words total storage (on disk) of N elements (N is very large) disk size unlimited (for our considerations)

GIS Data in ArcGIS. Pay Attention to Data!!!

GIS Data in ArcGIS Pay Attention to Data!!! 1 GIS Data Models Vector Points, lines, polygons, multi-part, multi-patch Composite & secondary features Regions, dynamic segmentation (routes) Raster Grids,

12 Abstract Data Types

12 Abstract Data Types 12.1 Source: Foundations of Computer Science Cengage Learning Objectives After studying this chapter, the student should be able to: Define the concept of an abstract data type (ADT).

Carroll County Public Schools Elementary Mathematics Instructional Guide (5 th Grade) August-September (12 days) Unit #1 : Geometry

Carroll County Public Schools Elementary Mathematics Instructional Guide (5 th Grade) Common Core and Research from the CCSS Progression Documents Geometry Students learn to analyze and relate categories

Glossary of Object Oriented Terms

Appendix E Glossary of Object Oriented Terms abstract class: A class primarily intended to define an instance, but can not be instantiated without additional methods. abstract data type: An abstraction

ALGEBRA. sequence, term, nth term, consecutive, rule, relationship, generate, predict, continue increase, decrease finite, infinite

ALGEBRA Pupils should be taught to: Generate and describe sequences As outcomes, Year 7 pupils should, for example: Use, read and write, spelling correctly: sequence, term, nth term, consecutive, rule,

Visualization of 2D Domains

Visualization of 2D Domains This part of the visualization package is intended to supply a simple graphical interface for 2- dimensional finite element data structures. Furthermore, it is used as the low

C programming: exercise sheet L2-STUE (2011-2012)

C programming: exercise sheet L2-STUE (2011-2012) Algorithms and Flowcharts Exercise 1: comparison Write the flowchart and associated algorithm that compare two numbers a and b. Exercise 2: 2 nd order

A HYBRID APPROACH FOR AUTOMATED AREA AGGREGATION

A HYBRID APPROACH FOR AUTOMATED AREA AGGREGATION Zeshen Wang ESRI 380 NewYork Street Redlands CA 92373 Zwang@esri.com ABSTRACT Automated area aggregation, which is widely needed for mapping both natural

Oracle8i Spatial: Experiences with Extensible Databases

Oracle8i Spatial: Experiences with Extensible Databases Siva Ravada and Jayant Sharma Spatial Products Division Oracle Corporation One Oracle Drive Nashua NH-03062 {sravada,jsharma}@us.oracle.com 1 Introduction

Scan-Line Fill. Scan-Line Algorithm. Sort by scan line Fill each span vertex order generated by vertex list

Scan-Line Fill Can also fill by maintaining a data structure of all intersections of polygons with scan lines Sort by scan line Fill each span vertex order generated by vertex list desired order Scan-Line

Persistent Data Structures and Planar Point Location

Persistent Data Structures and Planar Point Location Inge Li Gørtz Persistent Data Structures Ephemeral Partial persistence Full persistence Confluent persistence V1 V1 V1 V1 V2 q ue V2 V2 V5 V2 V4 V4

COMP175: Computer Graphics. Lecture 1 Introduction and Display Technologies

COMP175: Computer Graphics Lecture 1 Introduction and Display Technologies Course mechanics Number: COMP 175-01, Fall 2009 Meetings: TR 1:30-2:45pm Instructor: Sara Su (sarasu@cs.tufts.edu) TA: Matt Menke

Fast Sequential Summation Algorithms Using Augmented Data Structures

Fast Sequential Summation Algorithms Using Augmented Data Structures Vadim Stadnik vadim.stadnik@gmail.com Abstract This paper provides an introduction to the design of augmented data structures that offer

*1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles.

Students: 1. Students understand and compute volumes and areas of simple objects. *1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles. Review

EE602 Algorithms GEOMETRIC INTERSECTION CHAPTER 27

EE602 Algorithms GEOMETRIC INTERSECTION CHAPTER 27 The Problem Given a set of N objects, do any two intersect? Objects could be lines, rectangles, circles, polygons, or other geometric objects Simple to

Binary Heap Algorithms

CS Data Structures and Algorithms Lecture Slides Wednesday, April 5, 2009 Glenn G. Chappell Department of Computer Science University of Alaska Fairbanks CHAPPELLG@member.ams.org 2005 2009 Glenn G. Chappell

Lines That Pass Through Regions

: Student Outcomes Given two points in the coordinate plane and a rectangular or triangular region, students determine whether the line through those points meets the region, and if it does, they describe

Previous Lectures. B-Trees. External storage. Two types of memory. B-trees. Main principles

B-Trees Algorithms and data structures for external memory as opposed to the main memory B-Trees Previous Lectures Height balanced binary search trees: AVL trees, red-black trees. Multiway search trees:

Lecture 9: Geometric map transformations. Cartographic Transformations

Cartographic Transformations Analytical and Computer Cartography Lecture 9: Geometric Map Transformations Attribute Data (e.g. classification) Locational properties (e.g. projection) Graphics (e.g. symbolization)

Algebra Unpacked Content For the new Common Core standards that will be effective in all North Carolina schools in the 2012-13 school year.

This document is designed to help North Carolina educators teach the Common Core (Standard Course of Study). NCDPI staff are continually updating and improving these tools to better serve teachers. Algebra

Lecture 1: Data Storage & Index

Lecture 1: Data Storage & Index R&G Chapter 8-11 Concurrency control Query Execution and Optimization Relational Operators File & Access Methods Buffer Management Disk Space Management Recovery Manager

Fuzzy Spatial Data Warehouse: A Multidimensional Model

4 Fuzzy Spatial Data Warehouse: A Multidimensional Model Pérez David, Somodevilla María J. and Pineda Ivo H. Facultad de Ciencias de la Computación, BUAP, Mexico 1. Introduction A data warehouse is defined

Lesson 15 - Fill Cells Plugin

15.1 Lesson 15 - Fill Cells Plugin This lesson presents the functionalities of the Fill Cells plugin. Fill Cells plugin allows the calculation of attribute values of tables associated with cell type layers.

Introduction to GIS. Dr F. Escobar, Assoc Prof G. Hunter, Assoc Prof I. Bishop, Dr A. Zerger Department of Geomatics, The University of Melbourne

Introduction to GIS 1 Introduction to GIS http://www.sli.unimelb.edu.au/gisweb/ Dr F. Escobar, Assoc Prof G. Hunter, Assoc Prof I. Bishop, Dr A. Zerger Department of Geomatics, The University of Melbourne

2) What is the structure of an organization? Explain how IT support at different organizational levels.

(PGDIT 01) Paper - I : BASICS OF INFORMATION TECHNOLOGY 1) What is an information technology? Why you need to know about IT. 2) What is the structure of an organization? Explain how IT support at different

Plotting: Customizing the Graph

Plotting: Customizing the Graph Data Plots: General Tips Making a Data Plot Active Within a graph layer, only one data plot can be active. A data plot must be set active before you can use the Data Selector

Part-Based Recognition

Part-Based Recognition Benedict Brown CS597D, Fall 2003 Princeton University CS 597D, Part-Based Recognition p. 1/32 Introduction Many objects are made up of parts It s presumably easier to identify simple

Quickstart for Desktop Version

Quickstart for Desktop Version What is GeoGebra? Dynamic Mathematics Software in one easy-to-use package For learning and teaching at all levels of education Joins interactive 2D and 3D geometry, algebra,

Overview. Essential Questions. Grade 8 Mathematics, Quarter 4, Unit 4.3 Finding Volume of Cones, Cylinders, and Spheres

Cylinders, and Spheres Number of instruction days: 6 8 Overview Content to Be Learned Evaluate the cube root of small perfect cubes. Simplify problems using the formulas for the volumes of cones, cylinders,

Add-in application for fx-9860g series/ GRAPH 85 series calculators. Geometry. User s Guide.

Add-in application for fx-9860g series/ GRAPH 85 series calculators E Geometry User s Guide http://edu.casio.com Contents Contents 1 Geometry Mode Overview 2 Drawing and Editing Objects 3 Controlling the

5: Magnitude 6: Convert to Polar 7: Convert to Rectangular

TI-NSPIRE CALCULATOR MENUS 1: Tools > 1: Define 2: Recall Definition --------------- 3: Delete Variable 4: Clear a-z 5: Clear History --------------- 6: Insert Comment 2: Number > 1: Convert to Decimal

Topology. Shapefile versus Coverage Views

Topology Defined as the the science and mathematics of relationships used to validate the geometry of vector entities, and for operations such as network tracing and tests of polygon adjacency Longley

a) Three faces? b) Two faces? c) One face? d) No faces? What if it s a 15x15x15 cube? How do you know, without counting?

Painted Cube (Task) Imagine a large 3x3x3 cube made out of unit cubes. The large cube falls into a bucket of paint, so that the faces of the large cube are painted blue. Now suppose you broke the cube

What s New V 11. Preferences: Parameters: Layout/ Modifications: Reverse mouse scroll wheel zoom direction

What s New V 11 Preferences: Reverse mouse scroll wheel zoom direction Assign mouse scroll wheel Middle Button as Fine tune Pricing Method (Manufacturing/Design) Display- Display Long Name Parameters:

Classifying Large Data Sets Using SVMs with Hierarchical Clusters. Presented by :Limou Wang

Classifying Large Data Sets Using SVMs with Hierarchical Clusters Presented by :Limou Wang Overview SVM Overview Motivation Hierarchical micro-clustering algorithm Clustering-Based SVM (CB-SVM) Experimental

GEOGRAPHIC INFORMATION SYSTEMS CERTIFICATION

GEOGRAPHIC INFORMATION SYSTEMS CERTIFICATION GIS Syllabus - Version 1.2 January 2007 Copyright AICA-CEPIS 2009 1 Version 1 January 2007 GIS Certification Programme 1. Target The GIS certification is aimed

SolidWorks Implementation Guides. Sketching Concepts

SolidWorks Implementation Guides Sketching Concepts Sketching in SolidWorks is the basis for creating features. Features are the basis for creating parts, which can be put together into assemblies. Sketch

BALTIC OLYMPIAD IN INFORMATICS Stockholm, April 18-22, 2009 Page 1 of?? ENG rectangle. Rectangle

Page 1 of?? ENG rectangle Rectangle Spoiler Solution of SQUARE For start, let s solve a similar looking easier task: find the area of the largest square. All we have to do is pick two points A and B and

PROG0101 Fundamentals of Programming PROG0101 FUNDAMENTALS OF PROGRAMMING. Chapter 3 Algorithms

PROG0101 FUNDAMENTALS OF PROGRAMMING Chapter 3 1 Introduction to A sequence of instructions. A procedure or formula for solving a problem. It was created mathematician, Mohammed ibn-musa al-khwarizmi.

Hierarchical Data Visualization

Hierarchical Data Visualization 1 Hierarchical Data Hierarchical data emphasize the subordinate or membership relations between data items. Organizational Chart Classifications / Taxonomies (Species and

In mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data.

MATHEMATICS: THE LEVEL DESCRIPTIONS In mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data. Attainment target

Introduction. The Aims & Objectives of the Mathematical Portion of the IBA Entry Test

Introduction The career world is competitive. The competition and the opportunities in the career world become a serious problem for students if they do not do well in Mathematics, because then they are

Content. Chapter 4 Functions 61 4.1 Basic concepts on real functions 62. Credits 11

Content Credits 11 Chapter 1 Arithmetic Refresher 13 1.1 Algebra 14 Real Numbers 14 Real Polynomials 19 1.2 Equations in one variable 21 Linear Equations 21 Quadratic Equations 22 1.3 Exercises 28 Chapter

1. Relational database accesses data in a sequential form. (Figures 7.1, 7.2)

Chapter 7 Data Structures for Computer Graphics (This chapter was written for programmers - option in lecture course) Any computer model of an Object must comprise three different types of entities: 1.

The Essentials of CAGD

The Essentials of CAGD Chapter 2: Lines and Planes Gerald Farin & Dianne Hansford CRC Press, Taylor & Francis Group, An A K Peters Book www.farinhansford.com/books/essentials-cagd c 2000 Farin & Hansford

, each of which contains a unique key value, say k i , R 2. such that k i equals K (or to determine that no such record exists in the collection).

The Search Problem 1 Suppose we have a collection of records, say R 1, R 2,, R N, each of which contains a unique key value, say k i. Given a particular key value, K, the search problem is to locate the

External Memory Geometric Data Structures

External Memory Geometric Data Structures Lars Arge Department of Computer Science University of Aarhus and Duke University Augues 24, 2005 1 Introduction Many modern applications store and process datasets

Random Map Generator v1.0 User s Guide

Random Map Generator v1.0 User s Guide Jonathan Teutenberg 2003 1 Map Generation Overview...4 1.1 Command Line...4 1.2 Operation Flow...4 2 Map Initialisation...5 2.1 Initialisation Parameters...5 -w xxxxxxx...5

Binary Search Trees CMPSC 122

Binary Search Trees CMPSC 122 Note: This notes packet has significant overlap with the first set of trees notes I do in CMPSC 360, but goes into much greater depth on turning BSTs into pseudocode than

Digital Cadastral Maps in Land Information Systems

LIBER QUARTERLY, ISSN 1435-5205 LIBER 1999. All rights reserved K.G. Saur, Munich. Printed in Germany Digital Cadastral Maps in Land Information Systems by PIOTR CICHOCINSKI ABSTRACT This paper presents

Image Compression through DCT and Huffman Coding Technique

International Journal of Current Engineering and Technology E-ISSN 2277 4106, P-ISSN 2347 5161 2015 INPRESSCO, All Rights Reserved Available at http://inpressco.com/category/ijcet Research Article Rahul

Visibility Map for Global Illumination in Point Clouds

TIFR-CRCE 2008 Visibility Map for Global Illumination in Point Clouds http://www.cse.iitb.ac.in/ sharat Acknowledgments: Joint work with Rhushabh Goradia. Thanks to ViGIL, CSE dept, and IIT Bombay (Based

2) Write in detail the issues in the design of code generator.

COMPUTER SCIENCE AND ENGINEERING VI SEM CSE Principles of Compiler Design Unit-IV Question and answers UNIT IV CODE GENERATION 9 Issues in the design of code generator The target machine Runtime Storage

Glencoe. correlated to SOUTH CAROLINA MATH CURRICULUM STANDARDS GRADE 6 3-3, 5-8 8-4, 8-7 1-6, 4-9

Glencoe correlated to SOUTH CAROLINA MATH CURRICULUM STANDARDS GRADE 6 STANDARDS 6-8 Number and Operations (NO) Standard I. Understand numbers, ways of representing numbers, relationships among numbers,

Raster Data Structures

Raster Data Structures Tessellation of Geographical Space Geographical space can be tessellated into sets of connected discrete units, which completely cover a flat surface. The units can be in any reasonable

Investigating Area Under a Curve

Mathematics Investigating Area Under a Curve About this Lesson This lesson is an introduction to areas bounded by functions and the x-axis on a given interval. Since the functions in the beginning of the

Current Standard: Mathematical Concepts and Applications Shape, Space, and Measurement- Primary

Shape, Space, and Measurement- Primary A student shall apply concepts of shape, space, and measurement to solve problems involving two- and three-dimensional shapes by demonstrating an understanding of:

Introduction to the TI-Nspire CX

Introduction to the TI-Nspire CX Activity Overview: In this activity, you will become familiar with the layout of the TI-Nspire CX. Step 1: Locate the Touchpad. The Touchpad is used to navigate the cursor

Lecture 10: Regression Trees

Lecture 10: Regression Trees 36-350: Data Mining October 11, 2006 Reading: Textbook, sections 5.2 and 10.5. The next three lectures are going to be about a particular kind of nonlinear predictive model,

Oracle Database 10g: Building GIS Applications Using the Oracle Spatial Network Data Model. An Oracle Technical White Paper May 2005

Oracle Database 10g: Building GIS Applications Using the Oracle Spatial Network Data Model An Oracle Technical White Paper May 2005 Building GIS Applications Using the Oracle Spatial Network Data Model

Unit 6 Coordinate Geometry

Mathematics I Frameworks Student Edition Unit 6 Coordinate Geometry 2 nd Edition Table of Contents Introduction:... 3 Video Game Learning Task... 6 New York Learning Task... 11 Quadrilaterals Revisited

WFP Liberia Country Office

1 Oscar Gobbato oscar.gobbato@wfp.org oscar.gobbato@libero.it WFP Liberia Country Office GIS training - Summary Objectives 1 To introduce to participants the basic concepts and techniques in using Geographic

Section 1.1. Introduction to R n

The Calculus of Functions of Several Variables Section. Introduction to R n Calculus is the study of functional relationships and how related quantities change with each other. In your first exposure to

MATHS LEVEL DESCRIPTORS

MATHS LEVEL DESCRIPTORS Number Level 3 Understand the place value of numbers up to thousands. Order numbers up to 9999. Round numbers to the nearest 10 or 100. Understand the number line below zero, and

Big Ideas in Mathematics

Big Ideas in Mathematics which are important to all mathematics learning. (Adapted from the NCTM Curriculum Focal Points, 2006) The Mathematics Big Ideas are organized using the PA Mathematics Standards

Quiz 4 Solutions EECS 211: FUNDAMENTALS OF COMPUTER PROGRAMMING II. 1 Q u i z 4 S o l u t i o n s

Quiz 4 Solutions Q1: What value does function mystery return when called with a value of 4? int mystery ( int number ) { if ( number

Partitioning and Divide and Conquer Strategies

and Divide and Conquer Strategies Lecture 4 and Strategies Strategies Data partitioning aka domain decomposition Functional decomposition Lecture 4 and Strategies Quiz 4.1 For nuclear reactor simulation,

Everyday Mathematics. Grade 4 Grade-Level Goals CCSS EDITION. Content Strand: Number and Numeration. Program Goal Content Thread Grade-Level Goal

Content Strand: Number and Numeration Understand the Meanings, Uses, and Representations of Numbers Understand Equivalent Names for Numbers Understand Common Numerical Relations Place value and notation

Understand the Sketcher workbench of CATIA V5.

Chapter 1 Drawing Sketches in Learning Objectives the Sketcher Workbench-I After completing this chapter you will be able to: Understand the Sketcher workbench of CATIA V5. Start a new file in the Part

Introduction to GIS (Basics, Data, Analysis) & Case Studies. 13 th May 2004. Content. What is GIS?

Introduction to GIS (Basics, Data, Analysis) & Case Studies 13 th May 2004 Content Introduction to GIS Data concepts Data input Analysis Applications selected examples What is GIS? Geographic Information

Higher Education Math Placement

Higher Education Math Placement Placement Assessment Problem Types 1. Whole Numbers, Fractions, and Decimals 1.1 Operations with Whole Numbers Addition with carry Subtraction with borrowing Multiplication

STRAND: Number and Operations Algebra Geometry Measurement Data Analysis and Probability STANDARD:

how August/September Demonstrate an understanding of the place-value structure of the base-ten number system by; (a) counting with understanding and recognizing how many in sets of objects up to 50, (b)

NEW MEXICO Grade 6 MATHEMATICS STANDARDS

PROCESS STANDARDS To help New Mexico students achieve the Content Standards enumerated below, teachers are encouraged to base instruction on the following Process Standards: Problem Solving Build new mathematical

B-Trees. Algorithms and data structures for external memory as opposed to the main memory B-Trees. B -trees

B-Trees Algorithms and data structures for external memory as opposed to the main memory B-Trees Previous Lectures Height balanced binary search trees: AVL trees, red-black trees. Multiway search trees:

Introduction to Statistical Machine Learning

CHAPTER Introduction to Statistical Machine Learning We start with a gentle introduction to statistical machine learning. Readers familiar with machine learning may wish to skip directly to Section 2,

Lecture 3: Models of Spatial Information

Lecture 3: Models of Spatial Information Introduction In the last lecture we discussed issues of cartography, particularly abstraction of real world objects into points, lines, and areas for use in maps.

Distance based clustering

// Distance based clustering Chapter ² ² Clustering Clustering is the art of finding groups in data (Kaufman and Rousseeuw, 99). What is a cluster? Group of objects separated from other clusters Means

A Short Introduction to Computer Graphics

A Short Introduction to Computer Graphics Frédo Durand MIT Laboratory for Computer Science 1 Introduction Chapter I: Basics Although computer graphics is a vast field that encompasses almost any graphical

Everyday Mathematics. Grade 4 Grade-Level Goals. 3rd Edition. Content Strand: Number and Numeration. Program Goal Content Thread Grade-Level Goals

Content Strand: Number and Numeration Understand the Meanings, Uses, and Representations of Numbers Understand Equivalent Names for Numbers Understand Common Numerical Relations Place value and notation

Research And Development For GeoSpatial Data Security. CSRE, IIT Bombay

Research And Development For GeoSpatial Data Security P. Venkatachalam and B. Krishna Mohan CSRE, IIT Bombay July 2011 Introduction Advancements in sensor technology, satellite remote sensing and field

Algorithms, Flowcharts & Program Design. ComPro

Algorithms, Flowcharts & Program Design ComPro Definition Algorithm: o sequence of steps to be performed in order to solve a problem by the computer. Flowchart: o graphical or symbolic representation of

Converting a Number from Decimal to Binary

Converting a Number from Decimal to Binary Convert nonnegative integer in decimal format (base 10) into equivalent binary number (base 2) Rightmost bit of x Remainder of x after division by two Recursive

CAMI Education linked to CAPS: Mathematics

- 1 - TOPIC 1.1 Whole numbers _CAPS Curriculum TERM 1 CONTENT Properties of numbers Describe the real number system by recognizing, defining and distinguishing properties of: Natural numbers Whole numbers

Social Media Mining. Data Mining Essentials

Introduction Data production rate has been increased dramatically (Big Data) and we are able store much more data than before E.g., purchase data, social media data, mobile phone data Businesses and customers

Topographic Change Detection Using CloudCompare Version 1.0

Topographic Change Detection Using CloudCompare Version 1.0 Emily Kleber, Arizona State University Edwin Nissen, Colorado School of Mines J Ramón Arrowsmith, Arizona State University Introduction CloudCompare

MICHIGAN TEST FOR TEACHER CERTIFICATION (MTTC) TEST OBJECTIVES FIELD 050: COMPUTER SCIENCE

MICHIGAN TEST FOR TEACHER CERTIFICATION (MTTC) TEST OBJECTIVES Subarea Educational Computing and Technology Literacy Computer Systems, Data, and Algorithms Program Design and Verification Programming Language

INTERACTIVE COMPUTER GRAPHICS Data Structures, Algorithms, Languages

INTERACTIVE COMPUTER GRAPHICS Data Structures, Algorithms, Languages Wolfgang K. Glloi Technical University of Berlin and University of Minnesota Tochnisths BodischBle Dnrmstadt FACHEEKE1CH 1NFORMATIK

2 SYSTEM DESCRIPTION TECHNIQUES

2 SYSTEM DESCRIPTION TECHNIQUES 2.1 INTRODUCTION Graphical representation of any process is always better and more meaningful than its representation in words. Moreover, it is very difficult to arrange

Homework from Section Find two positive numbers whose product is 100 and whose sum is a minimum.

Homework from Section 4.5 4.5.3. Find two positive numbers whose product is 100 and whose sum is a minimum. We want x and y so that xy = 100 and S = x + y is minimized. Since xy = 100, x = 0. Thus we have

SAT Subject Math Level 1 Facts & Formulas

Numbers, Sequences, Factors Integers:..., -3, -2, -1, 0, 1, 2, 3,... Reals: integers plus fractions, decimals, and irrationals ( 2, 3, π, etc.) Order Of Operations: Aritmetic Sequences: PEMDAS (Parenteses

Number and Numeracy SE/TE: 43, 49, 140-145, 367-369, 457, 459, 479

Ohio Proficiency Test for Mathematics, New Graduation Test, (Grade 10) Mathematics Competencies Competency in mathematics includes understanding of mathematical concepts, facility with mathematical skills,

Students will understand 1. use numerical bases and the laws of exponents

Grade 8 Expressions and Equations Essential Questions: 1. How do you use patterns to understand mathematics and model situations? 2. What is algebra? 3. How are the horizontal and vertical axes related?

Lecture Notes, CEng 477

Computer Graphics Hardware and Software Lecture Notes, CEng 477 What is Computer Graphics? Different things in different contexts: pictures, scenes that are generated by a computer. tools used to make