Shearing

Duration: 3 min

This video lesson is available to enrolled students.

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Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. Section A: General Awareness: Polity, Physics, Biology, Chemistry, Static General Knowledge, History, Geography, Indian Economy, GK- Current Affairs, Evolution of Indian Banking (Banking & Financial Awareness), Environment
  3. Section A: General Intelligence & Reasoning ability: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Analytical Reasoning (Counting Figures Reasoning), Blood Relations, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Seating Arrangements, Directions (Direction Test), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Selection Decision Table (Decision Making), Logical Sequence Of Words, Crypt Arithmetic, Venn Diagram, Data Arrangement, Inequality, Analogy, Ranking, Order and Sequence, TCS NQT Advanced Reasoning Ability
  4. Section A: Arithmetical & Numerical Ability: Ratio and Proportion (Ratios), Divisibility Rules, Data Interpretation, Mixture and Alligation, Permutation and Combination, Logarithm, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Percentage, Average, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, Mensuration and Geometry, Powers and Exponents (Surds and Indices), Algebra, Probability, Mental Ability, Age Problems, Partnership, Statistics, Arithmetic, Speed Mathematics and Basic Mathematics, Miscellaneous
  5. Section A: English Language & Comprehension: Vocabulary, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Tenses, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Articles, Sentence Construction, Preposition, Direct and Indirect Speech, Sentence Completion (Fill in the blanks), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Modals, Active Passive Voice (Voice), Sentence Correction (Error Correction), Adverb, Conjunction, Cloze Test (Cloze Passage)
  6. Section A: Hindi Language & Comprehension: भाषा, लिपि, ध्वनि, वर्ण, अक्षर, स्वर, व्यंजन, मात्रा और संयुक्ताक्षर, वर्तनी, वर्ण-विन्यास, अनुस्वार, अनुनासिक, चंद्रबिंदु और ‘र’ के रूप, शब्द, पद और शब्द-भेद, संज्ञा और सर्वनाम, विशेषण और क्रिया, लिंग, वचन, पुरुष और कारक, काल, वाच्य, वाक्य और वाक्य-भेद, संधि, समास, विलोम शब्द, पर्यायवाची शब्द, सामान्य अशुद्धियाँ, अनेक शब्दों के लिए एक शब्द, मुहावरे और लोकोक्तियाँ, अपठित गद्यांश और अपठित पद्यांश, Multi-Topic Content (Cross-Concept Material), वर्णमाला
  7. Section B: Programming, Data Structures, OOP & Java: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Java, OOPS with C++, Language Design, Intro to Compilers, Visual Basics, Syntax Analysis: Bottom-Up, Object Oriented Technology
  8. Section B: Computer Networks, TCP/IP & Network Security: Introduction to CN, Data Communication, DLL: Flow Control, DLL: Access Control, DLL: Error Control, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics, Network Access Technologies, Network Security, Society, Law & Ethics, Mobile Computing, Net Layer:Routing Protocol, Cyber Safety and Security
  9. Section B: Teaching Methodology: Child Development, Concept of Pedagogy, Theories, Inclusive Education, Experiential Pedagogy, Assessment & Evaluation, Curriculum Framework & Reforms, National Education Policy (NEP) 2020, Psychology, Teaching-Learning Process, Personality Development, Teaching Methods & Strategies, Learning and Motivation, Learners & Learning Process, Factors Affecting Teaching, Methods of Teaching, Nature, Objectives & Characteristics of Teaching, Teaching-Learning Aids & ICT Integration, Classroom Management & Communication, Evaluation, Assessment & Measurement, Curriculum & School Environment, Inclusive Education & Special Needs, Professional Development & Ethics
  10. Section B: Digital Electronics / Boolean Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Analog-Digital Conversion
  11. Section B: Operating Systems & Linux: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, File Management, Disc Scheduling, Unix OS, Linux OS, Distributed Systems, Windows OS
  12. Section B: Data Base Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, File Organization & Indexing, Transaction Management, Concurrency Control, Database Security & Authorization, Database Recovery, Data Warehousing & Mining
  13. Section B: Internet & Web Technologies: Website, Browser & Services, Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, HTML Basics, CSS, Emerging Technologies, JavaScript-Basics, .Net Programming, Electronic Data Interchange and E-Commerce, XML
  14. Section B: Computer Fundamentals, IT Basics & Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Register Transfer and Microoperations, Control Unit Design, Programming the Basic Computer, Terms & Abbreviations, MS Office Applications, Instr Formats & Modes, Floating Point Rep
  15. Section B: Python Language: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  16. Section B: Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management, extras, Fundamentals of Systems and Information Systems
  17. Section B: Design & Analysis of Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
  18. Section B: Mathematics: Linear Algebra, Calculus, Trigonometry, Vectors, Set Theory, Functions, Relations, Propositional and Predicate Logic, Research Process Steps, Graph Theory
  19. Section B: Computer Graphics, Multimedia & Mobile Computing: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, 3-D Object Representation, Geometric Transformations and Viewing, Multimedia
  20. Section B: Emerging Trends: Emerging Tech Trends, Knowledge Representation, Natural Language Processing
  21. DSSSB Previous Year Paper:
  22. Business Studies and Management: Business Communication, Business Organization and Management, Financial Accounting, Business Economics, Management Information System (MIS), Knowledge Management & New Economy
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The video is a lecture on 2D geometric transformations, specifically focusing on shearing. It begins by defining shearing as a technique to change an object's shape in a 2D plane, where the object's size can be altered along the x and y directions. The lecture explains that shearing is achieved using off-diagonal elements (b and c) in a transformation matrix. It then presents the mathematical equations and matrix forms for shearing along the x-axis (x' = x + shx * y, y' = y) and the y-axis (x' = x, y' = y + shy * x). A worked example demonstrates applying a shear parameter of 2 along the x-axis to a triangle with vertices A(1,1), B(0,0), and C(1,0), calculating the new coordinates for each point. The final segment shows a multiple-choice question from a UGC NET paper, asking to match 3x3 transformation matrices with their corresponding 2D transformation diagrams.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video starts with a slide titled 'Other transformations' which introduces the concept of Shear. It displays two diagrams illustrating shearing along the x-direction and y-direction, each with its corresponding 3x3 transformation matrix. The matrix for x-direction shear is shown as [[1, shx, 0], [0, 1, 0], [0, 0, 1]], and for y-direction shear as [[1, 0, 0], [shy, 1, 0], [0, 0, 1]]. The lecture then transitions to a new slide defining 'Shearing' as a technique to change the shape of an object in a 2D plane. It explains that off-diagonal elements (b and c) are involved in shearing and provides the general matrix form [[a, c], [b, d]] for a 2D transformation. An example is given where a = d = 1, c = 0, and b = 2, leading to the equations x' = x and y' = 2x + y. The slide then details the equations and matrix form for 'Shearing along x-axis' (x' = x + shx * y, y' = y) and 'Shearing along y-axis' (x' = x, y' = y + shy * x).

  2. 2:00 – 2:36 02:00-02:36

    The lecture continues with a worked example. The problem states: 'Given a triangle with points as: A (1, 1), B (0, 0) and C (1, 0). Apply shear parameter 2 along the x-axis and find out the new coordinates of the object.' The solution is shown step-by-step. For point A(1,1), the new coordinates are calculated as x' = 1 + 2*1 = 3 and y' = 1, resulting in (3,1). For point B(0,0), x' = 0 + 2*0 = 0 and y' = 0, resulting in (0,0). For point C(1,0), x' = 1 + 2*0 = 1 and y' = 0, resulting in (1,0). The new coordinates of the triangle are A(3,1), B(0,0), C(1,0). The slide then shows a diagram illustrating the original triangle and the sheared triangle. The final part of the video presents a multiple-choice question from a UGC NET paper, asking to match List-I (3x3 matrices) with List-II (2D transformation diagrams).

The video provides a comprehensive overview of 2D shearing transformations. It begins with a conceptual definition and visual examples, then delves into the mathematical foundation by presenting the standard matrix forms for shearing along the x and y axes. The core of the lesson is a practical application, where a specific example demonstrates the step-by-step calculation of new coordinates for a triangle after a shear transformation. This progression from theory to practice solidifies the understanding of how shearing alters an object's shape. The video concludes with a relevant exam-style question, reinforcing the concepts and preparing the student for application in a test environment.

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