Reading. 8. Projections. 3D Geometry Pipeline. 3D Geometry Pipeline (cont d) Required: w Watt, Section
|
|
- Wilfrid Underwood
- 5 years ago
- Views:
Transcription
1 Reading Required: Watt, Section Further reading: 8. Projections Fole, et al, Chapter 5.6 and Chapter 6 David F. Rogers and J. Alan Adams, Mathematical Elements for Computer Graphics, 2 nd Ed., McGra-Hill, Ne York, 990, Chapter 2. 3D Geometr Pipeline 3D Geometr Pipeline (cont d) Before being turned into piels, a piece of geometr goes through a number of transformations... Ee space (Vie space) Model space (Object space) scale, translate, rotate,... Projective transformation, scale, translate World space (Object space) Normalied projection space Project, scale, translate rotate, translate Normalied device space (Screen space) Ee space (Vie space) scale Image space (Windo space) (Raster space) (Screen space) (Device space)
2 Projections Projections transform points in n-space to m-space, here m<n. In 3-D, e map points from 3-space to the projection plane () along projectors emanating from the center of projection (): The center of projection is eactl the same as the pinhole in apinhole camera. There are to basic tpes of projections: Perspective distance from to finite Parallel distance from to infinite DOP Parallel projections For parallel projections, e specif a direction of projection (DOP) instead of a. There are to tpes of parallel projections: Orthographic projection DOP perpendicular to Oblique projection DOP not perpendicular to We can rite orthographic projection onto the 0 plane ith a simple matri Normall, e do not drop the value right aa. Wh not? Oblique parallel projections There are to standard kinds of oblique projections: Properties of parallel projection Properties of parallel projection: Cavalier projection DOP makes 45 degree angle ith Does not foreshorten lines perpendicular to Cabinet projection DOP makes a 63.4 degree angle ith Foreshortens lines perpendicular to b onehalf Not realistic looking Good for eact measurements Are actuall a kind of affine transformation Parallel lines remain parallel Angles not (in general) preserved Most often used in CAD, architectural draings, etc., here taking eact measurement is important /2 N V Cavalier (2D) Cabinet (2D) Oblique projection geometr (3D)
3 Derivation of perspective projection Consider the projection of a point onto the projection plane: Homogeneous coordinates revisited Remember ho e said that affine transformations ork ith the last coordinate alas set to one. What happens if the coordinate is not one? d (', ', -d) (,, ) B similar triangles, e can compute ho much the and coordinates are scaled: We divide all the coordinates b : / / / If, then nothing changes. Sometimes e call this division step the perspective divide. Note: Watt uses a left-handed coordinate sstem, and he looks don the + ais, and the is at +d. Homogeneous coordinates and perspective projection No e can re-rite the perspective projection as a matri equation: / d 0 / d Projective normaliation After appling the perspective transformation and dividing b, e are free to do a simple parallel projection (drop the ) to get the 2D image. What does this impl about the shape of things after the perspective transformation + divide? After division b, e get: d d Again, projection implies dropping the coordinate to give a 2D image, but e usuall keep it around a little hile longer.
4 Vanishing points Vanishing points (cont d) What happens to to parallel lines that are not parallel to the projection plane? Think of train tracks receding into the horion... Dividing b : p + tv d p + tv p tv + d p + tv The equation for a line is: p v p v l p+ tv + t p v 0 After perspective transformation e get: p + tv p + tv ( p + tv)/ d Letting t go to infinit: We get a point! What happens to the line l q + tv? Each set of parallel lines intersect at a vanishing point on the. Q: Ho man vanishing points are there? Principal vanishing points If e define a set of principal aes in orld coordinates, i.e., the,, and aes, then it s possible to choose the viepoint such that these aes ill converge to different vanishing points. The vanishing points of the principal aes are called the principal vanishing points. Eample: vieer image Perspective draings are often classified b the number of principal vanishing points. One-point perspective simplest to dra To-point perspective gives better impression of depth Three-point perspective most difficult to dra All three tpes are equall simple ith computer graphics. Properties of perspective projections The perspective projection is an eample of a projective transformation. Here are some properties of projective transformations: Lines map to lines Parallel lines do not necessaril remain parallel Ratios are not preserved One of the advantages of perspective projection is that sie varies inversel ith distance looks realistic. A disadvantage is that e can't judge distances as eactl as e can ith parallel projections. Q: Wh did nature give us ees that perform perspective projections? Q: Do our ees ``see in 3D''?
5 Clipping and the vieing frustum The center of projection and the portion of the projection plane that map to the final image form an infinite pramid. The sides of the pramid are clipping planes. Frequentl, additional clipping planes are inserted to restrict the range of depths. These clipping planes are called the near and far or the hither and on clipping planes. D Summar What to take aa from this lecture: All the boldfaced ords. An appreciation for the various coordinate sstems used in computer graphics. Ho the persepctive transformation orks. Ho e use homogeneous coordinates to represent perspective projections. The classification of different tpes of projections. The concepts of vanishing points and one-, to-, and three-point perspective. The mathematical properties of projective transformations. Near (Hither) Far (Yon) All of the clipping planes bound the the vieing frustum.
Reading. Projections. Projections. Perspective vs. parallel projections. Foley et al. Chapter 6. Optional. Perspective projections pros and cons:
Reading Fole et al. Chapter 6 Optional Projections David F. Rogers and J. Alan Adams, Mathematical Elements for Computer Graphics, Second edition, McGra-Hill, Ne York, 990, Chapter 3. Projections Projections
More informationReading. Projections. The 3D synthetic camera model. Imaging with the synthetic camera. Angel. Chapter 5. Optional
Reading Angel. Chapter 5 Optional Projections David F. Rogers and J. Alan Adams, Mathematical Elements for Computer Graphics, Second edition, McGraw-Hill, New York, 1990, Chapter 3. The 3D snthetic camera
More informationReading. Angel. Chapter 5. Optional
Projections Reading Angel. Chapter 5 Optional David F. Rogers and J. Alan Adams, Mathematical Elements for Computer Graphics, Second edition, McGraw-Hill, New York, 1990, Chapter 3. The 3D synthetic camera
More information3D Viewing. Projections. Perspective A B B. Projectors. Center of Projection. Projection Plane
Projections Projectors A Center of Projection A B B Projection Plane Perspective Projections Projectors A A B At Infinit B Projection Plane Parallel Parallel Projections Orthographic 3D Viewing Top View
More informationGraphics and Interaction Perspective Geometry
433-324 Graphics and Interaction Perspective Geometr Department of Computer Science and Software Engineering The Lecture outline Introduction to perspective geometr Perspective Geometr Centre of projection
More information3D Viewing. Introduction to Computer Graphics Torsten Möller / Manfred Klaffenböck. Machiraju/Zhang/Möller
3D Viewing Introduction to Computer Graphics Torsten Möller / Manfred Klaffenböck Machiraju/Zhang/Möller Reading Chapter 5 of Angel Chapter 13 of Hughes, van Dam, Chapter 7 of Shirley+Marschner Machiraju/Zhang/Möller
More informationProjections Computer Graphics and Visualization
Planar Geometric Fall 2010 Standard projections project onto a plane Projectors are lines that either converge at a center of projection are parallel Nonplanar projections are needed for applications such
More informationGraphic Communications
Graphic Communications Lecture 8: Projections Assoc. Prof.Dr. Cengizhan İpbüker İTÜ-SUNY 2004-2005 2005 Fall ipbuker_graph06 Projections The projections used to display 3D objects in 2D are called Planar
More information3D COMPUTER GRAPHICS
3D COMPUTER GRAPHICS http://www.tutorialspoint.com/computer_graphics/3d_computer_graphics.htm Copyright tutorialspoint.com In the 2D system, we use only two coordinates X and Y but in 3D, an extra coordinate
More informationCS-184: Computer Graphics. Today
CS-84: Computer Graphics Lecture 5: Projection Prof. James O Brien Universit of California, Berkele V25-5-.3 Toda Windowing and Viewing Transformations Windows and viewports Orthographic projection Perspective
More informationTransform 3D objects on to a 2D plane using projections
PROJECTIONS 1 Transform 3D objects on to a 2D plane using projections 2 types of projections Perspective Parallel In parallel projection, coordinate positions are transformed to the view plane along parallel
More informationClassical Viewing. Ed Angel Professor of Computer Science, Electrical and Computer Engineering, and Media Arts University of New Mexico
Classical Viewing Ed Angel Professor of Computer Science, Electrical and Computer Engineering, and Media Arts University of New Mexico 1 Objectives Introduce the classical views Compare and contrast image
More informationIntroduction to Projection The art of representing a three-dimensional object or scene in a 2D space is called projection.
Introduction to Projection The art of representing a three-dimensional object or scene in a 2D space is called projection. Projection is carried out by passing projectors through each vertex and intersecting
More information3D Viewing I. Acknowledgement: Some slides are from the Dr. Andries van Dam lecture. CMSC 435/634 August D Viewing I # /27
3D Viewing I Acknowledgement: Some slides are from the Dr. Andries van Dam lecture. From 3D to 2D: Orthographic and Perspective Projection Part 1 Geometrical Constructions Types of Projection Projection
More informationCS354 Computer Graphics Viewing and Projections
Slide Credit: Donald S. Fussell CS354 Computer Graphics Viewing and Projections Qixing Huang February 19th 2018 Eye Coordinates (not NDC) Planar Geometric Projections Standard projections project onto
More informationAML710 CAD LECTURE Parallel Projections a) Orthographic Projections b) Axonometric Projections 2. Perspective Transformations and Projections
AML7 CAD LECTURE 8 PROJECTIONS. Parallel Projections a) Orthographic Projections b) Aonometric Projections. Perspective Transormations and Projections PROJECTIONS Aine, Rigid-bod/Euclidian Vs Perspective
More information3D Viewing I. From 3D to 2D: Orthographic and Perspective Projection Part 1
From 3D to 2D: Orthographic and Perspective Projection Part 1 3D Viewing I By Andries van Dam Geometrical Constructions Types of Projection Projection in Computer Graphics Jian Chen January 15, 2010 3D
More informationViewing. Perspective views. Parallel l views. Finite COP (center of projection) COP at infinity DOP (direction of projection) Parallel View
Viewing th Week, 29 Funamental Tes of Viewing views Finite COP (center of rojection) Parallel l views COP at infinit DOP (irection of rojection) View Parallel View Parallel View View Classical Viewing
More informationViewing. Perspective views. Parallel l views. Finite COP (center of projection) COP at infinity DOP (direction of projection) Parallel View
Viewing 3 r Week, 29 Funamental Tes of Viewing views Finite COP (center of rojection) Parallel l views COP at infinit DOP (irection of rojection) View Parallel View Parallel View View Taonom of Planar
More informationIntroduction to Computer Graphics (CS602) Lecture 19 Projections
Introduction to Computer Graphics (CS602) Lecture 19 Projections For centuries, artists, engineers, designers, drafters, and architects have been facing difficulties and constraints imposed by the problem
More informationProjections. Conceptual Model of the 3D viewing process
Projections Projections Conceptual Model of the 3D viewing process 3D Projections (Rays converge on eye position) (Rays parallel to view plane) Perspective Parallel Orthographic Oblique Elevations Axonometric
More informationVisual Imaging in the Electronic Age. Drawing Perspective Images
Visual Imaging in the Electronic Age Lecture # 2 Drawing Perspective Images Brunelleschi s Experiment August 27, 2015 Prof. Donald P. Greenberg http://www.graphics.cornell.edu/academic/art2907/ User Name:
More informationVisual Imaging in the Electronic Age. Drawing Perspective Images
Visual Imaging in the Electronic Age Lecture # 2 Drawing Perspective Images Brunelleschi s Experiment August 25, 2016 Prof. Donald P. Greenberg http://www.graphics.cornell.edu/academic/art2907/ User Name:
More informationLecture 2 Camera Models
Lecture 2 Camera Models Professor Silvio Savarese Computational Vision and Geometr Lab Silvio Savarese Lecture 2 - -Jan-8 Lecture 2 Camera Models Pinhole cameras Cameras lenses The geometr of pinhole cameras
More informationVisual Imaging in the Electronic Age. Drawing Perspective Images
Visual Imaging in the Electronic Age Lecture # 2 Drawing Perspective Images Brunelleschi s Experiment August 24, 2017 Prof. Donald P. Greenberg http://www.graphics.cornell.edu/academic/art2907/ User Name:
More informationProjections Josef Pelikán & Alexander Wilkie CGG MFF UK Praha
Projections 995-205 Josef Pelikán & Aleander Wilkie CGG MFF UK Praha pepca@cgg.mff.cuni.c http://cgg.mff.cuni.c/~pepca/ / 24 Basic Concepts plane of projection projection ras projection origin plane of
More informationCS475/CS675 Computer Graphics
CS475/CS675 Computer Graphics Viewing Perspective Projection Projectors Centre of Projection Object Image Plane or Projection Plane 2 Parallel Projection Projectors Centre of Projection? Object Image Plane
More informationVIEWING 1. CLASSICAL AND COMPUTER VIEWING. Computer Graphics
VIEWING We now investigate the multitude of ways in which we can describe our virtual camera. Along the way, we examine related topics, such as the relationship between classical viewing techniques and
More informationInteractive Computer Graphics A TOP-DOWN APPROACH WITH SHADER-BASED OPENGL
International Edition Interactive Computer Graphics A TOP-DOWN APPROACH WITH SHADER-BASED OPENGL Sixth Edition Edward Angel Dave Shreiner 228 Chapter 4 Viewing Front elevation Elevation oblique Plan oblique
More informationLecture 2 Camera Models
Lecture 2 Camera Models Professor Silvio Savarese Computational Vision and Geometr Lab Silvio Savarese Lecture 2-4-Jan-4 Announcements Prerequisites: an questions? This course requires knowledge of linear
More informationLecture 7: Camera Models
Lecture 7: Camera Models Professor Stanford Vision Lab 1 What we will learn toda? Pinhole cameras Cameras & lenses The geometr of pinhole cameras Reading: [FP]Chapters 1 3 [HZ] Chapter 6 2 What we will
More informationLecture 8 Camera Models
Lecture 8 Caera Models Professor Silvio Savarese Coputational Vision and Geoetr Lab Silvio Savarese Lecture 8-5-Oct-4 Lecture 8 Caera Models Pinhole caeras Caeras & lenses The geoetr of pinhole caeras
More informationLecture 2 of 41. Viewing 1 of 4: Overview, Projections
Viewing 1 of 4: Overview, Projections William H. Hsu Department of Computing and Information Sciences, KSU KSOL course pages: http://bit.ly/hgvxlh / http://bit.ly/evizre Public mirror web site: http://www.kddresearch.org/courses/cis636
More informationLecture 2 of 41. Viewing 1 of 4: Overview, Projections
Viewing 1 of 4: Overview, Projections William H. Hsu Department of Computing and Information Sciences, KSU KSOL course pages: http://bit.ly/hgvxlh / http://bit.ly/evizre Public mirror web site: http://www.kddresearch.org/courses/cis636
More information11/12/2015 CHAPTER 7. Axonometric Drawings (cont.) Axonometric Drawings (cont.) Isometric Projections (cont.) 1) Axonometric Drawings
CHAPTER 7 1) Axonometric Drawings 1) Introduction Isometric & Oblique Projection Axonometric projection is a parallel projection technique used to create a pictorial drawing of an object by rotating the
More informationMultiviews and Auxiliary Views
Multiviews and Auxiliary Views Multiviews and Auxiliary Views Objectives Explain orthographic and multiview projection. Identifying the six principal views. Apply standard line practices to multiviews
More informationExploring 3D in Flash
1 Exploring 3D in Flash We live in a three-dimensional world. Objects and spaces have width, height, and depth. Various specialized immersive technologies such as special helmets, gloves, and 3D monitors
More informationEngineering Drawing Lecture 5 PROJECTION THEORY
University of Palestine College of Engineering & Urban Planning First Level Engineering Drawing Lecture 5 PROJECTION THEORY Lecturer: Eng. Eman Al.Swaity Eng.Heba hamad PART 1 PROJECTION METHOD TOPICS
More information1 st Subject: Types of Pictorial Drawings (Isometric, Oblique, and Perspective)
Intermediate Engineering Graphics 4 th Week 1 st Meeting Lecture Notes Instructor: Edward N. Locke Topic: Types of pictorial drawings (isometric, oblique, and perspective), isometric sketching and drafting
More informationStudent Name: Teacher: Date: District: Rowan. Assessment: 9_12 T and I IC61 - Drafting I Test 1. Description: Unit C - Sketching - Test 2.
Student Name: Teacher: Date: District: Rowan Assessment: 9_12 T and I IC61 - Drafting I Test 1 Description: Unit C - Sketching - Test 2 Form: 501 1. The most often used combination of views includes the:
More informationUNIT 5a STANDARD ORTHOGRAPHIC VIEW DRAWINGS
UNIT 5a STANDARD ORTHOGRAPHIC VIEW DRAWINGS 5.1 Introduction Orthographic views are 2D images of a 3D object obtained by viewing it from different orthogonal directions. Six principal views are possible
More informationUnit 1: Image Formation
Unit 1: Image Formation 1. Geometry 2. Optics 3. Photometry 4. Sensor Readings Szeliski 2.1-2.3 & 6.3.5 1 Physical parameters of image formation Geometric Type of projection Camera pose Optical Sensor
More informationLecture 7: Camera Models
Lecture 7: Camera Models Professor Fei- Fei Li Stanford Vision Lab Lecture 7 -! 1 What we will learn toda? Pinhole cameras Cameras & lenses The geometr of pinhole cameras Reading: [FP] Chapters 1 3 [HZ]
More informationME 111: Engineering Drawing
ME 111: Engineering Drawing Lecture 5 12-08-2011 Orthographic projection and Projection of Points Indian Institute of Technology Guwahati Guwahati 781039 1 Orthographic Projection A parallel projection
More informationHomogeneous Representation Representation of points & vectors. Properties. Homogeneous Transformations
From Last Class Homogeneous Transformations Combines Rotation + Translation into one single matri multiplication Composition of Homogeneous Transformations Homogeneous Representation Representation of
More informationEquations of Parallel and Perpendicular Lines
COMMON CORE AB is rise - - 1 - - 0 - - 8 6 Locker LESSON. Equations of Parallel and Perpendicular Lines Name Class Date. Equations of Parallel and Perpendicular Lines Essential Question: How can ou find
More informationHistory of projection. Perspective. History of projection. Plane projection in drawing
History of projection Ancient times: Greeks wrote about laws of perspective Renaissance: perspective is adopted by artists Perspective CS 4620 Lecture 3 Duccio c. 1308 1 2 History of projection Plane projection
More informationGL5: Visualisation and reading drawings
436-105 Engineering Communications GL5:1 GL5: Visualisation and reading drawings Being able to both: represent a 3D object in multiview drawings interpret a multiview drawing to visualise a 3D object is
More informationChapter 8. Technical Drawings
Chapter 8 Technical Drawing Technical Drawings Multiview drawings Also called three-view drawings Simple objects take three views Front, top, one side Title block Identifies who did the design Gives date,
More informationIsometric Drawing Chapter 26
Isometric Drawing Chapter 26 Sacramento City College EDT 310 EDT 310 - Chapter 26 - Isometric Drawing 1 Drawing Types Pictorial Drawing types: Perspective Orthographic Isometric Oblique Pictorial - like
More informationME1105 Engineering Drawing & Design
City University London Term 1 Assessment 2008/2009 School of Engineering and Mathematical Sciences ME1105 Engineering Drawing & Design Student Name:.., Group: Examination duration: Reading time: This paper
More information8.2 Slippery Slopes. A Solidify Understanding Task
7 8.2 Slippery Slopes A Solidify Understanding Task CC BY https://flic.kr/p/kfus4x While working on Is It Right? in the previous module you looked at several examples that lead to the conclusion that the
More informationImage formation - Cameras. Grading & Project. About the course. Tentative Schedule. Course Content. Students introduction
About the course Instructors: Haibin Ling (hbling@temple, Wachman 35) Hours Lecture: Tuesda 5:3-8:pm, TTLMAN 43B Office hour: Tuesda 3: - 5:pm, or b appointment Textbook Computer Vision: Models, Learning,
More informationAuxiliary view KCEC1101
Auxiliary view KCEC1101 Introduction There are times when one of the six principal views will not completely describe an object. This is especially true when there are inclined or oblique planes or features
More informationBeginning Engineering Graphics 3 rd Week Lecture Notes Instructor: Edward N. Locke Topic: The Coordinate System, Types of Drawings and Orthographic
Beginning Engineering Graphics 3 rd Week Lecture Notes Instructor: Edward N. Locke Topic: The Coordinate System, Types of Drawings and Orthographic 1 st Subject: The Cartesian Coordinate System The Cartesian
More informationCS337 INTRODUCTION TO COMPUTER GRAPHICS. Viewing. Part I (History and Overview of Projections) Bin Sheng 1 / 46 10/04/2016
Viewing Part I (History and Overview of Projections) 1 / 46 Lecture Topics History of projection in art Geometric constructions Types of projection (parallel and perspective) 2 / 46 CS337 INTRODUCTION
More informationVISUALIZING CONTINUITY BETWEEN 2D AND 3D GRAPHIC REPRESENTATIONS
INTERNATIONAL ENGINEERING AND PRODUCT DESIGN EDUCATION CONFERENCE 2 3 SEPTEMBER 2004 DELFT THE NETHERLANDS VISUALIZING CONTINUITY BETWEEN 2D AND 3D GRAPHIC REPRESENTATIONS Carolina Gill ABSTRACT Understanding
More information(Ans:d) a. A0 b. A1 c. A2 d. A3. (Ans:b) (Ans:a) (Ans:d) (Ans:d)
Multiple Choice Questions (MCQ) on Engineering Drawing (Instruments) The mini drafter serves the purpose of everything except a. Scales b. Set square c. Protractor d. Compass (Ans:d) During operation,
More informationTSBB09 Image Sensors 2018-HT2. Image Formation Part 1
TSBB09 Image Sensors 2018-HT2 Image Formation Part 1 Basic physics Electromagnetic radiation consists of electromagnetic waves With energy That propagate through space The waves consist of transversal
More informationENGINEERING DRAWING. 1. Set squares are used to draw different angles. What is the angel a formed by the 45⁰ set square? Give a brief answer.
ENGINEERING DRAWING 1. Set squares are used to draw different angles. What is the angel a formed by the 45⁰ set square? Give a brief answer. 2. Which is the correct method of hatching a plane surface?
More informationCameras. CSE 455, Winter 2010 January 25, 2010
Cameras CSE 455, Winter 2010 January 25, 2010 Announcements New Lecturer! Neel Joshi, Ph.D. Post-Doctoral Researcher Microsoft Research neel@cs Project 1b (seam carving) was due on Friday the 22 nd Project
More information1. When sketching long, narrow objects in OBLIQUE, distortion can be lessened by placing the long dimension along:
Draft Student Name: Teacher: District: Date: Wake County Test: 9_12 T and I IC61 - Drafting I Test 2 Description: 3.03 Apply 3D sketching Form: 501 1. When sketching long, narrow objects in OBLIQUE, distortion
More informationPerspective. CS 4620 Lecture Steve Marschner. Cornell CS4620 Spring 2018 Lecture 5
Perspective CS 4620 Lecture 5 2018 Steve Marschner 1 Parallel projection To render an image of a 3D scene, we project it onto a plane Simplest kind of projection is parallel projection image projection
More informationIntorduction to light sources, pinhole cameras, and lenses
Intorduction to light sources, pinhole cameras, and lenses Erik G. Learned-Miller Department of Computer Science University of Massachusetts, Amherst Amherst, MA 01003 October 26, 2011 Abstract 1 1 Analyzing
More informationYou may recall from previous work with solving quadratic functions, the discriminant is the value
8.0 Introduction to Conic Sections PreCalculus INTRODUCTION TO CONIC SECTIONS Lesson Targets for Intro: 1. Know and be able to eplain the definition of a conic section.. Identif the general form of a quadratic
More informationPerspective. Announcement: CS4450/5450. CS 4620 Lecture 3. Will be MW 8:40 9:55 How many can make the new time?
Perspective CS 4620 Lecture 3 1 2 Announcement: CS4450/5450 Will be MW 8:40 9:55 How many can make the new time? 3 4 History of projection Ancient times: Greeks wrote about laws of perspective Renaissance:
More informationPROJECTIONS PARALLEL CONICAL PROJECTIONS PROJECTIONS OBLIQUE ORTHOGRAPHIC PROJECTIONS PROJECTIONS
PROJECTIONS CONICAL PROJECTIONS PARALLEL PROJECTIONS OBLIQUE PROJECTIONS ORTHOGRAPHIC PROJECTIONS ISOMETRIC MULTI-VIEW an object; The Description of Forms Behind every drawing of an object is space relationship
More informationUnderstanding Projection Systems
Understanding Projection Systems A Point: A point has no dimensions, a theoretical location that has neither length, width nor height. A point shows an exact location in space. It is important to understand
More informationCS123 INTRODUCTION TO COMPUTER GRAPHICS. Viewing. Part I (History and Overview of Projections) Andries van Dam 1 / 46 10/05/2017
Viewing Part I (History and Overview of Projections) 1 / 46 Lecture Topics History of projection in art Geometric constructions Types of projection (parallel and perspective) 2 / 46 CS123 INTRODUCTION
More informationORTHOGRAPHIC PROJECTIONS. Ms. Sicola
ORTHOGRAPHIC PROJECTIONS Ms. Sicola Objectives List the six principal views of projection Sketch the top, front and right-side views of an object with normal, inclined, and oblique surfaces Objectives
More informationChapter 4 ORTHOGRAPHIC PROJECTION
Chapter 4 ORTHOGRAPHIC PROJECTION 4.1 INTRODUCTION We, the human beings are gifted with power to think. The thoughts are to be shared. You will appreciate that different ways and means are available to
More informationPerspective Notes 8 th Grade Art
Perspective Notes 8 th Grade Art Perspective Perspective is the representation of three-dimensional objects on a flat twodimensional surface. In perspective drawing, objects are made to recede in space
More information60 Most Important Engineering Drawing Questions
1. If a client of yours is having difficulty visualizing a design, what type of drawing would be the easiest to understand? A. axonometric B. three-view orthographic C. one-view orthographic D. bimetric
More informationLecture 7: homogeneous coordinates
Lecture 7: homogeneous Dr. Richard E. Turner (ret26@cam.ac.uk) October 31, 2013 House keeping webpage: http://cbl.eng.cam.ac.uk/public/turner/teaching Recap of last lecture: Pin hole camera image plane
More informationTechnological Design Mr. Wadowski. Orthographic & Isometric Drawing Lesson
Technological Design Mr. Wadowski Orthographic & Isometric Drawing Lesson TOPICS Working Drawings, Isometric Drawings & Orthographic Drawings Glass box concept Multiview projection Orthographic projection
More informationReavis High School Curriculum Snapshot/Cover Page for Computer Aided Design (CAD)
Reavis High School Curriculum Snapshot/Cover Page for Computer Aided Design (CAD) Unit 1: Introduction In this unit, students will identify components of a Computer Aided Design (CAD) system and how to
More informationChapter 5 Pictorial sketching
Chapter 5 Pictorial sketching Contents Freehand sketching techniques Pictorial projections - Axonometric - Oblique Isometric projection vs isometric sketch Isometric sketch from an orthographic views Isometric
More informationDrawing sheet: - The various size of the drawing sheet used for engineering drawing as per IS Are listed in the table
Dronacharya Group of Institutions, Greater Noida Computer Aided Engineering Graphics (CAEG) (NCE 151/251) List of Drawing Sheets: 1. Letter writing & Dimensioning. 2. Projection of Points & Lines. 3. Projection
More informationENGINEERING GRAPHICS 1E9
Lecture 3 Monday, 15 December 2014 1 ENGINEERING GRAPHICS 1E9 Lecture 3: Isometric Projections Lecture 3 Monday, 15 December 2014 2 What is ISOMETRIC? It is a method of producing pictorial view of an object
More information6.1 INTRODUCTION Chapter 6 ORTHOGRAPHIC PROJECTIONS OF SIMPLE MACHINE BLOCKS We have already made you aware of many simple geometrical shapes (laminae), projected on such planes (vertical plane, horizontal
More informationMath 7 Notes - Unit 08B (Chapter 5B) Proportions in Geometry
Math 7 Notes - Unit 8B (Chapter B) Proportions in Geometr Sllabus Objective: (6.23) The student will use the coordinate plane to represent slope, midpoint and distance. Nevada State Standards (NSS) limits
More informationProjection. Announcements. Müller-Lyer Illusion. Image formation. Readings Nalwa 2.1
Announcements Mailing list (you should have received messages) Project 1 additional test sequences online Projection Readings Nalwa 2.1 Müller-Lyer Illusion Image formation object film by Pravin Bhat http://www.michaelbach.de/ot/sze_muelue/index.html
More information4.5 Equations of Parallel and Perpendicular Lines
Name Class Date.5 Equations of Parallel and Perpendicular Lines Essential Question: How can ou find the equation of a line that is parallel or perpendicular to a given line? Resource Locker Eplore Eploring
More informationMULTIPLE CHOICE QUESTIONS - CHAPTER 6
MULTIPLE CHOICE QUESTIONS - CHAPTER 6 1. The selection of the front view in executing a multiview drawing of an object is dependent upon the following factors: a. size and shape of the object and their
More informationElliptic Partial Differential Equations
Elliptic Partial Differential Equations http://numericalmethods.eng.usf.edu ransforming Numerical Methods Education for SEM Undergraduates 9/4/ http://numericalmethods.eng.usf.edu Defining Elliptic PDE
More informationUNIT 2 LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set 2: Relations Versus Functions/Domain and Range
UNIT LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set : Relations Versus Functions/Domain and Range Station You will be given a ruler and graph paper. As a group, use our ruler to determine
More informationHow do we see the world?
The Camera 1 How do we see the world? Let s design a camera Idea 1: put a piece of film in front of an object Do we get a reasonable image? Credit: Steve Seitz 2 Pinhole camera Idea 2: Add a barrier to
More informationTIME SCHEDULE. Module Topic Periods 1 Importance of Engineering Graphics Drawing Instruments Drawing Standards Lettering and Numbering
COURSE TITLE : ENGINEERING GRAPHICS (First Semester) COURSE CODE : COURSE CATEGORY : F PERIODS/WEEK : 3 PERIODS/SEMESTER : 54 CREDITS : Examination in the Second Semester RATIONALE: Engineering Graphics
More informationName Date. and y = 5.
Name Date Chapter Fair Game Review Evaluate the epression when = and =.... 0 +. 8( ) Evaluate the epression when a = 9 and b =.. ab. a ( b + ) 7. b b 7 8. 7b + ( ab ) 9. You go to the movies with five
More informationVirtual and Digital Cameras
CS148: Introduction to Computer Graphics and Imaging Virtual and Digital Cameras Ansel Adams Topics Effect Cause Field of view Film size, focal length Perspective Lens, focal length Focus Dist. of lens
More informationGraphical Communication
Chapter 9 Graphical Communication mmm Becoming a fully competent engineer is a long yet rewarding process that requires the acquisition of many diverse skills and a wide body of knowledge. Learning most
More informationTechnology Education Grades Drafting I
Technology Education Grades 9-12 Drafting I 46 Grade Level: 9, 10, 11, 12 Technology Education, Grades 9-12 Drafting I Prerequisite: None Drafting I is an elective course which provides students the opportunity
More informationSolutions to Exercise problems
Brief Overview on Projections of Planes: Solutions to Exercise problems By now, all of us must be aware that a plane is any D figure having an enclosed surface area. In our subject point of view, any closed
More informationA Concise Introduction to Engineering Graphics
Concise Introduction to Engineering Graphics ourth Edition Including Worksheet Series imothy J. Sexton, Professor Department of Industrial echnology Ohio University ONUS ook on CD: ECHNICL GRPHICS Meyers,
More informationInterpretation of Drawings. An Introduction to the Basic Concepts of Creating Technical Drawings
Interpretation of Drawings An Introduction to the Basic Concepts of Creating Technical Drawings Introduction In the design process drawings are the main way in which information about an object or product
More informationAutodesk Inventor. In Engineering Design & Drafting. By Edward Locke
Autodesk Inventor In Engineering Design & Drafting By Edward Locke Engineering Design Drafting Essentials Working Drawings: Orthographic Projection Views (multi-view, auxiliary view, details and sections)
More informationProjection. Readings. Szeliski 2.1. Wednesday, October 23, 13
Projection Readings Szeliski 2.1 Projection Readings Szeliski 2.1 Müller-Lyer Illusion by Pravin Bhat Müller-Lyer Illusion by Pravin Bhat http://www.michaelbach.de/ot/sze_muelue/index.html Müller-Lyer
More informationDr. Reham Karam. Perspective Drawing. For Artists & Designers. By : Dr.Reham Karam
Perspective Drawing For Artists & Designers By : Dr.Reham Karam Geometry and Art : What is perspective? Perspective, in the vision and visual perception, is : the way that objects appear to the eye based
More informationPerspective in 2D Games
Lecture 16 in 2D Games Take Away for Today What is game camera? How does it relate to screen space? Object space? How does camera work in a 2D game? 3D? How do we give 2D games depth? Advantages, disadvantages
More informationC.3 Review of Trigonometric Functions
C. Review of Trigonometric Functions C7 C. Review of Trigonometric Functions Describe angles and use degree measure. Use radian measure. Understand the definitions of the si trigonometric functions. Evaluate
More information