DOCSLIB.ORG

Engineering Drawing & Descriptive Geometry II Lecture 1

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Engineering Drawing & Descriptive Geometry II Lecture 1 Engineering Drawing & Descriptive Geometry II Lecture 1 Mr. AHMED SAMIR M.Sc. P. E. Material Science AHMED SAMIR [email protected] INRODUCTION Descriptive Geometry: It is a science deals with the treatment way of representation of geometrical solids having three dimensions (length, width (breadth), and thickness) on the paper plane surface which has only two dimensions (length, width) in another word the descriptive geometry is the graphical solution of point, line, and plane in space. Descriptive Geometry is a method to study three dimensions (3D) geometry through two dimensions (2D) images. It provides insight into structure and metrical properties of spatial objects, processes and principles. Applications of D.G.: This subject deals with graphic representation of solid objects having three dimensions (length, width (breadth), and thickness) upon a plan surface of paper which has only two dimensions (length, width), It deals with the graphical solution of problems which are difficult to solve analytically such as determination of: True length of lines and true shapes of objects for representations made on the paper; Pictorial drawing for example isometric, perspective, and oblique projections; Development of surfaces for sheet metal working; Paths traced out by curve surface along a straight path and along curved surfaces. AHMED SAMIR 2 DEFINITIONS Throughout our study, repeatedly we are using the following terms, understanding their meaning is imperative for proper study of descriptive geometry. SOLID OBJECT It is any system which occupying a displacement in the space. It has three dimensions (length, width (breadth), and thickness). The amount of occupying space is its volume. SURFACE It is the boundary which separates the object from surrounding. It has two dimensions (length, width). LINE It is the path of a moving point. Also it can be defined as a thing that surrounds (bounds) the surface. It has only one dimension which its length. There are many types of lines:- AHMED SAMIR 3 DEFINITIONS 1. Straight Line: It is the path of a point moving forward in one direction. It has a definite length which assigned by its two ends. Any two points on the line can be chosen and locate on the entire new line. a) Inclined Line: It is a line neither horizontal nor vertical. It can appear in its true length on either front or profile plane but its projection on the horizontal plane is shorter than its true length. b) Oblique (Skew) line: It is a line inclined to all three principal planes; it doesn’t appear in its true length on anyone of them. c) Vertical line: It is a line parallel to plumb line and it is perpendicular to a level plane. Its true length appears on any elevation view. d) Horizontal line: It is a line parallel to Still Water Lake; therefore all points which lie on the line are at the same elevation. It always appears in its true length on horizontal plane. AHMED SAMIR 4 DEFINITIONS e) Frontal line: It is a line parallel to the image front plane. It appears in its true length on front plane. f) Profile line: It is a line parallel to the image profile plane. It appears in its true length on profile plane. g) Principle Line: It is a line parallel to both of the two principal line planes (horizontal & vertical) and it is perpendicular to the profile plane, therefore its true length appears on the both horizontal and front planes, while its projection on the profile plane is a point. It is parallel to the ground line. h) Reference Line (Ground Line): It is a line originated from intersecting of two principal planes of projection, it is denoted by G.L. and it has a great importance in solving problems. 2. Contour Line: It is a straight-curved line or curved line used in topographical drawing while locates a series of points at the same elevation; therefore the counter line can be considered level line. This line has a wide usage in Earth Sciences & Physical Geography. AHMED SAMIR 5 DEFINITIONS 3. Line of Sight: It is an imaginary straight line joining the center of the eye of the observer with the object viewed. POINT A point is simply a location. It has no dimension (shape or size), is usually represented by a small dot, and named by a capital letter. SHAPE This word is released to a group of points, lines, and surfaces of an object. PLANE It is the simplest surface, if any two points taken on that surface and jointed by a line, this line is lie on that surface, and this surface is called plane. The plane can be classified to these types:- 1. Horizontal Plane: It is the plane that any point lies on it are at the same elevation, the top of plane view is determined by projection of the object on this plane. The sight lights for it are vertical, i.e. they are perpendicular to it. AHMED SAMIR 6 DEFINITIONS 2. Frontal (Vertical Plane): It is an image plane at 90º to the horizontal and profile planes. The front view (elevation) is determined by projection of the object on this plane. The sight lights for it are horizontal, i.e. they are perpendicular to it. 3. Profile Plane: It is an image plane at right angles to both horizontal and vertical planes, the right and left side elevation views are determined by projection of the object on this plane. The sight lights for it are horizontal and parallel to the front plane, i.e. they are perpendicular to it. 4. Image Plane: There are planes which they are perpendicular to the sight lines; they are located between the eye of the observer and the object which being viewed. NORMAL VIEW It is the view which shows the true length of line or true shape (Size) of the plane. The normal view of the plane shows true size of any angle which being in that plane and also the true length of any lines on that plane too. AHMED SAMIR 7 DEFINITIONS Right Profile Plane Left Profile Plane AHMED SAMIR 8 SLOPE OF THE LINE It is the tangent of the angle between the line and horizontal plane. The slope of line to be determined, two coordinated have to be present; first the line should be shown in an elevation view and second the line must be appears in its true length on elevation view. BEARING The true bearing to a point is the angle measured in degrees in a clockwise direction from the north line. We will refer to the true bearing simply as the bearing. For example, the bearing of point P is 065º which is the number of degrees in the angle measured in a clockwise direction from the north line to the line joining the center of the compass at O with the point P (i.e. OP). The bearing of point Q is 300º which is the number of degrees in the angle measured in a clockwise direction from the north line to the line joining the center of the compass at O with the point Q (i.e. OQ). Note: All bearings are measured in a horizontal plane. AHMED SAMIR 9 PROJECTION When representing a three-dimensional object on the two-dimensional surface of our retina, of a camera film or array of sensors, of a paper sheet, or of a TV or computer screen, the number of dimensions is reduced from three to two. The general process of reducing the number of dimensions of a given object is called projection. The planar image of an object in three-dimensional space is found by passing a line through each point of the object and finding the intersections of these lines with the projection plane. These lines, the projectors, emanate from a single point called the center of projection. When the center of projection is at infinity, so that the projectors are all parallel, the projection is known as a parallel projection. When the center of projection is at a finite distance from the projection plane, the projection is known as a perspective projection. AHMED SAMIR 10 PROJECTION The projection methods can be classified as following: Planer Geometric Projection Parallel Perspective One Two Three Orthographic Oblique point point Point Multi-view Axonometric Cavalier Cabinet orthographic Isometric Di-metric Trimetric AHMED SAMIR 11 PROJECTION 1. Perspective (Central) Projections: A perspective projection represents an object as it would be seen by an observer positioned at a certain vantage point. An object appears smaller as its distance from the observer increases, and parallel lines of an object converge in the drawing. • Observer is at finite distance. • Rays or Projectors are converging at observer’s eye. • It does not provide exact size and shape of object. 2. Parallel projection: In this type of projection the center of projection is at infinity, so the projectors are all parallel. The classification of parallel projections is determined by the angle between the projectors and the projection plane. When the projectors are perpendicular to the projection plane, the projection is orthographic; otherwise, it is oblique. Orthographic projections are represented either as multi-view orthographic projections or axonometric projections. AHMED SAMIR 12 PROJECTION 2.1. Oblique Projection: • Observer is at infinite distance. • Rays or Projectors are parallel to each other. • Rays or Projectors are not perpendicular to the Plane of projection (i.e. projectors are inclined to the plane of projection i.e. oblique). 2.2. Orthogonal Projection: is a means of representing a three-dimensional object in two dimensions. It is a form of parallel projection, where the view direction is orthogonal to the projection plane.
Load more

Recommended publications
  • Mathematics Is a Gentleman's Art: Analysis and Synthesis in American College Geometry Teaching, 1790-1840 Amy K
    Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 2000 Mathematics is a gentleman's art: Analysis and synthesis in American college geometry teaching, 1790-1840 Amy K. Ackerberg-Hastings Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Higher Education and Teaching Commons, History of Science, Technology, and Medicine Commons, and the Science and Mathematics Education Commons Recommended Citation Ackerberg-Hastings, Amy K., "Mathematics is a gentleman's art: Analysis and synthesis in American college geometry teaching, 1790-1840 " (2000). Retrospective Theses and Dissertations. 12669. https://lib.dr.iastate.edu/rtd/12669 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margwis, and improper alignment can adversely affect reproduction. in the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted.
    [Show full text]
  • Elements of Descriptive Geometry
    Livre de Lyon Academic Works of Livre de Lyon Science and Mathematical Science 2020 Elements of Descriptive Geometry Francis Henney Smith Follow this and additional works at: https://academicworks.livredelyon.com/sci_math Part of the Geometry and Topology Commons Recommended Citation Smith, Francis Henney, "Elements of Descriptive Geometry" (2020). Science and Mathematical Science. 13. https://academicworks.livredelyon.com/sci_math/13 This Book is brought to you for free and open access by Livre de Lyon, an international publisher specializing in academic books and journals. Browse more titles on Academic Works of Livre de Lyon, hosted on Digital Commons, an Elsevier platform. For more information, please contact [email protected]. ELEMENTS OF Descriptive Geometry By Francis Henney Smith Geometry livredelyon.com ISBN: 978-2-38236-008-8 livredelyon livredelyon livredelyon 09_Elements of Descriptive Geometry.indd 1 09-08-2020 15:55:23 TO COLONEL JOHN T. L. PRESTON, Professor of Latin Language and English Literature, Vir- ginia Military Institute. I am sure my associate Professors will vindicate the grounds upon which you arc singled out, as one to whom I may appro- priately dedicate this work. As the originator of the scheme, by which the public guard of a State Arsenal was converted into a Military School, you have the proud distinction of being the “ Father of the Virginia Military Institute ” You were a member of the first Board of Visitors, which gave form to the organization of the Institution; you were my only colleague during the two first and trying years of its being; and you have, for a period of twenty-eight years, given your labors and your influence, in no stinted mea- sure, not only in directing the special department of instruc- tion assigned to you, but in promoting those general plans of development, which have given marked character and wide- spread reputation to the school.
    [Show full text]
  • An Analytical Introduction to Descriptive Geometry
    An analytical introduction to Descriptive Geometry Adrian B. Biran, Technion { Faculty of Mechanical Engineering Ruben Lopez-Pulido, CEHINAV, Polytechnic University of Madrid, Model Basin, and Spanish Association of Naval Architects Avraham Banai Technion { Faculty of Mathematics Prepared for Elsevier (Butterworth-Heinemann), Oxford, UK Samples - August 2005 Contents Preface x 1 Geometric constructions 1 1.1 Introduction . 2 1.2 Drawing instruments . 2 1.3 A few geometric constructions . 2 1.3.1 Drawing parallels . 2 1.3.2 Dividing a segment into two . 2 1.3.3 Bisecting an angle . 2 1.3.4 Raising a perpendicular on a given segment . 2 1.3.5 Drawing a triangle given its three sides . 2 1.4 The intersection of two lines . 2 1.4.1 Introduction . 2 1.4.2 Examples from practice . 2 1.4.3 Situations to avoid . 2 1.5 Manual drawing and computer-aided drawing . 2 i ii CONTENTS 1.6 Exercises . 2 Notations 1 2 Introduction 3 2.1 How we see an object . 3 2.2 Central projection . 4 2.2.1 De¯nition . 4 2.2.2 Properties . 5 2.2.3 Vanishing points . 17 2.2.4 Conclusions . 20 2.3 Parallel projection . 23 2.3.1 De¯nition . 23 2.3.2 A few properties . 24 2.3.3 The concept of scale . 25 2.4 Orthographic projection . 27 2.4.1 De¯nition . 27 2.4.2 The projection of a right angle . 28 2.5 The two-sheet method of Monge . 36 2.6 Summary . 39 2.7 Examples . 43 2.8 Exercises .
    [Show full text]
  • Understanding Projection Systems
    Understanding 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 that a point is not an object, but a position. We represent a point by placing a dot with a pencil. A Line: A line is a geometric object that has length and direction but no thickness. A line may be straight or curved. A line may be infinitely long. If a line has a definite length it is called a line segment or curve segment. A straight line is the shortest distance between two points which is known as the true length of the line. A line is named using letters to indicate its endpoints. B B A A AB - Straight Line Segment AB – Curved Line Segment A line may be seen as the locus of a point as it travels between two points. A B A line can graphically represent the intersection of two surfaces, the edge view of a surface, or the limiting element of a surface. B A Plane: A plane is a flat surface which is infinitely large with zero thickness. Just as a point generates a line, a line can generate a plane. A A portion of a plane is referred to as a lamina. A Plane may be defined in a number of different ways. - 1 - Understanding Projection Systems A plane may be defined by; (i) 3 non-linear points (ii) A line and a point (iii) Two intersecting lines (iv) Two Parallel Lines (The point can not lie on the line) Descriptive Geometry: refers to the representation of 3D objects in a 2D format using points, lines and planes.
    [Show full text]
  • Descriptive Geometry Section 10.1 Basic Descriptive Geometry and Board Drafting Section 10.2 Solving Descriptive Geometry Problems with CAD
    10 Descriptive Geometry Section 10.1 Basic Descriptive Geometry and Board Drafting Section 10.2 Solving Descriptive Geometry Problems with CAD Chapter Objectives • Locate points in three-dimensional (3D) space. • Identify and describe the three basic types of lines. • Identify and describe the three basic types of planes. • Solve descriptive geometry problems using board-drafting techniques. • Create points, lines, planes, and solids in 3D space using CAD. • Solve descriptive geometry problems using CAD. Plane Spoken Rutan’s unconventional 202 Boomerang aircraft has an asymmetrical design, with one engine on the fuselage and another mounted on a pod. What special allowances would need to be made for such a design? 328 Drafting Career Burt Rutan, Aeronautical Engineer Effi cient travel through space has become an ambi- tion of aeronautical engineer, Burt Rutan. “I want to go high,” he says, “because that’s where the view is.” His unconventional designs have included every- thing from crafts that can enter space twice within a two week period, to planes than can circle the Earth without stopping to refuel. Designed by Rutan and built at his company, Scaled Composites LLC, the 202 Boomerang aircraft is named for its forward-swept asymmetrical wing. The design allows the Boomerang to fl y faster and farther than conventional twin-engine aircraft, hav- ing corrected aerodynamic mistakes made previously in twin-engine design. It is hailed as one of the most beautiful aircraft ever built. Academic Skills and Abilities • Algebra, geometry, calculus • Biology, chemistry, physics • English • Social studies • Humanities • Computer use Career Pathways Engineers should be creative, inquisitive, ana- lytical, detail oriented, and able to work as part of a team and to communicate well.
    [Show full text]
  • 3D Viewing Week 8, Lecture 15
    CS 536 Computer Graphics 3D Viewing Week 8, Lecture 15 David Breen, William Regli and Maxim Peysakhov Department of Computer Science Drexel University 1 Overview • 3D Viewing • 3D Projective Geometry • Mapping 3D worlds to 2D screens • Introduction and discussion of homework #4 Lecture Credits: Most pictures are from Foley/VanDam; Additional and extensive thanks also goes to those credited on individual slides 2 Pics/Math courtesy of Dave Mount @ UMD-CP 1994 Foley/VanDam/Finer/Huges/Phillips ICG Recall the 2D Problem • Objects exist in a 2D WCS • Objects clipped/transformed to viewport • Viewport transformed and drawn on 2D screen 3 Pics/Math courtesy of Dave Mount @ UMD-CP From 3D Virtual World to 2D Screen • Not unlike The Allegory of the Cave (Plato’s “Republic", Book VII) • Viewers see a 2D shadow of 3D world • How do we create this shadow? • How do we make it as realistic as possible? 4 Pics/Math courtesy of Dave Mount @ UMD-CP History of Linear Perspective • Renaissance artists – Alberti (1435) – Della Francesca (1470) – Da Vinci (1490) – Pélerin (1505) – Dürer (1525) Dürer: Measurement Instruction with Compass and Straight Edge http://www.handprint.com/HP/WCL/tech10.html 5 The 3D Problem: Using a Synthetic Camera • Think of 3D viewing as taking a photo: – Select Projection – Specify viewing parameters – Clip objects in 3D – Project the results onto the display and draw 6 1994 Foley/VanDam/Finer/Huges/Phillips ICG The 3D Problem: (Slightly) Alternate Approach • Think of 3D viewing as taking a photo: – Select Projection – Specify
    [Show full text]
  • Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (21St, Lahti, Finland, July 14-19, 1997)
    DOCUMENT RESUME ED 416 082 SE 061 119 AUTHOR Pehkonen, Erkki, Ed. TITLE Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (21st, Lahti, Finland, July 14-19, 1997). Volume 1. INSTITUTION International Group for the Psychology of Mathematics Education. ISSN ISSN-0771-100X PUB DATE 1997-00-00 NOTE 335p.; For Volumes 2-4, see SE 061 120-122. PUB TYPE Collected Works Proceedings (021) EDRS PRICE MF01/PC14 Plus Postage. DESCRIPTORS Communications; *Educational Change; *Educational Technology; Elementary Secondary Education; Foreign Countries; Higher Education; *Mathematical Concepts; Mathematics Achievement; *Mathematics Education; Mathematics Skills; Number Concepts IDENTIFIERS *Psychology of Mathematics Education ABSTRACT The first volume of the proceedings of the 21st annual meeting of the International Group for the Psychology of Mathematics Education contains the following 13 full papers: (1) "Some Psychological Issues in the Assessment of Mathematical Performance"(0. Bjorkqvist); (2) "Neurcmagnetic Approach in Cognitive Neuroscience" (S. Levanen); (3) "Dilemmas in the Professional Education of Mathematics Teachers"(J. Mousley and P. Sullivan); (4) "Open Toolsets: New Ends and New Means in Learning Mathematics and Science with Computers"(A. A. diSessa); (5) "From Intuition to Inhibition--Mathematics, Education and Other Endangered Species" (S. Vinner); (6) "Distributed Cognition, Technology and Change: Themes for the Plenary Panel"(K. Crawford); (7) "Roles for Teachers, and Computers" (J. Ainley); (8) "Some Questions on Mathematical Learning Environments" (N. Balacheff); (9) "Deepening the Impact of Technology Beyond Assistance with Traditional Formalisms in Order To Democratize Access To Ideas Underlying Calculus"(J. J. Kaput and J. Roschelle); (10) "The Nature of the Object as an Integral Component of Numerical Processes"(E.
    [Show full text]
  • Descriptive Geometry for CAD Users: Ribs Construction
    Journal for Geometry and Graphics Volume 18 (2014), No. 1, 115–124. Descriptive Geometry for CAD Users: Ribs Construction Evgeniy Danilov Department of Graphics, Dnepropetrovsk National University of Railway Transport 2, Lazaryan str., Dnepropetrovsk, 49010, Ukraine email: [email protected] Abstract. In 3D modeling CAD users often face problems that can be success- fully analyzed and solved only by the methods of Descriptive Geometry. One such problem is considered in this paper: the construction of structural elements of machine parts known as stiffening ribs. In addition, a possible geometry of ribs is analyzed and a review is performed of tools for its modeling available in up-to- date CAD packages. Some features are shown that are useful in representing parts with ribs in technical drawing manuals. An innovative approach is developed for educational purposes. Key Words: stiffening rib, Descriptive Geometry, CAD MSC 2010: 51N05, 97U50 1. Introduction Most current curricula suggest that Descriptive Geometry training be done concurrently with practicing the use of one or more CAD packages. As students begin to use the powerful 3D modeling capabilities of these packages for solving problems of classical Descriptive Geom- etry, they also are mastering CAD. They often solve positional and metrical problems by modeling geometrical objects and their interaction in virtual 3D space [3, 6], thereby avoiding Descriptive Geometry methods. Afterward students do not see the necessity of spatial prob- lems being solved by using plane images and they lose interest in the study of Descriptive Geometry. That impedes their academic progress and their training as engineers. It can be argued that the study of Descriptive Geometry is not possible without clear examples of how its apparatus works in solving problems that arise in the process of 3D modeling.
    [Show full text]
  • U. S. Department of Agriculture Technical Release No
    U. S. DEPARTMENT OF AGRICULTURE TECHNICAL RELEASE NO. 41 SO1 L CONSERVATION SERVICE GEOLOGY &INEERING DIVISION MARCH 1969 U. S. Department of Agriculture Technical Release No. 41 Soil Conservation Service Geology Engineering Division March 1969 GRAPHICAL SOLUTIONS OF GEOLOGIC PROBLEMS D. H. Hixson Geologist GRAPHICAL SOLUTIONS OF GEOLOGIC PROBLEMS Contents Page Introduction Scope Orthographic Projections Depth to a Dipping Bed Determine True Dip from One Apparent Dip and the Strike Determine True Dip from Two Apparent Dip Measurements at Same Point Three Point Problem Problems Involving Points, Lines, and Planes Problems Involving Points and Lines Shortest Distance between Two Non-Parallel, Non-Intersecting Lines Distance from a Point to a Plane Determine the Line of Intersection of Two Oblique Planes Displacement of a Vertical Fault Displacement of an Inclined Fault Stereographic Projection True Dip from Two Apparent Dips Apparent Dip from True Dip Line of Intersection of Two Oblique Planes Rotation of a Bed Rotation of a Fault Poles Rotation of a Bed Rotation of a Fault Vertical Drill Holes Inclined Drill Holes Combination Orthographic and Stereographic Technique References Figures Fig. 1 Orthographic Projection Fig. 2 Orthographic Projection Fig. 3 True Dip from Apparent Dip and Strike Fig. 4 True Dip from Two Apparent Dips Fig. 5 True Dip from Two Apparent Dips Fig. 6 True Dip from Two Apparent Dips Fig. 7 Three Point Problem Fig. 8 Three Point Problem Page Fig. Distance from a Point to a Line 17 Fig. Shortest Distance between Two Lines 19 Fig. Distance from a Point to a Plane 21 Fig. Nomenclature of Fault Displacement 23 Fig.
    [Show full text]
  • National 4 & 5 Graphic Communication
    Duncanrig Secondary School Department of Design, Engineering & Technology National 4 & 5 Graphic Communication - Revision Notes Contents Page 01 Exam Preparation and Techniques 02 - 03 The 3 P’s 04 British Standards Purpose, title blocks and scale 05 British Standards Line types & 3rd Angle Projection 06 - 08 British Standards Dimensioning 09 Drawing Types: Overview and Introduction 10 Drawing Types: Orthographic Views 11 Drawing Types: Sectional Views and Exploded Views 12 Sectional Drawing guide for answering questions 13 - 14 Drawing Types: Geometry 15 Answering true shape exam questions 16 A/C and A/F explained 17 - 18 Drawing Types: Pictorial drawings and exam questions 19 Interpreting/Reading Complex drawings 20 - 23 Building Drawings 24 - 27 Computer Terminology, Hardware Input, Output and Storage 28 - 29 Computer Software 30 Computer Aided Design Software 31 - 35 2D/3D CAD Features and Edits 36 - 37 Answering 3D CAD exam questions 38 CAD Assembly constraints 39 CAD Animation and Simulation 40 CAD illustration Techniques 41 - 42 Advantages and Limitations of CAD and Manual Techniques 43 Manual Graphics Techniques 44 - 49 DTP features and edits 50 - 52 DTP Elements and Principles 50 - 52 Colour Theory 53 - 55 Graphics Impact on Society 56 Graphs and Charts 1 Exam Preparation What makes up my grade in Graphic Communication? The exam has written questions to test Knowledge and Interpretation skills in Graphic Communication. A grade A, B, C or D is awarded at National 5. 33% of your course award is made up of the graphics assignment which you undertake in class over a period of 8 hours. The exam is worth 67%.
    [Show full text]
  • Lecture (1) Definition of Descriptive Geometry: DG Is a Method to Study 3D Geometry Through 2D Images. the Aim of Descriptive Ge
    Lecture (1) Definition of Descriptive Geometry: DG is a method to study 3D geometry through 2D images. The aim of Descriptive Geometry is to describe the three - dimensional objects by two - dimensional drawings so as to allow reconstituting their original forms. The Theory of Projection Projection is the representation on a plane surface of the image of an object as it is observed by a viewer and the plane on which the image is represented is known as the Plane of Projection. If the eye is directed towards a body in a space, rays or projectors will come from the visible parts of the body and gathered at the eye in a point. The type of projection that produces the image in our eye is called Central Projection. The images produced by central projection convey the sensation of depth. If a plate ABCD as illustrated in figure (1) is placed in front of a plane of projection, and if we imagine that rays will pass from point (o) to the different points of the object, then the view abcd will be obtained. In this type of projection, point (o) is called the centre of projection. Plane of Projection a A B O b D Centre of Projection d C c Figure (1). 1 Descriptive Geometry is based on another type of projection that is called Parallel Projection or Orthographic Projection on Two Orthogonal Planes which is one of the cases of the parallel projection in which the shape description of a three dimensional is represented on drawing paper which is a two dimensional plane surface, and If we imagine that point (o), the centre of projection goes far away to infinity, the rays or projectors will become parallel to each other and normal to the plane of projection, and the view obtained is orthographic as illustrated in figures (2) and (3).
    [Show full text]
  • Descriptive Geometry and Digital Representation: Memory and Innovation I
    M l i Michela Rossi (editor) c Michela Rossi (editor) h e Michela Rossi (editor) l a R Nexus Ph.D. Day. Relationships between o s s l i ( e Architecture and Mathematics d i t o he IX edition of the International Conference Nexus-Relationships between Architecture and Mathematics at r ) Politecnico di Milano, sponsored by Department of Industrial Design and Department of Mathematics compris- T N NDescriptiveexus Ph .GeometryD. Day. and es a workshop dedicated to Ph.D. students. i e The event is sponsored by the Politecnico Ph.D. School and the Design Ph.D. program of Department INDA- x CO and by the National (Italian) Ph.D. School in “Science of Represen tation and Architectural Survey”. u s RDigitalelati oRepresentation:nships betw een The “Nexus Ph.D. Day” is meant to be an international and multi-disciplinary meeting between Ph.D. students P involved in scientific researches in the fields that are connected to the topic of the Conference. It intends to promote h . didactic and research exchanges trough interactions between various schools from different countries. D . AMemoryrchit eandct uInnovationre and This will give the opportunity to Ph.D. students and young Ph.D. fellow, who have di fensed their thesis in 2010 H or later, to show their work to a large international academic community, by the oral presentation of selected lecture D a and a poster session related to the conference one, to improve a meeting among people working on similar issues, y General Investigator Prof. Riccardo Migliari . Mathematics generally concerning the relationships between Architecture and Mathematics in all the different scales of design.
    [Show full text]