DOCSLIB.ORG

Engineering Computer Graphics

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Engineering Computer Graphics ENGR126 – Engineering Computer Graphics Lecture 6 Jaehwan Choi, Ph.D. Adjunct Faculty Department of Mechanical Engineering Today’s Topics Fundamentals of Descriptive Geometry 1/2/2014 2 INTRODUCTION Descriptive geometry is the graphic representation of plane, solid, and analytical geometry used to describe real or imagined technical devices and objects. The concepts of descriptive geometry can be applied to solving spatial problems. The basic geometric elements of points, lines, and planes are defined by example problems. 1/2/2014 3 Descriptive Geometry Methods The application of descriptive geometry is used in the design of chemical plants. 1/2/2014 4 Descriptive Geometry Methods Direct view method Revolution method Fold-line method 1/2/2014 5 Descriptive Geometry Methods The direct view method, sometimes referred to as the natural method, places the observer at an infinite distance from the object, with the observer's line of sight perpendicular to the geometry in question. 1/2/2014 6 Descriptive Geometry Methods In the revolution method geometry, such as a point, line, plane, or entire object is revolved about an axis until that geometry is parallel to the plane of projection that will show the true shape of the revolved geometry. 1/2/2014 7 Descriptive Geometry Methods An oblique face has been revolved to bring it parallel to the profile plane, in which the true shape of that surface is shown. The revolution method is satisfactory when a single entity or simple geometry is revolved; however, when the geometry is complex, this method tends to be confusing. 1/2/2014 8 Descriptive Geometry Methods The folding line method is also referred to as the glass box method, which was discussed in previous classes. Using the folding line method the oblique face is projected onto an auxiliary plane, which is placed parallel to it. The difference between this method and the revolution method In the revolution method, the geometry is revolved to one of the principal projection planes, while the fold-line method uses an auxiliary plane parallel to the desired geometry. The auxiliary projection plane then is "unfolded" so the projection plane is perpendicular to the line of sight. 1/2/2014 9 Descriptive Geometry Methods 1/2/2014 10 Points A point has no width, height, or depth. A point represents a specific position in space as well as the end view of a line or the intersection of two lines. The graphical representation of a point is a small symmetrical cross. 1/2/2014 11 The Coordinate System With the Cartesian coordinate system, points are located with respect to the origin (0,0,0) and to each other. 1/2/2014 12 LINES A line is a geometric primitive that has no thickness, only length and direction. A line can graphically represent the intersection of two surfaces, the edge view of a surface, or the limiting element of a surface. Lines are either vertical, horizontal, or inclined. 1/2/2014 13 LINES A vertical line is defined as a line that is perpendicular to the horizontal plane. 1/2/2014 14 LINES A line is defined as horizontal if all points are at the same height or elevation. Multiview representation of horizontal lines 1/2/2014 15 LINES An inclined line has one end higher than the other (but not at 90 degrees). An inclined line can only be described as inclined in a front or side view; in the top view, it can appear in a variety of positions. 1/2/2014 16 LINES A true length line is the actual straight-line distance between two points. In orthographic projection, a true-length line must be parallel to a projection plane. 1/2/2014 17 LINES A line can also appear as a point, called an end or point view. This occurs when the line of sight is parallel to the true-length line. The point view of a line cannot be orthographically determined without first drawing the line in a true length position. 1/2/2014 18 LINES Z X Y Z Y X 1/2/2014 19 LINES 1/2/2014 20 LINES In orthographic projection, the point view of a line is found in an adjacent view of the true-length line view. 1/2/2014 21 LINES A principal line is parallel to one of the three principal projection planes. A line that is not parallel to any of the three projection planes is called an oblique line and will appear foreshortened in any of these planes. A frontal line is a principal line that is parallel to, and therefore true length in, a frontal plane. 1/2/2014 22 LINES Frontal Line 1/2/2014 23 LINES A horizontal line is a principal line that is parallel to, and therefore true length in, a horizontal plane. 1/2/2014 24 LINES A profile line is a principal line that is parallel to, and therefore true length in, a profile plane. 1/2/2014 25 LINES If a point lies on a line, it must appear as a point on that line in all views of the line. 1/2/2014 26 LINES If a line is positioned parallel to a projection plane and the line of sight is perpendicular to that projection plane, the line will appear as true length. 1/2/2014 27 LINES Finding the true length of a line by the auxiliary view method. 1/2/2014 28 LINES 1/2/2014 29 LINES An application of finding the true length of a line. Exhaust system 1/2/2014 30 LINES It sometimes is more practical to find the true length of a line by the revolution method. 1/2/2014 31 LINES Finding the true length of a line by the revolution method. 1/2/2014 32 LINES 1/2/2014 33 PLANES A plane is positioned by locating any three points on the plane that are not in a straight line. Theoretically, planes are limitless; in actual practice, planes are bounded by straight or curved lines. In orthographic projection planes can appear as: (1) edges, (2) true size and shape, or (3) foreshortened. 1/2/2014 34 PLANES Planes can be graphically represented in four ways: (1) two intersecting lines, (2) two parallel lines, (3) three points not in a straight line, or (4) a point and a line. 1/2/2014 35 PLANES 1/2/2014 36 PLANES Planes are classified as horizontal, vertical, or inclined. A horizontal plane always appears true size and shape (TSP) in the top and bottom views, and as an edge in the front, back, and profile views. 1/2/2014 37 PLANES A vertical plane always appears as an edge in the top and bottom views, however it may appear in several positions in the front and profile views. When a vertical plane appears as an edge view in the front view and is parallel to the profile projection plane it called a profile plane. A vertical plane that is parallel to the frontal plane and appears as an edge in the profile view is called a frontal plane. 1/2/2014 38 PLANES 1/2/2014 39 PLANES An inclined plane is perpendicular to a principal projection plane but not parallel. A inclined plane never appears true size and shape in a principal view. 1/2/2014 40 PLANES A plane that appears as a surface in all three principal views is called an oblique plane. 1/2/2014 41 PLANES Any surface view of a plane must have a similar configuration as the plane (i.e., the same number of sides and similar shape.) 1/2/2014 42 PLANES The edge view of a plane occurs when your line of sight is parallel to the plane. If a line in the plane appears as a point, a plane appears as an edge. 1/2/2014 43 PLANES Finding the edge view of a plane using the auxiliary view method. 1/2/2014 44 PLANES A true-size plane must be perpendicular to the line of sight and must appear as an edge in all adjacent views. Finding a true-size plane view of a plane using the auxiliary view method. 1/2/2014 45 PLANES 1/2/2014 46 PLANES To measure the angle between two planes or surfaces, you must construct a view where both planes are on edge. Angle between surfaces – windshields on airplane Intersection of the two sloping sections of the roof on a house 1/2/2014 47 PLANES 1/2/2014 48 .
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]
  • Viewing in 3D
    Viewing in 3D Viewing in 3D Foley & Van Dam, Chapter 6 • Transformation Pipeline • Viewing Plane • Viewing Coordinate System • Projections • Orthographic • Perspective OpenGL Transformation Pipeline Viewing Coordinate System Homogeneous coordinates in World System zw world yw ModelViewModelView Matrix Matrix xw Tractor Viewing System Viewer Coordinates System ProjectionProjection Matrix Matrix Clip y Coordinates v Front- xv ClippingClipping Wheel System P0 zv ViewportViewport Transformation Transformation ne pla ing Window Coordinates View Specifying the Viewing Coordinates Specifying the Viewing Coordinates • Viewing Coordinates system, [xv, yv, zv], describes 3D objects with respect to a viewer zw y v P v xv •A viewing plane (projection plane) is set up N P0 zv perpendicular to zv and aligned with (xv,yv) yw xw ne pla ing • In order to specify a viewing plane we have View to specify: •P0=(x0,y0,z0) is the point where a camera is located •a vector N normal to the plane • P is a point to look-at •N=(P-P)/|P -P| is the view-plane normal vector •a viewing-up vector V 0 0 •V=zw is the view up vector, whose projection onto • a point on the viewing plane the view-plane is directed up Viewing Coordinate System Projections V u N z N ; x ; y z u x • Viewing 3D objects on a 2D display requires a v v V u N v v v mapping from 3D to 2D • The transformation M, from world-coordinate into viewing-coordinates is: • A projection is formed by the intersection of certain lines (projectors) with the view plane 1 2 3 ª x v x v x v 0 º ª 1 0 0 x 0 º « » «
    [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]
  • Squaring the Circle in Panoramas
    Squaring the Circle in Panoramas Lihi Zelnik-Manor1 Gabriele Peters2 Pietro Perona1 1. Department of Electrical Engineering 2. Informatik VII (Graphische Systeme) California Institute of Technology Universitat Dortmund Pasadena, CA 91125, USA Dortmund, Germany http://www.vision.caltech.edu/lihi/SquarePanorama.html Abstract and conveying the vivid visual impression of large panora- mas. Such mosaics are superior to panoramic pictures taken Pictures taken by a rotating camera cover the viewing with conventional fish-eye lenses in many respects: they sphere surrounding the center of rotation. Having a set of may span wider fields of view, they have unlimited reso- images registered and blended on the sphere what is left to lution, they make use of cheaper optics and they are not be done, in order to obtain a flat panorama, is projecting restricted to the projection geometry imposed by the lens. the spherical image onto a picture plane. This step is unfor- The geometry of single view point panoramas has long tunately not obvious – the surface of the sphere may not be been well understood [12, 21]. This has been used for mo- flattened onto a page without some form of distortion. The saicing of video sequences (e.g., [13, 20]) as well as for ob- objective of this paper is discussing the difficulties and op- taining super-resolution images (e.g., [6, 23]). By contrast portunities that are connected to the projection from view- when the point of view changes the mosaic is ‘impossible’ ing sphere to image plane. We first explore a number of al- unless the structure of the scene is very special.
    [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]
  • CS 4204 Computer Graphics 3D Views and Projection
    CS 4204 Computer Graphics 3D views and projection Adapted from notes by Yong Cao 1 Overview of 3D rendering Modeling: * Topic we’ve already discussed • *Define object in local coordinates • *Place object in world coordinates (modeling transformation) Viewing: • Define camera parameters • Find object location in camera coordinates (viewing transformation) Projection: project object to the viewplane Clipping: clip object to the view volume *Viewport transformation *Rasterization: rasterize object Simple teapot demo 3D rendering pipeline Vertices as input Series of operations/transformations to obtain 2D vertices in screen coordinates These can then be rasterized 3D rendering pipeline We’ve already discussed: • Viewport transformation • 3D modeling transformations We’ll talk about remaining topics in reverse order: • 3D clipping (simple extension of 2D clipping) • 3D projection • 3D viewing Clipping: 3D Cohen-Sutherland Use 6-bit outcodes When needed, clip line segment against planes Viewing and Projection Camera Analogy: 1. Set up your tripod and point the camera at the scene (viewing transformation). 2. Arrange the scene to be photographed into the desired composition (modeling transformation). 3. Choose a camera lens or adjust the zoom (projection transformation). 4. Determine how large you want the final photograph to be - for example, you might want it enlarged (viewport transformation). Projection transformations Introduction to Projection Transformations Mapping: f : Rn Rm Projection: n > m Planar Projection: Projection on a plane.
    [Show full text]
  • Perspective Projection
    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 lines. In perspective projection, object position are transformed to the view plane along lines that converge to a point called projection reference point (center of projection) 2 Perspective Projection 3 Parallel Projection 4 PROJECTIONS PARALLEL PERSPECTIVE (parallel projectors) (converging projectors) One point Oblique Orthographic (one principal (projectors perpendicular (projectors not perpendicular to vanishing point) to view plane) view plane) Two point General (Two principal Multiview Axonometric vanishing point) (view plane parallel (view plane not parallel to Cavalier principal planes) to principal planes) Three point (Three principal Cabinet vanishing point) Isometric Dimetric Trimetric 5 Perspective v Parallel • Perspective: – visual effect is similar to human visual system... – has 'perspective foreshortening' • size of object varies inversely with distance from the center of projection. Projection of a distant object are smaller than the projection of objects of the same size that are closer to the projection plane. • Parallel: It preserves relative proportion of object. – less realistic view because of no foreshortening – however, parallel lines remain parallel. 6 Perspective Projections • Characteristics: • Center of Projection (CP) is a finite distance from object • Projectors are rays (i.e., non-parallel) • Vanishing points • Objects appear smaller as distance from CP (eye of observer) increases • Difficult to determine exact size and shape of object • Most realistic, difficult to execute 7 • When a 3D object is projected onto view plane using perspective transformation equations, any set of parallel lines in the object that are not parallel to the projection plane, converge at a vanishing point.
    [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]