Technical Drawing School of Art, Design and Architecture Nust – Spring 2011
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Alvar Aalto's Associative Geometries
Alvar Aalto Researchers’ Network Seminar – Why Aalto? 9-10 June 2017, Jyväskylä, Finland Alvar Aalto’s associative geometries Holger Hoffmann Prof. Dipl.-Ing., Architekt BDA Fay Jones School of Architecture and Design Why Aalto?, 3rd Alvar Aalto Researchers Network Seminar, Jyväskylä 2017 Prof. Holger Hoffmann, Bergische Universität Wuppertal, April 30th, 2017 Paper Proposal ALVAR AALTO‘S ASSOCIATIVE GEOMETRIES This paper, written from a practitioner’s point of view, aims at describing Alvar Aalto’s use of associative geometries as an inspiration for contemporary computational design techniques and his potential influence on a place-specific version of today’s digital modernism. In architecture the introduction of digital design and communication techniques during the 1990s has established a global discourse on complexity and the relation between the universal and the specific. And however the great potential of computer technology lies in the differentiation and specification of architectural solutions, ‘place’ and especially ‘place-form’ has not been of greatest interest since. Therefore I will try to build a narrative that describes the possibilities of Aalto’s “elastic standardization” as a method of well-structured differentiation in relation to historical and contemporary methods of constructing complexity. I will then use a brief geometrical analysis of Aalto’s “Neue Vahr”-building to hint at a potential relation of his work to the concept of ‘difference and repetition’ that is one of the cornerstones of contemporary ‘parametric design’. With the help of two projects (one academic, one professional) I will furthermore try to show the capability of such an approach to open the merely generic formal vocabulary of so-called “parametricism” to contextual or regional necessities in a ‘beyond-digital’ way. -
CS 543: Computer Graphics Lecture 7 (Part I): Projection Emmanuel
CS 543: Computer Graphics Lecture 7 (Part I): Projection Emmanuel Agu 3D Viewing and View Volume n Recall: 3D viewing set up Projection Transformation n View volume can have different shapes (different looks) n Different types of projection: parallel, perspective, orthographic, etc n Important to control n Projection type: perspective or orthographic, etc. n Field of view and image aspect ratio n Near and far clipping planes Perspective Projection n Similar to real world n Characterized by object foreshortening n Objects appear larger if they are closer to camera n Need: n Projection center n Projection plane n Projection: Connecting the object to the projection center camera projection plane Projection? Projectors Object in 3 space Projected image VRP COP Orthographic Projection n No foreshortening effect – distance from camera does not matter n The projection center is at infinite n Projection calculation – just drop z coordinates Field of View n Determine how much of the world is taken into the picture n Larger field of view = smaller object projection size center of projection field of view (view angle) y y z q z x Near and Far Clipping Planes n Only objects between near and far planes are drawn n Near plane + far plane + field of view = Viewing Frustum Near plane Far plane y z x Viewing Frustrum n 3D counterpart of 2D world clip window n Objects outside the frustum are clipped Near plane Far plane y z x Viewing Frustum Projection Transformation n In OpenGL: n Set the matrix mode to GL_PROJECTION n Perspective projection: use • gluPerspective(fovy, -
Axonometric (Isometric Projection)
AXONOMETRIC (ISOMETRIC PROJECTION) Representation Systems Isometric Into the ISOMETRIC PERSPECTIVE, the isometric axes form a 120º angle between one another Elevation Profile Plan Isometric Into the ISOMETRIC PERSPECTIVE, the isometric axes form a 120º angle between one another Front View Isometric Into the ISOMETRIC PERSPECTIVE, the isometric axes form a 120º angle between one another Front View Isometric Into the ISOMETRIC PERSPECTIVE, the isometric axes form a 120º angle between one another Front View Isometric Into the ISOMETRIC PERSPECTIVE, the isometric axes form a 120º angle between one another Front View Isometric Into the ISOMETRIC PERSPECTIVE, the isometric axes form a 120º angle between one another Front View Isometric Into the ISOMETRIC PERSPECTIVE, the isometric axes form a 120º angle between one another Front View Isometric Into the ISOMETRIC PERSPECTIVE, the isometric axes form a 120º angle between one another Front View Isometric Into the ISOMETRIC PERSPECTIVE, the isometric axes form a 120º angle between one another Front View Isometric Into the ISOMETRIC PERSPECTIVE, the isometric axes form a 120º angle between one another Front View Isometric Into the ISOMETRIC PERSPECTIVE, the isometric axes form a 120º angle between one another Front View Isometric Into the ISOMETRIC PERSPECTIVE, the isometric axes form a 120º angle between one another Front View Isometric Into the ISOMETRIC PERSPECTIVE, the isometric axes form a 120º angle between one another Front View Isometric Into the ISOMETRIC PERSPECTIVE, the isometric axes form a 120º angle between one another Front View Isometric Into the ISOMETRIC PERSPECTIVE, the isometric axes form a 120º angle between one another Front View Isometric Into the ISOMETRIC PERSPECTIVE, the isometric axes form a 120º angle between one another Front View Isometric Into the ISOMETRIC PERSPECTIVE, the isometric axes form a 120º angle between one another Front View Technical Drawing Name and Surname: Axonometric System Draw the AXONOMETRIC PERSPECTIVE of these pieces. -
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 « » « -
'The "Perfyt Scyens" of the Map; a Study of the Meaning and Interpretation of Local Maps in Early Tudor England 1509-1547'
'The "Perfyt Scyens" of the Map; a Study of the Meaning and Interpretation of Local Maps in Early Tudor England 1509-1547' Lewis John Kaye Roberts Queen Mary, University of London 70,056 words (excluding bibliography) This work was supported by the AHRC (BGP award reference: 0673) A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy, University of London 1 Statement of Originality. I, Lewis Roberts, confirm that the research included within this thesis is my own work or that where it has been carried out in collaboration with, or supported by others, that this is duly acknowledged below and my contribution indicated. Previously published material is also acknowledged below. I attest that I have exercised reasonable care to ensure that the work is original, and does not to the best of my knowledge break any UK law, infringe any third party’s copyright or other Intellectual Property Right, or contain any confidential material. I accept that the College has the right to use plagiarism detection software to check the electronic version of the thesis. I confirm that this thesis has not been previously submitted for the award of a degree by this or any other university. The copyright of this thesis rests with the author and no quotation from it or information derived from it may be published without the prior written consent of the author. Signature: Date: 16th January 2014 2 Abstract. This thesis begins by examining an unexplored contextual background for sixteenth century local maps. It argues that the architectural drawing techniques developed by master masons in the late twelfth century continued to be taught to the King’s masons well into the sixteenth, and that these drawing techniques lie behind the innovations in sixteenth century topographical mapping. -
Implementation of Projections
CS488 Implementation of projections Luc RENAMBOT 1 3D Graphics • Convert a set of polygons in a 3D world into an image on a 2D screen • After theoretical view • Implementation 2 Transformations P(X,Y,Z) 3D Object Coordinates Modeling Transformation 3D World Coordinates Viewing Transformation 3D Camera Coordinates Projection Transformation 2D Screen Coordinates Window-to-Viewport Transformation 2D Image Coordinates P’(X’,Y’) 3 3D Rendering Pipeline 3D Geometric Primitives Modeling Transform into 3D world coordinate system Transformation Lighting Illuminate according to lighting and reflectance Viewing Transform into 3D camera coordinate system Transformation Projection Transform into 2D camera coordinate system Transformation Clipping Clip primitives outside camera’s view Scan Draw pixels (including texturing, hidden surface, etc.) Conversion Image 4 Orthographic Projection 5 Perspective Projection B F 6 Viewing Reference Coordinate system 7 Projection Reference Point Projection Reference Point (PRP) Center of Window (CW) View Reference Point (VRP) View-Plane Normal (VPN) 8 Implementation • Lots of Matrices • Orthographic matrix • Perspective matrix • 3D World → Normalize to the canonical view volume → Clip against canonical view volume → Project onto projection plane → Translate into viewport 9 Canonical View Volumes • Used because easy to clip against and calculate intersections • Strategies: convert view volumes into “easy” canonical view volumes • Transformations called Npar and Nper 10 Parallel Canonical Volume X or Y Defined by 6 planes -
Basic Engineering Drawings
Today’s Thoughts The thing that’s so wonderful about using beautiful, appropriate [CAD] tools is that they become an extension of you, your body, you fingertips, and your mind. They get out of the way and let you directly interact with the problem you are solving. Everyone’s tried to remove a screw without a screwdriver; a task quickly becomes impossible that otherwise would be trivial. — Luke Crawford Here is one of the few effective keys to the design problem — the ability of the designer to recognize as many of the constraints as possible — his willingness and enthusiasm for working within these constraints. Constraints of price, of size, of strength, of balance, of surface, of time and so forth. — Charles Eames Section Views ME 172 Outline • Full Section • Half Section • Offset Section • Broken-out Section • Revolved Section • Removed Section • Sectioning Problems • Sectioning Quiz A Section View Technical Drawing– by Giesecke Visualizing a Section View Technical Drawing– by Giesecke Visualizing a Section View Technical Drawing– by Giesecke A Cut Plane Line Technical Drawing– by Giesecke Full Section View Blueprint Reading Basics – by Warren Hammer Full Section View Technical Drawing– by Giesecke Correct Full Section View Technical Drawing– by Giesecke Correct Full Section View Technical Drawing– by Giesecke Correct Full Section View Technical Drawing– by Giesecke Sectioning Symbols Technical Drawing– by Giesecke Correct Sectioning Lines Technical Drawing– by Giesecke ProblemAligned Full with Section a Full Section Blueprint Reading -
EX NIHILO – Dahlgren 1
EX NIHILO – Dahlgren 1 EX NIHILO: A STUDY OF CREATIVITY AND INTERDISCIPLINARY THOUGHT-SYMMETRY IN THE ARTS AND SCIENCES By DAVID F. DAHLGREN Integrated Studies Project submitted to Dr. Patricia Hughes-Fuller in partial fulfillment of the requirements for the degree of Master of Arts – Integrated Studies Athabasca, Alberta August, 2008 EX NIHILO – Dahlgren 2 Waterfall by M. C. Escher EX NIHILO – Dahlgren 3 Contents Page LIST OF ILLUSTRATIONS 4 INTRODUCTION 6 FORMS OF SIMILARITY 8 Surface Connections 9 Mechanistic or Syntagmatic Structure 9 Organic or Paradigmatic Structure 12 Melding Mechanical and Organic Structure 14 FORMS OF FEELING 16 Generative Idea 16 Traits 16 Background Control 17 Simulacrum Effect and Aura 18 The Science of Creativity 19 FORMS OF ART IN SCIENTIFIC THOUGHT 21 Interdisciplinary Concept Similarities 21 Concept Glossary 23 Art as an Aid to Communicating Concepts 27 Interdisciplinary Concept Translation 30 Literature to Science 30 Music to Science 33 Art to Science 35 Reversing the Process 38 Thought Energy 39 FORMS OF THOUGHT ENERGY 41 Zero Point Energy 41 Schools of Fish – Flocks of Birds 41 Encapsulating Aura in Language 42 Encapsulating Aura in Art Forms 50 FORMS OF INNER SPACE 53 Shapes of Sound 53 Soundscapes 54 Musical Topography 57 Drawing Inner Space 58 Exploring Inner Space 66 SUMMARY 70 REFERENCES 71 APPENDICES 78 EX NIHILO – Dahlgren 4 LIST OF ILLUSTRATIONS Page Fig. 1 - Hofstadter’s Lettering 8 Fig. 2 - Stravinsky by Picasso 9 Fig. 3 - Symphony No. 40 in G minor by Mozart 10 Fig. 4 - Bird Pattern – Alhambra palace 10 Fig. 5 - A Tree Graph of the Creative Process 11 Fig. -
Drawing the “Boundaries”, the Start of an Urban Planning Project
Geographia Technica, Vol. 12, Issue 2, 2017, pp 73 to 81 DRAWING THE “BOUNDARIES”, THE START OF AN URBAN PLANNING PROJECT Jordi GOMIS1, Carlos TURÓN DOI: 10.21163/GT_2017.122.07 ABSTRACT: The graphic representation of the boundaries of urban planning areas is a sufficiently important element of the representation of urban planning as not to allow the slightest hint of doubt or imprecision to arise in regard to the dividing lines it indicates. It can include everything from the growth limit of the urban land as a whole to small inner areas of the city subject to improvement, renovation or change of planning conditions. It is this first concept that the town planner must include/draw on his working plan to begin his task. Throughout the history of urban planning, this first “boundary” has been represented in various ways using different graphic and/or visual mechanisms. This article presents a journey through the history of the resources used by technicians for their representation and their evolution. Key-words: Graphic representation, Technical drawing, Urban Planning, City drawing, Urbanism. 1. INTRODUCTION The demarcation of geographical, territorial, municipal, regional, etc. areas has never been a problem dissociated from society. Since ancient times the specification of geographic boundaries and limits of influence has occupied and preoccupied people. “Boundaries” and “frontiers” have always given rise to disputes that people have attempted to resolve and settle, sometimes graphically, many others, unfortunately, through the use of force. Various inventories of land, people, property, crops, etc. were made ever since ancient times to inform kings and noblemen of the quantity and quality of their belongings and properties. -
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. -
Map Projections
Map Projections Chapter 4 Map Projections What is map projection? Why are map projections drawn? What are the different types of projections? Which projection is most suitably used for which area? In this chapter, we will seek the answers of such essential questions. MAP PROJECTION Map projection is the method of transferring the graticule of latitude and longitude on a plane surface. It can also be defined as the transformation of spherical network of parallels and meridians on a plane surface. As you know that, the earth on which we live in is not flat. It is geoid in shape like a sphere. A globe is the best model of the earth. Due to this property of the globe, the shape and sizes of the continents and oceans are accurately shown on it. It also shows the directions and distances very accurately. The globe is divided into various segments by the lines of latitude and longitude. The horizontal lines represent the parallels of latitude and the vertical lines represent the meridians of the longitude. The network of parallels and meridians is called graticule. This network facilitates drawing of maps. Drawing of the graticule on a flat surface is called projection. But a globe has many limitations. It is expensive. It can neither be carried everywhere easily nor can a minor detail be shown on it. Besides, on the globe the meridians are semi-circles and the parallels 35 are circles. When they are transferred on a plane surface, they become intersecting straight lines or curved lines. 2021-22 Practical Work in Geography NEED FOR MAP PROJECTION The need for a map projection mainly arises to have a detailed study of a 36 region, which is not possible to do from a globe. -
189 09 Aju 03 Bryon 8/1/10 07:25 Página 31
189_09 aju 03 Bryon 8/1/10 07:25 Página 31 Measuring the qualities of Choisy’s oblique and axonometric projections Hilary Bryon Auguste Choisy is renowned for his «axonometric» representations, particularly those illustrating his Histoire de l’architecture (1899). Yet, «axonometric» is a misnomer if uniformly applied to describe Choisy’s pictorial parallel projections. The nomenclature of parallel projection is often ambiguous and confusing. Yet, the actual history of parallel projection reveals a drawing system delineated by oblique and axonometric projections which relate to inherent spatial differences. By clarifying the intrinsic demarcations between these two forms of parallel pro- jection, one can discern that Choisy not only used the two spatial classes of pictor- ial parallel projection, the oblique and the orthographic axonometric, but in fact manipulated their inherent differences to communicate his theory of architecture. Parallel projection is a form of pictorial representation in which the projectors are parallel. Unlike perspective projection, in which the projectors meet at a fixed point in space, parallel projectors are said to meet at infinity. Oblique and axonometric projections are differentiated by the directions of their parallel pro- jectors. Oblique projection is delineated by projectors oblique to the plane of pro- jection, whereas the orthographic axonometric projection is defined by projectors perpendicular to the plane of projection. Axonometric projection is differentiated relative to its angles of rotation to the picture plane. When all three axes are ro- tated so that each is equally inclined to the plane of projection, the axonometric projection is isometric; all three axes are foreshortened and scaled equally.