Main Architecture: Form, Space, and Order
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This is one of the best basic architectural reference works I've read. I got mine from an architect friend of my parents who had used it for years, when I was applying to a school of architecture many years ago, and still have my very old print copy that predates me. It's a useful reference, and the illustrations make it even a beautiful coffee table book, if your household does coffee table books.
08 May 2020 (01:05)
This is exactly what you need to understand the meaning of design and deliver your ideas as you wish for them since it breaks designs to it's basic elements
11 June 2020 (18:42)
ARCHITECTURE Form, Space, & Order Fourth Edition ARCHITECTURE Form, Space, & Order Fourth Edition Francis D.K. Ching Cover design: Wiley Cover image: Courtesy of Francis D.K. Ching This book is printed on acid-free ∞ paper. Copyright © 2015 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 646-8600, or on the web at www.copyright.com. 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If you wish to purchase access to the Interactive Resource Center, you can go to www.wiley.com/go/formspaceorder4e, click on "Student Companion Website" and then "Register," which will allow you to enter a code or to purchase access if you do not have a code. If you've purchased an e-Book version of this title please contact our Customer Care Department: Customer Care Center - Consumer Accounts 10475 Crosspoint Blvd. Indianapolis, IN 46256 Phone: (877) 762-2974 Fax: (800) 597-3299 Web: http://support.wiley.com Library of Congress Cataloging-in-Publication Data: Ching, Frank, 1943Architecture : form, space, & order / Francis D.K. Ching. -- Fourth edition. pages cm Includes bibliographical references and index. ISBN 978-1-118-74508-3 (paperback); 978-1-118-74513-7 (ebk); 978-1-118-74519-9 (ebk) 1. Architecture--Composition, proportion, etc. 2. Space (Architecture) I. Title. NA2760.C46 2014 720.1--dc23 201402021 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 C ON T E N T S Preface vii Acknowledgments viii Introduction ix 1 Primary Elements Primary Elements 2 Point 4 Point Elements 5 Two Points 6 Line 8 Linear Elements 10 Linear Elements Defining Planes 15 From Line to Plane 14 Plane 18 Planar Elements 20 Volume 28 Volumetric Elements 30 2 Form Form 34 Properties of Form 35 Shape 36 Primary Shapes 38 Circle 39 Triangle 40 Square 41 Surfaces 42 Curved Surfaces 43 Primary Solids 46 Regular & Irregular Forms 50 Transformation of Form 54 Dimensional Transformation 56 Subtractive Form 58 Subtractive & Additive Forms 61 Additive Form 62 Centralized Form 64 Linear Form 66 Radial Form 70 Clustered Form 72 Grid Form 76 Formal Collisions of Geometry 78 Circle & Square 80 Rotated Grid 82 Articulation of Form 84 Edges & Corners 86 Corners 87 Surface Articulation 92 3 Form & Space Form & Space 100 Form & Space: Unity of Opposites 102 Form Defining Space 110 Horizontal Elements Defining Space 111 Base Plane 112 Elevated Base Plane 114 Depressed Base Plane 120 Overhead Plane 126 Vertical Elements Defining Space 134 Vertical Linear Elements 136 Single Vertical Plane 144 L-Shaped Configuration of Planes 148 L-Shaped Planes 149 Parallel Vertical Planes 154 Parallel Planes 155 U-Shaped Planes 160 Four Planes: Closure 166 Four Planes: Enlosure 170 Openings in Space-Defining Elements 174 Openings within Planes 176 Openings at Corners 178 Openings between Planes 180 Qualities of Architectural Space 182 Degree of Enclosure 184 Light 186 View 190 4 Organization Organization of Form & Space 196 Spatial Relationships 197 Space within a Space 198 Interlocking Spaces 200 Adjacent Spaces 202 Spaces Linked by a Common Space 204 Spatial Organizations 206 Centralized Organizations 208 Linear Organizations 218 Radial Organizations 228 Clustered Organizations 234 Grid Organizations 242 C ON T E N TS 5 Circulation Circulation: Movement through Space 252 Circulation Elements 253 Approach 254 Entrance 262 Configuration of the Path 276 Path-Space Relationships 290 Form of the Circulation Space 294 6 Proportion & Scale Proportion & Scale 306 Material Proportions 307 Structural Proportions 308 Manufactured Proportions 310 Proportioning Systems 311 Golden Section 314 Regulating Lines 318 Classical Orders 320 Renaissance Theories 326 Modulor 330 Ken 334 Anthropometry 338 Scale 341 Visual Scale 342 Human Scale 344 A Scalar Comparison 346 7 Principles Ordering Principles 350 Axis 352 Symmetry 360 Hierarchy 370 Datum 380 Rhythm 396 Repetition 397 Transformation 418 Conclusion 422 A Selected Bibliography 425 Glossary 427 Index of Buildings 435 Index of Designers 441 Index of Subject Matter 443 P RE FA C E The original edition of this study introduced the student of architecture to form and space and the principles that guide their ordering in the built environment. Form and space are the critical means of architecture comprising a design vocabulary that is both elemental and timeless. The second edition continued to be a comprehensive primer on the ways form and space are interrelated and organized in the shaping of our environment, and was refined by editing the text and incorporating diagrams for greater clarity, adding selected examples of architectural works, expanding the sections on openings, stairways, and scale, and finally, by including a glossary and an index to designers. The third edition persisted in illustrating the ways the fundamental elements and principles of architectural design manifest themselves over the course of human history but added an electronic component to introduce the aspects of time and movement to the exposition of elements and principles. In this fourth edition, major changes consist of the addition of more than two dozen contemporary examples, selected to illustrate the new forms that go beyond the timeless elements of basic statics—the columns, beams, and load-bearing walls of stable constructions that are fixed in time and space. Five more modules have also been added to the electronic component to animate certain design decisions regarding scale and proportion, the type of visual, often subtle judgements that designers face in the development of a project. The historical models in this book span time and cross cultural boundaries. While the juxtaposition of styles may appear to be abrupt at times, the diverse range of examples is deliberate. The collage is intended to persuade the reader to look for likenesses among seemingly unlike constructions and bring into sharper focus the critical distinctions that reflect the time and place of their making. Readers are encouraged to take note of additional examples encountered or recalled within the context of their individual experiences. As the design elements and principles become more familiar, new connections, relationships, and levels of meaning may be established. The illustrated examples are neither exhaustive nor necessarily the prototypes for the concepts and principles discussed. Their selection merely serves to illuminate and clarify the formal and spatial ideas being explored. These seminal ideas transcend their historical context and encourage speculation: How might they be analyzed, perceived, and experienced? How might they be transformed into coherent, useful, and meaningful structures of space and enclosure? How might they be reapplied to a range of architectural problems? This manner of presentation attempts to promote a more evocative understanding of the architecture one experiences, the architecture one encounters in literature, and the architecture one imagines while designing. P REFACE / V II A C K NOWL E D G ME NTS I will always be indebted to the following people for their invaluable contributions to the original edition of this work: Forrest Wilson, whose insights into the communication of design principles helped clarify the organization of the material, and whose support made its initial publication possible; James Tice, whose knowledge and understanding of architectural history and theory strengthened the development of this study; Norman Crowe, whose diligence and skill in the teaching of architecture encouraged me to pursue this work; Roger Sherwood, whose research into the organizational principles of form fostered the development of the chapter on ordering principles; Daniel Friedman, for his enthusiasm and careful editing of the final copy; Diane Turner and Philip Hamp, for their assistance in researching material for the illustrations; and to the editorial and production staff at Van Nostrand Reinhold, for their exceptional support and service during the making of the first edition. For the second edition, my appreciation extends to the many students and their teachers who have used this book over the years and offered suggestions for its improvement as a reference and tool for study and teaching. I want to especially thank the following educators for their careful critique of the first edition: L. Rudolph Barton, Laurence A. Clement, Jr., Kevin Forseth, Simon Herbert, Jan Jennings, Marjorie Kriebel, Thomas E. Steinfeld, Cheryl Wagner, James M. Wehler, and Robert L. Wright. In preparing the third edition, I am grateful to Michele Chiuini, Ahmeen Farooq, and Dexter Hulse for their thoughtful reviews of the second edition. While I attempted to incorporate much of their wise counsel, I remain solely responsible for any deficiencies remaining in the text. I especially want to express my gratitude to the editorial and production staff at John Wiley & Sons for their invaluable support and encouragement, and to Nan-ching Tai for his creative contributions and technical assistance in preparing the electronic component of the third edition. Dr. Karen Spence, Gary Crafts, Lohren Deeg, and Dr. Ralph Hammann provided valuable insights and suggestions for this fourth edition. I want to especially recognize Paul Drougas and Lauren Olesky of John Wiley & Sons for their continuing editorial assistance and support, which made this publication not only possible but also an enjoyable endeavor. V I I I / A R C HIT EC T UR E: FOR M , S PA C E , & O R D E R To Debra, Emily, and Andrew, whose love of life it is ultimately the role of architecture to nourish. IN T RODUC T I ON Architecture is generally conceived—designed—realized—built—in response to an existing set of conditions. These conditions may be purely functional in nature, or they may also reflect in varying degrees the social, political, and economic climate. In any case, it is assumed that the existing set of conditions—the problem—is less than satisfactory and that a new set of conditions—a solution—would be desirable. The act of creating architecture, then, is a problem-solving or design process. The initial phase of any design process is the recognition of a problematic condition and the decision to find a solution to it. Design is above all a willful act, a purposeful endeavor. A designer must first document the existing conditions of a problem, define its context, and collect relevant data to be assimilated and analyzed. This is the critical phase of the design process since the nature of a solution is inexorably related to how a problem is perceived, defined, and articulated. Piet Hein, the noted Danish poet and scientist, puts it this way: “Art is solving problems that cannot be formulated before they have been solved. The shaping of the question is part of the answer.” Designers inevitably and instinctively prefigure solutions to the problems they are confronted with, but the depth and range of their design vocabulary influence both their perception of a question and the shaping of its answer. If one’s understanding of a design language is limited, then the range of possible solutions to a problem will also be limited. This book focuses, therefore, on broadening and enriching a vocabulary of design through the study of its essential elements and principles and the exploration of a wide array of solutions to architectural problems developed over the course of human history. As an art, architecture is more than satisfying the purely functional requirements of a building program. Fundamentally, the physical manifestations of architecture accommodate human activity. However, the arrangement and ordering of forms and spaces also determine how architecture might promote endeavors, elicit responses, and communicate meaning. So while this study focuses on formal and spatial ideas, it is not intended to diminish the importance of the social, political, or economic aspects of architecture. Form and space are presented not as ends in themselves but as means to solve a problem in response to conditions of function, purpose, and context—that is, architecturally. The analogy may be made that one must know and understand the alphabet before words can be formed and a vocabulary developed; one must understand the rules of grammar and syntax before sentences can be constructed; one must understand the principles of composition before essays, novels, and the like can be written. Once these elements are understood, one can write poignantly or with force, call for peace or incite to riot, comment on trivia or speak with insight and meaning. In a similar way, it might be appropriate to be able to recognize the basic elements of form and space and understand how they can be manipulated and organized in the development of a design concept, before addressing the more vital issue of meaning in architecture. I NTROD UCTION / IX I N T R O D U CTION In order to place this study in proper context, the following is an overview of the basic elements, systems, and orders that constitute a work of architecture. All of these constituents can be perceived and experienced. Some may be readily apparent while others are more obscure to our intellect and senses. Some may dominate while others play a secondary role in a building’s organization. Some may convey images and meaning while others serve as qualifiers or modifiers of these messages. In all cases, however, these elements and systems should be interrelated to form an integrated whole having a unifying or coherent structure. Architectural order is created when the organization of parts makes visible their relationships to each other and the structure as a whole. When these relationships are perceived as mutually reinforcing and contributing to the singular nature of the whole, then a conceptual order exists—an order that may well be more enduring than transient perceptual visions. Architectural Systems The Architecture of Space Structure Enclosure t PSHBOJ[BUJPOBMQBUUFSO SFMBUJPOTIJQT DMBSJUZ IJFSBSDIZ t GPSNBMJNBHFBOETQBUJBMEFGJOJUJPO t RVBMJUJFTPGTIBQF DPMPS UFYUVSF TDBMF QSPQPSUJPO t RVBMJUJFTPGTVSGBDFT FEHFT BOEPQFOJOHT Experienced through Movement in Space-Time t BQQSPBDIBOEFOUSZ t QBUIDPOGJHVSBUJPOBOEBDDFTT t TFRVFODFPGTQBDFT t MJHIU WJFX UPVDI TPVOE BOETNFMM Achieved by means of Technology t TUSVDUVSFBOEFODMPTVSF t FOWJSPONFOUBMQSPUFDUJPOBOEDPNGPSU t IFBMUI TBGFUZ BOEXFMGBSF t EVSBCJMJUZBOETVTUBJOBCJMJUZ Accommodating a Program t VTFSSFRVJSFNFOUT OFFET BTQJSBUJPOT t TPDJPDVMUVSBMGBDUPST t FDPOPNJDGBDUPST t MFHBMDPOTUSBJOUT t IJTUPSJDBMUSBEJUJPOBOEQSFDFEFOUT Compatible with its Context t TJUFBOEFOWJSPONFOU t DMJNBUFTVO XJOE UFNQFSBUVSF QSFDJQJUBUJPO t HFPHSBQIZTPJMT UPQPHSBQIZ WFHFUBUJPO XBUFS t TFOTPSZBOEDVMUVSBMDIBSBDUFSJTUJDTPGUIFQMBDF X / ARCHIT EC T UR E: FOR M , S PA C E , & O R D E R IN T RODUC T I ON …& Orders Physical Form and Space tTPMJETBOEWPJET tJOUFSJPSBOEFYUFSJPS Systems and organizations of t TQBDF t TUSVDUVSF t FODMPTVSF t NBDIJOFT Perceptual Sensory perception and recognition of the physical elements by experiencing them sequentially in time t t t t t BQQSPBDIBOEEFQBSUVSF FOUSZBOEFHSFTT NPWFNFOUUISPVHIUIFPSEFSPGTQBDFT GVODUJPOJOHPGBOEBDUJWJUJFTXJUIJOTQBDFT RVBMJUJFTPGMJHIU DPMPS UFYUVSF WJFX BOETPVOE Conceptual Comprehension of the ordered or disordered relationships among a building’s elements and systems, and responding to the meanings they evoke t t t t JNBHFT QBUUFSOT TJHOT TZNCPMT t DPOUFYU SPACE FUNCTION FORM TECHNICS* * Technics refers to the theory, principles, or study of an art or a process. I NTROD UCTION / X I I N T R O D U CTION Spatial System Structural System t 5IFUISFFEJNFOTJPOBMJOUFHSBUJPOPGQSPHSBNFMFNFOUTBOETQBDFT accommodates the multiple functions and relationships of a house. t "HSJEPGDPMVNOTTVQQPSUTIPSJ[POUBMCFBNTBOETMBCT t 5IFDBOUJMFWFSBDLOPXMFEHFTUIFEJSFDUJPOPGBQQSPBDIBMPOHUIF longitudinal axis. Enclosure System t 'PVSFYUFSJPSXBMMQMBOFTEFGJOFBSFDUBOHVMBSWPMVNFUIBUDPOUBJOT the program elements and spaces. Villa Savoye, Poissy, east of Paris, 1923–31, Le Corbusier XI I / AR C HIT EC T UR E: FOR M , S PA C E , & O R D E R This graphic analysis illustrates the way architecture embodies the harmonious integration of interacting and interrelated parts into a complex and unified whole. IN T RODUC T I ON Circulation System Context t 5IFTUBJSBOESBNQQFOFUSBUFBOEMJOLUIFUISFFMFWFMT BOEIFJHIUFO the viewer’s perception of forms in space and light. t 5IFDVSWFEGPSNPGUIFFOUSBODFGPZFSSFGMFDUTUIFNPWFNFOUPG the automobile. t "TJNQMFFYUFSJPSGPSNXSBQTBSPVOEBDPNQMFYJOUFSJPSPSHBOJ[BUJPO of forms and spaces. t &MFWBUJOHUIFNBJOGMPPSQSPWJEFTBCFUUFSWJFXBOEBWPJETUIFIVNJEJUZ of the ground. t "HBSEFOUFSSBDFEJTUSJCVUFTTVOMJHIUUPUIFTQBDFTHBUIFSFEBSPVOEJU “Its severe, almost square exterior surrounds an intricate interior configuration glimpsed through openings and from protrusions above. . . . Its inside order accommodates the multiple functions of a house, domestic scale, and partial mystery inherent in a sense of privacy. Its outside order expresses the unity of the idea of house at an easy scale appropriate to the green field it dominated and possibly to the city it will one day be part of.” Robert Venturi, Complexity and Contradiction in Architecture, 1966 I N T ROD UCTION / X III XI V / AR C HIT EC T UR E: FORM , S PA C E , & O R D E R 1 Primary Elements “All pictorial form begins with the point that sets itself in motion… The point moves . . . and the line comes into being—the first dimension. If the line shifts to form a plane, we obtain a two-dimensional element. In the movement from plane to spaces, the clash of planes gives rise to body (three-dimensional) . . . A summary of the kinetic energies which move the point into a line, the line into a plane, and the plane into a spatial dimension.” Paul Klee The Thinking Eye: The Notebooks of Paul Klee (English translation) 1961 P R I M A RY E L E ME N T S This opening chapter presents the primary elements of form in the order of their growth from the point to a one-dimensional line, from the line to a twodimensional plane, and from the plane to a three-dimensional volume. Each element is first considered as a conceptual element, then as a visual element in the vocabulary of architectural design. As conceptual elements, the point, line, plane, and volume are not visible except to the mind’s eye. While they do not actually exist, we nevertheless feel their presence. We can sense a point at the meeting of two lines, a line marking the contour of a plane, a plane enclosing a volume, and the volume of an object that occupies space. When made visible to the eye on paper or in three-dimensional space, these elements become form with characteristics of substance, shape, size, color, and texture. As we experience these forms in our environment, we should be able to perceive in their structure the existence of the primary elements of point, line, plane, and volume. 2 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R PR IMA RY E L E M E N T S As the prime generator of form, the Point indicates a position in space. A point extended becomes a Line with properties of: t MFOHUI t EJSFDUJPO t QPTJUJPO A line extended becomes a Plane with properties of: t MFOHUIBOEXJEUI t TIBQF t TVSGBDF t PSJFOUBUJPO t QPTJUJPO Volume A plane extended becomes a with properties of: t MFOHUI XJEUI BOEEFQUI t GPSNBOETQBDF t TVSGBDF t PSJFOUBUJPO t QPTJUJPO Point Line Plane Volume PRI M ARY ELEMENTS / 3 POINT t A point marks a position in space. Conceptually, it has no length, width, or depth, and is therefore static, centralized, and directionless. As the prime element in the vocabulary of form, a point can serve to mark: t t t t UIFUXPFOETPGBMJOF UIFJOUFSTFDUJPOPGUXPMJOFT UIFNFFUJOHPGMJOFTBUUIFDPSOFSPGBQMBOFPSWPMVNF UIFDFOUFSPGBGJFME Although a point theoretically has neither shape nor form, it begins to make its presence felt when placed within a visual field. At the center of its environment, a point is stable and at rest, organizing surrounding elements about itself and dominating its field. When the point is moved off-center, however, its field becomes more aggressive and begins to compete for visual supremacy. Visual tension is created between the point and its field. 4 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R P O INT E L E M E N T S A point has no dimension. To visibly mark a position in space or on the ground plane, a point must be projected vertically into a linear form, as a column, obelisk, or tower. Any such columnar element is seen in plan as a point and therefore retains the visual characteristics of a point. Other point-generated forms that share these same visual attributes are the: t $JSDMF 5IPMPTPG1PMZDMFJUPT, Epidauros, Greece, c. 350 B.C. t $ZMJOEFS #BQUJTUFSZBU1JTB, Italy, 1153–1265, Diotisalvi t 4QIFSF $FOPUBQIGPS4JS*TBBD/FXUPO, Project, 1784, Étienne-Louis Boulée Piazza del Campidoglio, Rome, c. 1544, Michelangelo Buonarroti. The equestrian statue of Marcus Aurelius marks the center of this urban space. Mont St. Michel, France, 13th century and later. The pyramidal composition culminates in a spire that serves to establish this fortified monastery as a specific place in the landscape. PRI M ARY ELEMENTS / 5 TW O POIN TS Two points describe a line that connects them. Although the points give this line finite length, the line can also be considered a segment of an infinitely longer path. Two points further suggest an axis perpendicular to the line they describe and about which they are symmetrical. Because this axis may be infinite in length, it can be at times more dominant than the described line. In both cases, however, the described line and the perpendicular axis are optically more dominant than the infinite number of lines that may pass through each of the individual points. 6 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R T W O P OI N T S Two points established in space by columnar elements or centralized forms can define an axis, an ordering device used throughout history to organize building forms and spaces. 5PSJJ *TF4ISJOF, Mie Prefecture, Japan, A.D. 690 In plan, two points can denote a gateway signifying passage from one place to another. Extended vertically, the two points define both a plane of entry and an approach perpendicular to it. The Mall, Washington, D.C., lies along the axis established by the Lincoln Memorial, the Washington Monument, and the United States Capitol building. PRI M ARY ELEMENTS / 7 LINE A point extended becomes a line. Conceptually, a line has length, but no width or depth. Whereas a point is by nature static, a line, in describing the path of a point in motion, is capable of visually expressing direction, movement, and growth. A line is a critical element in the formation of any visual construction. A line can serve to: t KPJO MJOL TVQQPSU TVSSPVOE PS intersect other visual elements t EFTDSJCFUIFFEHFTPGBOEHJWFTIBQFUPQMBOFT t BSUJDVMBUFUIFTVSGBDFTPGQMBOFT 8 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R LINE Although a line theoretically has only one dimension, it must have some degree of thickness to become visible. It is seen as a line simply because its length dominates its width. The character of a line, whether taut or limp, bold or tentative, graceful or ragged, is determined by our perception of its length–width ratio, its contour, and its degree of continuity. Even the simple repetition of like or similar elements, if continuous enough, can be regarded as a line. This type of line has significant textural qualities. The orientation of a line affects its role in a visual construction. While a vertical line can express a state of equilibrium with the force of gravity, symbolize the human condition, or mark a position in space, a horizontal line can represent stability, the ground plane, the horizon, or a body at rest. An oblique line is a deviation from the vertical or horizontal. It may be seen as a vertical line falling or a horizontal line rising. In either case, whether it is falling toward a point on the ground plane or rising to a place in the sky, it is dynamic and visually active in its unbalanced state. PRI M ARY ELEMENTS / 9 L I N E A R E L E ME N TS Vertical linear elements, such as columns, obelisks, and towers, have been used throughout history to commemorate significant events and establish particular points in space. #FMM5PXFS $IVSDIBU7VPLTFOOJTLB, Imatra, Finland, 1956, Alvar Aalto .FOIJS, a prehistoric monument consisting of an upright megalith, usually standing alone but sometimes aligned with others. $PMVNOPG.BSDVT"VSFMJVT, Piazza Colonna, Rome, A.D. 174. This cylindrical shaft commemorates the emperor’s victory over Germanic tribes north of the Danube. 0CFMJTLPG-VYPS, Place de la Concorde, Paris. The obelisk, which marked the entrance to the Amon Temple at Luxor, was given by the viceroy of Egypt, Mohamed Ali, to Louis Phillipe and was installed in 1836. Vertical linear elements can also define a transparent volume of space. In the example illustrated to the left, four minaret towers outline a spatial field from which the dome of the Selim Mosque rises in splendor. Selim Mosque, Edirne, Turkey, A.D. 1569–1575 1 0 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R LIN EA R E L E M E N T S Linear members that possess the necessary material strength can perform structural functions. In these three examples, linear elements: t FYQSFTTNPWFNFOUBDSPTTTQBDF t QSPWJEFTVQQPSUGPSBOPWFSIFBEQMBOF t GPSNBUISFFEJNFOTJPOBMTUSVDUVSBMGSBNF for architectural space $BSZBUJE1PSDI, The Erechtheion, Athens, 421–405 B.C., Mnesicles. The sculptured female figures stand as columnar supports for the entablature. 4BMHJOBUPCFM#SJEHF, Switzerland, 1929–1930, Robert Maillart. Beams and girders have the bending strength to span the space between their supports and carry transverse loads. ,BUTVSB*NQFSJBM7JMMB, Kyoto, Japan, 17th century. Linear columns and beams together form a three-dimensional framework for architectural space. PRI M ARY ELEMENTS / 1 1 L I N E A R E L E ME N TS A line can be an imagined element rather than a visible one in architecture. An example is the axis, a regulating line established by two distant points in space and about which elements are symmetrically arranged. 7JMMB"MEPCSBOEJOJ, Italy, 1598–1603, Giacomo Della Porta )PVTF, 1966, John Hejduk Although architectural space exists in three dimensions, it can be linear in form to accommodate the path of movement through a building and link its spaces to one another. Buildings also can be linear in form, particularly when they consist of repetitive spaces organized along a circulation path. As illustrated here, linear building forms have the ability to enclose exterior spaces as well as adapt to the environmental conditions of a site. $PSOFMM6OJWFSTJUZ6OEFSHSBEVBUF)PVTJOH (Project), Ithaca, New York, 1974, Richard Meier 1 2 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R LIN EA R E L E M E N T S 5PXO)BMM 4ÊZOÊUTBMP, Finland, 1950–1952, Alvar Aalto At a smaller scale, lines articulate the edges and surfaces of planes and volumes. These lines can be expressed by joints within or between building materials, by frames around window or door openings, or by a structural grid of columns and beams. How these linear elements affect the texture of a surface will depend on their visual weight, spacing, and direction. $SPXO)BMM, School of Architecture and Urban Design, Illinois Institute of Technology, Chicago, 1956, Mies van der Rohe 4FBHSBN#VJMEJOH, New York City, 1956–1958, Mies van de Rohe and Philip Johnson PRI M ARY ELEMENTS / 1 3 FR O M L I N E TO PL ANE Two parallel lines have the ability to visually describe a plane. A transparent spatial membrane can be stretched between them to acknowledge their visual relationship. The closer these lines are to each other, the stronger will be the sense of plane they convey. A series of parallel lines, through their repetitiveness, reinforces our perception of the plane they describe. As these lines extend themselves along the plane they describe, the implied plane becomes real and the original voids between the lines revert to being mere interruptions of the planar surface. The diagrams illustrate the transformation of a row of round columns, initially supporting a portion of a wall, then evolving into square piers which are an integral part of the wall plane, and finally becoming pilasters—remnants of the original columns occurring as a relief along the surface of the wall. “The column is a certain strengthened part of a wall, carried up perpendicular from the foundation to the top … A row of columns is indeed nothing but a wall, open and discontinued in several places.” Leon Battista Alberti 1 4 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R LIN EA R ELEMEN T S D EF INI N G P L A N E S "MUFT.VTFVN, Berlin, 1823–1830, Karl Friedrich Schinkel A row of columns supporting an entablature—a colonnade—is often used to define the public face or facade of a building, especially one that fronts on a major civic space. A colonnaded facade can be penetrated easily for entry, offers a degree of shelter from the elements, and forms a semi-transparent screen that unifies individual building forms behind it. The Basilica, Vicenza, Italy. Andrea Palladio designed this two-story loggia in 1545 to wrap around an existing medieval structure. This addition not only buttressed the existing structure but also acted as a screen that disguised the irregularity of the original core and presented a uniform but elegant face to the Piazza del Signori. 4UPBPG"UUBMVT fronting the Agora in Athens PRI M ARY ELEMENTS / 1 5 L I N E A R E L E ME N TS DEFINING PLANES Cloister of .PJTTBD"CCFZ, France, c. 1100 In addition to the structural role columns play in supporting an overhead floor or roof plane, they can articulate the penetrable boundaries of spatial zones which mesh easily with adjacent spaces. These two examples illustrate how columns can define the edges of an exterior space defined within the mass of a building as well as articulate the edges of a building mass in space. 5FNQMFPG"UIFOB1PMJBT, Priene, c. 334 B.C., Pythius 4U1IJMJCFSU, Tournus, France, 950–1120. This view of the nave shows how rows of columns can provide a rhythmic measure of space. 1 6 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R LIN EA R ELEMEN T S D EF INI N G P L A N E S $BSZ)PVTF, Mill Valley, California, 1963, Joseph Esherick Trellised Courtyard, (FPSHJB0,FFGF3FTJEFODF, Abiquiu, northwest of Sante Fe, New Mexico The linear members of trellises and pergolas can provide a moderate degree of definition and enclosure for outdoor spaces while allowing filtered sunlight and breezes to penetrate. Vertical and horizontal linear elements together can define a volume of space such as the solarium illustrated to the right. Note that the form of the volume is determined solely by the configuration of the linear elements. Solarium of $POEPNJOJVN6OJU 4FB3BODI, California, 1966, Moore, Lyndon, Turnbull, Whitaker (MLTW) PRI M ARY ELEMENTS / 1 7 P LA N E A line extended in a direction other than its intrinsic direction becomes a plane. Conceptually, a plane has length and width, but no depth. Shape is the primary identifying characteristic of a plane. It is determined by the contour of the line forming the edges of a plane. Because our perception of shape can be distorted by perspective foreshortening, we see the true shape of a plane only when we view it frontally. The supplementary properties of a plane—its surface color, pattern, and texture—affect its visual weight and stability. In the composition of a visual construction, a plane serves to define the limits or boundaries of a volume. If architecture as a visual art deals specifically with the formation of threedimensional volumes of mass and space, then the plane should be regarded as a key element in the vocabulary of architectural design. 1 8 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R PLANE Planes in architecture define three-dimensional volumes of mass and space. The properties of each plane—size, shape, color, texture —as well as their spatial relationship to one another ultimately determine the visual attributes of the form they define and the qualities of the space they enclose. In architectural design, we manipulate three generic types of planes: Overhead Plane The overhead plane can be either the roof plane that spans and shelters the interior spaces of a building from the climatic elements, or the ceiling plane that forms the upper enclosing surface of a room. Wall Plane The wall plane, because of its vertical orientation, is active in our normal field of vision and vital to the shaping and enclosure of architectural space. Base Plane The base plane can be either the ground plane that serves as the physical foundation and visual base for building forms, or the floor plane that forms the lower enclosing surface of a room upon which we walk. PRI M ARY ELEMENTS / 1 9 P LA N AR E L E ME N TS The ground plane ultimately supports all architectural construction. Along with climate and other environmental conditions of a site, the topographical character of the ground plane influences the form of the building that rises from it. The building can merge with the ground plane, rest firmly on it, or be elevated above it. The ground plane itself can be manipulated as well to establish a podium for a building form. It can be elevated to honor a sacred or significant place; bermed to define outdoor spaces or buffer against undesirable conditions; carved or terraced to provide a suitable platform on which to build; or stepped to allow changes in elevation to be easily traversed. Scala de Spagna (Spanish Steps), Rome, 1721–1725. Alessandro Specchi designed this civic project to connect the Piazza di Spagna with SS. Trinita de’ Monti; completed by Francesco de Sanctis. .PSUVBSZ5FNQMFPG2VFFO)BUTIFQTVU, Dêr el-Bahari, Thebes, 1511–1480 B.C., Senmut. Three terraces approached by ramps rise toward the base of the cliffs where the chief sanctuary is cut deep into the rock. Machu Picchu, an ancient Incan city established c.1500 in the Andes Mountains on a saddle between two peaks, 8000 ft. above the Urubamba River in south-central Peru. 2 0 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R P LA N A R E L E M E N T S Sitting Area, -BXSFODF)PVTF, Sea Ranch, California, 1966, MLTW The floor plane is the horizontal element that sustains the force of gravity as we move around and place objects for our use on it. It may be a durable covering of the ground plane or a more artificial, elevated plane spanning the space between its supports. In either case, the texture and density of the flooring material influences both the acoustical quality of a space and how we feel as we walk across its surface. While the pragmatic, supportive nature of the floor plane limits the extent to which it can be manipulated, it is nonetheless an important element of architectural design. Its shape, color, and pattern determine to what degree it defines spatial boundaries or serves as a unifying element for the different parts of a space. Like the ground plane, the form of a floor plane can be stepped or terraced to break the scale of a space down to human dimensions and create platforms for sitting, viewing, or performing. It can be elevated to define a sacred or honorific place. It can be rendered as a neutral ground against which other elements in a space are seen as figures. &NQFSPShT4FBU *NQFSJBM1BMBDF, Kyoto, Japan, 17th century #BDBSEJ0GGJDF#VJMEJOH (Project), Santiago de Cuba, 1958, Mies van der Rohe PRI M ARY ELEMENTS / 2 1 P LA N AR E L E ME N TS 4.BSJB/PWFMMB, Florence, 1456–1470. The Renaissance facade by Alberti presents a public face to a square. Exterior wall planes isolate a portion of space to create a controlled interior environment. Their construction provides both privacy and protection from the climatic elements for the interior spaces of a building, while openings within or between their boundaries reestablish a connection with the exterior environment. As exterior walls mold interior space, they simultaneously shape exterior space and describe the form, massing, and image of a building in space. 6GGJ[J1BMBDF, 1560–1565, Giorgio Vasari. This Florentine street defined by the two wings of the Uffizi Palace links the Piazza della Signoria with the River Arno. As a design element, the plane of an exterior wall can be articulated as the front or primary facade of a building. In urban situations, these facades serve as walls that define courtyards, streets, and such public gathering places as squares and marketplaces. 1JB[[B4BO.BSDP, Venice. The continuous facades of buildings form the “walls” of the urban space. 2 2 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R PLA N AR E L E M E N T S A compelling way to use the vertical wall plane is as a supporting element in the bearing-wall structural system. When arranged in a parallel series to support an overhead floor or roof plane, bearing walls define linear slots of space with strong directional qualities. These spaces can be related to one another only by interrupting the bearing walls to create perpendicular zones of space. 1FZSJTTBD3FTJEFODF, Cherchell, Algeria, 1942, Le Corbusier $PVOUSZ)PVTFJO#SJDL (Project), 1923, Mies van der Rohe In the project to the right, freestanding brick bearing walls, together with L-shaped and T-shaped configurations of planes, create an interlocking series of spaces. PRI M ARY ELEMENTS / 2 3 P LA N AR E L E ME N TS $PODFSU)BMM (Project), 1942, Mies van der Rohe Interior wall planes govern the size and shape of the internal spaces or rooms within a building. Their visual properties, their relationship to one another, and the size and distribution of openings within their boundaries determine both the quality of the spaces they define and the degree to which adjoining spaces relate to one another. As a design element, a wall plane can merge with the floor or ceiling plane, or be articulated as an element isolated from adjacent planes. It can be treated as a passive or receding backdrop for other elements in the space, or it can assert itself as a visually active element within a room by virtue of its form, color, texture, or material. While walls provide privacy for interior spaces and serve as barriers that limit our movement, doorways and windows reestablish continuity with neighboring spaces and allow the passage of light, heat, and sound. As they increase in size, these openings begin to erode the natural sense of enclosure walls provide. Views seen through the openings become part of the spatial experience. 'JOOJTI1BWJMJPO, New York World’s Fair, 1939, Alvar Aalto 2 4 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R PLA N AR E L E M E N T S )BOHBS %FTJHO*, 1935, Pier Luigi Nervi. The lamella structure expresses the way forces are resolved and channeled down to the roof supports. While we walk on a floor and have physical contact with walls, the ceiling plane is usually out of our reach and is almost always a purely visual event in a space. It may be the underside of an overhead floor or roof plane and express the form of its structure as it spans the space between its supports, or it may be suspended as the upper enclosing surface of a room or hall. #SJDL)PVTF, New Canaan, Connecticut, 1949, Philip Johnson. The detached vaulted ceiling plane appears to float above the bed. As a detached lining, the ceiling plane can symbolize the sky vault or be the primary sheltering element that unifies the different parts of a space. It can serve as a repository for frescoes and other means of artistic expression or be treated simply as a passive or receding surface. It can be raised or lowered to alter the scale of a space or to define spatial zones within a room. Its form can be manipulated to control the quality of light or sound within a space. $IVSDIBU7VPLTFOOJTLB, Imatra, Finland, 1956, Alvar Aalto. The form of the ceiling plane defines a progression of spaces and enhances their acoustical quality. PRI M ARY ELEMENTS / 2 5 P LA N AR E L E ME N TS The roof plane is the essential sheltering element that protects the interior of a building from the climatic elements. The form and geometry of its structure is established by the manner in which it spans across space to bear on its supports and slopes to shed rain and melting snow. As a design element, the roof plane is significant because of the impact it can have on the form and silhouette of a building within its setting. Dolmen, a prehistoric monument consisting of two or more large upright stones supporting a horizontal stone slab, found especially in Britain and France and usually regarded as a burial place for an important person. 3PCJF)PVTF, Chicago,1909, Frank Lloyd Wright. The low sloping roof planes and broad overhangs are characteristic of the Prairie School of Architecture. 4IPEIBO)PVTF, Ahmedabad, India, 1956, Le Corbusier. A grid of columns elevates the reinforced concrete roof slab above the main volume of the house. 2 6 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R The roof plane can be hidden from view by the exterior walls of a building or merge with the walls to emphasize the volume of the building mass. It can be expressed as a single sheltering form that encompasses a variety of spaces beneath its canopy, or comprise a number of hats that articulate a series of spaces within a single building. A roof plane can extend outward to form overhangs that shield door and window openings from sun or rain, or continue downward further still to relate itself more closely to the ground plane. In warm climates, it can be elevated to allow cooling breezes to flow across and through the interior spaces of a building. PLA N AR E L E M E N T S 'BMMJOHXBUFS ,BVGNBOO)PVTF , near Ohiopyle, Pennsylvania ,1936–1937, Frank Lloyd Wright. Reinforced concrete slabs express the horizontality of the floor and roof planes as they cantilever outward from a central vertical core. The overall form of a building can be endowed with a distinctly planar quality by carefully introducing openings that expose the edges of vertical and horizontal planes. These planes can be further differentiated and accentuated by changes in color, texture, or material. 4DISÚEFS)PVTF, Utrecht, 1924–1925, Gerrit Thomas Rietveld. Asymmetrical compositions of simple rectangular forms and primary colors characterized the de Stijl School of Art and Architecture. PRI M ARY ELEMENTS / 2 7 VOL U M E A plane extended in a direction other than its intrinsic direction becomes a volume. Conceptually, a volume has three dimensions: length, width, and depth. All volumes can be analyzed and understood to consist of: t QPJOUTPSWFSUJDFTXIFSFTFWFSBMQMBOFTDPNFUPHFUIFS t MJOFTPSFEHFTXIFSFUXPQMBOFTNFFU t QMBOFTPSTVSGBDFTUIBUEFGJOFUIFMJNJUTPS boundaries of a volume Form is the primary identifying characteristic of a volume. It is established by the shapes and interrelationships of the planes that describe the boundaries of the volume. As the three-dimensional element in the vocabulary of architectural design, a volume can be either a solid—space displaced by mass—or a void—space contained or enclosed by planes. 2 8 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R V OL UM E Plan and Section Space defined by wall, floor, and ceiling or roof planes In architecture, a volume can be seen to be either a portion of space contained and defined by wall, floor, and ceiling or roof planes, or a quantity of space displaced by the mass of a building. It is important to perceive this duality, especially when reading orthographic plans, elevations, and sections. &MFWBUJPO Space displaced by the mass of a building /PUSF%BNF%V)BVU, Ronchamp, France, 1950–1955, Le Corbusier PRI M ARY ELEMENTS / 2 9 VOL U M E TRIC E L E MENTS Building forms that stand as objects in the landscape can be read as occupying volumes in space. %PSJD5FNQMFBU4FHFTUB, Sicily, c. 424–416 B.C. 7JMMB(BSDIFT, Vaucresson, France, 1926–1927, Le Corbusier #BSO in Ontario, Canada 3 0 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R V O LU MET R I C E L E M E N T S Building forms that serve as containers can be read as masses that define volumes of space. 1JB[[B.BHHJPSF, Sabbioneta, Italy. A series of buildings enclose an urban square. Palazzo Thiene, Vicenza, Italy, 1545, Andrea Palladio. The interior rooms surround a cortile— the principal courtyard of an Italian palazzo. #VEEIJTU$IBJUZB)BMMBU,BSMJ, Maharashtra, India, A.D. 100–125. The sanctuary is a volume of space carved out of the mass of solid rock. PRI M ARY ELEMENTS / 3 1 /PUSF%BNF%V)BVU, Ronchamp, France, 1950–1955, Le Corbusier 3 2 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R 2 Form “Architectural form is the point of contact between mass and space … Architectural forms, textures, materials, modulation of light and shade, color, all combine to inject a quality or spirit that articulates space. The quality of the architecture will be determined by the skill of the designer in using and relating these elements, both in the interior spaces and in the spaces around buildings.” Edmund N. Bacon The Design of Cities 1974 FOR M Form is an inclusive term that has several meanings. It may refer to an external appearance that can be recognized, as that of a chair or the human body that sits in it. It may also allude to a particular condition in which something acts or manifests itself, as when we speak of water in the form of ice or steam. In art and design, we often use the term to denote the formal structure of a work—the manner of arranging and coordinating the elements and parts of a composition so as to produce a coherent image. In the context of this study, form suggests reference to both internal structure and external outline and the principle that gives unity to the whole. While form often includes a sense of three-dimensional mass or volume, shape refers more specifically to the essential aspect of form that governs its appearance—the configuration or relative disposition of the lines or contours that delimit a figure or form. Shape The characteristic outline or surface configuration of a particular form. Shape is the principal aspect by which we identify and categorize forms. In addition to shape, forms have visual properties of: 3 4 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R Size The physical dimensions of length, width, and depth of a form. While these dimensions determine the proportions of a form, its scale is determined by its size relative to other forms in its context. Color A phenomenon of light and visual perception that may be described in terms of an individual’s perception of hue, saturation, and tonal value. Color is the attribute that most clearly distinguishes a form from its environment. It also affects the visual weight of a form. Texture The visual and especially tactile quality given to a surface by the size, shape, arrangement, and proportions of the parts. Texture also determines the degree to which the surfaces of a form reflect or absorb incident light. P R O P ERT I E S OF F ORM Forms also have relational properties that govern the pattern and composition of elements: Position The location of a form relative to its environment or the visual field within which it is seen. Orientation The direction of a form relative to the ground plane, the compass points, other forms, or to the person viewing the form. Visual Inertia The degree of concentration and stability of a form. The visual inertia of a form depends on its geometry as well as its orientation relative to the ground plane, the pull of gravity, and our line of sight. All of these properties of form are in reality affected by the conditions under which we view them. t t t t "DIBOHJOHQFSTQFDUJWFPSBOHMFPGWJFXQSFTFOUTEJGGFSFOUTIBQFTPSBTQFDUTPGBGPSNUPPVSFZFT 0VSEJTUBODFGSPNBGPSNEFUFSNJOFTJUTBQQBSFOUTJ[F 5IFMJHIUJOHDPOEJUJPOTVOEFSXIJDIXFWJFXBGPSNBGGFDUTUIFDMBSJUZPGJUTTIBQFBOETUSVDUVSF 5IFWJTVBMGJFMETVSSPVOEJOHBGPSNJOGMVFODFTPVSBCJMJUZUPSFBEBOEJEFOUJGZJU FORM / 3 5 SHA P E Shape refers to the characteristic outline of a plane figure or the surface configuration of a volumetric form. It is the primary means by which we recognize, identify, and categorize QBSUJDVMBSGJHVSFTBOEGPSNT0VSQFSDFQUJPOPG shape depends on the degree of visual contrast that exists along the contour separating a figure from its ground or between a form and its field. Bust of Queen Nefertiti The pattern of eye movement of a person viewing the figure, from research by Alfred L. Yarbus of the Institute for Problems of Information Transmission in Moscow. In architecture, we are concerned with the shapes of: t GMPPS XBMM BOEDFJMJOHQMBOFTUIBUFODMPTF space t EPPSBOEXJOEPXPQFOJOHTXJUIJOBTQBUJBM enclosure t TJMIPVFUUFTBOEDPOUPVSTPGCVJMEJOHGPSNT 3 6 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R SHAPE These examples illustrate how shaping the juncture between mass and space expresses the manner in which the contours of a building mass rise from the ground plane and meet the sky. Central Pavilion, Horyu-Ji Temple, Nara, Japan, A.D. 607 Villa Garches, Vaucresson, France, 1926–1927, Le Corbusier. This architectural composition illustrates the interplay between the shapes of planar solids and voids. Suleymaniye Mosque, Constantinople (Istanbul), 1551–1558, Mimar Sinan FORM / 3 7 P R I M ARY SHAPE S Gestalt psychology affirms that the mind will simplify the visual environment in order to understand it. Given any composition of forms, we tend to reduce the subject matter in our visual field to the simplest and most regular shapes. The simpler and more regular a shape is, the easier it is to perceive and understand. From geometry we know the regular shapes to be the circle, and the infinite series of regular QPMZHPOTUIBUDBOCFJOTDSJCFEXJUIJOJU0GUIFTF UIFNPTUTJHOJGJDBOUBSFUIFQSJNBSZTIBQFT the circle, the triangle, and the square. Circle A plane curve every point of which is equidistant from a fixed point within the curve Triangle A plane figure bounded by three sides and having three angles Square 3 8 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R A plane figure having four equal sides and four right angles C I RC L E Plan of the Ideal City of Sforzinda, 1464, Antonio Filarete Compositions of circles and circular segments Neutral Stable Unstable Equilibrium Stable Self-centered Dynamic Fixed in place The circle is a centralized, introverted figure that is normally stable and self-centering in its environment. Placing a circle in the center of a field reinforces its inherent centrality. Associating it with straight or angular forms or placing an element along its circumference, however, can induce in the circle an apparent rotary motion. Roman Theater according to Vitruvius FORM / 3 9 TR I A NG L E The triangle signifies stability. When resting on one of its sides, the triangle is an extremely stable figure. When tipped to stand on one of its vertices, however, it can either be balanced in a precarious state of equilibrium or be unstable and tend to fall over onto one of its sides. Modern Art Museum, Caracas 1SPKFDU 7FOF[VFMB 0TDBS/JFNFZFS Vigo Sundt House, Madison, Wisconsin, 1942, Frank Lloyd Wright 4 0 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R Great Pyramid of Cheops at Giza, Egypt, c. 2500 B.C. S QUA RE Compositions resulting from the rotation and modification of the square The square represents the pure and the rational. It is a bilaterally symmetrical figure having two equal and perpendicular axes. All other rectangles can be considered variations of the square—deviations from the norm by the addition of height or width. Like the triangle, the square is stable when resting on one of its sides and dynamic when standing on one of its corners. When its diagonals are vertical and horizontal, however, the square exists in a balanced state of equilibrium. Bathhouse, Jewish Community Center, Trenton, New Jersey, 1954–1959, Louis Kahn Agora of Ephesus, Asia Minor, 3rd century B. C. FORM / 4 1 SU R FAC E S In the transition from the shapes of planes to the forms of volumes is situated the realm of surfaces. Surface first refers to any figure having only two dimensions, such as a flat plane. The term, however, can also allude to a curved two-dimensional locus of points defining the boundary of a three-dimensional solid. There is a special class of the latter that can be generated from the geometric family of curves and straight lines. This class of curved surfaces include the following: t $ZMJOESJDBMTVSGBDFTBSFHFOFSBUFECZTMJEJOHBTUSBJHIUMJOF along a plane curve, or vice versa. Depending on the curve, a cylindrical surface may be circular, elliptic, or parabolic. Because of its straight line geometry, a cylindrical surface can be regarded as being either a translational or a ruled surface. t 5SBOTMBUJPOBMTVSGBDFTBSFHFOFSBUFECZTMJEJOHBQMBOFDVSWF along a straight line or over another plane curve. t 3VMFETVSGBDFTBSFHFOFSBUFECZUIFNPUJPOPGBTUSBJHIU line. Because of its straight line geometry, a ruled surface is generally easier to form and construct than a rotational or translational surface. t 3PUBUJPOBMTVSGBDFTBSFHFOFSBUFECZSPUBUJOHBQMBOFDVSWF about an axis. t 1BSBCPMPJETBSFTVSGBDFTBMMPGXIPTFJOUFSTFDUJPOTCZQMBOFT are either parabolas and ellipses or parabolas and hyperbolas. Parabolas are plane curves generated by a moving point that remains equidistant from a fixed line and a fixed point not on the line. Hyperbolas are plane curves formed by the intersection of a right circular cone with a plane that cuts both halves of the cone. t )ZQFSCPMJDQBSBCPMPJETBSFTVSGBDFTHFOFSBUFECZTMJEJOH a parabola with downward curvature along a parabola with upward curvature, or by sliding a straight line segment with its ends on two skew lines. It can thus be considered to be both a translational and a ruled surface. 4 2 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R C U RV E D S URFA C E S Saddle surfaces have an upward curvature in one direction and a downward curvature in the perpendicular EJSFDUJPO3FHJPOTPGEPXOXBSEDVSWBUVSFFYIJCJUBSDIMJLF action while regions of upward curvature behave as a cable structure. If the edges of a saddle surface are not supported, beam behavior may also be present. The type of structural system that can best take advantage of this doubly curved geometry is the shell structure—a thin, plate structure, usually of reinforced concrete, which is shaped to transmit applied forces by compressive, tensile, and shear stresses acting in the plane of the curved surface. Restaurant Los Manantiales, Xochimilco, Mexico, 1958, Felix Candela. The structure consists of a radial arrangement of eight hyperbolic paraboloid segments. 3FMBUFEUPTIFMMTUSVDUVSFTBSFHSJETIFMM structures, which were pioneered by the 3VTTJBOFOHJOFFS7MBEJNJS4IVLIPWJOUIFMBUF 19th century. Like shell structures, gridshells rely on their double curvature geometry for their strength but are constructed of a grid or lattice, usually of wood or steel. Gridshells are capable of being formed into irregular curved surfaces, relying on computer modeling programs for their structural analysis and optimization and sometimes their fabrication and assembly as well. See also pages 172–173 for a related discussion of diagrids. FORM / 4 3 C U RV ED SU R FACE S The fluid quality of curved surfaces contrasts with the angular nature of rectilinear forms and is appropriate for describing the form of shell structures as well as non-loadbearing elements of enclosure. Symmetrical curved surfaces, such as domes and barrel vaults, are inherently stable. Asymmetrical curved surfaces, on the other hand, can be more vigorous and expressive in nature. Their shapes change dramatically as we view them from different perspectives. Olympic Velodrome, Athens, Greece, 2004 (renovation of original 1991 structure), Santiago Calatrava Walt Disney Concert Hall -PT"OHFMFT $BMJGPSOJB o 'SBOL0(FISZ1BSUOFST 4 4 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R C U RV E D S URFA C E S Banff Community Recreation Center, Banff, Alberta, Canada, 2011, GEC Architecture Tenerife Concert Hall, Canary Islands, Spain 1997–2003, Santiago Calatrava FORM / 4 5 P R I M A RY SOL I DS “…cubes, cones, spheres, cylinders, or pyramids are the great primary forms that light reveals to advantage; the image of these is distinct and tangible within us and without ambiguity. It is for this reason that these are beautiful forms, the most beautiful forms.” Le Corbusier The primary shapes can be extended or rotated to generate volumetric forms or solids that are distinct, regular, and easily recognizable. Circles generate spheres and cylinders; triangles generate cones and pyramids; squares generate cubes. In this context, the term “solid” does not refer to firmness of substance but rather to a three-dimensional geometric body or figure. Sphere A solid generated by the revolution of a semicircle about its diameter, whose surface is at all points equidistant from the center. A sphere is a centralized and highly concentrated form. Like the circle from which it is generated, it is self-centering and normally stable in its environment. It can be inclined toward a rotary motion when placed on a sloping plane. From any viewpoint, it retains its circular shape. Cylinder A solid generated by the revolution of a rectangle about one of its sides. A cylinder is centralized about the axis passing through the centers of its two circular faces. Along this axis, it can be easily extended. The cylinder is stable if it rests on one of its circular faces; it becomes unstable when its central axis is inclined from the vertical. 4 6 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R P R IM A RY S OL I DS Cone A solid generated by the revolution of a right triangle about one of its sides. Like the cylinder, the cone is a highly stable form when resting on its circular base, and unstable when its vertical axis is tipped or overturned. It can also rest on its apex in a precarious state of balance. Pyramid A polyhedron having a polygonal base and triangular faces meeting at a common point or vertex. The pyramid has properties similar to those of the cone. Because all of its surfaces are flat planes, however, the pyramid can rest in a stable manner on any of its faces. While the cone is a soft form, the pyramid is relatively hard and angular. Cube A prismatic solid bounded by six equal square sides, the angle between any two adjacent faces being a right angle. Because of the equality of its dimensions, the cube is a static form that lacks apparent movement or direction. It is a stable form except when it stands on one of its edges or corners. Even though its angular profile is affected by our point of view, the cube remains a highly recognizable form. FORM / 4 7 P R I M A RY SOL I DS Maupertius, Project for an Agricultural Lodge, 1775, Claude-Nicolas Ledoux Chapel, Massachusetts Institute of Technology, Cambridge, Massachusetts, 1955, Eero Saarinen and Associates Project for a Conical Cenotaph, 1784, Étienne-Louis Boulée 4 8 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R PR IM A RY S OL I DS Pyramids of Cheops, Chephren, and Mykerinos at Giza, Egypt, c. 2500 B.C. :H2?:"92D2E69AFC*:<C:, Palace Complex of Akbar the Great Mogul Emperor of India, 1569–1574 Hanselmann House, Fort Wayne, Indiana, 1967, Michael Graves FORM / 4 9 R E G U LA R & IR R E G ULAR FO RMS 3FHVMBSGPSNTSFGFSUPUIPTFXIPTFQBSUTBSF related to one another in a consistent and orderly manner. They are generally stable in nature and symmetrical about one or more axes. The sphere, cylinder, cone, cube, and pyramid are prime examples of regular forms. Forms can retain their regularity even when transformed dimensionally or by the addition or subtraction of elements. From our experiences with similar forms, we can construct a mental model of the original whole even when a fragment is missing or another part is added. Irregular forms are those whose parts are dissimilar in nature and related to one another in an inconsistent manner. They are generally asymmetrical and more dynamic than regular forms. They can be regular forms from which irregular elements have been subtracted or result from an irregular composition of regular forms. Since we deal with both solid masses and spatial voids in architecture, regular forms can be contained within irregular forms. In a similar manner, irregular forms can be enclosed by regular forms. 5 0 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R R EG U LA R & IR R EG U L A R F ORM S Irregular Forms: Philharmonic Hall, Berlin, 1956–1963, Hans Scharoun A Regular Composition of Regular Forms: Coonley Playhouse 3JWFSTJEF *MMJOPJT 'SBOL-MPZE8SJHIU An Irregular Composition of Regular Forms: Katsura Imperial Villa, Kyoto, Japan, 17th century Irregular Forms within a Regular Field: Courtyard House Project .JFTWBOEF3PIF Regular Forms within an Irregular Composition: Mosque of Sultan Hasan, Cairo, Egypt, 1356–1363 FORM / 5 1 R E G U LA R & IR R E G ULAR FO RMS An Irregular Array of Regular Forms in the Horizontal Dimension: City of Justice, Barcelona, Spain, 2010, David Chipperfield Architects, b720 Arquitectos An Irregular Array of Regular Forms in the Vertical Dimension: Poteries du Don, Le Fel, France, 2008, Lacombe–De Florinier 5 2 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R R EG U LA R & IR R EG UL A R F ORM S China Central Television Headquarters (CCTV), Beijing, $IJOB o 3FN,PPMIBBTBOE0MF4DIFFSFO0." What may appear to be a random pattern is often based on rational structural principles. Note how the diagrid pattern becomes more dense in areas where moment stresses are higher. Regular and Irregular Structural Patterns Busan Cinema Center #VTBO 4PVUI,PSFB $001)*..&-# M BV This example shows how irregular forms contrast with and play off of the horizontal ground and roof planes. FORM / 5 3 TR A NSFOR MATION O F FO RM All other forms can be understood to be transformations of the primary solids, variations which are generated by the manipulation of one or more dimensions or by the addition or subtraction of elements. Dimensional Transformation A form can be transformed by altering one or more of its dimensions and still retain its identity as a member of a family of forms. A cube, for example, can be transformed into similar prismatic forms through discrete changes in height, width, or length. It can be compressed into a planar form or be stretched out into a linear one. Subtractive Transformation A form can be transformed by subtracting a portion of its volume. Depending on the extent of the subtractive process, the form can retain its initial identity or be transformed into a form of another family. For example, a cube can retain its identity as a cube even though a portion of it is removed, or be transformed into a series of regular polyhedrons that begin to approximate a sphere. Additive Transformation A form can be transformed by the addition of elements to its volume. The nature of the additive process and the number and relative sizes of the elements being attached determine whether the identity of the initial form is altered or retained. 5 4 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R T R A N S F O R MAT IO N OF F ORM Dimensional Transformation of a Cube into a Vertical Slab: Unité d’Habitation, Firminy-Vert, France, 1963–1968, Le Corbusier Subtractive Transformation Creating Volumes of Space: Gwathmey Residence, Amagansett, New York, 1967, $IBSMFT(XBUINFZ(XBUINFZ4JFHFM Additive Transformation of a Parent Form by the Attachment of Subordinate Parts: Il Redentore, Venice, 1577–1592, Andrea Palladio FORM / 5 5 D I M E N SION A L TRANSFO RMATIO N A sphere can be transformed into any number of ovoid or ellipsoidal forms by elongating it along an axis. A pyramid can be transformed by altering the dimensions of the base, modifying the height of the apex, or tilting the normally vertical axis. A cube can be transformed into similar prismatic forms by shortening or elongating its height, width, or depth. 5 6 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R D IMEN S IO N A L T R A N S F ORM AT I ON Plan of an Elliptical Church, Pensiero Della Chiesa S. Carlo, Project, 17th century, Francesco Borromini St. Pierre, Firminy-Vert, France, 1965, Le Corbusier Project for Yahara Boat Club, Madison, Wisconsin, 1902, Frank Lloyd Wright FORM / 5 7 SU B TR A C TI VE FOR M We search for regularity and continuity in the forms we see within our field of vision. If any of the primary solids is partially hidden from our view, we tend to complete its form and visualize it as if it were whole because the mind fills in what the eyes do not see. In a similar manner, when regular forms have fragments missing from their volumes, they retain their formal identities if we perceive them as incomplete wholes. We refer to these mutilated forms as subtractive forms. Because they are easily recognizable, simple geometric forms, such as the primary solids, adapt readily to subtractive treatment. These forms will retain their formal identities if portions of their volumes are removed without deteriorating their edges, corners, and overall profile. Ambiguity regarding the original identity of a form will result if the portion removed from its volume erodes its edges and drastically alters its profile. In this series of figures, at what point does the square shape with a corner portion removed become an L- shaped configuration of two rectangular planes? 5 8 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R S U B T R AC T I V E F ORM Gorman Residence, Amagansett, New York, 1968, Julian and Barbara Neski House at Stabio, Ticino, Switzerland, 1981, Mario Botta Spatial volumes may be subtracted from a form to create recessed entrances, positive courtyard spaces, or window openings shaded by the vertical and horizontal surfaces of the recess. Khasneh al Faroun, Petra, 1st century A.D. FORM / 5 9 SU B TR A C TI VE FOR M Gwathmey Residence, Amagansett, New York, 1967, $IBSMFT(XBUINFZ(XBUINFZ4JFHFM"TTPDJBUFT Shodhan House, Ahmedabad, India, 1956, Le Corbusier Benacerraf House Addition, Princeton, New Jersey, 1969, Michael Graves 6 0 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R S U B T R A C T IV E & A D D I T I V E F ORM S Le Corbusier comments on form: “Cumulative Composition t BEEJUJWFGPSN t BSBUIFSFBTZUZQF t QJDUVSFTRVFGVMMPGNPWFNFOU t DBOCFDPNQMFUFMZEJTDJQMJOFECZDMBTTJGJDBUJPO and hierarchy” La Roche-Jeanneret Houses, Paris “Cubic Compositions (Pure Prisms) t WFSZEJGGJDVMU (to satisfy the spirit)” Villa at Garches t iWFSZFBTZ (convenient combining)” House at Stuttgart “Subtractive Form t WFSZHFOFSPVT t POUIFFYUFSJPSBOBSDIJUFDUVSBMXJMMJT confirmed t POUIFJOUFSJPSBMMGVODUJPOBMOFFETBSF satisfied (light penetration, continuity, circulation)” House at Poissy After a sketch, Four House Forms, by Le Corbusier for the cover of Volume Two of the Oeuvre Complète, published in 1935 FORM / 6 1 A D D I TIVE FORM While a subtractive form results from the removal of a portion of its original volume, an additive form is produced by relating or physically attaching one or more subordinate forms to its volume. The basic possibilities for grouping two or more forms are by: Spatial Tension This type of relationship relies on the close proximity of the forms or their sharing of a common visual trait, such as shape, color, or material. Edge-to-Edge Contact In this type of relationship, the forms share a common edge and can pivot about that edge. Face-to-Face Contact This type of relationship requires that the two forms have corresponding planar surfaces which are parallel to each other. Interlocking Volumes In this type of relationship, the forms interpenetrate each other’s space. The forms need not share any visual traits. 6 2 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R A D DI T I V E F ORM Additive forms resulting from the accretion of discrete elements can be characterized by their ability to grow and merge with other forms. For us to perceive additive groupings as unified compositions of form—as figures in our visual field—the combining elements must be related to one another in a coherent manner. These diagrams categorize additive forms according to the nature of the relationships that exist among the component forms as well as their overall configurations. This outline of formal organizations should be compared with a parallel discussion of spatial organizations in Chapter 4. Centralized Form A number of secondary forms clustered about a dominant, central parent-form Linear Form A series of forms arranged sequentially in a row Radial Form A composition of linear forms extending outward from a central form in a radial manner Clustered Form A collection of forms grouped together by proximity or the sharing of a common visual trait Lingaraja Temple, Bhubaneshwar, India, c. A.D. 1100 Grid Form A set of modular forms related and regulated by a three-dimensional grid FORM / 6 3 C E NTR A L I Z E D FORM St. Maria Della Salute, Venice, 1631–1682, Baldassare Longhena Beth Sholom Synagogue, Elkins Park, Pennsylvania, 1959, Frank Lloyd Wright 6 4 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R Villa Capra (The Rotunda), Vicenza, Italy, 1552–1567, Andrea Palladio C EN T R A L I Z E D F ORM Tempietto, S. Pietro in Montorio 3PNF %POBUP#SBNBOUF Centralized forms require the visual dominance of a geometrically regular, centrally located form, such as a sphere, cone, or cylinder. Because of their inherent centrality, these forms share the self-centering properties of the point and circle. They are ideal as freestanding structures isolated within their context, dominating a point in space, or occupying the center of a defined field. They can embody sacred or honorific places, or commemorate significant persons or events. Yume-Dono, Eastern precinct of Horyu-Ji Temple, Nara, Japan, A.D. 607 FORM / 6 5 L I N E A R FORM t "MJOFBSGPSNDBOSFTVMUGSPNBQSPQPSUJPOBMDIBOHF in a form’s dimensions or the arrangement of a series of discrete forms along a line. In the latter case, the series of forms may be either repetitive or dissimilar in nature and organized by a separate and distinct element such as a wall or path. t "MJOFBSGPSNDBOCFTFHNFOUFEPSDVSWJMJOFBSUP respond to topography, vegetation, views, or other features of a site. t "MJOFBSGPSNDBOGSPOUPOPSEFGJOFBOFEHFPGBO exterior space, or define a plane of entry into the spaces behind it. t "MJOFBSGPSNDBOCFNBOJQVMBUFEUPFODMPTFB portion of space. t "MJOFBSGPSNDBOCFPSJFOUFEWFSUJDBMMZBTBUPXFS element to establish or denote a point in space. t "MJOFBSGPSNDBOTFSWFBTBOPSHBOJ[JOHFMFNFOUUP which a variety of secondary forms are attached. 6 6 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R L I N E A R F ORM Runcorn New Town Housing, England,1967, James Stirling -JOFBS(SPXUIUISPVHIUIF3FQFUJUJPOPG'PSNT Linear Form Expressing Procession or Movement Burroughs Adding Machine Company, Detroit, Michigan, 1904, Albert Kahn FORM / 6 7 L I N E A R FORM Agora of Assos, Asia Minor, 2nd century B.C. Linear Forms Fronting on or Defining Exterior Space Queen’s College, Cambridge, England, 1709–1738, Nicholas Hawksmoor 6 8 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R 18th-century buildings fronting a tree-lined canal in Kampen, Holland LI N E A R F ORM Henry Babson House 3JWFSTJEF *MMJOPJT -PVJT4VMMJWBO Linear Organizations of Space Mile-High Illinois Skyscraper Project, Chicago, Illinois, 1956, Frank Lloyd Wright FORM / 6 9 R A D I A L FOR M A radial form consists of linear forms that extend outward from a centrally located core element in a radiating manner. It combines the aspects of centrality and linearity into a single composition. The core is either the symbolic or functional center of the organization. Its central position can be articulated with a visually dominant form, or it can merge with and become subservient to the radiating arms. The radiating arms, having properties similar to those of linear forms, give a radial form its extroverted nature. They can reach out and relate to or attach themselves to specific features of a site. They can expose their elongated surfaces to desirable conditions of sun, wind, view, or space. 3BEJBMGPSNTDBOHSPXJOUPBOFUXPSLPG centers linked by linear arms. 7 0 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R RA DI A L F ORM Aerial view Secretariat Building, UNESCO Headquarters, Place de Fontenoy, Paris, 1953–1958, Marcel Breuer Ground-level view The organization of a radial form can best be seen and understood from an aerial viewpoint. When viewed from ground level, its central core element may not be clearly visible and the radiating pattern of its linear arms may be obscured or distorted through perspective foreshortening. Skyscraper by the Sea, Project for Algiers, 1938, Le Corbusier FORM / 7 1 C L U STE R E D FORM While a centralized organization has a strong geometric basis for the ordering of its forms, a clustered organization groups its forms according to functional requirements of size, shape, or proximity. While it lacks the geometric regularity and introverted nature of centralized forms, a clustered organization is flexible enough to incorporate forms of various shapes, sizes, and orientations into its structure. Considering their flexibility, clustered organizations of forms may be organized in the following ways: t 5IFZDBOCFBUUBDIFEBTBQQFOEBHFTUPBMBSHFSQBSFOU form or space. t 5IFZDBOCFSFMBUFECZQSPYJNJUZBMPOFUPBSUJDVMBUFBOE express their volumes as individual entities. t 5IFZDBOJOUFSMPDLUIFJSWPMVNFTBOENFSHFJOUPBTJOHMF form having a variety of faces. A clustered organization can also consist of forms that are generally equivalent in size, shape, and function. These forms are visually ordered into a coherent, nonhierarchical organization not only by their close proximity to one another, but also by the similarity of their visual properties. 7 2 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R C LU S T E RE D F ORM A Cluster of Forms Attached to a Parent Form: Vacation House,4FB3BODI $BMJGPSOJB .-58 A Cluster of Interlocking Forms: G.N. Black House (Kragsyde), Manchester-by-the Sea, Massachusetts, o 1FBCPEZ4UFBSOT A Cluster of Articulated Forms: House Study +BNFT4UJSMJOH+BNFT(PXBO FORM / 7 3 C L U STE R E D FORM Trulli Village, Alberobello, Italy Traditional dry-stone shelters in existence since the 17th century. Numerous examples of clustered housing forms can be found in the vernacular architecture of various cultures. Even though each culture produced a unique style in response to differing technical, climatic, and sociocultural factors, these clustered housing organizations usually maintained the individuality of each unit and a moderate degree of diversity within the context of an ordered whole. Dogon Housing Cluster, Southeastern Mali, West Africa, 15th century–present 7 4 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R Taos Pueblo, New Mexico, 13th century C LU S T E RE D F ORM Ggantija Temple Complex, Malta, c. 3000 B.C. Habitat Israel, Project, Jerusalem, 1969, Moshe Safdie Vernacular examples of clustered forms can be readily transformed into modular, geometrically ordered compositions which are related to grid organizations of form. Habitat Montreal, 1967, Moshe Safdie FORM / 7 5 G R I D FOR M A grid is a system of two or more intersecting sets of regularly spaced parallel lines. It generates a geometric pattern of regularly spaced points at the intersections of the grid lines and regularly shaped fields defined by the grid lines themselves. The most common grid is based on the geometry of the square. Because of the equality of its dimensions and its bilateral symmetry, a square grid is essentially nonhierarchical and bidirectional. It can be used to break down the scale of a surface into measurable units and give it an even texture. It can be used to wrap several surfaces of a form and unify them with its repetitive and pervasive geometry. The square grid, when projected into the third dimension, generates a spatial network of reference points and lines. Within this modular framework, any number of forms and spaces can be visually organized. Conceptual Diagram, Museum of Modern Art, Gunma Prefecture, Japan, 1974, Arata Isozaki Nakagin Capsule Tower, Tokyo, 1972, Kisho Kurokawa 7 6 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R G RI D F ORM Cubic volumes Structural frame Frame with adjacent spaces Hattenbach Residence 4BOUB.POJDB $BMJGPSOJB o 3BZNPOE,BQQF FORM / 7 7 F O R MAL COL L I SI ONS O F GEO METRY When two forms differing in geometry or orientation collide and interpenetrate each other’s boundaries, each will vie for visual supremacy and dominance. In these situations, the following forms can evolve: Circle and Square Rotated Grid t 5IFUXPGPSNTDBOTVCWFSUUIFJSJOEJWJEVBM identities and merge to create a new composite form. t 0OFPGUIFUXPGPSNTDBOSFDFJWFUIFPUIFS totally within its volume. t 5IFUXPGPSNTDBOSFUBJOUIFJSJOEJWJEVBM identities and share the interlocking portion of their volumes. t 5IFUXPGPSNTDBOTFQBSBUFBOECFMJOLFECZ a third element that recalls the geometry of one of the original forms. 7 8 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R F O R MA L C O LLIS IO N S OF G E OM E T RY Forms differing in geometry or orientation may be incorporated into a single organization for any of the following reasons: t 5PBDDPNNPEBUFPSBDDFOUVBUFUIF differing requirements of interior space and exterior form t 5PFYQSFTTUIFGVODUJPOBMPSTZNCPMJD importance of a form or space within its context t 5PHFOFSBUFBDPNQPTJUFGPSNUIBU incorporates the contrasting geometries into its centralized organization t 5PJOGMFDUBTQBDFUPXBSEBTQFDJGJD feature of a building site t 5PDBSWFBXFMMEFGJOFEWPMVNFPGTQBDF from a building form t 5PFYQSFTTBOEBSUJDVMBUFUIFWBSJPVT constructional or mechanical systems that exist within a building form t 5PSFJOGPSDFBMPDBMDPOEJUJPOPGTZNNFUSZ in a building form t 5PSFTQPOEUPDPOUSBTUJOHHFPNFUSJFTPG the topography, vegetation, boundaries, or existing structures of a site t 5PBDLOPXMFEHFBOBMSFBEZFYJTUJOHQBUI of movement through a building site FORM / 7 9 C I R C LE & SQU A RE Plan for an Ideal City, 1615, Vincenzo Scamozzi A circular form can be freestanding in its context to express its ideal shape and still incorporate a more functional, rectilinear geometry within its boundaries. The centrality of a circular form enables it to act as a hub and unify forms of contrasting geometry or orientation about itself. Chancellery Building, French Embassy (Project),Brasilia, 1964–1965, Le Corbusier The Island Villa (Teatro Marittimo), Hadrian’s Villa, Tivoli, Italy, A.D. 118–125 8 0 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R C IR C L E & S QUA RE Museum for North Rhine–Westphalia (Project), Dusseldorf, (FSNBOZ +BNFT4UJSMJOH.JDIBFM8JMGPSE Lister County Courthouse, Solvesborg, Sweden, 1917–1921, Gunnar Asplund A circular or cylindrical space can serve to organize the spaces within a rectangular enclosure. Murray House, Cambridge, Massachusetts, 1969, Charles Moore FORM / 8 1 R O TATE D G R ID Pearl Mosque XJUIJOUIF3FE'PSU BOJNQFSJBMQBMBDFBU"HSB *OEJB 1658–1707. The interior space of this mosque is oriented exactly with the cardinal points so that the quibla wall faces in the direction of the holy city of Mecca, while its exterior conforms to the existing layout of the fort. Plan of the Ideal City of Sforzinda, 1464, Antonio Filarete St. Mark’s Tower, Project, New York City, 1929, Frank Lloyd Wright 8 2 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R R O TAT E D G RI D National Museum of Roman Art .ÏSJEB 4QBJO o 3BGBFM Moneo. The structural grid of the lower level of the museum floats over and DPOUSBTUTXJUIUIFHFPNFUSZPGUIFBODJFOU3PNBOSFNBJOTPG.ÏSJEB A Diagram of Architecture: Taliesin West, near Scottsdale, Arizona, 1938–1959, Frank Lloyd Wright A diagram by Bernhard Hoesli of the geometry regulating the layout of Taliesin West Diagram as Architecture: House III for Robert Miller, Lakeville, Connecticut, 1971, Design Development Drawings, Peter Eisenman FORM / 8 3 A RT I C U L ATI ON OF FO RM Palacio Güell, Barcelona, 1885–1889, Antonio Gaudi 8 4 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R A RT IC U LAT IO N OF F ORM Articulation refers to the manner in which the surfaces of a form come together to define its shape and volume. An articulated form clearly reveals the precise nature of its parts and their relationships to each other and to the whole. Its surfaces appear as discrete planes with distinct shapes and their overall configuration is legible and easily perceived. In a similar manner, an articulated group of forms accentuates the joints between the constituent parts in order to visually express their individuality. In opposition to the emphasis on joints and joinery, the corners of a form can CFSPVOEFEBOETNPPUIFEPWFSUPFNQIBTJ[FUIFDPOUJOVJUZPGJUTTVSGBDFT0S a material, color, texture, or pattern can be carried across a corner onto the adjoining surfaces to de-emphasize the individuality of the surface planes and emphasize instead the volume of a form. A form can be articulated by: t EJGGFSFOUJBUJOHBEKPJOJOHQMBOFTXJUIBDIBOHFJONBUFSJBM DPMPS UFYUVSF or pattern t EFWFMPQJOHDPSOFSTBTEJTUJODUMJOFBSFMFNFOUTJOEFQFOEFOUPGUIF abutting planes t SFNPWJOHDPSOFSTUPQIZTJDBMMZTFQBSBUFOFJHICPSJOHQMBOFT t MJHIUJOHUIFGPSNUPDSFBUFTIBSQDPOUSBTUTJOUPOBMWBMVFBMPOHFEHFT and corners FORM / 8 5 E D G E S & CORN E RS Since the articulation of a form depends to a great degree on how its surfaces meet each other at corners, how these edge conditions are resolved is critical to the definition and clarity of a form. While a corner can be articulated by simply contrasting the surface qualities of the adjoining planes, or obscured by layering their joining with an optical pattern, our perception of its existence is also affected by the laws of perspective and the quality of light that illuminates the form. For a corner to be formally active, there must be more than a slight deviation in the angle between the adjoining planes. Since we constantly search for regularity and continuity within our field of vision, we tend to regularize or smooth out slight irregularities in the forms we see. For example, a wall plane that is bent only slightly will appear to be a single flat plane, perhaps with a surface imperfection. A corner would not be perceived. At what point do these formal deviations become an acute angle? . . . a right angle? a segmented line? . . . a straight line? a circular segment? . . . a change in a line’s contour? 8 6 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R C ORN E RS Corners define the meeting of two planes. If the two planes simply touch and the corner remains unadorned, the presence of the corner will depend on the visual treatment of the adjoining surfaces. This corner condition emphasizes the volume of a form. A corner condition can be visually reinforced by introducing a separate and distinct element that is independent of the surfaces it joins. This element articulates the corner as a linear condition, defines the edges of the adjoining planes, and becomes a positive feature of the form. If an opening is introduced to one side of the corner, one of the planes will appear to bypass the other. The opening diminishes the corner condition, weakens the definition of the volume within the form, and emphasizes the planar qualities of the neighboring surfaces. If neither plane is extended to define the corner, a volume of space is created to replace the corner. This corner condition deteriorates the volume of the form, allows the interior space to leak outward, and clearly reveals the surfaces as planes in space. 3PVOEJOHPGGUIFDPSOFSFNQIBTJ[FTUIFDPOUJOVJUZPGUIFCPVOEJOH surfaces of a form, the compactness of its volume, and softness of its contour. The scale of the radius of curvature is important. If too small, it becomes visually insignificant; if too large, it affects the interior space it encloses and the exterior form it describes. FORM / 8 7 C OR NE RS Everson Museum, Syracuse, New York, 1968, I.M. Pei. The unadorned corners of the forms emphasize the volume of their mass. Corner Detail, Izumo Shrine, Shimane Prefecture, Japan, A.D. 717 (last rebuilt in 1744). The timber joinery articulates the individuality of the members meeting at the corner. 8 8 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R C ORN E RS Corner Detail, Commonwealth Promenade Apartments $IJDBHP o .JFTWBOEFS3PIF The corner member is recessed to be independent of the adjoining wall planes. Corner Detail, The Basilica, Vicenza, Italy, 1545, Andrea Palladio. The corner column emphasizes the edge of the building form. FORM / 8 9 C OR NE RS Einstein Tower, Potsdam, Germany, 1919, Eric Mendelsohn 3PVOEFEDPSOFSTFYQSFTTDPOUJOVJUZPGTVSGBDF compactness of volume, and softness of form. Laboratory Tower, Johnson Wax Building 3BDJOF 8JTDPOTJO Frank Lloyd Wright 9 0 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R C ORN E RS Kaufmann Desert House 1BMN4QSJOHT $BMJGPSOJB 3JDIBSE/FVUSB 0QFOJOHTBUDPSOFSTFNQIBTJ[FUIF definition of planes over volume. Architectural Design Study, 1923, Van Doesburg and Van Esteren FORM / 9 1 SU R FAC E ARTICU L ATIO N 0VSQFSDFQUJPOPGUIFTIBQF TJ[F TDBMF QSPQPSUJPO and visual weight of a plane is influenced by its surface properties as well as its visual context. t "EJTUJODUDPOUSBTUCFUXFFOUIFTVSGBDFDPMPSPGB plane and that of the surrounding field can clarify its shape, while modifying its tonal value can either increase or decrease its visual weight. t "GSPOUBMWJFXSFWFBMTUIFUSVFTIBQFPGBQMBOF oblique views distort it. t &MFNFOUTPGLOPXOTJ[FXJUIJOUIFWJTVBMDPOUFYU of a plane can aid our perception of its size and scale. t 5FYUVSFBOEDPMPSUPHFUIFSBGGFDUUIFWJTVBM weight and scale of a plane and the degree to which it absorbs or reflects light and sound. t %JSFDUJPOBMPSPWFSTJ[FEPQUJDBMQBUUFSOTDBO distort the shape or exaggerate the proportions of a plane. 9 2 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R S U R FA C E A RT I C UL AT I ON Vincent Street Flats, London, 1928, Sir Edwin Lutyens Palazzo Medici-Ricardo, Florence, Italy, 1444–1460, Michelozzi The color, texture, and pattern of surfaces articulate the existence of planes and influence the visual weight of a form. Hoffman House &BTU)BNQUPO /FX:PSL o 3JDIBSE.FJFS FORM / 9 3 SU R FAC E ARTICU L ATIO N John Deere & Company Building .PMJOF *MMJOPJT o &FSP4BBSJOFO"TTPDJBUFT The linear sun-shading devices accentuate the horizontality of the building form. CBS Building /FX:PSL$JUZ o &FSP4BBSJOFO"TTPDJBUFT Linear columnar elements emphasize the verticality of this high-rise structure. Linear patterns have the ability to emphasize the height or length of a form, unify its surfaces, and define its textural quality. Fukuoka Sogo Bank, Study of the Saga Branch, 1971, Arata Isozaki. A grid pattern unifies the surfaces of the three-dimensional composition. 9 4 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R S U R FA C E A RT I C UL AT I ON A transformation from a pattern of openings in a plane to an open facade articulated by a linear framework. IBM Research Center, La Guade, Var, France, 1960–1961, Marcel Breuer. The three-dimensional form of the openings creates a texture of light, shade, and shadows. First Unitarian Church 3PDIFTUFS /FX:PSL o -PVJT,BIO The pattern of openings and cavities interrupts the continuity of the exterior wall planes. FORM / 9 5 SU R FAC E ARTICU L ATIO N At a smaller scale, the surfaces of buildings owe their visual characteristics to the way their materials are joined and assembled in construction. From rough to smooth… 9 6 / ARC HIT EC T UR E: FOR M , S PA C E , & O R D E R S U R FA C E A RT I C UL AT I ON From orthogonal to skewed… Partial facade, Federation Square, Melbourne, Australia, -"#"SDIJUFDUVSF4UVEJP#BUFT4NBSU "SDIJUFDUT St. Andrew’s Beach House, Victoria, Australia, 2006, Sean Godsell Architects FORM / 9 7 3 Form & Space “We put thirty spokes together and call it a wheel; but it is on the space where there is nothing that the utility of the wheel depends. We turn clay to make a vessel; but it is on the space where there is nothing that the utility of the vessel depends. We pierce doors and windows to make a house; and it is on these spaces where there is nothing that the utility of the house depends. Therefore, just as we take advantage of what is, we should recognize the utility of what is not.” Lao-tzu Tao Te Ching 6th century B.C. 99 FOR M & SPACE Space constantly encompasses our being. Through the volume of space, we move, see forms, hear sounds, feel breezes, smell the fragrances of a flower garden in bloom. It is a material substance like wood or stone. Yet it is an inherently formless vapor. Its visual form, its dimensions and scale, the quality of its light—all of these qualities depend on our perception of the spatial boundaries defined by elements of form. As space begins to be captured, enclosed, molded, and organized by the elements of mass, architecture comes into being. Temple of Kailasnath at Ellora, near Aurangabad, India, A.D. 600–1000 1 0 0 / A R C HIT EC T UR E: FOR M , S PA C E , & O R D E R F O RM & S PA C E The Pantheon, Rome, A.D. 120–124 F O RM & SPACE / 1 0 1 FOR M & SPACE : THE UNITY O F O PPO SITES Our visual field normally consists of heterogeneous elements that differ in shape, size, color, or orientation. To better comprehend the structure of a visual field, we tend to organize its elements into two opposing groups: positive elements, which are perceived as figures and negative elements, which provide a background for the figures. Two Faces or a Vase? Our perception and understanding of a composition depends on how we interpret the visual interaction between the positive and negative elements within its field. On this page, for example, letters are seen as dark figures against the white background of the paper surface. Consequently, we are able to perceive their organization into words, sentences, and paragraphs. In the diagrams to the left, the letter “a” is seen as a figure not only because we recognize it as a letter in our alphabet but also because its profile is distinct, its value contrasts with that of its background, and its placement isolates it from its context. As it grows in size relative to its field, however, other elements within and around it begin to compete for our attention as figures. At times, the relationship between figures and their background is so ambiguous that we visually switch their identities back and forth almost simultaneously. White-on-Black or Black-on-White? In all cases, however, we should understand that figures, the positive elements that attract our attention, could not exist without a contrasting background. Figures and their background, therefore, are more than opposing elements. Together, they form an inseparable reality—a unity of opposites—just as the elements of form and space together form the reality of architecture. 1 0 2 / A R C HIT EC T UR E: FOR M , S PA C E , & O R D E R F O R M & S PA C E: T HE U N IT Y O F OP P OS I T E S Plan Diagrams,Taj Mahal, Agra, India, 1630–1653. Shah Jahan built this white marble mausoleum for his favorite wife, Muntaz Mahal. A. Line defining the boundary between solid mass and spatial void B. The form of solid mass rendered as a figure C. The form of the spatial void rendered as a figure Architectural form occurs at the juncture between mass and space. In executing and reading design drawings, we should be concerned with both the form of the mass containing a volume of space as well as the form of the spatial volume itself. Fragment of a Map of Rome, drawn by Giambattista Nolli in 1748 Depending on what we perceive to be positive elements, the figure-ground relationship of the forms of mass and space can be inverted in different parts of this map of Rome. In portions of the map, buildings appear to be positive forms that define street spaces. In other parts of the drawing, urban squares, courtyards, and major spaces within important public buildings read as positive elements seen against the background of the surrounding building mass. F O RM & SPACE / 1 0 3 FOR M & SPACE : THE UNITY O F O PPO SITES A The symbiotic relationship of the forms of mass and space in architecture can be examined and found to exist at several different scales. At each level, we should be concerned not only with the form of a building but also its impact on the space around it. At an urban scale, we should carefully consider whether the role of a building is to continue the existing fabric of a place, form a backdrop for other buildings, or define a positive urban space, or whether it might be appropriate for it to stand free as a significant object in space. At the scale of a building site, there are various strategies for relating the form of a building to the space around it. A building can: A. form a wall along an edge of its site and begin to define a positive outdoor space; B B. merge its interior space with the private outdoor space of a walled site; C. enclose a portion of its site as an outdoor room and shelter it from undesirable climatic conditions; C D. surround and enclose a courtyard or atrium space within its volume— an introverted scheme. D Building as an object in space Buildings defining space Monastery of St. Meletios on Mt. Kithairon, Greece, 9th century A.D. 1 0 4 / A R C HIT EC T UR E: FOR M , S PA C E , & O R D E R F O R M & S PA C E: T HE U N IT Y O F OP P OS I T E S E. stand as a distinct object in space and dominate its site through its form and topographical positioning—an extroverted scheme; E F. stretch out and present a broad face to address a view, terminate an axis, or define an edge of an urban space; F G. stand free within its site but extend its interior spaces to merge with private exterior spaces; G H. stand as a positive form in a negative space. H Buildings Defining Space: Piazza San Marco, Venice Building as an Object in Space: Boston City Hall, 1960, Kallmann, McKinnell & Knowles F O RM & SPACE / 1 0 5 FOR M & SPACE : THE UNITY O F O PPO SITES Building Embedded in the Landscape: Eyüp Cultural Center, Istanbul, Turkey, 2013, EAA-Emre Arolat Architects Building Dominating the Landscape: Cooroy Art Temple, Cooroy Mountain, Australia, 2008, Paolo Denti JMA Architects 1 0 6 / A R C HIT EC T UR E: FOR M , S PA C E , & O R D E R F O R M & S PA C E: T HE U N IT Y O F OP P OS I T E S Building as Landscape: Palafolls Public Library, Palafolls, Spain, 2009, Enric Miralles and Benedetta Tagliabue/Miralles Tagliabue EMBT Landscape as Building: Olympic Sculpture Park, Seattle Art Museum, Seattle, Washington, 2008, Weiss/Manfredi Architecture/Landscape/Urbanism F O RM & SPACE / 1 0 7 FOR M & SPACE : THE UNITY O F O PPO SITES At the scale of a building, we tend to read the configurations of walls as the positive elements of a plan. The white space in between, however, should not be seen simply as background for the walls, but also as figures in the drawing that have shape and form. Even at the scale of a room, articles of furnishings can either stand as forms within a field of space or serve to define the form of a spatial field. 1 0 8 / A R C HIT EC T UR E: FOR M , S PA C E , & O R D E R F O R M & S PA C E: T HE U N IT Y O F OP P OS I T E S Seinäjoki Theater, Finland,1968–1969, Alvar Aalto A B The form and enclosure of each space in a building either determines, or is determined by, the form of the spaces around it. In the Theater in Seinäjoki by Alvar Aalto, for example, we can distinguish several categories of spatial forms and analyze how they interact. Each category has an active or passive role in defining space. C A. Some spaces, such as offices, have specific but similar functions and can be grouped into single, linear, or clustered forms. B. Some spaces, such as concert halls, have specific functional and technical requirements, and require specific forms that will affect the forms of the spaces around them. C. Some spaces, such as lobbies, are flexible in nature and can therefore be freely defined by the spaces or grouping of spaces around them. F O RM & SPACE / 1 0 9 FOR M DE FIN I N G SPACE Square in Giron, Colombia, South America When we place a two-dimensional figure on a piece of paper, it influences the shape of the white space around it. In a similar manner, any three-dimensional form naturally articulates the volume of space surrounding it and generates a field of influence or territory which it claims as its own. The following section of this chapter looks at horizontal and vertical elements of form and presents examples of how various configurations of these formal elements generate and define specific types of space. 1 1 0 / A R C HIT EC T UR E: FOR M , S PA C E , & O R D E R HO R IZO N TA L ELEMEN T S D EF I N I N G S PA C E Base Plane A horizontal plane laying as a figure on a contrasting background defines a simple field of space. This field can be visually reinforced in the following ways. Elevated Base Plane A horizontal plane elevated above the ground plane establishes vertical surfaces along its edges that reinforce the visual separation between its field and the surrounding ground. Depressed Base Plane A horizontal plane depressed into the ground plane utilizes the vertical surfaces of the lowered area to define a volume of space. Overhead Plane A horizontal plane located overhead defines a volume of space between itself and the ground plane. F O RM & SPACE / 1 1 1 B A SE PL AN E For a horizontal plane to be seen as a figure, there must be a perceptible change in color, tone, or texture between its surface and that of the surrounding area. The stronger the edge definition of a horizontal plane is, the more distinct will be its field. Although there is a continuous flow of