DOCSLIB.ORG

Development of a 3D Viewer for Showing of House Models in a Web Browser – a Usability Evaluation of Navigation Techniques

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

Linköping University | Department of Computer and Information Science Master thesis, 30 ECTS | Datateknik 2021 | LIU-IDA/LITH-EX-A--21/016--SE Development of a 3D viewer for showing of house models in a web browser – A usability evaluation of navigation techniques Utveckling av en 3D visare för visning av husmodeller i en web- bläsare Pål Kastman Supervisor : Anders Fröberg Examiner : Erik Berglund Linköpings universitet SE–581 83 Linköping +46 13 28 10 00 , www.liu.se Copyright © 2021 Pål Kastman This work is licensed under CC BY 4.0 https://creativecommons.org/licenses/by/4.0/, unless otherwise stated. Abstract The architectural industry today struggles with how to best show their models to interested suitors opposite the construction industry which have the advantage of the fact that they can build physical models of houses which they can then show. This is where BIM comes into the picture. By extracting the graphics from these models and visualising them in a web browser this study has by creating a viewer with different navigation techniques sought to find out which techniques where most efficient for navigating models in the viewer. This was done with the help of user tests which results show that when it comes to projections, users were more efficient with perspective projection than orthogonal projections, however, user interviews show that users could still find a use for orthographic projection as it was better for displaying floor plans. Egocentric perspective were more efficient than allocentric perspective, but most users preferred egocentric perspective inside the models and allocentric projection outside of it. As for clipping objects and using clip planes, it is a closer race as users completed the task faster with clip plane but to a greater extent with culling of objects. However, most users wanted to use both technologies at the same time so that they could complement each other. Acknowledgments I would like to thank Erik Berglund and Anders Fröberg for their guidance and feedback during this work. I also want to give a special thanks to my family and friends for having kept inspiring me to finish this. iv Contents Abstract iii Acknowledgments iv Contents v List of Figures vii List of Tables viii Glossary ix 1 Introduction 1 1.1 Background . 1 1.2 Motivation . 1 1.3 Aim............................................ 2 1.4 Research questions . 2 1.5 Delimitations . 2 2 Theory 4 2.1 Spatial memory and virtual environments . 4 2.2 Navigation techniques . 5 2.2.1 Egocentric and Allocentric Perspectives . 5 2.2.2 Gimbal Lock . 6 2.3 Culling and Clipping . 6 2.4 Graphical projections . 6 2.4.1 Projection plane . 6 2.4.2 Ray . 7 2.4.3 Parallel projection . 7 2.4.4 Perspective projection . 8 2.5 Usability testing . 9 2.5.1 Summative studies . 9 2.5.2 Formative studies . 9 2.5.3 Usability testing metrics . 10 2.5.4 Planning the tests . 10 2.6 Usability measures . 11 2.6.1 Performance measures . 11 2.6.2 Perception-based measures . 12 2.7 Confidence intervals . 12 2.8 Test data . 13 2.8.1 Binary data . 13 2.8.2 Continuous data . 13 v 3 Method 15 3.1 Prestudy . 15 3.2 Implementation . 15 3.3 Usability study . 16 3.3.1 Test model . 16 3.3.2 Test users . 16 3.3.3 Test sessions . 16 3.3.4 User Tests . 16 3.3.5 User interviews . 17 4 Results 18 4.1 Prestudy . 18 4.2 Implementation . 18 4.2.1 Camera control . 20 4.2.2 Clip plane control . 20 4.2.3 Graphical projections . 21 4.3 Usability Study . 22 4.3.1 User Tests . 22 4.3.2 User Interviews . 24 5 Discussion 26 5.1 Method . 26 5.2 Results . 27 5.2.1 Prestudy . 27 5.2.2 Implementation . 28 5.2.3 Evaluation . 28 5.3 Societal and ethical aspects . 30 6 Conclusion 31 Bibliography 32 A Appendix A – Test plan 35 A.1 Purpose . 35 A.2 Research questions . 35 A.3 Method . 35 A.4 User profiles . 35 A.5 Tasks list . 36 A.6 Test environment & equipment . 36 A.7 Evaluation method . 36 A.8 Deliverables . 37 B Appendix B – Interview questions 38 vi List of Figures 1.1 Architectural models . 2 2.1 Six degrees of freedom of a ship . 5 2.2 View Frustum . 6 2.3 Various projections of cube above plane . 7 2.4 Axonometric projections . 8 2.5 Vanishing Points . 8 2.6 Problems found against users tested on in formative testing. 10 4.1 GUI used for testing . 19 4.2 Right click menu. 19 4.3 Clip plane control. 21 4.4 Implemented graphical projections . 22 4.5 Task success results . 23 4.6 Time on task results . 24 vii List of Tables 4.1 Characteristics of test participants . 23 viii Glossary BIM Building information modeling. 1, 2, 27 CAD Computer-aided design. 15 CSS Cascading style sheets. 15 DoF Degrees of freedom. 4, 5, 6 FPV First-person view. 5 glTFTM Graphics Language Transmission Format. 2, 28 GUI Graphical user interface. 15, 18, 20 HTML Hypertext Markup Language. 15 IFC Industry Foundation Classes. 27, 28 ISO International Organization for Standardization. 10 SaaS Software as a service. 1 VE Virtual Environment. 2, 4, 5, 31 VR Virtual Reality. 2, 27 WebGL Web Graphics Library. 1, 2, 15, 28 ix 1 Introduction This master thesis was done in collaboration with Sandell Collection AB – an architecture firm based in Stockholm, Sweden. From now on, this firm will be referred to as the client. 1.1 Background When buying a house in Sweden today, the customer normally contacts a building contractor which in turn contacts an architecture firm. This process makes it difficult for architecture firms to influence the customer to choose their designs. If the architecture firms wants to show their designs to the customer directly, they basically have two alternatives. They can either construct a miniature model of the design (see figure 1.1), or they can show a computer model of the design. Both of these alternatives means that they would have to invite all customers, one by one, to show the models at their office. That would be very time-consuming, and hence, very expensive too. If instead, they were able to make the models available online, so that anyone interested could explore them in their own pace, they would not only be able to save time, but they could also reach more potential buyers. 1.2 Motivation Building Information Modelling (BIM) is the process of collecting all the information about a building in one place. The data is stored in a BIM file that works as a database for the building. The database can be used to visualise the building in 3D as it contains all the geometries and coordinates of all the objects in the building. This makes it possible for architects, engineers and contractors to work collaboratively and in real-time on the same model. The software that is used by architects, to work in the BIM files are desktop applications that are very advanced and also very expensive, examples of these are Autodesk Revit1 and RhinoCeros2. 1https://www.autodesk.com/products/revit 2https://www.rhino3d.com/ 1 1.3. Aim (a) Interior model of a condo (b) Exterior model of a building Figure 1.1: Physical architectural models that can be shown to potential customers to promote the sale of a building. In (a) the focus is on the interior of the building, whereas in (b) the exterior is shown instead. There also exist some applications that are Software as a service (SaaS) applications (Au- todesk Forge3, bimsync4). These use Web Graphics Library5 (WebGL) which is a JavaScript6 library for visualising 2D and 3D graphics directly in a web browser without the need to in- stall additional software. These could.
Recommended publications
  • An Analytical Introduction to Descriptive Geometry

    An Analytical Introduction to Descriptive Geometry

    An analytical introduction to Descriptive Geometry Adrian B. Biran, Technion { Faculty of Mechanical Engineering Ruben Lopez-Pulido, CEHINAV, Polytechnic University of Madrid, Model Basin, and Spanish Association of Naval Architects Avraham Banai Technion { Faculty of Mathematics Prepared for Elsevier (Butterworth-Heinemann), Oxford, UK Samples - August 2005 Contents Preface x 1 Geometric constructions 1 1.1 Introduction . 2 1.2 Drawing instruments . 2 1.3 A few geometric constructions . 2 1.3.1 Drawing parallels . 2 1.3.2 Dividing a segment into two . 2 1.3.3 Bisecting an angle . 2 1.3.4 Raising a perpendicular on a given segment . 2 1.3.5 Drawing a triangle given its three sides . 2 1.4 The intersection of two lines . 2 1.4.1 Introduction . 2 1.4.2 Examples from practice . 2 1.4.3 Situations to avoid . 2 1.5 Manual drawing and computer-aided drawing . 2 i ii CONTENTS 1.6 Exercises . 2 Notations 1 2 Introduction 3 2.1 How we see an object . 3 2.2 Central projection . 4 2.2.1 De¯nition . 4 2.2.2 Properties . 5 2.2.3 Vanishing points . 17 2.2.4 Conclusions . 20 2.3 Parallel projection . 23 2.3.1 De¯nition . 23 2.3.2 A few properties . 24 2.3.3 The concept of scale . 25 2.4 Orthographic projection . 27 2.4.1 De¯nition . 27 2.4.2 The projection of a right angle . 28 2.5 The two-sheet method of Monge . 36 2.6 Summary . 39 2.7 Examples . 43 2.8 Exercises .
  • Viewing in 3D

    Viewing in 3D

    Viewing in 3D Viewing in 3D Foley & Van Dam, Chapter 6 • Transformation Pipeline • Viewing Plane • Viewing Coordinate System • Projections • Orthographic • Perspective OpenGL Transformation Pipeline Viewing Coordinate System Homogeneous coordinates in World System zw world yw ModelViewModelView Matrix Matrix xw Tractor Viewing System Viewer Coordinates System ProjectionProjection Matrix Matrix Clip y Coordinates v Front- xv ClippingClipping Wheel System P0 zv ViewportViewport Transformation Transformation ne pla ing Window Coordinates View Specifying the Viewing Coordinates Specifying the Viewing Coordinates • Viewing Coordinates system, [xv, yv, zv], describes 3D objects with respect to a viewer zw y v P v xv •A viewing plane (projection plane) is set up N P0 zv perpendicular to zv and aligned with (xv,yv) yw xw ne pla ing • In order to specify a viewing plane we have View to specify: •P0=(x0,y0,z0) is the point where a camera is located •a vector N normal to the plane • P is a point to look-at •N=(P-P)/|P -P| is the view-plane normal vector •a viewing-up vector V 0 0 •V=zw is the view up vector, whose projection onto • a point on the viewing plane the view-plane is directed up Viewing Coordinate System Projections V u N z N ; x ; y z u x • Viewing 3D objects on a 2D display requires a v v V u N v v v mapping from 3D to 2D • The transformation M, from world-coordinate into viewing-coordinates is: • A projection is formed by the intersection of certain lines (projectors) with the view plane 1 2 3 ª x v x v x v 0 º ª 1 0 0 x 0 º « » «
  • Squaring the Circle in Panoramas

    Squaring the Circle in Panoramas

    Squaring the Circle in Panoramas Lihi Zelnik-Manor1 Gabriele Peters2 Pietro Perona1 1. Department of Electrical Engineering 2. Informatik VII (Graphische Systeme) California Institute of Technology Universitat Dortmund Pasadena, CA 91125, USA Dortmund, Germany http://www.vision.caltech.edu/lihi/SquarePanorama.html Abstract and conveying the vivid visual impression of large panora- mas. Such mosaics are superior to panoramic pictures taken Pictures taken by a rotating camera cover the viewing with conventional fish-eye lenses in many respects: they sphere surrounding the center of rotation. Having a set of may span wider fields of view, they have unlimited reso- images registered and blended on the sphere what is left to lution, they make use of cheaper optics and they are not be done, in order to obtain a flat panorama, is projecting restricted to the projection geometry imposed by the lens. the spherical image onto a picture plane. This step is unfor- The geometry of single view point panoramas has long tunately not obvious – the surface of the sphere may not be been well understood [12, 21]. This has been used for mo- flattened onto a page without some form of distortion. The saicing of video sequences (e.g., [13, 20]) as well as for ob- objective of this paper is discussing the difficulties and op- taining super-resolution images (e.g., [6, 23]). By contrast portunities that are connected to the projection from view- when the point of view changes the mosaic is ‘impossible’ ing sphere to image plane. We first explore a number of al- unless the structure of the scene is very special.
  • CS 4204 Computer Graphics 3D Views and Projection

    CS 4204 Computer Graphics 3D Views and Projection

    CS 4204 Computer Graphics 3D views and projection Adapted from notes by Yong Cao 1 Overview of 3D rendering Modeling: * Topic we’ve already discussed • *Define object in local coordinates • *Place object in world coordinates (modeling transformation) Viewing: • Define camera parameters • Find object location in camera coordinates (viewing transformation) Projection: project object to the viewplane Clipping: clip object to the view volume *Viewport transformation *Rasterization: rasterize object Simple teapot demo 3D rendering pipeline Vertices as input Series of operations/transformations to obtain 2D vertices in screen coordinates These can then be rasterized 3D rendering pipeline We’ve already discussed: • Viewport transformation • 3D modeling transformations We’ll talk about remaining topics in reverse order: • 3D clipping (simple extension of 2D clipping) • 3D projection • 3D viewing Clipping: 3D Cohen-Sutherland Use 6-bit outcodes When needed, clip line segment against planes Viewing and Projection Camera Analogy: 1. Set up your tripod and point the camera at the scene (viewing transformation). 2. Arrange the scene to be photographed into the desired composition (modeling transformation). 3. Choose a camera lens or adjust the zoom (projection transformation). 4. Determine how large you want the final photograph to be - for example, you might want it enlarged (viewport transformation). Projection transformations Introduction to Projection Transformations Mapping: f : Rn Rm Projection: n > m Planar Projection: Projection on a plane.
  • Ac 2008-325: an Architectural Walkthrough Using 3D Game Engine

    Ac 2008-325: an Architectural Walkthrough Using 3D Game Engine

    AC 2008-325: AN ARCHITECTURAL WALKTHROUGH USING 3D GAME ENGINE Mohammed Haque, Texas A&M University Dr. Mohammed E. Haque is a professor and holder of the Cecil O. Windsor, Jr. Endowed Professorship in Construction Science at Texas A&M University at College Station, Texas. He has over twenty years of professional experience in analysis, design, and investigation of building, bridges and tunnel structural projects of various city and state governments and private sectors. Dr. Haque is a registered Professional Engineer in the states of New York, Pennsylvania and Michigan, and members of ASEE, ASCE, and ACI. Dr. Haque received a BSCE from Bangladesh University of Engineering and Technology, a MSCE and a Ph.D. in Civil/Structural Engineering from New Jersey Institute of Technology, Newark, New Jersey. His research interests include fracture mechanics of engineering materials, composite materials and advanced construction materials, architectural/construction visualization and animation, computer applications in structural analysis and design, artificial neural network applications, knowledge based expert system developments, application based software developments, and buildings/ infrastructure/ bridges/tunnels inspection and database management systems. Pallab Dasgupta, Texas A&M University Mr. Pallab Dasgupta is a graduate student of the Department of Construction Science, Texas A&M University. Page 13.173.1 Page © American Society for Engineering Education, 2008 An Architectural Walkthrough using 3D Game Engine Abstract Today’s 3D game engines have long been used by game developers to create dazzling worlds with the finest details—allowing users to immerse themselves in the alternate worlds provided. With the availability of the “Unreal Engine” these same 3D engines can now provide a similar experience for those working in the field of architecture.
  • Perspective Projection

    Perspective Projection

    Transform 3D objects on to a 2D plane using projections 2 types of projections Perspective Parallel In parallel projection, coordinate positions are transformed to the view plane along parallel lines. In perspective projection, object position are transformed to the view plane along lines that converge to a point called projection reference point (center of projection) 2 Perspective Projection 3 Parallel Projection 4 PROJECTIONS PARALLEL PERSPECTIVE (parallel projectors) (converging projectors) One point Oblique Orthographic (one principal (projectors perpendicular (projectors not perpendicular to vanishing point) to view plane) view plane) Two point General (Two principal Multiview Axonometric vanishing point) (view plane parallel (view plane not parallel to Cavalier principal planes) to principal planes) Three point (Three principal Cabinet vanishing point) Isometric Dimetric Trimetric 5 Perspective v Parallel • Perspective: – visual effect is similar to human visual system... – has 'perspective foreshortening' • size of object varies inversely with distance from the center of projection. Projection of a distant object are smaller than the projection of objects of the same size that are closer to the projection plane. • Parallel: It preserves relative proportion of object. – less realistic view because of no foreshortening – however, parallel lines remain parallel. 6 Perspective Projections • Characteristics: • Center of Projection (CP) is a finite distance from object • Projectors are rays (i.e., non-parallel) • Vanishing points • Objects appear smaller as distance from CP (eye of observer) increases • Difficult to determine exact size and shape of object • Most realistic, difficult to execute 7 • When a 3D object is projected onto view plane using perspective transformation equations, any set of parallel lines in the object that are not parallel to the projection plane, converge at a vanishing point.
  • Subsymmetry Analysis of Archiectural Designs, Some Examples

    Subsymmetry Analysis of Archiectural Designs, Some Examples

    Environment and Planning B: Planning and Design 2000, volume 27, pages 121- 136 Sub symmetry analysis of architectural designs: some examples Jin-Ho Park Department of Architecture and Urban Design, University of California, Los Angeles, CA 90095, USA; e-mail: [email protected] Received 1 December 1998; in revised form 28 April 1999 Abstract. An analytic method founded on the mathematical structure of symmetry groups is defined and some applications to the analysis of architectural designs are shown. In earlier work by March and Park, architectural designs were analyzed with respect to a partial ordering of subsymmetries associated with the symmetry of the square and then classified by lattice diagrams of the subsymmetries. The analytic approach dem- onstrates how different subsymmetries may be revealed in each part of the design and how various symmetric transformations combine to achieve the whole design. At first glance, the individual designs seem intricate and without obvious symmetry. However, an analysis of the sub symmetries and symmetric transformations clearly exposes the underlying structure. In this paper, the methodology employed in previous papers is substantially recounted, but new architectural examples have been added. The methodology of subsymmetry analysis In the methodology, various types of symmetry, or subsymmetries, are superimposed in individual designs and illustrate how symmetry may be employed strategically in the design process. An account of the mathematical structure of symmetry groups in analyzing architectural designs has been given over the last ten years by Lionel March in his graduate lectures at UCLA on the Fundamentals of Architectonics: Symmetry (reading materials for this course include Baglivo and Graver, 1976; March, 1995; + March and Steadman, 1971; see also Budden, 1972; Grossman and Magnus, 1964; Griinbaum and Shephard, 1987; Shubnikov and Kopstik, 1974; Weyl, 1952).
  • A Resting Place: Notes on Optimism and Shadows

    A Resting Place: Notes on Optimism and Shadows

    OAC PRESS Working Paper Series #3 How Knowledge Grows An Anthropological Anamorphosis Alberto Corsín Jiménez CSIC, Spain’s National Research Council © 2010 Alberto Corsín Jiménez Open Anthropology Cooperative Press www.openanthcoop.net/press This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-nd/3.0/ 1 ‘the most admirable operations derive from very weak means’ Galileo Galilei (1968: 109) ‘Not just judgments about analogy but judgments about proportion inform any organization of data.’ Marilyn Strathern (2004 [1991]: 24) ‘A strange thing full of water’ Michel Serres (1995: 122) I open with a myth of origins: All political thought evinces an aesthetic of sorts. Dioptric anamorphosis, for instance, was the ‘science of miracles’ through which Hobbes imagined his Leviathan. An example of the optical wizardry of seventeenth century clerical mathematicians, a dioptric anamorphic device used a mirror or lens to refract an image that had deliberately been distorted and exaggerated back into what a human eye would consider a natural or normal perspective. Many such artefacts played with pictures of the faces of monarchs or aristocrats. Here the viewer would be presented with a panel made up of a multiplicity of images, often emblems representing the patriarch’s genealogical ancestors or the landmarks of his estate. A second look at the panel through the optical glass, however, would recompose the various icons, as if by magical transubstantiation, into the master’s face. Noel Malcolm has exposed the place that the optical trickery of anamorphosis played in Hobbes’ political theory of the state (Malcolm 2002).
  • Subsymmetry Analysis and Synthesis of Architectural Designs

    Subsymmetry Analysis and Synthesis of Architectural Designs

    BRIDGES Mathematical Connections in Art, Music, and Science Subsymmetry Analysis and Synthesis of Architectural Designs Jin-Ho Park School of Architecture University of Hawaii at Manoa Honolulu, HI 96822, U.S.A. E-mail: [email protected] Abstract This paper presents an analytic and synthetic method founded on the algebraic structure of symmetry groups of a regular polygon. With the method, an architectural design is analyzed to demonstrate the use of symmetry in formal composition, and then a new design is constructed with its hierarchical structure of the method. 1. Introduction The approach of subsymmetry analysis and synthesis of architectural designs shows how various types of symmetry, or subsymmetries, are superimposed in individual designs, and illustrates how symmetry may be employed strategically in the design process. Analytically, by viewing architectural designs in this way, symmetry which is superimposed in several layers in a design and which may not be immediately recognizable become transparent. Synthetically, architects can benefit from being conscious of using group operations and spatial transformations associated with symmetry in compositional and thematic development. The advantage of operating the symmetric idea in this way is to provide architects·a method for analysis and description of sophisticated designs, and inspiration for the creation of new designs. The objective of the research resides in searching out the fundamental principles of architecture. A study of the fundamental principles of spatial forms in architecture is an essential prerequisite to the wider understanding of complex designs as well as the creation of new architectural forms. In this I stand by the Goethe's theory of metamorphosis in The Metamorphosis of Plants.
  • Anamorphosis: Optical Games with Perspective’S Playful Parent

    Anamorphosis: Optical Games with Perspective’S Playful Parent

    Anamorphosis: Optical games with Perspective's Playful Parent Ant´onioAra´ujo∗ Abstract We explore conical anamorphosis in several variations and discuss its various constructions, both physical and diagrammatic. While exploring its playful aspect as a form of optical illusion, we argue against the prevalent perception of anamorphosis as a mere amusing derivative of perspective and defend the exact opposite view|that perspective is the derived concept, consisting of plane anamorphosis under arbitrary limitations and ad-hoc alterations. We show how to define vanishing points in the context of anamorphosis in a way that is valid for all anamorphs of the same set. We make brief observations regarding curvilinear perspectives, binocular anamorphoses, and color anamorphoses. Keywords: conical anamorphosis, optical illusion, perspective, curvilinear perspective, cyclorama, panorama, D¨urermachine, color anamorphosis. Introduction It is a common fallacy to assume that something playful is surely shallow. Conversely, a lack of playfulness is often taken for depth. Consider the split between the common views on anamorphosis and perspective: perspective gets all the serious gigs; it's taught at school, works at the architect's firm. What does anamorphosis do? It plays parlour tricks! What a joker! It even has a rather awkward dictionary definition: Anamorphosis: A distorted projection or drawing which appears normal when viewed from a particular point or with a suitable mirror or lens. (Oxford English Dictionary) ∗This work was supported by FCT - Funda¸c~aopara a Ci^enciae a Tecnologia, projects UID/MAT/04561/2013, UID/Multi/04019/2013. Proceedings of Recreational Mathematics Colloquium v - G4G (Europe), pp. 71{86 72 Anamorphosis: Optical games.
  • Site Plan Creation

    Site Plan Creation

    GRAPHISOFT WORKFLOW GUIDE SERIES Site Plan Creation Workflow Guide 2019/5 Customer Support Services Department February 2019 Exclusively for SSA Customer Use The Workflow Guide Series are know-how documents providing solutions recommended for BIM workflows and project management related challenges. The Site Plan Creation guide is offering an overview of the different data types and methods in ARCHICAD to create a site plan drawing as per the required documentation package. This document was created with the aim to support the efficiency of your work. If you have any feedback, please send it to [email protected]. Visit the GRAPHISOFT website at www.graphisoft.com for local distributor and product availability information. Workflow Guide Series Site Plan Creation (International English Version) Copyright © 2019 by GRAPHISOFT, all rights reserved. Reproduction, paraphrasing or translation without express prior written permission is strictly prohibited. Trademarks ARCHICAD® is a registered trademark of GRAPHISOFT. All other trademarks are the property of their respective holders. Credits Authors Máté Marozsán – GRAPHISOFT SE Gordana Radonić – GRAPHISOFT SE Contributors Pantelis Ioannidis – GRAPHISOFT SE Ákos Karóczkai – GRAPHISOFT SE Enzyme - Hong Kong 1 Table of contents 1. Site planning ....................................................................................................................................... 3 2. Site plan data types ..........................................................................................................................
  • Anamorphic Projection: Analogical/Digital Algorithms

    Anamorphic Projection: Analogical/Digital Algorithms

    Nexus Netw J (2015) 17:253–285 DOI 10.1007/s00004-014-0225-5 RESEARCH Anamorphic Projection: Analogical/Digital Algorithms Francesco Di Paola • Pietro Pedone • Laura Inzerillo • Cettina Santagati Published online: 27 November 2014 Ó Kim Williams Books, Turin 2014 Abstract The study presents the first results of a wider research project dealing with the theme of ‘‘anamorphosis’’, a specific technique of geometric projection of a shape on a surface. Here we investigate how new digital techniques make it possible to simplify the anamorphic applications even in cases of projections on complex surfaces. After a short excursus of the most famous historical and contemporary applications, we propose several possible approaches for managing the geometry of anamorphic curves both in the field of descriptive geometry (by using interactive tools such as Cabrı` and GeoGebra) and during the complex surfaces realization process, from concept design to manufacture, through CNC systems (by adopting generative procedural algorithms elaborated in Grasshopper). Keywords Anamorphosis Anamorphic technique Descriptive geometry Architectural geometry Generative algorithms Free form surfaces F. Di Paola (&) Á L. Inzerillo Department of Architecture (Darch), University of Palermo, Viale delle Scienze, Edificio 8-scala F4, 90128 Palermo, Italy e-mail: [email protected] L. Inzerillo e-mail: [email protected] F. Di Paola Á L. Inzerillo Á C. Santagati Department of Communication, Interactive Graphics and Augmented Reality, IEMEST, Istituto Euro Mediterraneo di Scienza e Tecnologia, 90139 Palermo, Italy P. Pedone Polytechnic of Milan, Bulding-Architectural Engineering, EDA, 23900 Lecco, Italy e-mail: [email protected] C. Santagati Department of Architecture, University of Catania, 95125 Catania, Italy e-mail: [email protected] 254 F.