Advances in Intelligent Systems and Computing

Volume 809

Series editor Janusz Kacprzyk, Polish Academy of Sciences, Warsaw, Poland e-mail: [email protected] The series “Advances in Intelligent Systems and Computing” contains publications on theory, applications, and design methods of Intelligent Systems and Intelligent Computing. Virtually all disciplines such as engineering, natural sciences, computer and information science, ICT, economics, business, e-commerce, environment, healthcare, life science are covered. The list of topics spans all the areas of modern intelligent systems and computing such as: computational intelligence, soft computing including neural networks, fuzzy systems, evolutionary computing and the fusion of these paradigms, social intelligence, ambient intelligence, computational neuroscience, artificial life, virtual worlds and society, cognitive science and systems, Perception and Vision, DNA and immune based systems, self-organizing and adaptive systems, e-Learning and teaching, human-centered and human-centric computing, recommender systems, intelligent control, robotics and mechatronics including human-machine teaming, knowledge-based paradigms, learning paradigms, machine ethics, intelligent data analysis, knowledge management, intelligent agents, intelligent decision making and support, intelligent network security, trust management, interactive entertainment,Web intelligence and multimedia. The publications within “Advances in Intelligent Systems and Computing” are primarily proceedings of important conferences, symposia and congresses. They cover significant recent developments in the field, both of a foundational and applicable character. An important characteristic feature of the series is the short publication time and world-wide distribution. This permits a rapid and broad dissemination of research results. Advisory Board Chairman Nikhil R. Pal, Indian Statistical Institute, Kolkata, India e-mail: [email protected] Members Rafael Bello Perez, Universidad Central “Marta Abreu” de Las Villas, Santa Clara, Cuba e-mail: [email protected] Emilio S. Corchado, University of Salamanca, Salamanca, Spain e-mail: [email protected] Hani Hagras, University of Essex, Colchester, UK e-mail: [email protected] László T. Kóczy, Széchenyi István University, Győr, Hungary e-mail: [email protected] Vladik Kreinovich, University of Texas at El Paso, El Paso, USA e-mail: [email protected] Chin-Teng Lin, National Chiao Tung University, Hsinchu, Taiwan e-mail: [email protected] Jie Lu, University of Technology, Sydney, Australia e-mail: [email protected] Patricia Melin, Tijuana Institute of Technology, Tijuana, Mexico e-mail: [email protected] Nadia Nedjah, State University of Rio de Janeiro, Rio de Janeiro, Brazil e-mail: [email protected] Ngoc Thanh Nguyen, Wroclaw University of Technology, Wroclaw, Poland e-mail: [email protected] Jun Wang, The Chinese University of Hong Kong, Shatin, Hong Kong e-mail: [email protected]

More information about this series at http://www.springer.com/series/11156 Luigi Cocchiarella Editor

ICGG 2018—Proceedings of the 18th International Conference on Geometry and Graphics 40th Anniversary—Milan, Italy, August 3–7, 2018

123 Editor Luigi Cocchiarella Department of Architecture and Urban Studies—DASTU, School of Architecture Urban Planning and Construction Engineering—AUIC Politecnico di Milano Milan, Italy

ISSN 2194-5357 ISSN 2194-5365 (electronic) Advances in Intelligent Systems and Computing ISBN 978-3-319-95587-2 ISBN 978-3-319-95588-9 (eBook) https://doi.org/10.1007/978-3-319-95588-9

Library of Congress Control Number: 2018948129

© Springer International Publishing AG, part of Springer Nature 2019, corrected publication 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Preface

This book publishes the scientific contributions submitted for the 18th International Conference on Geometry and Graphics, celebrating the 40th anniversary from the first edition held in Vancouver at the University of British Columbia in 1978. At that time, it was the International Conference on Descriptive Geometry (ICDG), but in the second edition organized in Beijing in 1984, the name began to change, until the International Conference on Engineering Computer Graphics and Descriptive Geometry (ICECGDG) appeared in the 4th edition held in Miami in 1990, aiming at keeping the scientific event in step with the times, given the pervasive diffusion of the digital, and with the aim of widening the disciplinary spectrum of interest for the meeting. In due course, the revolutionary power of the computerized geometry and graphics, and the new sensitivity towards the role of geometry and graphics in about every theoretical and operational field, claimed for a more representative denomi- nation, reflecting the ever-widening thematics that the conference intended to pursue. Then, in 2000, the 9th edition was finally organized as an International Conference on Geometry and Graphics (ICGG), taking the name from the International Society for Geometry and Graphics (ISGG), constituted in 1990 and promoting the event biannually at different venues around the world. By the way, I had the privilege to participate as a guest speaker in the Panel Session on The Taxonomy of Geometry and Graphics, which concluded the 8th edition held at the University of Austin in Texas, and contributed to the decision to give a new name to the Conference. The references mentioned above may be useful for understanding the structure of the Proceedings for those who are new to the ICGGs Conferences. A series of scientific essays authored by the Guest Lecturers introduces the volume, representative of the variety of topics and research inherent to Geometry and Graphics, carried out in the three regions of the world, Asia/Australia/Oceania, Europe/Near East/Africa, and North America/South America, according to the geographic areas mapped by the ISGG.

v vi Preface

All the scientific contributions submitted by the authors are organized by topics, namely Theoretical Graphics and Geometry, Applied Geometry and Graphics, Engineering Computer Graphics, Graphics Education, and the new topic Geometry and Graphics in History, proposed for this edition. Poster papers presented in the plenary poster sessions at the Conference on the mentioned topics conclude the volume. On the Conference website, available at the web address www.icgg2018.polimi.it,aseriesof subtopics is also listed, together with a statement inviting prospective authors to submit papers even if not strictly related to the topics listed, which is consistent with the aim to promote Geometry and Graphics worldwide and in all the interested fields of research, education, industrial applications and profession, as one can also read on the official webpage of the International Society for Geometry and Graphics at the web address www.isgg.net. As in our tradition since 1997, an extended version of some selected contributions, recommended by the Session Chairs during the Conference, will also be published on the Journal for Geometry and Graphics (JGG), webpage www.heldermann.de/JGG/jggcover.htm. Being these the Proceedings of the 40th anniversary of the Conference, we like to recall the preface to the first Proceedings published in 1978, where professor Stephen Slaby of the Princeton University referred to the genuine spirit of geometry.Aswe can clearly see, this powerful spirit, and let us say, the spirit of geometry and graphics seem to be universally, and even strongly, confirmed nowadays. For the reasons mentioned, this volume is addressed to all those who have a direct interest in Geometry and Graphics, as well as in any fields, however related to Geometry and Graphics. For the same reasons, it can be of interest for scholars, researchers, teachers, Ph.D. students, students in general, as well as professionals. We also hope that the book may somehow reach other readers, stimulating interest in Geometry and Graphics. The SCOPUS indexing provided by Springer should be of help in this direction. This publication is the result of the generous joint effort of a large community of authors submitting their contributions; chairs and cochairs, namely Yasushi Ya-maguchi, Baoling Han, Ema Jurkin, Aura Conci, members of the steering and program committees, and reviewers, who have respectively led, supported, and collaborated in the reviewing process. The local editorial activity has particularly benefited from the engagement of some members of the Conference committee, who helped me in preparing the final editorial master, they are my colleagues Giampiero Mele, Daniela Oreni, Barbara E. Piga, Nicole De Togni, and Matteo Romanato. I would also thank for their advice the colleagues Raffaele Ardito, Dario Angelo Maria Coronelli, Damiano Cosimo Iacobone, Roberto Notari, Graziano Mario Valenti, and the Conference Staff and the Offices at the Politecnico di Milano in relation to the administrative aspects of the event. My special personal gratitude goes to Mrs. Sarah Pye for the competent support in the translation of some key documents, and for her frequent prompt helps on the matter. And my students Matteo Cavaglià, Chiara Gargan, Innocent Hembi Hembi, Freeda Jane Madius, Aurora Moreschi, Hanxi Xie, Di Yan, and Yangxing Zhang, for their admirable kind availability. Preface vii

Finally, as the Editor of the volume, I would like to express my thanks to Springer, and personally to our Springer’s Editor/Engineering, Pierpaolo Riva, for the constant support offered during the entire editorial process. Hoping this book will offer you a pleasant immersion into the fascinating universe of Geometry and Graphics!

Milan, Italy Prof. Luigi Cocchiarella ICGG2018 Executive Chairman Politecnico di Milano Department of Architecture and Urban Studies - DASTU Welcome Addresses from Politecnico di Milano

Welcome Address by the Rector Politecnico di Milano is glad to hold “The 18th International Conference on Geometry and Graphics” (ICGG2018) and to celebrate its 40th anniversary at its premises. Politecnico wishes the best to the International Society for Geometry and Graphics (ISGG), under whose auspices the Conference is organized. My warmest welcome to all the participants! Topics and goals of the International Conference on Geometry and Graphics are, by tradition, relevant for our academic community, dealing with our common language across the various fields of Engineering, Architecture, and Design. Research and technology transfer—carried out in our 12 Departments, through the educational programmes of our 4 Schools, by means of 27 bachelor courses and 45 master courses, together with our 18 Ph.D. Programmes, as well as several other Post Graduate Programmes—make Geometry and Graphics familiar with our everyday activities. Politecnico di Milano was founded in 1863. Nowadays, it counts 7 Campuses, located in Como, Cremona, Lecco, Mantova, Piacenza, and two in Milan, namely the Bovisa Campus and the Leonardo Campus, headquarter and Conference venue. Thanks to the passionate and competent dedication of researchers and teachers, as well as administrative and technical staff, benefited from students coming from all over the world, Politecnico di Milano ranks as the first Technical University in Italy, with recognized international reputation. I hope the participants to the ICGG 2018 feel at home at our university. I am glad for such a large presence of delegates and accompanying persons coming from about forty countries in the world. I wish you all a worthy celebration of this 40th anniversary, whose initial meeting was held in Vancouver at the University of British Columbia in 1978. I am sure this will turn out to be an inspiring and memorable experience at Politecnico di Milano and an enjoyable stay in Italy, surrounded by the historical beauties and fashionable modern atmospheres of Milan!

Prof. Ferruccio Resta Milan, Italy

ix x Welcome Addresses from Politecnico di Milano

Welcome Address by the Head of Department of Architecture and Urban Studies When Milan was chosen to host the 18th International Conference on Geometry and Graphics, I was very happy to receive this opportunity. The approach, the themes, and the program of the Conference are really an extraordinary occasion for interdisciplinary dialogues and scientific exchange between scholars, scientists, and teachers coming from all over the world. I am sure that Politecnico di Milano, with its schools of Engineering, Architecture and Design, and their experimental approach to research and teaching, can be an interesting set for this important international event. On the other hand, I think that the ICGG Conference will enrich transdisciplinary research at Politecnico and between our University and the ICGG network. I would like to welcome all the participants and the accompanying persons here in Milan. I am sure that aside from the scientific work, you will enjoy our vibrant city, that is living in these years real urban and cultural renaissance. We thank all the participants for the papers submitted, and we hope that this event will contribute to further development of geometry and new interactions between geometry, arts, and sciences.

Prof. Gabriele Pasqui Milan, Italy

Welcome Address by the Dean of School of Architecture Urban Planning Construction Engineering It is a pleasure to express my welcome to the participants of the 18th International Conference on Geometry and Graphics, to whose organization several teachers and students of the School of Architecture Urban Studies and Construction Engineering (AUIC) of the Politecnico di Milano contributed as members of the ICGG2018 Local Organizing Committee, as well as that of the supporting staff. The Conference topic is indeed of relevant importance for an education in Architecture, as well as in the related fields of Urban Studies and Construction Engineering, providing the bases for a common language to support and carry out the design processes involved, at any latitude and dimensional scale of the spatial contexts of human life. Moreover, the importance of Geometry and Graphics has become more and more important with the advent and the massive diffusion of Computer Graphics, imposing heavy changes in research, profession, and of course in education. Our School has recently fundamentally renovated its Bachelor and Master Programs, introducing important innovations in the curricula, as well as in the educational models and styles, including targeted elective initiative in order to appropriately promote and improve digital literacy at the various educational levels, in line with the foremost goals of our University. Welcome Addresses from Politecnico di Milano xi

Our School has also been a leader in the process of internationalization, attracting teachers and students from all over the world, which should make our international academic atmosphere familiar to the many international participants of the ICGG2018, and most of all, as we hope be, inspiring.

Prof. Ilaria Valente Milan, Italy

Welcome Address by the Coordinator of the Unit of Graphic Representation On behalf of the Unit of Graphic Representation in the School of Architecture Urban Planning and Construction Engineering, I would like to say thanks and extend a warm greeting to all participants of the 18th International Conference on Geometry and Graphics, hosted by Politecnico di Milano in 2018. As a group of professors and researchers practicing drawing and architectural representation, the Unit of Graphic Representation is particularly interested in the activities of the Society of Geometry and Graphics. Similarly, the Conference represents an interesting opportunity to listen to presentations on Geometry and Graphics, faced also from different points of view in respect of what is taught in our School of Architecture. Our training as scholars in representation subject is deeply rooted in Geometry, or better said, in Geometries, even if our disciplines involve many different com- ponents from the theoretical approach to the technological one. As Professors we teach representation disciplines not only in Architecture courses but also in Urban Design, Preservation, Landscape Architecture, only to recall the most important contribution: our shared commitment is to focus on both qualitative and quantitative features of graphic representation. The present conference is a significant occasion, on one hand it is the beginning of new international relationships and on the other, to deepen those already exist- ing: in fact how graphic and geometric disciplines and research are practiced in foreign schools and research centers are crucial for all of us. Furthermore, as a member of the Board of the Unione Italiana per il Disegno, I think that this is a significant occurrence to make the relationship between the two scientific society stronger. Last but not least, I am particularly glad that Milan is the location for the Conference of Geometry and Graphics in the 40th anniversary from the first one: it’s a singular and welcome coincidence that the Politecnico of Milano will also host, next September, the 40th UID CONFERENCE devoted to Representation/ Material/Immaterial. Drawing as (in)tangible representation.

Prof. Rossella Salerno Milan, Italy Welcome Addresses from the Board of Chairs

Welcome Address by the President of ISGG (and Conference Chairman of ICGG 2018) On behalf of the International Society for Geometry and Graphics (ISGG), it is my honor and pleasure to welcome you to Milan for the 18th International Conference on Geometry and Graphics (ICGG). ICGG has a series of international conferences held in every even-numbered year. The first conference took place in Vancouver, Canada, in 1978, and was hosted by the Engineering Design Graphics Division (EDGD) of the American Society for Engineering Education (ASEE). Therefore, this is the fortieth anniversary of the conference series. During the first four con- ferences, the core members confirmed the importance of having an international academic forum concerning geometry and graphics. ISGG was established at the 5th conference in Melbourne in 1992. Since then, it is our tradition to hold ICGG hosted by our members from the three regions all over the world, namely, Asia/Oceania, Europe/Africa, and North/South America. We are grateful to have the opportunity to meet in Milan, Italy, for a memorable conference. Milan is one of the most suitable cities for its historical/cultural background in terms of geometry and graphics. Also, Italy is one of the countries which provides the most active members of our society. At the last conferences, Italy was the first or second country for the number of participants excepting the host country. I hope to maintain the great relationship with Italian colleagues and the national body of Italy, Unione Italiana Disegno (UID), for the future. As a president of ISGG, it is important to take this opportunity to promote ISGG. This series of conference is one of our main events for the presentation and dis- cussion of research related to geometry and graphics. ISGG covers a broad spec- trum of geometry and graphics as does the conference, which includes theoretical graphics and geometry, applied geometry and graphics, engineering computer graphics, graphics education, and geometry and graphics in history. The ISGG also sponsors the Journal for Geometry and Graphics (JGG). It is a peer-reviewed scientific journal. The excellent papers presented in the conference will be selected for the further reviewing process for publication in JGG. The journal appears in one volume per year, consisting of two issues. All members of ISGG receive JGG free

xiii xiv Welcome Addresses from the Board of Chairs of charge. Please, ask our members about the society and consider joining ISGG, if you are not a member as yet. Finally, I would like to extend my sincere gratitude to the individuals and groups who have been organizing the conference. I would like to thank all of the societies, companies, organizations, and institutions that have helped to fund the conference. I am grateful to the local organizing committee and the host, Politecnico di Milano. It would be impossible for us to have the conference without their support. Last but certainly not least, I wish to express my true appreciation to Luigi Cocchiarella because of his dedicated work as the executive chair. Again, allow me to extend my welcome to all the conference participants. I wish you a pleasant stay in Milan and a productive and successful participation in the conference.

Prof. Yasushi Yamaguchi The University of Tokyo, Japan

Welcome Address by the former President of ISGG (and Honorary Conference Chairman of ICGG 2018) It is a cherished family tradition within the International Society for Geometry and Graphics to hold a biennial International Conference. For the upcoming conference in 2018 our colleagues from the Polytecnico di Milano with the executive chair Luigi Cocchiarella kindly offered to arrange this great event. Obviously, the exchange of information via modern media is much easier today than it once was. The oral presentation and face-to-face meetings and discussions, though, can give an indelible impression of new conceptions and of the motivation behind them. The immediate, personal mode of scientific exchange sparks off lots of new ideas, much more than any electronic exchange of data can do. Discussions following the presentations and the personal contact between dedicated scientists can inspire further research and encourage new teaching approaches. At this conference you can also embrace the opportunity to exceed the limits of your personal focus of interest by listening to lectures from various fields of geometry and graphics. Grab the chance to enjoy and let geometry inspire your mind at the ICGG2018! The venue of this year’s ICGG conference is Milano, the famous capital of Lombardy, one of the most prolific regions in Italy. Milano is renowned as a city of culture, music and design. The cultural heritage of this city is tremendous. Not only is there magnificent architecture to be admired like the Duomo di Milano, that is, the Milan’s cathedral; the immaterial legacy of this magical city is appreciated all over the world. Let me mention the famed painting ‘The Last Supper’ by Leonardo da Vinci. The famous opera house ‘Teatro alla Scala’ is the venue of the premieres of such legendary operas as ‘Nabucco’, ‘Otello’, ‘Falstaff’ by Giuseppe Verdi or ‘Madama Butterfly’ and ‘Turandot’ by Giacomo Puccini. More recently, the uni- versal exposition EXPO with the general theme ‘Feeding the Planet, Energy for Life’ was hosted by Milano in 2015. In the field of design and fashion labels I just want to quote the names of ‘Gucci’, ‘Versace’, ‘Prada’ and ‘Armani’. Whatever I mention here, I am sure our organizors will be able to introduce us to the history of the venue in a much more impressive way. Welcome Addresses from the Board of Chairs xv

To organize such a big conference is a demanding, and tough job. It will be done by the highly qualified and motivated geometry group of the Politecnico di Milano. I deeply appreciate what they have already achieved and what they will be accomplishing in the course of the conference. Many, many thanks to all of them! I wish you all a pleasant stay and a successful participation at the International Conference on Geometry and Graphics at Milano!

Prof. Otto Röschel Graz University of Technology, Austria

Welcome Address by the President of UID (and Honorary Conference Chairman of ICGG 2018) The UID, Unione Italiana per il Disegno, our national scientific society, literally the Italian Union for Drawing, has very willingly granted the Patronage to the ICGG 2018. For many reasons. First of all the ICGG are, among the scientific meetings on graphic represen- tation, the ones with the wider international audience; as the ISGG, the International Society for Geometry and Graphics, which promotes the ICGG is, probably the most international within the scientific communities in our field. For some years, our national scientific society has been committed to making a mighty effort towards the internationalization of its own scientific meetings, as well as to promote educational and research activities of Italian members and professors of graphic representation in international contexts. During the last year edition of our annual national meeting organized by the UID, namely the 39th meeting, celebrated in Naples in September 2017, a very numerous participation of international delegates was registered. They sent 20% of the 300 abstracts received in total (the double if compared to 2016, the meeting with the highest number of international participants until then). At the end of the double reviewing process operated on full abstracts and papers, almost the same percentage was confirmed in the number of contributions accepted for publication on the Proceedings, including international contributions in collaboration with Italian authors, and from Italian authors on research conducted in other countries (such as Argentina, Chins, Finland, Georgia, Oman and Slovenia). Many interna- tional scholars coming from 12 countries participated in person, and for the first time also important ISGG’s representatives attended our Italian conference, namely the ISGG President, prof. Yasushi Yamaguchi, who gave the ISGG Welcome (besides sending a scientific contribution), and prof. Hellmuth Stachel, managing editor of the Journal for Geometry and Graphics, the scientific review of the ISGG, who attended the Round Table with the editors of other international scientific reviews in the field of graphic representation. The 2017 Conference in Naples has therefore been the most international among all those previously celebrated by the UID. We hope that the next UID Conference, which will be held in Milan from 13 to 15 September 2018, will also confirm the same trend. The next UID Conference in Milan will be the 40th in the cycle, just as 40 years have now passed since the first ICGG organized in Vancouver in 1978, at that time xvi Welcome Addresses from the Board of Chairs it was entitled International Conference on Descriptive Geometry. In 1980, two years after the first Italian conference, the UID was founded, which is indeed one of the older scientific societies worldwide in the field of graphic representation: maybe even the oldest, after the Brazilian ABEG (Associação Brasileira de ExpressãoGráfica, founded in 1963), and the Japanese JSGS (Japan Society for Graphic Science, founded in the 1967), both institutional members of the ISGG. Five years ago the UID has also joined the ISGG. Moreover, for some years now, the Italian members of the UID are among the major groups of participants in the ICGG, in the last two editions probably the second largest group after those from the organizing countries. In the present edition, they are obviously the largest: 30% of abstracts, corresponding to a fourth of the total in terms of individuals, came from Italian authors, where 20% of them are Italian professors in the field of graphic representation, almost all members of UID. We can say that topics and fields of interest of our scientific society are to some extent even wider than those of ISGG and ICGG. Indeed, Geometry is only one of the basic sciences at the base of the science of representation related to the technical field, which is our specific field, with special focus on architectural and civil engineering, representation of the landscape, environment and, the territory, but it is not the only one. In recent years, with growing conviction, our interest has moved towards the study and the elaboration of any kind of visual image, in every field and independently of the practical scope, starting from Science and Art, therefore beyond the limits of Architecture, Design, and Engineering fields. Nevertheless, even in this new light, Geometry—mainly Descriptive Geometry, but not only that—, remains an essential part of the reference research field of the UID. Geometry continues to be the subject to which many colleagues, carrying out historical studies, and research on the most recent topics, as well as on the future disciplinary developments, are dedicated. I like to think that having assigned to Luigi Cocchiarella the responsibility for organizing the ICGG 2018 in Milan, besides being a recognition of his commitment to the ISGG, also rewards the very great attention of our Italian scientific com- munity to the ICGG themes. I thank him on behalf of the entire UID for the extensive and excellent work carried out for this ICGG. For many years now Luigi has made the activities inside the ISGG and the ICGG an important aspect of his career as a professor and a researcher, and thanks to the scientific relationships established this way at an international level, he is today among the most fully engaged in the effort towards the internationalization of the UID. Since a few years ago he is the secretary of the committee for the international relationships of the UID, nowadays presided by prof. Stefano Bertocci, who on the last 14 and 15th June organized the Symposium of Representation, Scientific Area of Multidisciplinary International Programs in Florence. The aim of this meeting was to start a discussion with work groups organized by geographical areas and development programs, in order to analyse characters and specific constraints of the various cultural (and administrative) international contexts involved, of potential interest for the UID, and to investigate, through direct discussions, opportunities and channels for promoting and empowering our international activities in terms of Welcome Addresses from the Board of Chairs xvii research, education, seminars and conferences, and scientific publications with diffusion at an international level. I hope that on the occasion of the current ICGG 2018 some further and actual steps could be taken in this direction, consolidating existing relationships and generating new ones. I am however convinced that this edition of the ICGG will live up to the expectations, ours as well as of the ISGG. Good work to everyone.

Prof. Vito Cardone Università degli Studi di Salerno, Italy

Welcome Address by the Executive Conference Chairman of ICGG 2018 With profound sentiments of honor and happiness, as Executive Chairman of the ICGG2018, I address my warmest welcome to all the participants of The 18th International Conference on Geometry and Graphics, on the special occasion of the celebrations of its 40th anniversary in Milano! This edition is held in Italy at the Politecnico di Milano and here granted and organized at the Department of Architecture and Urban Studies (DASTU) under the auspices of the International Society for Geometry and Graphics (ISGG), financially supported by the aforementioned institutions, together with the Japan Society for Graphic Science (JSGS); the School of Architecture Urban Planning Construction Engineering (AUIC) and the Department of Mathematics of the Politecnico di Milano (DIMAT); and other generous sponsors listed on the ICGG2018 webpage www.icgg2018.polimi.it. The conference has also obtained the patronage of the Unione Italiana per il Disegno (UID) and the following Italian patrons: Istituto Lombardo Accademia di Scienze e Lettere; Istituto di Studi Superiori dell’Insubria Gerolamo Cardano; Fondazione Fratelli Confalonieri; Associazione Guido Ucelli Amici del Museo Nazionale della Scienza e della Tecnologia Leonardo da Vinci. As a significant symbolic link to its origins, and as a good wish for the 40th anniversary, the University of British Columbia (UBC) and the Engineering Design Graphics Division (EDGD) of the American Society for Engineering Education (ASEE), which respectively organized and sponsored the first edition in 1978, has also honored us with their patronage. Patrons and Sponsors are listed by active links to the corresponding websites on a dedicated section of the ICGG2018 webpage www.icgg2018.polimi.it. Our event was welcomed by the Councillor for Labour Policies, Business, Commerce and Human Resources of the Municipality of Milan. Personally speaking, the responsibility of undertaking the organization of such an important event will be part of the unforgettable records of my academic career, as well as a private memory. I wish that something of this feeling could also pervade our welcome participants, delegates and accompanying persons. When at the 17th ICGG in Beijing, at the beginning of August 2016, quite unexpectedly the events started moving in the direction of a Conference in Europe again in 2018, and namely in Italy at the Politecnico di Milano, it was clear that the time to organize the event was much shorter than usual, and in addition the upcoming 40th anniversary would increase our concern. On the other hand some occurrences of numbers and coincidences—a kind of kabbalah as we liked to say— xviii Welcome Addresses from the Board of Chairs seemed to encourage us: indeed, eighteenth edition would have been in two thou- sand and eighteen, the 40th anniversary would be in the 20th from my first atten- dance in 1998 at the Austin Conference, the last with the old name ICECGDG and in turn celebrating then the 20th anniversary from the Vancouver’s edition in 1978, which again coincided with an anniversary, namely the 50th of the American Society for Engineering Education. The proposal was immediately supported by the Head of the Department DASTU, with the agreement of the Rector of the Politecnico di Milano. Finally, although it was not possible to announce the Venue of the 2018 meeting at the closing ceremony in Beijing; thanks to the support of the Politecnico di Milano and the guidance of ISGG, the generous engagement of Chairs and Co-Chairs, Members of Steering and Program Committees, as well as to the special dedication of some members of our Local Organizing Board and Staff, and students, the Conference was scheduled and organized, and it ended up being one of the greatest participation in the series. My heartfelt thanks go to all the individuals and institutions contributing to make this result possible. Some names need to be mentioned. From the ISGG, Hans-Peter Schröcker, member of the Board of Regents organizing with Manfred Husty the 16thICGG in Innsbruck, especially for the initial detailed recommendations and advice, and Hirotaka Suzuki, ISGG treasurer and organizer of the 14th ICGG in Kyoto, for visiting in advance our Conference Venue. Here in Milano, in my University, I cite Pierfranco Galliani, to whom no words would suffice for diverse appropriate advice on every aspect of the Conference; Dario Angelo Maria Coronelli, Luisa Rossi Costa, and Damiano Cosimo Iacobone, for the help on the program; Susanna Sancassani and Bruno Aliprandi for the support on the online services; Mascia Sgarlata and Cristina Giannetto for the relations with institutions and services; Gloria Paoluzzi, Giuseppe Piampiano and Gianluca Ferrante for the administrative issues. And many others, including colleagues, students, and friends could be mentioned for their kind encouragement and help. On the private side my grateful thoughts go to my wife Francesca Scherillo, for her lovely patience, her constant wise presence, and help. At the Austin’s Conference in 1998, just after my Ph.D., I was the only Italian delegate. I met there, for the first time, Hellmuth Stachel, Kenjiro Suzuki, and Gunter Weiss, who have since then been key reference persons in the process of fostering the international relationships between the Italian scientific community and the ISGG. Over time, the number of the Italian participants has gradually increased, until becoming the highest one after those of the organizing countries in the last two editions, and the highest in this edition. The engagement of the Unione Italiana per il Disegno (UID) and the personal commitment of the president in office Vito Cardone in front of the Italian academic community have been crucial in this process, during which also the affiliation of the UID as an institutional member of the ISGG, between 2013 and 2014, could be finally possible. In this period I had the great privilege—and I still have it today- to be member, at the same time, of the Board of Regents of the ISGG and of the Commission for the International Relationships of the UID. Welcome Addresses from the Board of Chairs xix

The present Conference is Held at the Politecnico di Milano, at the Leonardo Campus, the main historical district of our University, where participants attend the technical sessions and most of the plenaries, and can also relax in the gardens and public spaces of the Campus, which is in the urban area of Città Studi and Lambrate. The Opening Ceremony at the Triennale di Milano and the Closing Ceremony at the Museo Nazionale della Scienza e della Tecnologia Leonardo da Vinci, involve two relevant cultural institutions of our City, both located in the city center, where participants can enjoy masterpieces of Modern Art and History of Science and Technique. According to the Conference focus, 7 Invited Speaker of high scientific profile coming from various disciplinary fields related to Geometry and Graphics will open and close the scheduled working sessions. Several plenary sessions are also scheduled, including poster sessions, round tables with the session-chairs, a panel session, and of course opening and closing ceremony, aiming at further stimulating the scientific cross fertilization in our international community during the Conference days. The annual meeting of the ICGG Board of Regents is also part of the official program. More than 280 scientific contributions have been submitted to the review, by about 450 authors from 43 Countries of the Five Continents, concerning Geometry and Graphics in several disciplinary fields, about 80% of them are published in these Proceedings, grouped according to the following ICGG2018 topics: Theoretical Graphics, Applied Geometry and Graphics, Engineering Computer Graphics, Graphics Education, and Geometry and Graphics in History, a new topic added for this edition. As in our Conference tradition, a welcoming party, a conference dinner, a conference tour and accom- panying persons’ tours are also organized, including a leave taking snack at the end of the closing ceremony. As also the Conference Logo tries to synthesize, we liked to dedicate this conference to Leonardo Da Vinci, after whom our Campus is named and to whom we would pay homage as a genius among the greatest showing the widest power of Geometry and Graphics in investigation and creativity between Science and Art, and to Giulio Natta, professor at the Politecnico di Milano and Nobel prizewinner for Chemistry in 1963, together with Karl Ziegler, as a mentor on the profound function—and beauty!—of Geometry and Graphics in Science and Technology, even at the invisible scale of the molecular world: from these thoughts the choice to include Geometry and Graphics in History in the list of the 2018 conference topics. On the Conference website, the 3D configuration originating the graphic logo appears, suspended and oscillating in the virtual graphic space of the webpage, as a clear sign of the present statute of Geometry and Graphics, digital and still human centered. My sincere thanks go to Otto Röschel, the ISGG President in office in 2016, when it has been proposed to organize the ICGG2018 in Milano, and to the members of the ISGG Board of Regents, for their trust in us, as well as in me personally, and to Yasushi Yamaguchi, the estimeed present President in office of the ISGG, for his secure leadership and reliable support. My deepest gratitude is addressed to all the participants to the ICGG2018, authors, delegates, students, and accompanying persons, adults and often kids, since without their interest, xx Welcome Addresses from the Board of Chairs engagement, and participation, this Conference, one of the most attended up to now, would have simply not been possible. I sincerely hope that you all could have rich and profitable academic benefits from the 18th International Conference on Geometry and Graphics, a memorable experience at our University, and an enjoyable time in Milano. Once more, also on behalf of the ICGG2018 Organizing Board, WELCOME!

Prof. Luigi Cocchiarella Politecnico di Milano, Italy Special Addresses for the 40th Anniversary

Welcome Address by the President and Vice Chancellor of the University of British Columbia As president and vice chancellor of the University of British Columbia, the host university for the first International Conference on Descriptive Geometry at the University of British Columbia, held in June 1978, it gives me great pleasure to extend best wishes for the 18th International Conference on Geometry and Graphics. The world has changed greatly since scholars gathered for that first conference in 1978, and even more so since Leonardo Da Vinci used geometry and graphics to try to understand nature 500 years ago. However, the spirit of discovery and of application of geometry to real-world problem remains unchanged. My best wishes for a productive and fruitful conference.

Prof. Santa J. Ono UBC, Vancouver, Canada

Welcome Address by the Chair of EDGS (ASEE) On behalf of the Engineering Design Graphics Division (EDGD) of the American Society for Engineering Education (ASEE), it’s my pleasure to extend a warm and hearty welcome to all 18th International Conference on Geometry and Graphics (ICGG) attendees. I’d also like to congratulate and thank all the societies involved for continuing the tradition of this international conference for the past 40 years. We have seen many changes since 1978 when the first conference was founded by Steve M. Slaby, emeritus professor, Princeton University, and hosted by EDGD in Vancouver. The Engineering Design Graphics Division itself was founded in 1928 and is the oldest division within the American Society for Engineering Education. While not limited to, Division members are drawn principally from engineering— technical universities and community/junior colleges throughout this country and from abroad. The Division exists to coordinate and promote interests and activities that pertain to engineering graphics, design, and education and activities such as teaching, research, discussion, and communication. This is accomplished princi- pally through the Engineering Design Graphics Journal, which is published three

xxi xxii Special Addresses for the 40th Anniversary times a year by the Division, and conferences: the annual, which takes place in conjunction with the Society’s annual conference, and a midyear, which takes place annually between October 1 and January 31. The division also sponsors or cosponsors workshops and short courses in areas which broaden the skill and knowledge of those engaged in the teaching of design and graphics. According the ASEE, the Society itself was founded in 1893 initially as the Society for the Promotion of Engineering Education (SPEE) in responses to pro- fessors of engineering questioning whether they should adopt a more rigorous approach to teaching the fundamentals of their field. The need was grounded in 30 years’ worth of observation during the period following passage of the Morrill Land-Grant Act in 1862. That Act provided money for states to establish public institutions of higher education and focused on providing practical skills, especially “for the benefit of Agriculture and the Mechanic Arts.” In response to the Act’s passage, more Americans began entering the workforce with advanced training in applied fields of knowledge. However, those entering the workforce often lacked a grounding in scientific and engineering principles underlying this practical knowledge. In response, SPEE was founded with a focus on the premise that engineering curricula should stress fundamental scientific and mathematical prin- ciples, not hands-on apprenticeship experiences. Thus, ASEE’s birth. And yes, ASEE is celebrating its 125th birthday this year. Since the 1978 ICGG in Vancouver, and like ISGG and ICGG, EDGD has experienced numerous changes and continues to evolve socially and technically. It has successfully negotiated and continues to negotiate the adoption of leading-edge digital graphics and communication as it applies to all stages of design and engi- neering process. It continues to broaden its interest base. The Division continues to increase its range of incentives to stimulate interest, involvement, engagement, diversity, the pursuit of excellence, and to acknowledge member and nonmember contributions. More recently, EDGD took the plunge and transitioned from the print only dissemination of its official publication, the Engineering Design Graphics Journal, to the dissemination of digital only copies with the publication of its Fall 2009 issue. This has implications and opens opportunities for the Journal and the Division to tap. I am certain there are opportunities ISGG and ICGG have yet to identify and tap, and I am confident, this conference will result in considerable progress. Congratulations to the founding members of ISGG and ICGG, all ISGG and ICGG members, the 18th International Conference authors and presenters for your continued interest and your contributions, and to all others for being part of the Conference to share.

Prof. Robert A. Chin East Carolina University Greenville, NC, USA Special Addresses for the 40th Anniversary xxiii

Welcome Address by the President of JSGS As president of the Japan Society for Graphic Science, it is a great honor and pleasure to greet the participants of the 18th International Conference on Geometry and Graphics. We are happy to support this conference as a cosponsor and I would like to congratulate the 40th anniversary of this conference from the first edition in Vancouver. The progress of computing and information technology in recent years is tremendous and has brought about a great change in many aspects of our field of graphic science. In engineering fields, technological drawings are changing to digital modeling and now it is becoming an era of artificial intelligence. However, geometry still remains as a basis of digital modeling and graphics as ever. Moreover, geometry and graphic science are playing an even greater role in the highly computerized multimedia era. I believe that the Milan Conference will provide a valuable opportunity for the discussion on science, technology and educational aspects of geometry and graphics. I also hope that the Conference will contribute to the promotion of mutual understanding among people from diverse expertise. Finally, I would like to express my sincere gratitude to the Organizing Board at Politecnico di Milano, and to the International Scientific Committee of ISGG. My special thanks go to Prof. Luigi Cocchiarella, the Conference Executive Chair, and to all the delegates for their hard work in contributing to make this conference a successful one.

Prof. Hirokazu Abe University of Osaka, Japan

Welcome Address by the Councillor for Labour Policies, Business, Commerce and Human Resources of the Municipality of Milan As the councillor in charge for Labour Policies, Business, Commerce and Human Resources of the municipality of Milan, I am glad to welcome all the participants of the 18th International Conference on Geometry and Graphics in this special occasion of the 40th anniversary of the academic event, which we have the pleasure to hold and celebrate in our city. Since Geometry and Graphics are at the bases of Art and Science, conference topics are also in line with the spirit of Milano, which by tradition has been, and still is, a leading city in the fields of culture and innovation at an international level. Therefore, we wish that the participants to this edition, coming from about 40 countries in the world, will feel at home here, and will keep nice records from their stay. The venue of the Conference, held at the Politecnico di Milano, our well-known leading technical university, and also involves other important cultural institutions, like the Triennale di Milano and the National Museum of Science and Technology Leonardo Da Vinci, will offer a special and inspiring atmosphere to the guests, complemented by the wide spectrum of possible touristic programs avail- able in the city as well as in the surrounding region. xxiv Special Addresses for the 40th Anniversary

As a referenced geographic and historic crossroad for culture and commerce, Milano offers a unique experience to the visitors, integrating cultural heritage and genuine moods with examples of cutting edge modernity and a strong propensity towards the future. Avant-gardes have been often attracted to this city indeed, which has also been the scenery for important controversies and public disputes and debates in key moments of history. Nowadays, the teeming series of cultural activities and events, always swarming in the city, reflects the renovated multi- cultural profile of Milan, which in the last decades has exploded with a new energy thanks to the sensitivity of the citizens and the engagement of the municipality. For all these reasons, I wish profitable scientific results and an enjoyable touristic experience to all the participants to the ICGG 2018.

Mrs. Cristina Tajani Municipality of Milan, Italy Committees

Honorary Chairs Otto Röschel, Outgoing President of the International Society for Geometry and Graphics—ISGG, Graz University of Technology, Austria Vito Cardone, President in office of the Unione Italiana Disegno—UID, Università degli Studi di Salerno, Italy Chair Yasushi Yamaguchi, President in office of the ISGG, The University of Tokyo, Japan Executive Chair Luigi Cocchiarella, ISGG Director for Europe/Near East/Africa, Politecnico di Milano, Italy Co-Chairs Baoling Han, ISGG Vice-President for Asia/Australia/Oceania, Beijing Institute of Technology, China Ema Jurkin, ISGG Vice-President for Europe/Near East/Africa, University of Zagreb, Croatia Aura Conci, ISGG Vice-President for North America/South America, Universidade Federal Fluminense, Niteroi, Brazil Steering Committee Asia/Australia/Oceania Hirotaka Suzuki, ISGG Secretary and Treasurer in office, Kobe University, Japan Kenjiro Suzuki, Former ISGG President, Professor Emeritus, The University of Tokyo, Japan Emiko Tsutsumi, Former ISGG President, Otsuma Women’s University, Tokyo, Japan

xxv xxvi Committees

Europe/Near East/Africa Cornelie Leopold, Former ISGG Director, TU Kaiserslautern, Germany Hans-Peter Schröcker, ISGG Director, University of Innsbruck, Austria Hellmuth Stachel, Editor in Chief of the Journal for Geometry and Graphics—JGG, University of Technology Vienna, Austria Gunter Weiss, Former ISGG President, Technical University of Dresden, Germany North America/South America Ted Branoff, Former ISGG President, Illinois State University, Normal, USA Frank Maxfield Croft, The Ohio State University, Columbus, USA Eduardo Toledo Santos, ISGG Director, Sao Paulo University, Brazil Program Committee International Board Naomi Ando, Hosei University, Tokyo, Japan Gilson Braviano, President of the Associação Brasileira de ExpressãoGráfica, Brazil Fabiana Carbonari, Universidad Nacional de La Plata, Argentina Larry Cooperman, University of California Irvine, USA, and Open Education Consortium Yüksel Demir, Istanbul Technical University, Turkey Magdalena Dragovic, University of Belgrade, Serbia Douglas Dunham, University of Minnesota, Duluth, USA Sergio Gavino, Universidad de La Plata, Argentina Georg Glaeser, University of Applied Arts, Vienna, Austria Sonia Gorjanc, University of Zagreb, Croatia Renata Gorska, Cracow University of Technology, Poland Marco Hemmerling, Cologne University of Applied Sciences, Germany Miklós Hoffmann, ISGG Director, Karoly Esterhazy College, Eger, Hungary Manfred Husty, University of Innsbruck, Austria Pedro António Janeiro, Universidade de Lisboa, Portugal Mine Özkar Kabakçioğlu, Istanbul Technical University, Turkey Michio Kato, The University of Tokyo, Japan Ashraf Khattab, Ain Shams University, Cairo, Egypt Kunio Kondo Tokyo University of Technology, Japan Rimvydas Krasauskas, Vilnius University, Lithuania Sonja Krasic, University of Nis, Serbia Daniel Lordick, Technical University of Dresden, Germany Daiva Makuteniene, Vilnius Gediminas Technical University, Lithuania Bhekie Mamba, University of South Africa, Pretoria, South Africa Michael Manevich, Ariel University Center of Samaria, Israel Kazuko Mende Joshibi, University of Art and Design, Tokyo, Japan Emil Molnar, Budapest University of Technology and Economics, Hungary Zhendong Niu, Beijing Institute of Technology, China Committees xxvii

Boris Odehnal, Vienna University of Applied Arts, Austria Marius Paun Transilvania, University of Brasov, Romania José Ignacio Rojas Sola, Universidad de Jaén, Spain Pawel Rubinowicz, West Pomerian University of Technology Szczecin, Poland Peeraya Sripian ISGG Director, Shibaura Institute of Technology, Tokyo, Japan Milena Stavric, Graz University of Technology, Austria Tomohiro Tachi, ISGG Director, The University of Tokyo, Japan Antonio Álvaro Tordesillas, Universidad de Valladolid, Spain Susana Toscano, President of the Asociación Internacional de Matemática y Diseño, Argentina Daniela Velichova, Slovak University of Technology in Bratislava, Slovakia Vera Viana, Universidade do Porto, Portugal Krassimira Vlachkova, University of Sofia St. Kliment Ohridski, Bulgaria Laszlo Voros, University of Pécs, Hungary Srdjan Vukmirovic, University of Belgrade, Serbia Norman Wildberger, ISGG Director, The University of New South Wales, Sydney, Australia Cheng Liang Yee, ISGG Director, Sao Paulo University, Brazil Emil Zagar, University of Ljubljana, Slovenia Paul Zsombor-Murray, ISGG Director, McGill University, Montreal, Canada National Board Salvatore Barba, Università degli Studi di Salerno Stefano Bertocci, Università di Firenze Andrea Bonarini, Politecnico di Milano Monica Bordegoni, Politecnico di Milano Fausto Brevi, Politecnico di Milano Raffaella Brumana, Politecnico di Milano Franca Caliò, Politecnico di Milano Mario Centofanti, Università di L’Aquila Michela Cigola, Università di Cassino o del Lazio Meridionale Sara Comai, Politecnico di Milano Ugo Cosentino, Università di Milano Bicocca Antonella Di Luggo, Università degli Studi di Napoli Federico II Ruggero Eugeni, Università Cattolica del Sacro Cuore Federico Fallavollita, Alma Mater Studiorum Università di Bologna Andrea Giordano, Università degli Studi di Padova Simone Giostra, Politecnico di Milano Gabriele Guidi, Politecnico di Milano Sereno Innocenti, Università degli Studi di Brescia Elena Ippoliti, Università degli Studi di Roma La Sapienza Marcella Lorenzi, Università della Calabria Elena Marchetti, Politecnico di Milano Eugenio Morello, Politecnico di Milano Roberto Notari, Politecnico di Milano xxviii Committees

Ingrid Paoletti, Politecnico di Milano Nicola Pisacane, Università degli Studi della Campania Luigi Vanvitelli Andrea Rolando, Politecnico di Milano Michela Rossi, Politecnico di Milano Luisa Rossi Costa, Politecnico di Milano Rossella Salerno, Politecnico di Milano Laura Tedeschini Lalli, Università degli Studi Roma Tre Graziano Mario Valenti, Università degli Studi di Roma La Sapienza Maurizio Stefano Vianello, Politecnico di Milano Organizing Board at Politecnico di Milano Giuseppe Amoruso, Raffaele Ardito, Alessandro Bianchi, Federico Alberto Brunetti, Cecilia Maria Bolognesi, Giuliana Cardani, Camilla Casonato, Claudio Umberto Comi, Dario Angelo Maria Coronelli, Carlo De Falco, Nicole De Togni, Damiano Cosimo Iacobone, Maria Pompeiana Iarossi, Paola Magnaghi Delfino, Giampiero Mele, Marco Muscogiuri, Tullia Norando, Daniela Oreni, Daniele Giovanni Papi, Barbara Ester Adele Piga, Matteo Giuseppe Romanato, Tan Shilong Daniele Villa Staff and Offices Cristina Giannetto, Communication Staff Gianluca Ferrante, Administration and Accounting Staff—DASTU Gloria Paoluzzi, Department Manager—DASTU Susanna Sancassani, Support Service for Research and Innovation Didactics— METID Grant ICGG 2018 has been granted by the Department of Architecture and Urban Studies (DASTU). Department Head, Prof. Gabriele Pasqui Contents

Part I Introduction to ISGG Community and the 2018 Conference Giving Birth to the International Society for Geometry and Graphics—A Documentation of the Years 1988–1994 ...... 3 Hellmuth Stachel Geometry and Graphics for the Graphic Identity of a Conference on Geometry and Graphics: About the ICGG2018 Conference Logo .... 7 Luigi Cocchiarella

Part II Invited Lectures Rational Estimates for Irrational Problems: Proportional Geometry in the Work of Leonardo da Vinci ...... 19 Matthew Landrus Molecular Geometry and Molecular Graphics: Natta’s Polypropylene and Beyond ...... 55 Guido Raos Geometric Thinking and the Geometry of Conics and Quadrics ..... 63 Paul Zsombor-Murray Designing with Shadow/in Architectural Lighting Design ...... 78 Kaoru Mende Higher Dimensional Geometries. What Are They Good For? ...... 94 Boris Odehnal Computational Visual Illusion and Its Application ...... 106 Peeraya Sripian Blindness of Seeing. On the Origin of the Images ...... 114 Agostino De Rosa

xxix xxx Contents

Part III Theoretical Graphics and Geometry Composition and Deconstruction of Spaces Depicted in Shinji Somai’s Films ...... 129 Naomi Ando, Motoharu Taneda, Shota Ishii, and Nobuhiro Yamahata Graphical Model of the Biquadratic Transformation ...... 147 Auyez Baidabekov, Seriktay Baymukhanov, and Elmira Kemelbekova Graphics and Quantum Mechanics—The Necker Cube as a Quantum-like Two-Level System ...... 161 Giorgio Benedek and Giuseppe Caglioti Surface and Curves: A Dialogue Between Nature and Structural Analysis ...... 173 Otello Bergamo On One Locus in the Plane ...... 184 Jiří Blažek and Pavel Pech Integration Between Perspective Images and BIM Models: Projective Geometry Is Still Alive ...... 197 Paolo Borin, Andrea Giordano, and Federico Panarotto Geometric Constructive Traces in Drawings by Francesco Borromini ...... 208 Marco Canciani, Giovanna Spadafora, María del Pilar Pastor Altaba, Giovanni Formica, Marco D’Angelico, and Camilla Lebboroni Using Topological Transformations to Construct the Intercepting Lines ...... 219 Gocha Chavleshvili and Gaioz Partskhaladze A Property of Area and Perimeter ...... 228 Douglas Dunham and John Shier Quasifocal Line and “Burning Curve” ...... 238 Aleksandr Dvoretskii and Tetiana Denysova Detection of Critical Direction for Feature Line Extraction on Meshes Based on Local Integral Invariants ...... 252 Qiqi Gao and Yasushi Yamaguchi A Spatial Version of the Theorem of the Angle of Circumference .... 265 Georg Glaeser, Boris Odehnal, and Hellmuth Stachel Equidistant Sets of Conic and Line ...... 277 Mirela KatićŽlepalo and Ema Jurkin Isotomic Transformation with Respect to a Family of Triangles ..... 290 Helena Koncul Contents xxxi

The Geometry of Quadratic Quaternion Polynomials in Euclidean and Non-euclidean Planes ...... 298 Zijia Li, Josef Schicho, and Hans-Peter Schröcker Geometric Algorithms for Constructing the Algebraic Surfaces on the Basis of Grassmann’s Ideas and Their Extensive Equations ... 310 Michael Manevich and Elizabeth Itskovich Hyperbolic Space Forms with Crystallographic Applications and Visualizations ...... 320 Emil Molnár and Jenő Szirmai Optimized Ruled Surfaces with an Application to Thin-Walled Concrete Shells ...... 338 Kevin Noack and Daniel Lordick Examples of Autoisoptic Curves ...... 350 Boris Odehnal The Properties of Special Points on the Brocard Circle in a Triangle ...... 362 Victor Oxman, Avi Sigler, and Moshe Stupel Structure Functions of Ruled Surfaces with Null Rulings ...... 371 Ljiljana Primorac Gajčić, Ivana Protrka, and Željka Milin Šipuš Curved Folding with Pairs of Cones ...... 381 Otto Röschel Relationship Between Time and Typical Buildings Depicted in KASUGA GONGEN GENKI ...... 389 Noriko Sato Two Remarkable Spherical Arrangements of Circles ...... 401 Hellmuth Stachel Study and Practice on Double Deck Folding Structure Mobile Home Design Development ...... 410 Shin Tsuchiya and Toshikazu Ishida Logicometry: Graphical Representations of Logical Space Interrelations ...... 426 Panayiotis Varoutsos Minkowski Triples of Curve Segments ...... 437 Daniela Velichová Some Theorems of the Euclidean Geometry in Pentagonal Quasigroups ...... 445 Stipe Vidak xxxii Contents

Geometrical Structures of Planar and Spatial Tessellations Based on 3D Models of Higher Dimensional Cubes ...... 458 László Vörös The Cube: Its Relatives, Geodesics, Billiards, and Generalisations .... 471 Gunter Weiss Duality in Non-polyhedral Bodies Part I: Polyliner ...... 484 Eva Wohlleben Quadric Sections of Four-Dimensional Cones ...... 500 Michal Zamboj Curves and Surfaces in the Churches with Ovate Plant in Naples. Geometric Analogies and Differences ...... 514 Ornella Zerlenga and Vincenzo Cirillo

Part IV Applied Geometry and Graphics A Suggestion of the Optical Illusion Blocks for an Architectural Theory: Toward an Architecture in the Near Future ...... 529 Daiki Amanai, Tomoko Ohtani, and Kazushi Maruya Perspective and the Blind ...... 541 Barbara Ansaldi The Korean Alphabet (Hangeul) and the Translation Processes in Design ...... 553 Andrea Arosa “Ultima Dea”: A Laser Scanner Application for 3D Modelling ...... 559 Salvatore Barba, Francesco Villecco, and Alessandro Naddeo Margin’s Landscapes Between Po and Trebbia Rivers in Piacenza Area: Geometrical Descriptions ...... 570 Alessandro Bianchi Immersive Visions. Some Paradigm a of an Exceeding Iconography. Capture and Monitoring by Spherical Cameras and Interactive Smartglasses ...... 579 Federico Alberto Brunetti Imperial Porphiry and Golden Leaf: Sierpinski Triangle in a Medieval Roman Cloister ...... 595 Paola Brunori, Paola Magrone, and Laura Tedeschini Lalli A Storage Model for Large Scale Web-Based Learning Systems Based on Concept Tree ...... 610 Hongming Cai, Zheng Wang, Jingjing Li, Haiyan Yu, Yuanjun He, and Yonggen Gu Contents xxxiii

An Unlikely Rome. Towards Performative Geometry ...... 620 Carlos Campos and Alessandra Cirafici Cellular Automata Between Life Science and Parametric Design: Examples of Stochastic Models to Simulate Natural Processes and Generate Morphogenetic Artefacts ...... 632 Irene Cazzaro Smart Artefacts and Spaces to Interact, Promote and Transfer Cultural Knowledge ...... 644 Mauro Ceconello The Role of the Graphic Element in the Context of Playful Games for Cultural Heritage ...... 653 Valeria Cera Unfolding Geometry from Unity: Digital Survey and 3D Modeling of Islamic Decorative Apparatus in Generalife Palace, Alhambra .... 664 Raffaella De Marco Triangular Proportional Scheme and Concept of the Two Serbian Medieval Churches ...... 677 Magdalena Dragović, Aleksandar Čučaković, Jelena Bogdanović, Svetlana Čičević, and Aleksandar Trifunović Best-Fit Analysis for the Geometry Characterization of Domes ...... 690 Laura Floriano, Mariangela Liuzzo, and Giuseppe Margani The Evolutionary Mechanism of Unit Cell: Parameterizations of Polyhedron Sandwich Structure Based on Rigid Origami ...... 701 Hao Qiu, Yicong Gao, Yixiong Feng, Hao Zheng, and Jianrong Tan Converting 3D-CAD Data into FRP Parts ...... 711 Sande Gao and Loulin Huang A Quest for the Structural Response Through Geometric Representation of the Design of Built Heritage...... 722 Maria Chiara Giangregorio, Giuliana Cardani, and Dario Coronelli Geometric Representation of Turbulent Macrostructure in 3D Jets .... 739 Olena Gumen, Volodymyr Dovhaliuk, and Viktor Mileikovskyi An Algebraic Version of the Input-Output Equation of Planar Four-Bar Mechanisms ...... 746 Manfred Husty and Martin Pfurner Collection and Visualization of Pedestrian Navigation Routes with Parametric Tools ...... 758 Maja Ilić xxxiv Contents

Between Architecture and Writing: Graphical Geometry to Decipher Systems of Signs. Campo Verano in Rome ...... 769 Elena Ippoliti and Francesca Guadagnoli Visualized Analysis of Spatial Distribution of Dissolved Oxygen and Nitrogen Removal Efficiency in Constructed Wetland ...... 781 Aichen Jia and Huixue Yan Study on the Modeling Converting Methods of Complex Mechanical Product Exterior Design ...... 790 Jing Gan and Lei Ma Examination of the Experience of Biomorphic Form Materialized in Urban Design Model ...... 798 Biljana S. Jović, Aleksandar A. Čučaković, Jelena T. Tomićević- Dubljević, and Anđela D. Mitić Repetition of Triangle Fountain of Aldo Rossi: Geometrical Analogy of Architecture ...... 809 Yuji Katagiri Toward a New Capital by Le Corbusier—A Synthesis of Images with Different Origins ...... 820 Michio Kato Generic Fitting in Point Clouds ...... 832 Daniel Klawitter, Oliver Bringmann, and Christian Tonn Identification Method of Topographic Surfaces Models ...... 842 Dilarom F. Kuchkarova and Dilnoza A. Achilova Geometry of Stairs ...... 849 Cornelie Leopold Exempla Imperfecta: The “Curious” Image of the Platonic Solid .... 862 Gabriella Liva The Design of JLAMT: An Aided Tool for Large-Scale Complex Physical Modeling ...... 877 Yan Ma, Yuanguang Fu, and GuiMing Qin Geometric Links Between 2d Patterns and 3d Structures in Islamic Architectures of Andalusia ...... 884 Barbara Messina and Stefano Chiarenza Extended Morphological Closing Using Geodesic Filtering ...... 896 Takashi Michikawa and Satoshi Wada 3D Printer of Five-Axis Laminate-Shaping with FDM Method and Its Application ...... 903 Tatsuya Mochizuki and Takehiro Kawamura Contents xxxv

A Program to Seek Drawing Methods for Descriptive Geometry in Prolog ...... 912 Shinobu Nagashima Alternative Interpretation of the Plücker Quadric’s Ambient Space and Its Application ...... 918 Georg Nawratil Visualization of Infants’ Behavior at Home Using Augmented Reality for Promotion of Development and Prevention of Accidents ...... 930 Miho Nishizaki Modularity of Concave Polyhedra of the Second Sort with Octagonal Bases ...... 942 Marija Obradović Introduction to “Architectural Geometry”: Through Analysis of Architecture Made of Square Plan ...... 955 Takahiro Ohmura Visual Paradoxes in Video Games: Spatial Reconstructions and Geometric Analysis ...... 968 Alessandro Olivieri and Ramona Feriozzi Directorial Surfaces and Potential Applications in Cupola Design .... 980 Maja M. Petrović, Radovan B. Stulic, Marko P. Vučić, and Radomir M. Mijailović 3D Modeling of the Biological Form of the Green Chinche ...... 989 Dina Rochman and America Sánchez From Voxels to Parts: Hierarchical Discrete Modeling for Design and Assembly ...... 1001 Andrea Rossi and Oliver Tessmann Visualisation of DSM as 3D-Mesh for Urban Analyses ...... 1013 Paweł Rubinowicz Research on Video Representation by Unexperienced Viewpoint Using 360-Degree Movie ...... 1023 Yuya Sato and Tsukasa Kikuchi Application of Middle-Out Design Based on Multi-body Method ..... 1038 Song Hongxia Geometrically Controlled Digital Workflow from Scratch to Fabrication ...... 1050 Milena Stavric, Albert Wiltsche, Markus Bartaky, and Elmar Hess xxxvi Contents

Graphical Analysis of the Structural Behavior, According Hypothesis of Rankine-Schwedler, of a Large Stone Dome in Granada (Spain)...... 1062 Javier Suarez, Rafael Bravo, and José A. González Utilization of Plane Tessellation for Paper Folding and Geometrical Transmittance Pattern for Lampshade Design ...... 1075 Hirotaka Suzuki The Geometry of the Ramps in Frank Lloyd Wright’s Organic Architecture ...... 1084 Ana Tagliari and Wilson Florio Geometric Basis of the Use of “Green Constructions” for Sun Protection of Glazing ...... 1096 Tetiana Tkachenko and Viktor Mileikovskyi Making Fulldome Images Using Camera with Fisheye Lens and Fulldome Picture on Bowl ...... 1108 Hidekazu Tsujiai, Megumi Takenaka, and Tadashi Hayashi Interactive Expansion of Achiral Polyhedra ...... 1116 Vera Viana, João Pedro Xavier, Ana Paula Aires, and Helena Campos Parametric Modelling and Geometry for the Study of Groins in Compound Vaults ...... 1129 Marco Vitali A Geometric Look at 3D Illusionist Techniques ...... 1139 Maria Helena Wyllie L. Rodrigues, Madalena R. Grimaldi, and Daniel W. L. Rodrigues Suggestions for New Content in the Planetarium ...... 1152 Kosei Yamamura, Satoshi Cho, and Hisashi Sato Interactive Visualization for Analysis of Air Traffic Model ...... 1161 Kensuke Yasufuku and Shinsuke Nagaoka Geometrical Universality of Truss-Z System ...... 1167 Machi Zawidzki Interaction Between 3D Printing and Geometry Studies ...... 1177 Marianna Zichar and Ildikó Papp The Story of NanoJesus: Combining 3D Scanning and Femtosecond Laser Nanolithography for the Fabrication of the Smallest Nativity Scene in the World ...... 1191 RytėŽiūrienė, Linas Jonušauskas, Eimantas Auglys, Darius Gailevičius, and Eglė Girdzijauskaitė Contents xxxvii

Part V Engineering Computer Graphics Geometrically Constrained Surface (Re)Construction ...... 1205 Gudrun Albrecht, Franca Caliò, and Edie Miglio Challenges in Modelling Complex Geometry in Historical Buildings for Numerical Simulations ...... 1218 Grigor Angjeliu, Dario Coronelli, and Giuliana Cardani Transient Finite Elements Analysis of Thin-Walled Structure in Selective Laser Melting Process ...... 1231 Linshan Ding, Li Zhang, Chunhong Ruan, and Zaizhuo Jiang Three-Dimensional Modeling and Finite Element Analysis of Cycloid Hyperbolic Arch Dam ...... 1241 Tingna Du and Bo Li Mixing of Fluids with Space-Filling Curves ...... 1255 Martin Friedrich Eichenauer, Kevin Noack, and Daniel Lordick Electronic Geometric Modeling Is the Basis of Modern Geometric-Graphic Education in the Technical University ...... 1268 Vladimir Guznenkov and Pavel Zhurbenko The Optimization Algorithm for Gait Planning and Foot Trajectory on the Quadruped Robot ...... 1274 Baoling Han, Xiao Luo, Rui Zhao, Qingsheng Luo, and Guanhao Liang Analytic Approach to Finding Lines in Images and Estimating Their Uncertainty ...... 1280 Matthew Harker and Paul O’Leary Geometric Fitting, Registration and Identification for Large Sets of Spatial Measurement Data ...... 1292 Matthew Harker and Paul O’Leary 3-D Reconstruction of Bubbles Inside Valve Based on Multi-mirrors Imaging ...... 1304 Liye Jiao, He Xu, Haihang Wang, Zitong Zhao, and Pooneeth Vishwanath Facial Expression Recognition Base on Weighted KNN and RF ..... 1315 Kaiping Feng, Siyuan Lai, Quanjie Li, and Junwen Wen Directing Scheme Support Method Based on Analysis of Angry Characters...... 1324 Yoshihisa Kanematsu, Ryuta Motegi, Naoya Tsuruta, Koji Mikami, and Kunio Kondo Generating Videos Based on Convolutional Recurrent Generative Adversarial Networks ...... 1334 Yachao Li and Toshihiro Komma xxxviii Contents

Study on Adaptive Threshold Image Processing Method for Detection of Vaccine Activity ...... 1340 Yancong Liu and Chao Huang A Creo-Based Modeling and Toolpath Generating System for the NC Whirling Process of Propeller Blades ...... 1350 Xinfeng Liu and Riliang Liu Aircraft Target Recognition in Remote Sensing Images Based on Saliency Maps and Invariant Moments ...... 1358 Jie Luo, Jiexian Zeng, Jun Fu, Xiang Fu, and Lu Leng The Configuration Design and Analysis of a Small Air-Land Amphibious Detecting Robot ...... 1366 Xiao Luo, Qingsheng Luo, Chen Zhu, and Baoling Han Curves with Special Aesthetics Generated by an Original Mechanism ...... 1377 Iulian Popescu, Ludmila Sass, Alina Duță, Marcela Popescu, and Gabriel Marinescu Tensile Structure Form-Finding on the Basis of Properties of Frame-Grid Template ...... 1391 Eugene Vladimirovich Popov, Marina Victorovna Lagunova, and Sergey Igorevich Rotkov Orthographic Drawings Minting: Testing for Indeterminate Solid Models Caused by Underrepresentation ...... 1404 Peter Rosso, Ben Hicks, and Michael Patterson From Orthographic Drawings to Editable Models of Simple Solid Using “Reconstruction-Recomposition” Coupled with Feature Recognition ...... 1414 Peter Rosso, Ben Hicks, and Michael Patterson Solving Applied Geometric Design Problems with the Use of 3D-CAD ...... 1423 Kenjiro Suzuki Research on Parametric Modeling of Cable-Stayed Bridge Based on BIM ...... 1434 Ziru Wang, Yuanjun He, and Baiyu Ma Attribute in Formation on Three-Dimensional Annotated Models .... 1443 Masahiro Yasui, Susumu Kise, Sozo Sekiguchi, Kazuya Okusaka, Shigeo Hirano, and Tsutomu Araki Contents xxxix

Part VI Graphics Education From the Plan to the 3D Model Through Folding. Case Studies in Fashion Design ...... 1455 Alessandra Avella Byrne’s Euclidean Geometry Revisited with Geogebra...... 1468 Giorgio Bolondi and Alessandro Luigini Drawing Geometry: A Laborious History in Italian School ...... 1474 Giorgio Bolondi Formation of Competence in Students of Technical University for 3D-Modeling and Prototyping of the Objects ...... 1481 Tatiana Boshchenko and Natalia Kaygorodtseva A Course on Geometric Dimensioning and Tolerancing: Overview and Initial Assessment ...... 1488 Theodore J. Branoff Design-Based Learning Supported by Empirical-Concrete Learning Objects in Descriptive Geometry ...... 1502 Fernando Batista Bruno, Régio Pierre da Silva, Tânia Luisa Koltermann da Silva, and Fábio Gonçalves Teixeira Mathegraphics ...... 1511 Enrico Cicalò, Andrea Causin, and Margherita Solci Teaching Geometry and Surfaces Evaluation Through Graphic Representation and Dynamic Paper Models ...... 1523 Caterina Cumino, Martino Pavignano, Maria Luisa Spreafico, and Urzula Zich Geometrography Revised and Enlarged: A Brazilian Geometer’s Approach to Émile Lemoine’s Work ...... 1533 Marcelo da Silva Bueno Is the Constructional Drawing an International Language for Engineers? ...... 1542 Modris Dobelis, Piotr Polinceusz, Monika Sroka-Bizon, Krzysztof Tytkowski, Daniela Velichova, and Antanas Vansevicius Application of Augmented Reality in the Compilation and Publication of Cartographic Textbooks ...... 1553 Hongliang Fan New Analog for the Digital Age: Adjusting Simultaneousness for Self-explanatory Delineation of Architectural and Urban Projects in Public Presentations or: a “Nolli Isometric” ...... 1560 Niels-Christian Fritsche xl Contents

Biomimetical Approach in Training Students of Technical Institutes in Graphic Disciplines with Aim of Developing Creativity and Formation of Professional Culture of the Engineer ...... 1572 Galina Gavrilenko and Uliana Danilova Shell Tessellation—Research-Based Design Strategies Between Architecture and Mathematics ...... 1582 Marco Hemmerling, Carlo de Falco, and Elena Angeli Research on the Effect of Providing User Interaction for Graphic Education ...... 1593 Biljana S. Jović, Takashi Ohta, and Noriko Sato Practical Skills in AutoCAD Through a Mass Open Online Course .... 1603 Natalia Kaygorodtseva and Valeriia Luzgina Comparative Analysis of Teaching in Geometric Surfaces at Architectural Faculties in Niš and Tokyo ...... 1611 Sonja Krasić, Naomi Ando, Petar Pejić, and Zlata Tošić Quality Management of Engineering Graphics Teaching ...... 1624 Dilarom F. Kuchkarova and Dilnoza A. Achilova Digitizing Spatial Visualization Tests ...... 1631 Domen Kušar, Mateja Volgemut, and Lidija Pletenac Creative Graphics Education Potential for Creativity of Hospitality Students via Virtual Environment ...... 1643 Zhen Liu Reinterpret Whith Estrus. Creativity and Science in the Drawing Workshops of the Degree Course in Communication Design ...... 1655 Maria Paola Marabotto Character Making Education by DREAM Process ...... 1663 Ryuta Motegi, Yoshihisa Kanematsu, Naoya Tsuruta, Koji Mikami, and Kunio Kondo Teaching 3D Character Animation Through Four Related Tasks .... 1671 Ratko Obradović, Miloš Vujanović, and Igor Kekeljević The Effect of a Two-Dimensional Optical Illusion Pattern on the Three-Dimensional Interpretation of Objects Using Café Wall “Illusion Blocks” ...... 1682 Tomoko Ohtani, Daiki Amanai, and Kazushi Maruya Non-conventional Representation for Urban Design: Depicting the Intangible ...... 1694 Barbara E. A. Piga and Rossella Salerno Contents xli

A Revised Project-Based Learning Program on Geometry—Maximizing the Volume of Solid ...... 1706 Ichiro Tanaka A Multiview Interactive Interface for the Solution of Descriptive Geometry Problems ...... 1716 Fábio G. Teixeira, Sérgio L. Dos Santos, and Fernando B. Bruno Physical—Digital. Defining the Architectural Space ...... 1727 Jolanta Tofil Challenges and Promises of Mobile Devices Usage for Spatial Visualization Skills Assessment in Technical Drawing for Engineering Course ...... 1740 Aleksandar Trifunović, Svetlana Čičević, Dragan Lazarević, Magdalena Dragović, and Aleksandar Čučaković Basic Modelling Education to Obtain 3D Spatial Perception for Design Beginners ...... 1751 Maiko K. Tsujii and Ayako Kita Systematic Review of a Flipped Learning Model for the Courses of Descriptive Geometry, Engineering and Computer Graphics ...... 1765 Marianna Vladimirovna Voronina, Sergei Anatolyevich Ignatiev, and Viktoriya Anatolyevna Merkulova The Importance of Circular References, Architectural Modeling, Digital Project and Collaborative Actions in the Architecture Learning ...... 1777 Ivan Xavier, Philipe Cantreva, and Igor Klein Didactic Experiences on Digital Modeling. Anamorphosis ...... 1789 João Pedro Xavier, José Pedro Sousa, and Alexandra Castro Research and Practice of the Mixed Teaching Mode for Engineering Graphics Based on MOOC ...... 1801 Jingying Zhang, Wei Yang, Xianying Tong, and Hui Zhang

Part VII Geometry and Graphics in History Graph Theory and Music: A Mathematical Tool for Musicians ...... 1813 Giovanni Albini and Marco Paolo Bernardi A Contribution to the History of Representation. The Unpublished Treatise by Matteo Zaccolini ...... 1825 Leonardo Baglioni, Marco Fasolo, and Matteo Flavio Mancini Phonurgia Nova. Geometrical Acoustics in the 17th Century ...... 1837 Alessio Bortot xlii Contents

Perspective Analysis of the Inlaid Wood Panel from Duomo of Bergamo ...... 1849 Giorgio Buratti and Giampiero Mele De l’Orme’s Graphics Language: Between Stereotomy and Orthogonal Proto-Projection ...... 1859 Antonio Calandriello Ludovico Cardi Said “Il Cigoli”. Practical Treaty of Perspective: Innovative Aspects and Intuitions ...... 1870 Daniele Calisi Drawings and Models in English Perspective Treatises of the XVII and XVIII Centuries ...... 1882 Cristina Càndito Geometry as a Tool to Manage the Territory. Nicolaas Cruquius and the Map of the Merwede ...... 1895 Laura Carlevaris The Quincunx as Architectural Structure. Geometry and Digital Reconstructions After Leonardo Da Vinci’s Centralized Plan Temples ...... 1907 Marco Carpiceci and Fabio Colonnese La Géométrie Pratique. Survey Manuals in France Between the 18th and 19th Centuries ...... 1919 Camilla Casonato DIN-DON-DAN—Bells and Their Geometry ...... 1930 Graciela Marina Colagreco and Günter Weiss Geometry/Time Measurement/Sundials Graphical Resolution via Algorithmic and Parametric Processes ...... 1945 Francesco Di Paola Digital Renovation and Archives of Japanese Ancient Ritual Performance at the World Cultural Heritage; Niutsuhime Shrine .... 1958 Kohei Furukawa, Kazuya Kojima, and Kozaburo Hachimura A Study on Site Planning of Mountain Temples Through Scene Transition Along the Visiting Route by MOTATION: Case Study of Muroji, Hasedera, and Kinpusenji Temples in Japan ...... 1972 Momoko Kato, Hirokazu Abe, and Kensuke Yasufuku The Study of “Deconstructivism” in the Field of Architecture ...... 1984 Masanao Kitamura, Kensuke Yasufuku, and Hirokazu Abe Sharawadgi and Penetrating Space in Chinese Classic Gardens ..... 1994 Luyi Liu Contents xliii

Geometry in Advertising Graphics ...... 2000 Massimo Malagugini Leonardo da Vinci as a Scientist in Assessing the Encyclopedic Literature of Imperial Russia, the Soviet Union and the Russian Federation ...... 2009 Mikhail Mashkarin and Natalia Kaygorodtseva Astronomy of Shadows and Light: Athanasius Kircher’s Sundials Between Geometry, Perspective and Science ...... 2019 Cosimo Monteleone and Isabella Friso Design Method of Original Motifs and Decorative Patterns Using Geometric Baseline Derived from Japanese Crafts ...... 2031 Kuniko Ohtomo Material Models of Ruled Surfaces as Witnesses to the Development of Mathematical Teaching ...... 2041 Robert Päßler and Daniel Lordick The Masonry Domes Over the Centuries: The Important Role of Geometry ...... 2051 Raffaella Pavani and Luisa Rossi-Costa Theater and The Towns ...... 2061 Enrica Pieragostini and Salvatore Santuccio Digital Approach to Michelangelo’s Design. The Inner Light of Neoplatonic Geometry ...... 2074 Matteo Giuseppe Romanato Abraham Bosse and the Perspective in Practice ...... 2083 Marta Salvatore The Triad of Vitruvius in the Modern World ...... 2095 Elena I. Shangina Geometry, Arithmetic, Architecture. Calculation Methods for Vault Surfaces in the Modo di Misurare le Fabriche by Guarini ...... 2108 Roberta Spallone The Influence of the Discovery of Prehistoric Pile Dwellings Around the Alps on Architect Hannes Meyer ...... 2120 Hideo Tomita Between Survey and Interpretation: The Ideal Shape of Flavian Amphitheater According to Carlo Lucangeli ...... 2127 Jessica Romor and Graziano Mario Valenti xliv Contents

Simulation of the Giant Wild Goose Pagoda in Immersive Virtual Reality Environment ...... 2139 Fei Yang, Shilun Hao, Adrian Tan, Jin Yang, Fabian Tan, and Michael Parke

Part VIII Posters The Golden Ratio and Jewelry Design ...... 2159 Claudia Regina Batista and Adhemar Maria do Valle Filho Federated Parametric Models for Seismic Risk Analysis in Existing Buildings ...... 2163 Carlo Biagini and Paolo Ottobri Wallace-Simson Line in Four Cayley-Klein Planes ...... 2167 Ivana Božić Dragun Geometry of Conjugation of Curvilinear Channels of the Parts ...... 2171 Aleksandr Yurievich Brailov Designing by Rules: Parametric Workflow Behind ICGG 2018 Conference Logo ...... 2176 Matteo Cavaglià The Alexander Mosaic and the House of the Faun. The Iconic Light of Geometric Relationships ...... 2180 Luisa Ferro MRT as a Testing Instrument in Research on a Singular Aptitude Among Architecture Students...... 2184 Renata A. Górska, Agnieszka Wojtowicz, and Barbara Wojtowicz Visual Simulation of Erosion Terrain Considering Different Materials ...... 2188 Tomoya Ito and Tsukasa Kikuchi Study on Analysis Support of Lubrication Phenomenon by Three-Dimensional CAD Development of Auxiliary Analysis Tool for CAD ...... 2192 Toshiaki Kanda, Masatoshi Niizeki, and Toshihiro Ozasa Parametrizing 3-Webs of Circles on Darboux Cyclides ...... 2196 Rimvydas Krasauskas Representation of an Object as a Semiotic Sign in Engineering ...... 2201 Harri Lille and Aime Ruus Luca Pacioli: A Friend of Leonardo da Vinci De Divina Proportione in Capital Letters ...... 2205 Paola Magnaghi-Delfino and Tullia Norando Contents xlv

Vilnius Cathedral Ceiling Interactive 3D Models—Exploration and Digitalization ...... 2209 Daiva Makutėnienė Comparison with Expression on “Rakuchu Rakugai-zu”, Scenes in and Around the Capital of Kyoto ...... 2214 Kazuko Mende Visual Art as Science ...... 2218 Antonio Mollicone Spatial Analysis and 3D Modeling: Drawing the Cathedral of Brasilia in Different Software ...... 2223 Luciana Nemer and Igor Klein Learning Creative, Learning MOOC ...... 2227 Maria Ines Pascariello Projections: Applications from Geometric and Project Design Education ...... 2232 Caio Cesar Pereira, Guacira Macedo dos Santos, and Sandra de Araujo Barata Gomes Kinematical Ruled Surfaces Based on Interrelated Movements in Axoids’ Triad “Torse–Cone–Cone” ...... 2236 Galina S. Rachkovskaya, Yuriy N. Kharabayev, and Natalya S. Rachkovskaya Building Types and Narrative Development in Emaki—Comparing the Compositions of KASUGA GONGEN GENKI and Ishiyama-dera Engi Emaki ...... 2241 Noriko Sato A Study on Automatic Generation of Heating Patterns of Contour Maps for 2.5D Printing ...... 2245 Hiromasa Suzuki, Yutaka Ohtake, and Yuta Miwa Quadratic Characteristics of Workspace Curves of Generalized Planar Cable-Driven Parallel Mechanisms ...... 2249 Lewei Tang Getting the Smallest Sphere Which is Tangent to Four Non-parallel Unlimited Skew Lines in General Positions Based on MATLAB ..... 2253 Ye Tao, Sheng Wen, and Kai Zhang Features of Teaching the Graphic Discipline Courses for Different Specialty Students ...... 2257 Iryna Taras xlvi Contents

A Study on Monozukuri Education in Karakuri Doll Production ..... 2262 Hiroki Tominaga, Masayuki Mori, Naoki Iida, and Kenichi Hirose Determining Features of Volumes of Interest of Medical Ultrasound Images ...... 2266 Robert Tornai, Péter Török, János P. Pálmai, and Botond Balogh The Modeling for Numerical Simulation of a Benchmark Model Based on CAD System ...... 2270 MinLe Xu and YuanGuang Fu Geometric Analysis and Engineering Application of Conic Section ...... 2274 Xu Yaqi, Zhang Chengfang, and Mi Xinwu An Algorithm for Computing Geodesic Curve Based on Digital Experiment of Point Clouds ...... 2282 Peng-Fei Zheng, Qing Liu, Ju-Di Zhao, Da-Jun Lin, and Qi An Correction to: Geometrical Universality of Truss-Z System ...... C1 Machi Zawidzki Author Index...... 2295