ICGG 2018 - Proceedings of the 18th International Conference on Geometry and Graphics

Name: ICGG 2018 - Proceedings of the 18th International Conference on Geometry and Graphics | 40th Anniversary - Milan, Italy, August 3-7, 2018
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40th Anniversary - Milan, Italy, August 3-7, 2018

Luigi Cocchiarella(Editor)

Springer (Publisher)

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Published on 6. July 2018

XLVI, 2300 pages

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Content

Intro
Preface
Welcome Addresses from Politecnico di Milano
Welcome Addresses from the Board of Chairs
Special Addresses for the 40th Anniversary
Committees
Contents
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
1 1988-1990: Brainstorming
2 1990-1994: Decisions
Reference
Geometry and Graphics for the Graphic Identity of a Conference on Geometry and Graphics: About the ICGG2018 Conference Logo
Abstract
1 Conference Dedication
2 Leonardo's and Natta's Diagrams as Sources
3 Merging Leonardo's and Natta's Diagrams
4 Designing, Branding, Prototyping: Use and Abuse
5 Conclusion
Acknowledgements
References
II Invited Lectures
Rational Estimates for Irrational Problems: Proportional Geometry in the Work of Leonardo da Vinci
Abstract
1 Proportional Geometry and Rules of Nature
1.1 Pyramidal Law
1.2 Form and Balance
1.3 Form and Force
1.4 Motion
2 Proportional Design
2.1 The Last Supper
2.2 The Last Supper's Proportions
2.3 The Giant Crossbow
References
Molecular Geometry and Molecular Graphics: Natta's Polypropylene and Beyond
1 Introduction: The Birth of Stereochemistry
2 Natta's Polypropylene: The Breaking of Nature's Monopoly
3 Outlook: Structure and Self-assembly in Biology and Materials
References
Geometric Thinking and the Geometry of Conics and Quadrics
1 Introduction
2 Point on Line Ruling Three
3 Degenerate Quadrics
4 Eigenvalues, Eigenvectors and Standard Form Quadric
4.1 Translation
4.2 Rotation
5 Relation to Planar Lines and Conics
6 Stationary Distances and Quadrics
7 Conclusion
References
Designing with Shadow/in Architectural Lighting Design
Abstract
1 The Shadow's Identity/Under the Natural Light
2 Gradation
2.1 Cast on White Wall
2.2 What Is Ideal: Uniformity or Gradation?
2.3 Sharing Japan's Unique Shadow Aesthetic with the West
2.4 The Art of Grayscale Drawing
3 Contrast
3.1 Thinking About Perceptual Contrast Effect: shiruko and shio-konbu
3.2 Contrast: Basic Principles
3.3 Light and Shadow in Dry and Sunny Climates
4 Utsuroi
4.1 Light Is Always in Flux
4.2 The Subtlety and Breadth of the Japanese Word Utsuroi
4.3 The Light Operation Diagram
Appendix
References
Higher Dimensional Geometries. What Are They Good For?
1 Introduction
2 A Huge Variety of Higher Dimensional Geometries
2.1 What is a Dimension?
2.2 Some Examples of Higher Dimensional Geometries
3 Model Spaces
3.1 Various Geometries and Their Models
3.2 What Makes a Model Space?
4 Applications - Benefiting from Model Spaces
4.1 Interpolation with Ruled an Channel Surfaces
4.2 Recognition and Reconstruction of Surfaces
4.3 Interpolation of Poses by Smooth Motions
5 Conclusion
References
Computational Visual Illusion and Its Application
1 Introduction
2 Hybrid Image
2.1 The Composition of a Hybrid Image
2.2 Problems With the Conventional Method
3 An Edge-Alignment Free Hybrid Image
3.1 The Synthesis Algorithm
3.2 The Assessment Method
4 The Application of a Hybrid Image
4.1 Hybrid Image as Visual Acuity Assessment Tool
4.2 Hybrid Image as a Security Prevention Measure
5 Other Visual Illusions and Their Applications
5.1 The Illusion of Sex
5.2 Mirror Therapy Using Visual Illusion
6 Conclusion
References
Blindness of Seeing. On the Origin of the Images
Abstract
1 Introduction
2 A Girl Who Saw Too Much, a Prehistoric Tent, and Some Dark Rooms
3 A Distant Island, a Picture Seen Close Up
References
III Theoretical Graphics and Geometry
Composition and Deconstruction of Spaces Depicted in Shinji Somai's Films
Abstract
1 Introduction
2 Composition and Deconstruction of Spaces
2.1 Composition of Spaces in Film
2.2 Composition and Deconstruction in Somai Films
2.3 Composition and Deconstruction in Architecture
3 Long Takes in Somai Films
3.1 Transformation of Somai Films
3.2 Characteristics of Long Takes
3.3 Deconstruction in Long Takes
4 Conclusion
References
Graphical Model of the Biquadratic Transformation
Abstract
1 The Method of Constructing a Graphical Model of Biquadratic Transformations of the Plane
2 The Development of Graphical Models Biquadratic Transformations Obtained by Binary Mapping of Two Nonruled Surfaces of the Second Order
2.1 Graphical Model Biquadratic Transformation L1
2.2 Graphical Model of Biquadratic Transformation L2
2.3 Graphical Model of Biquadratic Transformation L3
2.4 Graphical Model of Biquadratic Transformation L4
3 The Development of Graphical Models of Biquadratic Transformations Obtained Binary Mapping Pair of Bevel Surfaces
3.1 Graphical Model of Biquadratic Transformation L5
3.2 Graphical Model of Biquadratic Transformation L6
3.3 Building a Graphical Model of Biquadratic Transformation L7
3.4 Graphical Model of Biquadratic Transformation L8
4 The Development of Graphical Models of Biquadratic Transformations Obtained Binary Mapping Ruled Two Hyperbolic Surfaces
4.1 Graphical Model of Biquadratic Transformations L9
4.2 Graphical Model of Biquadratic Transformations L10
4.3 Graphical Model Biquadratic Transformations L11
4.4 Graphical Model Biquadratic Transformation L12
5 Conclusion
References
Graphics and Quantum Mechanics-The Necker Cube as a Quantum-like Two-Level System
Abstract
1 Introduction
2 A Quantum Representation
3 In Search of the Eigenstates: The Bloch Sphere
4 A Neurophysiological Action
5 Conclusion
Acknowledgements
References
Surface and Curves: A Dialogue Between Nature and Structural Analysis
Abstract
1 Fractal and Biomimetic
1.1 Nature, Shapes, Geometry and Structure: Prediction and Description
1.2 Biomimetic: Systemic Architecture
2 Nature Design
2.1 Unconsorable or Designed Architectures? The Architecture Made by Animals as an Example for Human Beings
2.2 Historical Examples of Architectures Inspired by Those of Animals
References
On One Locus in the Plane
1 Introduction
2 Locus Equation
3 Decomposability
4 Singular Points
5 Further Properties of the Curve G
6 Conclusions
References
Integration Between Perspective Images and BIM Models: Projective Geometry Is Still Alive
Abstract
1 Introduction
2 Literature Review
3 Methodology
4 Case Study
5 Conclusion
References
Geometric Constructive Traces in Drawings by Francesco Borromini
Abstract
1 On Some Drawings by Borromini
1.1 Sant'Agnese
1.2 Sant'Andrea delle Fratte
1.3 San Carlino
2 Construction Phases and Temporary Constructions for the Dome of San Carlino: Reconstructive Hypothesis of the System of Centring
2.1 The Construction of the 3D Model for the Construction of the Centrings
References
Using Topological Transformations to Construct the Intercepting Lines
Abstract
1 Introduction
2 The Graphical Representation of Topological Transformations
3 Conclusions
References
A Property of Area and Perimeter
1 Introduction
2 The New Algorithm
3 Discs Within a Circle: A Case Study
4 Other Dimensions
5 Squares Within a Square
6 Larger Values of
7 Discussion and Future Work
References
Quasifocal Line and "Burning Curve"
Abstract
1 Introduction
2 Quasifocal Line and "Burning Curve"
2.1 "Burning Curve"
2.2 Quasifocal Line
2.2.1 Reflecting Surface Is a Straight Circular Cylinder
2.2.2 Reflecting Surface Is a Cone
2.2.3 Reflecting Surface Is a Sphere
2.2.4 Reflecting Surface Is Paraboloid of Revolution
2.2.5 Reflecting Surface Is Torus
2.3 Receiver Surface for a Torus
2.4 Comparing Reflecting Properties of Torus and Circular Reflectors
2.5 Energy Map for Torus Reflector on the Flat Receiver
3 Conclusions and Further Work
References
Detection of Critical Direction for Feature Line Extraction on Meshes Based on Local Integral Invariants
Abstract
1 Introduction
2 Related Work
3 A Framework for Classifying Critical Directions Defined Over Local Neighborhoods
3.1 Definition of Neighborhood
3.2 Definition of "Normal" for {\varvec N}_{{\varvec r}} \left( {\varvec p} \right)
3.3 A Framework for Defining Critical Directions Over Local Neighborhoods
4 Analysis of Approaches
4.1 PCA of Local Neighborhoods
4.2 Find Critical Direction Over the Convex Hull of the Planar Curve (Spherical Curve's Projection onto Plane)
4.3 Find Critical Directions Over Gauss Map's Spherical Convex Hull
4.4 Find Critical Directions from a Sequence of Angle/Distance
5 Results
5.1 Effectiveness
5.2 Robustness
5.3 Computational Cost
6 Conclusion
Acknowledgements
References
A Spatial Version of the Theorem of the Angle of Circumference
1 Introduction
2 Equation of the Ruled Surface
3 Properties of
4 Special Cases
4.1 One-Sheeted Hyperboloids
References
Equidistant Sets of Conic and Line
1 Introduction
1.1 Equidistant Sets of an Ellipse and a Line
2 Equidistant Sets of a Hyperbola and a Line
3 Equidistant Sets of a Parabola and a Line
References
Isotomic Transformation with Respect to a Family of Triangles
1 Preliminaries
1.1 Barycentric Coordinates
1.2 Isotomic Transformation
2 Isotomic Transformation on a Family of Triangles
References
The Geometry of Quadratic Quaternion Polynomials in Euclidean and Non-euclidean Planes
1 Introduction
2 Quaternions and Quaternion Polynomials
3 Universal Hyperbolic Geometry
4 The Kinematics of Polynomial Factorization
5 A Conic and Its Focal Points
6 Comparison with the Euclidean Case
References
Geometric Algorithms for Constructing the Algebraic Surfaces on the Basis of Grassmann's Ideas and Their Extensive Equations
Abstract
1 Introduction
2 Basis for Construction of Surface O2
3 Basis for Construction of Surface O3
4 Other Basis for Construction of Surface O3
5 Basis for Construction of Surface O4
6 Basis for Construction of Surface O5
References
Hyperbolic Space Forms with Crystallographic Applications and Visualizations
1 Introduction
2 An Euclidean Example for the Space Group P212121
3 The {5,6,6} Football Manifold and its Extremal Properties
4 Cobweb or Tube Manifolds
4.1 Construction of the Cobweb (tube) Manifold Series Cw(2z = 8p-2), 2 P N
4.2 Construction of Cobweb (tube) Manifold Cw(10) and Cw(2z = 8q + 2), 1 q N, in General
5 Manifolds for the Archimedean Solids {4, 6, 8} and {4, 6, 10}
5.1 {4, 6, 8}
5.2 A Hyperbolic Archimedean Manifold {4,6,10}
References
Optimized Ruled Surfaces with an Application to Thin-Walled Concrete Shells
Abstract
1 Introduction
2 The Line Geometry Model: Study Sphere
2.1 Dual Vectors
2.2 Geodesics and Minimal Ruled Surfaces
3 Kinematics of Rulings
3.1 Dual Rodrigues Formula
3.2 Piecewise Geodesic Interpolation
4 Interpolation Algorithms
5 Building the Footbridge
6 Conclusions
Acknowledgements
References
Examples of Autoisoptic Curves
1 Introduction
2 Curve Representation via Support Function
3 Delay Differential Equations for Autoisoptic Curves
4 Exact Solutions
4.1 One Equation
4.2 Autoevolutes: ==2
4.3 Autoevolutoides ==2
5 Two Equations and Approximations
5.1 Approximation in the Space of Elementary Solutions
5.2 Approximation with power series
6 Conclusion
References
The Properties of Special Points on the Brocard Circle in a Triangle
Abstract
1 Introduction
2 The Special Point O1 in Triangle {{\bf ABC}}:\angle {\varvec AO}_{1} {\varvec B} = \angle {\varvec AO}_{1} {\varvec C} = \angle {\varvec B} {\,+\,} \angle {{\bf C}}
3 When a Symmedian Is a Tangent to the Brocard Circle?
4 A Right Angle Triangle
5 An Isosceles Triangle
References
Structure Functions of Ruled Surfaces with Null Rulings
1 Introduction
2 Preliminaries
3 Structure Functions of Non-null Ruled Surfaces in Lorentz-Minkowski Space
4 Structure Functions of Ruled Surfaces with Null Rulings
4.1 Helicoidal B-scrolls
References
Curved Folding with Pairs of Cones
1 Introduction
2 Cone-Cone-Origami
3 The Characterization Theorem
4 Construction of the Corresponding Spatial Curves
5 An Example
6 Summary and Conclusions
References
Relationship Between Time and Typical Buildings Depicted in KASUGA GONGEN GENKI
Abstract
1 Introduction
2 Visualization of Time
3 Expressions Conveying Time
4 Methods of Analysis
4.1 Dates Recorded in the Emaki
4.2 Depicted Locations
4.3 Iji-Dozu-Ho
5 Analysis and Results
5.1 Dates
5.2 Locations
5.3 Iji-Dozu-Ho
5.3.1 Type I: Same Time, Same Setting
5.3.2 Type II: Different Time, Same Setting
5.3.3 Type III: Same Time, Different Setting
5.3.4 Type IV: Different Time, Different Setting
5.3.5 Type V: Mixed Type
6 Discussion
7 Conclusion
References
Two Remarkable Spherical Arrangements of Circles
1 Introduction
2 A Polyhedron with Hexagonal Faces and a Circumsphere
3 An Incircular Net on the Sphere
References
Study and Practice on Double Deck Folding Structure Mobile Home Design Development
Abstract
1 Introduction
1.1 Background
1.2 Related Work
1.3 Objectives of This Research
2 Designing the Prototype
2.1 Summary of the Prototype
2.2 Design Specification
2.3 Geometry of the Prototype
3 The Process of Expanding Upper Deck
4 Case Study
4.1 Case Study as Exhibition Space
4.2 Case Study as Exhibition Control Tower
5 Conclusion
References
Logicometry: Graphical Representations of Logical Space Interrelations
Abstract
1 Introduction
2 Analysis
2.1 The Logical Proposition of the Human Agency and Its Form
2.2 Defining Logical Space Through Geometry
2.3 Symbolical Analogies Between Logical and Metaphysical Objects
2.4 The Values of the Metaphysical Conscience of Human Agency
3 Methodology
3.1 The Cartesian Model of Logical Space
3.2 The Polar Model of Logical Space
4 Conclusion
References
Minkowski Triples of Curve Segments
Abstract
1 Basic Concepts
1.1 Minkowski Point Set Operations
1.2 Minkowski Triples
2 Minkowski Circular Triples
3 Conclusions
References
Some Theorems of the Euclidean Geometry in Pentagonal Quasigroups
1 Introduction
2 Geometry of Pentagonal Quasigroups
3 Some Old and New Theorems of the Euclidean Geometry in Pentagonal Quasigroups
4 Conclusion
References
Geometrical Structures of Planar and Spatial Tessellations Based on 3D Models of Higher Dimensional Cubes
Abstract
1 The Considered 3D Model of Higher-Dimensional Cubes
2 Space-Filling Periodical Tessellations of 3-Models of k and 2 lessthan j lessthan k-Cubes
3 Reconstruction of the Spatial Tessellations
3.1 Compound Elements with Multiplied Edge Length
3.2 Models Composed by Models of Lower-Dimensional Elements
3.3 Reconstructions Related to the Model Edges
4 Planar Tessellations Based on the Spatial Models and Mosaics
4.1 Parallel Projections of the Models
4.2 Planar Intersections of the Space-Filling Mosaics
5 Concluding Remarks
References
The Cube: Its Relatives, Geodesics, Billiards, and Generalisations
Abstract
1 Introduction: The Cube and Related Polyhedra
2 Reflections and Shortest Paths
3 Geodesics, Pseudo- and Quasi-geodesics
4 Square, Cube, and Hypercube: Closed Geodesics and Billiards
5 Conclusion
References
Duality in Non-polyhedral Bodies Part I: Polyliner
Abstract
1 Duality
1.1 Duality in Form
1.2 Synthesis
1.3 Duality in Transformation Process
2 Further Structures Corresponding to Dual Pairs
2.1 Folding Down the Hull into Bundles
2.2 From the Kernel to Knots and Links
3 Simplest Cases of Dual Pairs, Knots, Links and Bundles
3.1 Polyliner with Duogon
3.2 Polyliner with Monogon
3.3 Loops-Unknotting with Monogon
3.4 Graphic Representation
Quadric Sections of Four-Dimensional Cones
1 Introduction
2 Analytic Approach
2.1 Quadric Sections of an Ellipsoidal Cone
2.2 Quadric Sections of a One-Sheet Hyperboloidal Cone
3 Synthetic Approach
3.1 A Spherical Cone
3.2 A One-Sheet Hyperboloidal Cone
4 Conclusion
References
Curves and Surfaces in the Churches with Ovate Plant in Naples. Geometric Analogies and Differences
Abstract
1 Introduction (OZ)
2 Oval Shape Between Polycentric Curve and Ellipse (OZ)
3 Churches Spatial Morphology and 3D Modeling (VC)
4 Conclusion (VC)
References
IV Applied Geometry and Graphics
A Suggestion of the Optical Illusion Blocks for an Architectural Theory: Toward an Architecture in the Near Future
Abstract
1 Architectural Theory for Our Blocks
1.1 Optical Illusion Block
1.2 Two Points from Architectural Theories
1.3 The Third Point: Phenomenal Transparency
2 The Lessons of Our Blocks
2.1 Depth from Wider Angles
2.2 Versatility
3 Semi-transparency and Frequency of Change
3.1 Kunstwollen for Semi-transparency
3.2 Technical Allowance for Frequency
3.3 Semi-transparency Versus Equivocalness
3.4 Super Imposing Layers
4 Two Points of Importance
4.1 Historical Tension: Transparency Versus Semi-transparency
4.2 Aesthetic Significance: Crisis of Harmony
References
Perspective and the Blind
Abstract
1 Introduction
1.1 Art and Visual Impairment
1.2 Aesthetic Experience in Non-sighted People
2 Pictorial Artworks' Main Challenges
2.1 Perspective and the Blind. Two Psychological Theories
2.2 The Problem of Light and Colour
3 Conclusion
3.1 A Proposed Research Methodology
References
The Korean Alphabet (Hangeul) and the Translation Processes in Design
Abstract
1 Introduction
2 Hangeul: The Korean Writing System
3 The Letters. Experience Aims and Methodology
4 Final Considerations
References
"Ultima Dea": A Laser Scanner Application for 3D Modelling
Abstract
1 "Ultima Dea"
1.1 The Designer: Renato (Sonny) Levi
2 Engine Compartment 3D Scanning
2.1 Scans' Pre-processing
2.2 Fine Registration and Output
3 Meshing the Cloud
3.1 Surface Modelling
4 Conclusions
References
Margin's Landscapes Between Po and Trebbia Rivers in Piacenza Area: Geometrical Descriptions
Abstract
1 Roman's "Centuriazione": From Metric Measure to Photography
2 Methodologies of Measure by Photography and Video
3 Geometry and Perception of the Landscape: A Multiple Point of View
4 Final Considerations: Layers of the Landscape
References
Immersive Visions. Some Paradigm a of an Exceeding Iconography. Capture and Monitoring by Spherical Cameras and Interactive Smartglasses
Abstract
1 The Sphere as a Landscape
2 The Sphere as an Image
3 The Sphere as a Visual Representation
4 Connections-Interfaces. The Sphere as a Device
4.1 Capture and Monitoring by Spherical Cameras and Interactive Smartglasses
5 Case Studies. Survey Examples
6 Case Studies
7 The Frame Is You. Conclusions
Acknowledgements
References
Imperial Porphiry and Golden Leaf: Sierpinski Triangle in a Medieval Roman Cloister
Abstract
1 Introduction: Our Mental Eyes, Bridging Across Times
2 The Sierpinski Triangles in the Cloister of St. John
3 The Cloister of St John in Lateran and the Role of the Marmorari
3.1 Bibliographic Note
4 The Sierpinski Triangle, Its Mathematical Values
4.1 The Sierpinski Triangle Has a Non-integer Number of "Dimensions" (A Fractal)
5 Conclusions
Acknowledgements
References
A Storage Model for Large Scale Web-Based Learning Systems Based on Concept Tree
Abstract
1 Introduction
2 Framework of Collaborative Editing Platform
3 Storage Model Based on Conception Tree
3.1 Electronic Resource Model Definition
3.2 Concept Tree Model Construction
3.3 Electronic Resource Association Based on Concept Tree
3.4 Resources Extraction Mechanism Based on Hash Table
3.5 Cloud Storage Based on the Combination of Distributed Files and Rational Database
4 System Development and Discussion
5 Conclusion
Acknowledgements
References
An Unlikely Rome. Towards Performative Geometry
Abstract
1 An Evening with Monge
2 Representation in Contemporaneity
3 Non-representation, the Field of Performative Geometry
4 An Unlikely Rome
5 Rethoric of Representation and Design Strategies
6 Geometry as an Event
7 Maps. Diagrammatic Representation of Data Complexity
References
Cellular Automata Between Life Science and Parametric Design: Examples of Stochastic Models to Simulate Natural Processes and Generate Morphogenetic Artefacts
Abstract
1 From Deterministic to Stochastic Cellular Automata
1.1 Introduction
1.2 From Elementary Cellular Automata to Complexity
2 Applications in the Study of Stochastic Development
2.1 Alan Turing's Morphogenetic Model and Cellular Automata
2.2 Morphogenesis in Nature and Its Digital Replication
2.3 Parametric Design and Urban Morphogenesis
3 Conclusions
References
Smart Artefacts and Spaces to Interact, Promote and Transfer Cultural Knowledge
Abstract
1 Introduction
2 Responsive and Intelligent Objects
3 Interacting with the Body
4 A Case Study: Leonardo Racconta Leonardo
5 Conclusions
References
The Role of the Graphic Element in the Context of Playful Games for Cultural Heritage
Abstract
1 Video Games as Teaching and Learning Tool
2 Environment and Space Design in Video Games
3 A Video Game Project for a Chartehouse. Some Critical Issues
3.1 Game Environment Design: Real Data Collection
3.2 Game Environment Design: Data Processing
3.3 Game Environment Design: Visual, Graphic and Architectural Elements for Narrative Purposes
4 Conclusions
Acknowledgements
References
Unfolding Geometry from Unity: Digital Survey and 3D Modeling of Islamic Decorative Apparatus in Generalife Palace, Alhambra
Abstract
1 Islamic Decoration: Genesis of Geometrical Approach
2 Geometry into Mudéjar Art: Al-Andalus and Al-Hambra
3 Alhambra Documentation Project: Digital Methodologies for the Representation of Architectural Apparatuses
4 Unfolding Unity: Geometric Constancy in Morphological Variation of Alhambra Decorations
5 Ornamental Apparatus in Generalife Palace: Surfaces and Complexity of Models for a Representative Analysis
5.1 Decomposition and Design of Decorative Matrices
5.2 Ornamental Models and Morphological Hierarchies
6 Conclusions
References
Triangular Proportional Scheme and Concept of the Two Serbian Medieval Churches
Abstract
1 Introduction
1.1 Historical Frame and Architectural Concept of the Two Churches
2 Proportional Analysis
2.1 Documentation Sources
2.2 Proportional Analysis Guided by Regular Polygons
2.3 Proportional Analysis of "Empty" Spaces by Classical Constructions
3 Conclusion
Acknowledgements
References
Best-Fit Analysis for the Geometry Characterization of Domes
Abstract
1 Introduction
2 The Case Study of Catania's Cathedral
3 Best-Fit Analysis: Geometric Procedure
4 Best-Fit Analysis: Analytic Procedure
5 Conclusion
References
The Evolutionary Mechanism of Unit Cell: Parameterizations of Polyhedron Sandwich Structure Based on Rigid Origami
Abstract
1 Introduction
2 Regular Polyhedral Unit Cell
3 Evolutionary Mechanism of Polyhedral Unit Cell Based on Origami
3.1 Origami Geometric Crease Transformation
3.2 Basic Unit Cell and Basic Circles
3.3 Similarity Transformation
4 Conclusions
Funding
References
Converting 3D-CAD Data into FRP Parts
Abstract
1 Instruction
2 Computer Aided Modeling
3 Numerical Control Machining
4 FRP Making
5 Tensile Strength Testing
6 Conclusions
References
A Quest for the Structural Response Through Geometric Representation of the Design of Built Heritage
Abstract
1 Introduction
2 Complex Structure Geometry
3 How to Reconstruct the Masonry Vaults Geometry
3.1 Actual Methods of Survey
3.2 G. Scott and J. Heyman
3.3 Application: Milan Cathedral
4 Simplification of the Model: Venustas-Utilitas-Firmitas
5 Integrated Approach
5.1 The Cathedral of Milan
5.2 Experimental Observation: Surveys
5.3 A Digital Code for Structural Calculation
6 Conclusions
Acknowledgements
References
Geometric Representation of Turbulent Macrostructure in 3D Jets
1 Introduction
2 3D Jet Representation and Averaging of Flow Parameters
3 Description of a Puff
4 Results and Continuation of the Work
5 Conclusions
References
An Algebraic Version of the Input-Output Equation of Planar Four-Bar Mechanisms
1 Introduction
2 Input-Output Equation
2.1 Special Cases
3 Design Parameter Space
4 Conclusions
References
Collection and Visualization of Pedestrian Navigation Routes with Parametric Tools
Abstract
1 Introduction
1.1 Experiments in Virtual Environment
2 Survey
3 Digital Parametric Model
4 Results and Implementation
5 Discussion
6 Conclusion
References
Between Architecture and Writing: Graphical Geometry to Decipher Systems of Signs. Campo Verano in Rome
Abstract
1 Introduction
2 Analysis Method
3 Analysis of the Funerary Micro-architecture
4 Analysis of the Displayed Writing
5 Conclusions
References
Visualized Analysis of Spatial Distribution of Dissolved Oxygen and Nitrogen Removal Efficiency in Constructed Wetland
Abstract
1 Introduction
2 Experimental Basis
2.1 Map Obtainment
2.2 Data Obtainment
2.3 Preparation of Excel Chart for DO and TN
3 Data Visualization
3.1 Spatial Interpolation Methods
3.2 Spatial Interpolation Principle
3.3 Visual Chart Productions
4 Analysis of the Distribution of DO and Nitrogen Removal in the Wetlands
4.1 Visualization of the Plane Distribution of DO and Denitrification Effect in the Wetlands
4.2 Facade Distribution Visualized Analysis of DO in the Wetlands
5 Conclusions
References
Study on the Modeling Converting Methods of Complex Mechanical Product Exterior Design
Abstract
1 Overview
2 Industrial Design Process of Complex Mechanical Product
3 The Export of the Structure Model
3.1 Several Data Conversion Formats of Structure Model
3.2 Selection of Structure Model Transformation Mode
4 Several Modes to Import Exterior Model into Pro/E Engineering Modeling Software
5 Structure Model Export Mode Verification by Example
6 Conclusion
References
Examination of the Experience of Biomorphic Form Materialized in Urban Design Model
Abstract
1 Introduction
2 Implementing Biomorphic Forms in Urban Design
3 Materials and Methods
3.1 Parametric Tools for Modeling Biomorphic Forms into Urban Design Model
3.2 The Visual Questionnaire for Examination of the Experience of Urban Design Model-Bench
4 Results
5 Conclusion
Acknowledgements
References
Repetition of Triangle Fountain of Aldo Rossi: Geometrical Analogy of Architecture
Abstract
1 Introduction
2 Method
3 Discussion
3.1 The Type "Lifted by Pillar"
3.2 The type "Cantilevered"
3.3 The Type "Synthesized"
4 Conclusion
4.1 Formula of Geometrical Analogy
4.2 Relationship with Drawings
References
Toward a New Capital by Le Corbusier-A Synthesis of Images with Different Origins
Abstract
1 Introduction
2 Purpose and Method
3 Development Crossing Over the Genres
3.1 Reflection of Pictorial Images
3.2 Development of Architectural Images
3.3 Development of City Images
3.4 Linkage of Images of lessthan Birth greaterthan via Chandigarh
4 From the Acropolis Toward Chandigarh-A Synthesis of Images with Different Origins
References
Generic Fitting in Point Clouds
1 Introduction
2 Generic Fitting
2.1 RANSAC Algorithms for Primitive Detection
2.2 Massive RANSAC Primitive Detection
2.3 Extended Boundary Graph Representation
2.4 From Model to Boundary Graph Representation
2.5 Graph-Matching
3 Application
3.1 2D Polygon Fit
3.2 Application to Catalogue-Based Models
4 Conclusion
References
Identification Method of Topographic Surfaces Models
Abstract
1 Introduction
2 Literature Review
3 Aim and Research Problems
4 Materials and Methods
5 Conclusion
References
Geometry of Stairs
Abstract
1 Stairs-Function, History and Design Rules
2 Typologies of Stairs
3 Stair Geometries and Directions
4 Spiral Stairs
5 Sinus Stairs
6 Conclusions
Acknowledgements
References
Exempla Imperfecta: The "Curious" Image of the Platonic Solid
Abstract
1 First Section
1.1 Introduction
2 Second Section
2.1 Discussion
References
The Design of JLAMT: An Aided Tool for Large-Scale Complex Physical Modeling
Abstract
1 Introduce
2 The Visual Modeling Tool JLAMT Based on Field Oriented Development
3 The Architecture and Design Principles of JLAMT
4 The Application Example of JLAMT
5 Conclusion
Acknowledgements
References
Geometric Links Between 2d Patterns and 3d Structures in Islamic Architectures of Andalusia
Abstract
1 Introduction
2 The Geometry, Between Theory and Practice
3 The Geometric Drawing as a Matrix of Decorative Patterns
4 Andalusian Vaults with Interwoven Arches
5 Conclusions
Acknowledgements
References
Extended Morphological Closing Using Geodesic Filtering
1 Introduction
2 Mathematical Morphology
3 Method
3.1 Extended Closing Operator
3.2 Extended Opening Operator
4 Results and Discussion
5 Conclusion
References
3D Printer of Five-Axis Laminate-Shaping with FDM Method and Its Application
Abstract
1 Introduction
2 Hardware and Control of Hybrid Machine
3 Software for Five-Axis Laminate-Shaping
4 Simulation for of Five-Axis Laminate-Shaping
5 Integration of Additive Manufacturing to CAM
6 Case Study
7 Summary
Reference
A Program to Seek Drawing Methods for Descriptive Geometry in Prolog
Abstract
1 Descriptive Geometry
1.1 Handwriting Drawing
1.2 Database of Descriptive Geometry
2 A Trial Program to Seek Drawing Method
2.1 Consideration About Program
2.2 Simple Example
2.3 Perpendicular Line Drawing by the Same Radius Circles
2.4 Perpendicular Line Drawing by Different Radius Circles
3 Conclusion
References
Alternative Interpretation of the Plücker Quadric's Ambient Space and Its Application
1 Introduction
1.1 Lines and Line-Elements of Euclidean 3-Space
1.2 Outline
2 Lines in Euclidean 4-Space
2.1 Quaternionic Representation
2.2 Alternative Interpretation
2.3 Projection on the Plücker Quadric
3 Lines-Elements in Euclidean 4-Space
3.1 Lower-Dimensional Analogue
4 Straight Lines
4.1 Straight Lines in P5L
4.2 Straight Lines in P6G
4.3 Kinematic Relevance of
5 Application
5.1 Study Sphere
5.2 Review
5.3 Concluding Algorithm
References
Visualization of Infants' Behavior at Home Using Augmented Reality for Promotion of Development and Prevention of Accidents
Abstract
1 Introduction
1.1 Augmented Reality and Real Environment
1.2 Home and Affordances
2 Methods
2.1 Participants
2.2 Procedure
2.3 Data Analysis
2.4 Ethical Considerations
3 Results
3.1 Observational Data
3.2 Vision-Based Tracking
3.3 User Experience
4 Discussion
4.1 Observational Data
5 Conclusions and Future Work
Acknowledgements
References
Modularity of Concave Polyhedra of the Second Sort with Octagonal Bases
Abstract
1 Introduction
2 Previous Research
3 Joining the Compatible C II with the Octagonal Bases
3.1 Connecting the Bases in the Same Plane
3.2 Joining the Polyhedra by the Common Bases
3.3 Using Truncated Cube as a Mediator
4 Ideas for the Application of C II-8 in Architecture
5 Conclusions
Acknowledgement
References
Introduction to "Architectural Geometry": Through Analysis of Architecture Made of Square Plan
Abstract
1 Introduction
2 Three Categories of Architectural Geometry
2.1 Compositional Geometry
2.2 Projective Geometry
2.3 Signified Geometry (Non-euclidean Geometry)
2.4 Geometric Order as "Fiction"
3 Architectural Geometry and Scale
3.1 Embodied Geometry
3.2 Scale of Architecture
4 Analysis of Architecture Made of Square Plan
4.1 Method and Results
4.2 Discussion
5 Conclusion
References
Visual Paradoxes in Video Games: Spatial Reconstructions and Geometric Analysis
Abstract
1 Introduction
2 Research and Classification
3 Analysis by Type
3.1 Parallel Projection: Axonometric View
3.2 Parallel Projection: Orthographic View
3.3 Central Projection: Perspective
4 Conclusion and Possible Developments
References
Directorial Surfaces and Potential Applications in Cupola Design
Abstract
1 Introduction
2 Mathematical Formulation
2.1 Weberian Approach in Surface Definition
2.2 Directorial Surfaces
3 Geometrical Model and Results
3.1 Line Directors as the Sides of the Regular Polygons
3.2 Line Directors as the Non-parallel Diagonals of Regular Upright Prisms
3.3 Line Directors as the Edges of Platonic Polyhedrons
4 Architectural Applicability
5 Conclusion
Acknowledgements
References
3D Modeling of the Biological Form of the Green Chinche
Abstract
1 Introduction
2 Separation and Identification of the Insect Parts
3 Capture and Accommodation of the Images
4 Tagged Points
5 Numerical Values of the "Landmarks"
6 3D Modeling
7 Results
8 Contributions
9 Conclusions
References
From Voxels to Parts: Hierarchical Discrete Modeling for Design and Assembly
Abstract
1 Introduction
2 Background
2.1 Volumetric Modelling
2.2 Digital Fabrication with Digital Materials
3 Methods
3.1 Wasp: Discrete Modelling Framework
3.2 Gradient Fields
3.3 Constraints Modelling
3.4 Hierarchical Discrete Modelling
3.5 Implementation
4 Results
5 Conclusion and Outlook
Acknowledgements
References
Visualisation of DSM as 3D-Mesh for Urban Analyses
Abstract
1 Introduction
2 Brief Typology of 3D-City-Models
2.1 CAD-Models
2.2 CityGML
2.3 LiDAR and DSM
2.4 Reality Mesh Models
3 Application of DSM
3.1 Data & Geometric Structure
3.2 Visualisation
3.3 Computation Aspects
3.4 Urban Analyses
4 Conclusions
References
Research on Video Representation by Unexperienced Viewpoint Using 360-Degree Movie
Abstract
1 Introduction
2 Related Works
3 What Is a 360-Degree Movie?
3.1 Features of 360-Degree Movies
3.2 Understanding of Image Production
3.3 Production Flow
4 Video Production and Evaluation Experiment Based on Unexperienced Viewpoint
4.1 Taking 360-Degree Movies
4.2 Evaluation Experiment
4.3 Evaluation Result
5 Discussion
6 Conclusion and Future Works
References
Application of Middle-Out Design Based on Multi-body Method
Abstract
1 Introduction
2 Overview of Design Approaches
2.1 Bottom-Up Design
2.2 Top-Down Design
2.3 Middle-Out Design
3 Multi-body Layouts
3.1 Layout Based on Split
3.2 Layout Based on Creating Independent Solid Bodies
4 Parameter Correlation in Multi-body Layout
4.1 Full Parameter Correlation
4.2 Cross-Feature Parameter Correlation
4.3 Cross-Component Parameter Correlation
4.4 Cross-Part Parameter Correlation
5 Case Study
6 Conclusion
References
Geometrically Controlled Digital Workflow from Scratch to Fabrication
Abstract
1 Introduction
1.1 Digital Fabrication
1.2 Parametric and Algorithmic Design
1.3 State of Art at the Universities
2 Didactical Approach
2.1 Conceptual Phase
2.2 Elaboration Phase
2.3 Realization Phase
2.4 Exhibition Phase
3 Realized Projects
4 Splitterwerk
4.1 Form-Finding Process and Geometry
4.2 Parametric Model and Statics
4.3 The Workflow
4.4 Fabrication
4.5 Construction Site
4.6 Result
5 Summary
Acknowledgements
References
Graphical Analysis of the Structural Behavior, According Hypothesis of Rankine-Schwedler, of a Large Stone Dome in Granada (Spain)
Abstract
1 Introduction
2 Historical Context
3 Geometric Modelling
4 Materials
5 Structural Behaviour
5.1 Analysis of Meridional and Hoop Forces
5.2 Graphical Procedure
6 Conclusions
References
Utilization of Plane Tessellation for Paper Folding and Geometrical Transmittance Pattern for Lampshade Design
Abstract
1 Introduction
2 Principle of SQEF Method and Related Works
3 Single Tessellation Method
4 Multiple Tessellation Method
5 Conclusion and Future Works
References
The Geometry of the Ramps in Frank Lloyd Wright's Organic Architecture
Abstract
1 Introduction
1.1 Ramps, Geometry and Modern Architecture
2 Ramps in Modern Architecture
3 Frank Lloyd Wright's Designs with Ramp Element: Geometric and Graphic Analysis
3.1 Residential Designs
3.2 Religious Spaces Designs
3.3 Commercial Designs
3.4 Institutional Buildings Designs
4 Discussion
5 Final Remarks
Illustration credits
References
Geometric Basis of the Use of "Green Constructions" for Sun Protection of Glazing
Abstract
1 Introduction
2 Literature Analysis
3 Plants Assortment
4 Optimized Algorithms for Sun Position
5 Building a Figure to Fill by Plants
6 Conclusions
References
Making Fulldome Images Using Camera with Fisheye Lens and Fulldome Picture on Bowl
Abstract
1 Introduction
2 Fulldome Images Using Fisheye Lens and Bowl
2.1 Equipment and Materials
2.2 The Bowl Used in This Experiment
2.3 The Image Processing in This Experiment
3 Workshop for Children at Planetarium
3.1 Schedule
3.2 Photography
3.3 Results of Workshop
4 Conclusion
References
Interactive Expansion of Achiral Polyhedra
Abstract
1 Digital Tools to Work in Space
2 Expansion and Contraction of Polyhedra
3 Expansion e1
4 Expansion e2
Acknowledgements
References
Parametric Modelling and Geometry for the Study of Groins in Compound Vaults
Abstract
1 Introduction
2 Main Focus
2.1 Cylindric Groins
2.2 Cylindroidic Groins
2.3 Groins Improperly Named Spherical, Generated by a Circular Arc of Variable Shape
3 Discussion of the Results
4 Conclusion
References
A Geometric Look at 3D Illusionist Techniques
Abstract
1 Introduction
2 The Sense of Space
3 From Traditional Perspective Techniques to Anamorphosis
4 A Magic Visual Adventure
5 Conclusions
References
Suggestions for New Content in the Planetarium
Abstract
1 Introduction
1.1 Dome Master Format
2 Production of a Kaleidoscope
2.1 Purpose and Background
2.2 Approach
2.3 Algorithm
2.3.1 Placement of Polygons
2.3.2 Splitting Polygons
2.3.3 Mesh Deformation
3 Content Creation by Unity
3.1 Used Software/Equipment
3.2 Interactive Content
3.3 Advantages of Planetarium
3.4 Display with Unity
3.4.1 Approach
3.4.2 Create Planetarium at Unity
4 Result
5 Conclusions
References
Interactive Visualization for Analysis of Air Traffic Model
Abstract
1 Introduction
2 Method
2.1 Air Traffic Model
2.2 Visualization Program
2.3 Large-Scale Visualization Using the Fly-Through Program
3 Results and Discussions
3.1 Visualization Results
3.2 Large-Scale Visualization
4 Conclusion
Acknowledgements
References
Geometrical Universality of Truss-Z System
Abstract
1 Introduction
1.1 What Is an Extremely Modular System?
2 Why the Truss-Z Module Is Trapezoidal in the XY Plane?
2.1 Tiling of TZMs in the Horizontal Plane
2.2 Branching
3 The Measurement of Universality of a Single-Branch TZ
4 Conclusions
Acknowledgements
References
Interaction Between 3D Printing and Geometry Studies
Abstract
1 Introduction
1.1 3D Printing
1.2 3D Modeling
1.3 Relationship to Education
2 Visual Modeler-Tinkercad
2.1 Primitives in Tinkercad
2.2 Design with Applying Boolean Operators
3 Modeling with Codes-OpenSCAD
3.1 3D Primitives
3.2 Transformations and Boolean Operators
4 New Concepts Needed to Design 3D Printable Solids in FDM
4.1 Raft
4.2 Support
4.3 Orientation and Splitting Models
5 Case Study
5.1 Tinkercad
5.2 OpenSCAD
6 Conclusions
References
The Story of NanoJesus: Combining 3D Scanning and Femtosecond Laser Nanolithography for the Fabrication of the Smallest Nativity Scene in the World
Abstract
1 Introduction
2 The Scanning Process
2.1 3D Modeling Process
3 Nano Fabrication
3.1 Technology
3.2 Size of the Model (Sculpture)
3.3 Process
4 Result
5 Business and Academia Partnership
6 Conclusions
References
V Engineering Computer Graphics
Geometrically Constrained Surface (Re)Construction
1 Introduction
2 The Rational Cubic Gregory Patch (RCGP) Model
3 The Modified Rational Cubic Gregory Patch (RCGP) Model
4 Fairing the Modified Rational Cubic Gregory Patch (RCPG) Model
5 Numerical Results
6 Conclusions
References
Challenges in Modelling Complex Geometry in Historical Buildings for Numerical Simulations
1 Introduction
2 Recording the Complexity of Existing Buildings
3 Approach to Structural Modelling
3.1 Modelling Geometric Complexity
3.2 Modelling Approximation and Improvement
3.3 Speeding up Modelling Process: Automated Modelling
4 Application and Results
4.1 Simple Banded Vault Over Walls and Buttresses
4.2 Application to Masonry Vaults
4.3 Application to Complex System: Milan Cathedral
5 Conclusions
References
Transient Finite Elements Analysis of Thin-Walled Structure in Selective Laser Melting Process
Abstract
1 Introduction
2 Basic Steps and Theory of Transient Finite Element Analysis
3 Arrangement of Scanning Strategies
4 Analysis of Temperature Field
5 Analysis of Stress Field and Warping Deformation
6 Conclusions
Acknowledgements
References
Three-Dimensional Modeling and Finite Element Analysis of Cycloid Hyperbolic Arch Dam
Abstract
1 Introduction
2 Modeling of Mathematical Model of Cycloid Arch Dam
2.1 The Establishment of the Arch Dam Engineering Coordinate System
2.2 Calculation of Arch Ring of Cycloid Arch Dam
3 Stress Calculation of Cycloid Arch Dam
3.1 Shear Force Calculation of Arch Crown Beam
3.2 Axial Force Calculation of the Arch Crown Beam
3.3 Bending Moment Calculation of Arch Crown Beam
3.4 Radial Displacement Calculation of Cantilever Beam Under Loading
4 Finite Element Stress Analysis of Cycloid Arch Dam
4.1 The Establishment of ANSYS 3D Model
4.2 Stress Analysis Results Under Various Loads
5 Conclusion
References
Mixing of Fluids with Space-Filling Curves
Abstract
1 Space Filling Curves
2 Lindenmayer System
2.1 Turtle Graphics
3 Curve Generator
4 Coding
4.1 Basic Structures
4.2 Proof
4.3 Binarity
5 Applications
6 Conclusion
References
Electronic Geometric Modeling Is the Basis of Modern Geometric-Graphic Education in the Technical University
Abstract
1 Introduction
2 Geometric Modeling
3 The Content of the Academic Discipline
4 Conclusion
References
The Optimization Algorithm for Gait Planning and Foot Trajectory on the Quadruped Robot
Abstract
1 Introduction
2 Static Gait Stability and Parameter Design
3 Simulation Experiment and Comparison
4 Conclusion
References
Analytic Approach to Finding Lines in Images and Estimating Their Uncertainty
1 Introduction
2 General Paradigm for Finding Geometric Curves
3 Analysis for Lines
4 Numerical Analysis
4.1 Nyquist Sampling Rate
4.2 Analytic Maxima from Candidate Peaks
4.3 Covariance Propagation and Confidence Envelopes
5 Numerical Testing
6 Future Work and Conclusions
References
Geometric Fitting, Registration and Identification for Large Sets of Spatial Measurement Data
1 Introduction
2 Cylinder Fitting by Orthogonal Distance Regression
3 Rasterization and Morphological Operations
4 Regularized Derivative and Curvature Computation
5 Identification and Registration
6 Conclusion and Future Work
References
3-D Reconstruction of Bubbles Inside Valve Based on Multi-mirrors Imaging
Abstract
1 Introduction
2 3D Measurement Model
2.1 Camera Model
2.2 Extraction of Features
3 Experiment
3.1 Experimental Setup
3.2 Calibration and 3D Reconstruction
4 CBR-Based Cavitation Analysis
4.1 Establishment of the CBR Database
4.2 Parameter Design and Cavitation Analysis
5 Conclusion
Acknowledgements
References
Facial Expression Recognition Base on Weighted KNN and RF
Abstract
1 Related Algorithm Description
1.1 The Basic Principle of Weighted KNN Algorithm
1.2 The Basic Principle of Random Forest
2 Weighted KNN Combined with Random Forest Algorithm
2.1 Algorithm Description
2.2 Validate Classifier Validity
3 Experimental Results and Analysis
4 Conclusion
References
Directing Scheme Support Method Based on Analysis of Angry Characters
Abstract
1 Introduction
2 Related Work
3 Preliminary Investigation on Anger
3.1 Classification in Related Work
3.2 Analysis of Anger Elements
4 Development of Template Data
4.1 Development of Lighting Template
4.2 Development of Camera Work Template
5 Development of Angry Scrapbook
5.1 Overview of Angry Scrapbook
5.2 Instructions for Using Angry Scrapbook
6 Experiment
6.1 Overview of Experiment
6.2 Experimental Result
7 Conclusion
References
Generating Videos Based on Convolutional Recurrent Generative Adversarial Networks
1 Introduction
2 Related Works
2.1 Convolutional Neural Networks
2.2 Recurrent Neural Networks
2.3 Generative Adversarial Networks
3 Experiments
4 Future Works
References
Study on Adaptive Threshold Image Processing Method for Detection of Vaccine Activity
Abstract
1 First Section
2 Segmentation of Embryo Egg Contour
3 Embryo Egg Blood Vessel Extraction
4 Creating a Model for the Identification of Egg Activity
5 Experiment and Result Analysis
6 Conclusion
References
A Creo-Based Modeling and Toolpath Generating System for the NC Whirling Process of Propeller Blades
Abstract
1 Introduction
2 Overview of the Proposed Approach
2.1 The Whirling Process of Propeller Blade Surface
2.2 Basic Structure of the CAD/CAM System for the Whirling Process
3 Parametric Modeling of a Propeller Blade
4 Toolpath Generation
5 Implementation
6 Conclusion
Acknowledgements
References
Aircraft Target Recognition in Remote Sensing Images Based on Saliency Maps and Invariant Moments
Abstract
1 Introduction
2 The Algorithm Flowsheet
3 Experiment Comparison and Analysis
4 Conclusion
Acknowledgements
References
The Configuration Design and Analysis of a Small Air-Land Amphibious Detecting Robot
Abstract
1 Overall Design of the Small Air-Land Amphibious Robot
2 Overall Design of the Integrated Air-Land Amphibious Robot
2.1 Configuration Scheme Based on 2-DOF Leg Mechanism
2.2 Configuration Scheme Based on 3-DOF Leg Mechanism
3 Overall Design of the Combinatorial Air-Land Robot
4 Comparison and Selection of Design Schemes
5 Conclusion
References
Curves with Special Aesthetics Generated by an Original Mechanism
Abstract
1 Introduction
2 The Generating Mechanism
3 The Kinematics of the Mechanism
4 Aesthetic Curves Plotted for n Taking Integer Values
4.1 Coefficient n = 2 k + 1, k ? N
4.2 Coefficient n = 2k, k ? N
5 Aesthetic Curves Plotted for n Taking Fractional Values
5.1 Coefficient n Is a Multiple of 2
5.2 Coefficient n not Divided by 2
6 Some Mathematical Properties of the Curves Generated
6.1 The Calculation of the Curvature in a Current Point of the Curve
6.2 The Calculation of the Curvature Radius of the Curve (C) in a Current Point
6.3 The Equation of the Tangent to the Curve (C) in a Current Point
6.4 The Equation of the Normal to the Curve (C) in a Current Point
6.5 The Study of the Symmetries of the Curve (C) with Respect to the Coordinate Axes (Ox axis and Oy axis) and with Respect to the Origin O
7 Conclusions
References
Tensile Structure Form-Finding on the Basis of Properties of Frame-Grid Template
Abstract
1 Introduction
2 Frame-Grid Template
3 Relaxation
4 Grid Adaptation
5 Elimination of Negative Effect
6 Quick Structure Editing
7 Pre-stress Orthotropy
8 Conclusion
Acknowledgements
References
Orthographic Drawings Minting: Testing for Indeterminate Solid Models Caused by Underrepresentation
Abstract
1 Introduction
1.1 Background
2 Underrepresentation Case Studies
2.1 Underrepresentation by "Deficiency"
2.2 Underrepresentation by Superposition
2.3 Solid Analysis
2.4 Multipartite Analysis
3 Conclusion
References
From Orthographic Drawings to Editable Models of Simple Solid Using "Reconstruction-Recomposition" Coupled with Feature Recognition
Abstract
1 Introduction
2 Reconstruction with Design Intent
2.1 Reconstruction
2.2 Features and Design Intent
3 Solid Modelling
4 Reconstruction-Recomposition
5 Case Study
5.1 Manufacturing Features
5.2 Results
6 Conclusions
References
Solving Applied Geometric Design Problems with the Use of 3D-CAD
Abstract
1 Introduction
2 Characteristic Features of Descriptive Geometry and 3D-CAD
3 Applied Geometric Design Problems
3.1 Use of Projection from a Specified Direction
3.2 Use of Development
3.3 Use of Sectioning
3.4 Use of Assembly Constraints in 3D-CAD
4 Summary and Conclusions
References
Research on Parametric Modeling of Cable-Stayed Bridge Based on BIM
Abstract
1 Introduction
2 Revit Secondary Development Process
2.1 Program Development Process
2.2 Interface Generation and Plug-in Module Design
3 Model Construction of Various Parts of Cable-Stayed Bridges
3.1 Modeling Ideas
3.2 Key Technologies of Parametric Modeling
4 Application Examples
5 Conclusion
References
Attribute in Formation on Three-Dimensional Annotated Models
Abstract
1 Introduction
2 Examination of Designing and Transmission of Design Information Using 3D Annotated Models
2.1 Lack of Information Other Than Shape That Are Indispensable for Manufacturing
2.2 No Unified Rules
2.3 Representation of Attribute Information
3 Advantages of Developing 3D Annotated Models
4 Basic Requirements for 3D Mechanical Design
4.1 Comprehension of Drawings
4.2 Origin of Mechanical Design
4.3 Passing on of Skills
5 Application of 3D Annotated Models
5.1 Planning Phase
5.2 Conceptual Design Phase
5.3 Basic Design Phase
5.4 Detailed Design Phase
6 Training Method and Contents for Beginners in Mechanical Design
7 Examples of Practical Training Method for Beginners in Mechanical Design
7.1 To Improve 3D Space Recognition Ability
7.2 Contriving of Shapes
7.3 Use of Examples of Determining Ambiguities in Designing
7.4 Design Skills and Know-How
8 Conclusions
VI Graphics Education
From the Plan to the 3D Model Through Folding. Case Studies in Fashion Design
Abstract
1 Introduction
2 Study Topic
2.1 Folding Surface. from Its Origins to Its Development in Contemporary Fashion Design
3 Materials and Methods
3.1 "Between the Lines": From the Folding Surface to the Fashion Project
4 Conclusions
References
Byrne's Euclidean Geometry Revisited with Geogebra
Abstract
1 Oliver Byrne's Euclid
1.1 Byrne's Semiotic Approach
1.2 Byrne's System
2 Theoretical Framework
2.1 The Theory of Semiotic Mediation
2.2 The Role of Dynamic Geometry Softwares
3 The Experiment
3.1 The Classes
3.2 The Activities
4 Results and Further Issues
References
Drawing Geometry: A Laborious History in Italian School
Abstract
1 The Role of Drawing in the Teaching and Learning of Geometry
1.1 The Archetype
1.2 Modern Theoretical Approaches
2 Geometry and Drawing in Italian Curricula
2.1 Luigi Cremona
2.2 The Gentile Reform
2.3 Le Nuove Indicazioni
3 Epistemological Debates
3.1 Vailati and Enriques
3.2 Italian Schools and the New Maths
4 Conclusion: Didactic Issues and the Role of Dynamic Geometry Softwares
References
Formation of Competence in Students of Technical University for 3D-Modeling and Prototyping of the Objects
Abstract
1 Introduction
2 Participation in Olympiads on Geometric Modeling and Prototyping
3 The Program of Support of Talented Students
4 Conclusion
References
A Course on Geometric Dimensioning and Tolerancing: Overview and Initial Assessment
Abstract
1 Introduction
2 Course Description
2.1 Course Objectives
2.2 Outline of Main Topics and Structure of Course
2.3 Example of Laboratory Activity
3 Summary of Assessments
3.1 Pretest
3.2 Online Quizzes
3.3 Tests and Final Exam
4 Analysis of Student Performance
4.1 Analysis of Pretest Items, Tests, Quizzes, and Exam
4.2 Analysis of Laboratory Assignments
5 Conclusions and Recommendations
References
Design-Based Learning Supported by Empirical-Concrete Learning Objects in Descriptive Geometry
Abstract
1 Introduction
1.1 Early Initiatives
1.2 A New Development
2 Empirical-Concrete Learning Objects
3 Using the Objects
4 Discussion
5 Conclusions
References
Mathegraphics
1 From Interdisciplinarity to Dialogical Educational Models
2 The Mathegraphic Workshop
2.1 Tessellation Between Geometry and Graphics
2.2 Tessellation and Déco Hydraulic Mosaic
2.3 The Dialogic Approach to the Study of the Hydraulic Mosaic Through Geometry and Graphics
3 Through the Algebraic Mirror and What Alice Found There
3.1 Isometries of the Plane: A Linear Algebra Description
3.2 Tessellations of the Plane
4 Conclusions
References
Teaching Geometry and Surfaces Evaluation Through Graphic Representation and Dynamic Paper Models
Abstract
1 Introduction
2 Premises
3 Context
4 The Lesson
4.1 Brief Description of the Tools
4.2 Procedures
4.3 Topics Insights
5 Conclusions
References
Geometrography Revised and Enlarged: A Brazilian Geometer's Approach to Émile Lemoine's Work
Abstract
1 Introduction
2 Lemoine's Original Concept of Geometrography and Some of Its Variations
3 Pinheiro's Approach to Geometrography
4 Pinheiro's Geometrography Today
References
Is the Constructional Drawing an International Language for Engineers?
Abstract
1 Introduction
2 DIAD-Tools Project-General Principles
3 Graphic Symbols Applied in Countries of Project Partners-Comparison of Source Materials
3.1 Lines
3.2 Dimensioning
3.3 Projection Methods
3.4 Construction Drawings
4 CAD Systems in Technical Drawing Are Giving the Universal Language for Engineers?
5 Conclusions
References
Application of Augmented Reality in the Compilation and Publication of Cartographic Textbooks
Abstract
1 Introduction
2 Features and Advantages of Augmented Reality Technology
2.1 Needs to Improve the Function of University Textbooks
2.2 Requirements for the Development of Drawing Textbooks in the Mobile Internet Era
3 The Use of Cartographic Materials Based on Augmented Reality Technology
4 The Advantages of Augmented Reality Technology in the Publication of Cartography Textbooks
4.1 Increase the Dynamics
4.2 Enhance Interactivity
4.3 Produce Fun
5 The Application of Augmented Reality Technology in the Publication of Textbooks
5.1 Amalgamation of Augmented Reality and Publishing
5.2 The Basic Paradigm of Augmented Reality Publications
6 Summary
References
New Analog for the Digital Age: Adjusting Simultaneousness for Self-explanatory Delineation of Architectural and Urban Projects in Public Presentations or: a "Nolli Isometric"
Abstract
1 New Analog for the Digital Age: What for?
2 New Expectations
3 Rules of Thumb for an Appealing Simultaneousness Plan
4 Anatomy of a Simultaneousness Plan
5 Let Us Draw Isometric Nolli Maps: Buildings in X-Ray Vision
6 Graphic Recommendations
7 Importance, Cognitive Biases and Factors of Intelligibility
8 Meta Effects: Learn to Reduce Complexity by Means of Freehand Drawing and Amplify Campus Understanding
References
Biomimetical Approach in Training Students of Technical Institutes in Graphic Disciplines with Aim of Developing Creativity and Formation of Professional Culture of the Engineer
Abstract
1 Introduction
2 Methodology
3 Results
4 Conclusions
References
Shell Tessellation-Research-Based Design Strategies Between Architecture and Mathematics
Abstract
1 Introduction
1.1 Methodology
1.2 Tessellations and Shells
2 Case Studies
2.1 Wafer Saddle
2.2 Reciprocal Tubes
2.3 Zebra Pattern
3 Conclusion
References
Research on the Effect of Providing User Interaction for Graphic Education
Abstract
1 Introduction
2 Background and Motivation
3 Related Research
4 Approach
4.1 Digital Content Interaction
4.2 Design Workshops
5 Observation and Discussion
5.1 Effects of Watching the Interaction Video
5.2 Additional Observations
6 Conclusion and Future Plan
Acknowledgements
References
Practical Skills in AutoCAD Through a Mass Open Online Course
Abstract
1 Introduction
2 Structure of the Course
3 Structure of the Course
3.1 Demonstration: Learning Is Promoted When Learners Observe a Demonstration of the Skill to Be Learned
3.2 Problem-Centred: Learning Advances When Students Acquire Skills in the Context of Real Problems
3.3 Activation: Learning Is Promoted When Learners Activate Existing Knowledge and Skill as a Foundation for New Skill
3.4 Application and Integration
4 Advantages and Disadvantages of Learning Through the MOOC
5 Conclusion
References
Comparative Analysis of Teaching in Geometric Surfaces at Architectural Faculties in Nis and Tokyo
Abstract
1 Introduction
2 Program of the Subject GSA on the Faculties in Nis and Tokyo
2.1 Comparative Analysis of Program of the Subject GSA on Faculties in Nis and Tokyo
3 Content of the Subject GSA
3.1 Content of the Subject GSA on FCEA in Nis
3.2 Content of the Subject GSA on FEDHU in Tokyo
3.3 Comparative Analysis of Subject's Content
4 Methodology of Teaching of the Subject GSA on the Faculties in Nis and Tokyo
4.1 Comparative Analysis of Teaching Methodology of Subject GSA
5 Evaluation of the Subject GSA on the Faculties in Nis and Tokyo
5.1 Evaluation of the Subject GSA on FCEA in Nis
5.2 Evaluation of the Subject GSA on FEDHU in Tokyo
5.3 Comparative Analysis of Evaluation of the Subject GSA
6 Models of Teaching the Subject GSA
7 Conclusion
References
Quality Management of Engineering Graphics Teaching
Abstract
1 Introduction
2 Literature Review
3 Aim and Research Problems
4 Materials and Methods
5 Results of the Research
6 Conclusion
References
Digitizing Spatial Visualization Tests
Abstract
1 Introduction
2 Digitalization of MRT and MCT
3 Application of the Test
4 Analysis of Results
5 Results of Both Tests from the FA
5.1 Results in the 2016/2017 Academic Year
5.2 Results of MRT and DMRT
5.3 Results of DMCT
5.4 Comparison of DMRT and DMCT Results
5.5 Correlation Between (D)MRT and DMCT Results
6 Results of Both Tests from the CE
6.1 Results of DMRT and DMCT
6.2 Correlation Between DMRT and DMCT Results
7 Conclusion
References
Creative Graphics Education Potential for Creativity of Hospitality Students via Virtual Environment
Abstract
1 Introduction
2 Methodology
3 Case Experiment
3.1 Interactive Graphic Changing
3.2 Guest Room Design Example
4 Results
5 Discussion and Conclusion
Acknowledgements
References
Reinterpret Whith Estrus. Creativity and Science in the Drawing Workshops of the Degree Course in Communication Design
Abstract
1 Introduction
2 Graphic Representation and Drawing
References
Character Making Education by DREAM Process
Abstract
1 Introduction
2 Related Work
3 Educational Tool for Character Making
4 Educational Case Examples
5 Conclusion
References
Teaching 3D Character Animation Through Four Related Tasks
Abstract
1 Introduction
2 Four Tasks Topics
2.1 Project
2.2 First Project Task
2.3 Second Project Task
2.4 Final Project
3 Results
4 Conclusion
References
The Effect of a Two-Dimensional Optical Illusion Pattern on the Three-Dimensional Interpretation of Objects Using Café Wall "Illusion Blocks"
Abstract
1 Introduction
2 Materials and Methods
2.1 "Illusion Block WS"
2.2 The Café Wall Illusion and Illusionary Blocks
3 A New Idea About 3D Interpretation of the Café Wall Illusion
4 Analysis of Knowledge Accumulation on the Café Wall Illusion in the WS Series
5 Conclusion
References
Non-conventional Representation for Urban Design: Depicting the Intangible
Abstract
1 Introduction
2 Conventional and Non-conventional Representation
3 The Application in Higher Architectural and Planning Education
4 Reflections on the Representation Outcomes
References
A Revised Project-Based Learning Program on Geometry-Maximizing the Volume of Solid
Abstract
1 Introduction
1.1 Background
1.2 The Course Structure
2 The Small PBL on Geometry in 2017
2.1 The Schedule
2.2 The Problem
2.3 Expected Subtasks
2.4 The First-Year Result
3 The Expected Optimal Solution
3.1 The Optimal Height of the Triangular Faces
3.2 The Optimal Proportion of the Bottom Face
3.3 The Optimal Net Orientation
4 The Revised Small PBL on Geometry in 2018
4.1 Week-1: The Preliminary Project
4.2 Subsequent Weeks
4.3 Expected Subtasks
4.4 Self-evaluation Rubric and Reports by Facilitators
5 Temporary Result in 2018
5.1 Week-1: The Preliminary Project (A4 Container)
5.2 Week-2: The Main Project (Elongated Square Pyramid)
6 Conclusion
References
A Multiview Interactive Interface for the Solution of Descriptive Geometry Problems
Abstract
1 Introduction
2 New Methodology
3 The Software
4 Applications
5 Conclusion
References
Physical-Digital. Defining the Architectural Space
Abstract
1 Introduction
2 Education
3 Representation
4 Triangulation
5 Creation
6 Conclusions
References
Challenges and Promises of Mobile Devices Usage for Spatial Visualization Skills Assessment in Technical Drawing for Engineering Course
Abstract
1 Introduction
2 Methodology
2.1 Collecting and Processing Data
3 Results and Discussion
3.1 Descriptive Statistics
3.2 Mobile Devices Versus PC
3.3 Gender Differences
4 Conclusion
Acknowledgements
References
Basic Modelling Education to Obtain 3D Spatial Perception for Design Beginners
Abstract
1 Introduction
1.1 Background and Purpose
1.2 Preceding Studies
2 Methods
2.1 Methods and Materials
2.2 Overview of Materials
2.3 Pre-analysis
3 Results and Discussion
3.1 Analysis on Appearance Frequency
3.2 Evaluation Structure
4 Conclusions
Acknowledgements
References
Systematic Review of a Flipped Learning Model for the Courses of Descriptive Geometry, Engineering and Computer Graphics
Abstract
1 Introduction
2 Literature Review
3 Results
4 Discussion
5 Conclusion
References
The Importance of Circular References, Architectural Modeling, Digital Project and Collaborative Actions in the Architecture Learning
Abstract
1 Architectural Scenery
2 References Circulars
3 Collaborative Actions
4 Architectural Modeling
5 Bibliographic Review
6 Creative Potential
7 Conclusion
References
Didactic Experiences on Digital Modeling. Anamorphosis
Abstract
1 Introduction
2 Didactic Strategy
3 Anamorphosis
3.1 Methodology
3.2 Results
3.3 Implementation
4 Conclusion
Acknowledgements
References
Research and Practice of the Mixed Teaching Mode for Engineering Graphics Based on MOOC
Abstract
1 Introduction
2 Construction and Application
3 Characteristics of the Two MOOCs
3.1 Integrating Teaching Content
3.2 Providing Diverse Online Teaching Resources
3.3 Online Interactive Discussion Questions
3.4 Various Online Job Evaluation Models
3.5 Learning Statistics
3.6 Asynchronous SPOC Mode Based on MOOC
4 Online and Offline Mixed Teaching Mode
5 Effectiveness
5.1 Student' Feedback
5.2 Social Influence
References
VII Geometry and Graphics in History
Graph Theory and Music: A Mathematical Tool for Musicians
1 Introduction
2 Graph Theory and Music in the 17th, 18th and 19th Centuries
3 Graph Theory and Music in the 20th Century
4 Generalized Tone-Networks
5 Generalized Chord-Networks
6 Conclusions
References
A Contribution to the History of Representation. The Unpublished Treatise by Matteo Zaccolini
Abstract
1 Reading the Past to Understand the Present Looking at the Future
2 The Theory of Shadows Generated by Point Sources of Light on Planes, Cylinders, and Cones
3 The Theory of Shadows Generated by Extended Luminous Bodies
4 Conclusion
Acknowledgements
References
Phonurgia Nova. Geometrical Acoustics in the 17th Century
Abstract
References
Perspective Analysis of the Inlaid Wood Panel from Duomo of Bergamo
Abstract
1 The Choir of Santa Maria Maggiore
2 Analysis of L'Annunciazione
3 Conclusion
References
De l'Orme's Graphics Language: Between Stereotomy and Orthogonal Proto-Projection
Abstract
References
Ludovico Cardi Said "Il Cigoli". Practical Treaty of Perspective: Innovative Aspects and Intuitions
Abstract
1 Introduction
2 The Second Perspective Rule
2.1 On How to Built il luogo della sciena
2.2 On Scenic Illusions: piani in maestà, piani in sfuggita e piani obliqui
2.3 De gl'aggetti nelle pareti per scorcio (About the Overhang of Walls in Foreshortened), 66v
2.4 Conclusion
References
Drawings and Models in English Perspective Treatises of the XVII and XVIII Centuries
Abstract
1 Books and Moveable Elements
2 English Treatises on Perspective
3 Some Possible Origins
4 Conclusion
References
Geometry as a Tool to Manage the Territory. Nicolaas Cruquius and the Map of the Merwede
Abstract
1 Cartography in the Netherlands: Quantity and Quality
2 The Cruquius Brothers and the Map of Delfland
3 Edmund Halley's Map of Magnetic Declination
4 Nicolaas Cruquius and the Map of the Merwede
5 The Map of the Merwede as an Example
6 Conclusions
References
The Quincunx as Architectural Structure. Geometry and Digital Reconstructions After Leonardo Da Vinci's Centralized Plan Temples
Abstract
1 Introduction
2 History and Evolution of the Quincunx
3 Leonardo's Studies on the Quincunx
3.1 Enquiring, Reconstructing, Modeling
4 Considerations on Leonardo's Design Concepts
4.1 The Question of the Wall Thickness
5 Considerations
6 Conclusions
Acknowledgements
References
La Géométrie Pratique. Survey Manuals in France Between the 18th and 19th Centuries
Abstract
1 Architectural Survey Practices in France Between the 18th and 19th Centuries: Manuals as a Documentary Source
2 Technical Manuals on Surveying
2.1 The Topics
2.2 The Authors
2.3 The Addressees
2.4 Content Structure and Organisation
3 Geometry and Practical Geometry: Instruments and Methods
4 Conclusions
References
DIN-DON-DAN-Bells and Their Geometry
Abstract
1 Introduction
2 Development
2.1 Definition
2.2 Bronze Bells
2.3 Bells, Their Parts and Sounds
2.4 Geometric Modelling of Bell Ribbons
2.5 Phenomena Occurring When Ringing the Bell
References
Geometry/Time Measurement/Sundials Graphical Resolution via Algorithmic and Parametric Processes
Abstract
1 Introduction
1.1 Aim and Structure of the Paper
2 Materials and Methods
2.1 The Celestial Vault/Earth System, a Parametric Approach
2.2 Constructions Employing Monge's Orthogonal Projection Method
2.3 Homological Transformations Between Dials
2.4 The Gnomonic Column and the Cylindrical "Filtering Hat" Dial
2.5 Proposal for a "Filtering Hat" Variant
3 Conclusion
Acknowledgements
References
Digital Renovation and Archives of Japanese Ancient Ritual Performance at the World Cultural Heritage
Niutsuhime Shrine
Abstract
1 Introduction
2 About Niutsuhime Shrine and Bugaku Mandala-Ku
3 Method of Reproduction
3.1 Sogon-Zu
3.2 The Modeling of Building and Niutsuhime Shrine Grounds
3.2.1 Modeling of the Topography
3.2.2 Modeling and Arrangement of Buildings
4 CG Animation
4.1 Video Shooting and Motion Capture of Bugaku
4.2 Bugaku Animation
5 Conclusion
Acknowledgements
References
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
Abstract
1 Introduction
2 Method
2.1 MOTATION
2.2 Sites Studied
2.2.1 Muroji Temple
2.2.2 Hasedera Temple
2.2.3 Kinpusenji Temple
3 Results and Discussion
4 Conclusion
References
The Study of "Deconstructivism" in the Field of Architecture
Abstract
1 Introduction
2 Methods
3 Results and Discussion
3.1 Definition of "Deconstructivist Architecture" by Two Curators
3.2 Comparison of Thought and Discourse Between Derrida and Tschumi
3.3 Application of the "Deconstruction" Theory Seen in Tschumi's Work
4 Conclusion
References
Sharawadgi and Penetrating Space in Chinese Classic Gardens
Abstract
1 A Misreading: Sharawadgi
1.1 Literature Review of Sharawadgi Research
1.2 The Possible Positive Meaning from Misreading
2 Brief Introduction of Wangshi Garden
3 Penetrating Space in Chinese Classic Gardens
3.1 Basic Data Review of Wangshi Garden
3.2 Penetrating Space in Irregular Spatial Organization
References
Geometry in Advertising Graphics
Abstract
1 Geometry Between Painting and Graphics
1.1 From Painting to Graphics
1.2 The Maîtres de l'affiche
2 A Critical Reading
2.1 Relationships, Proportions and Relations
2.2 A Reading from a New Point of View
2.3 From Photography to Digital Graphics
3 Conclusions
References
Leonardo da Vinci as a Scientist in Assessing the Encyclopedic Literature of Imperial Russia, the Soviet Union and the Russian Federation
Abstract
1 Introduction
2 Leonardo da Vinci in the Encyclopedia of Imperial Russia
3 Evaluation of the Work of Leonardo da Vinci in the Encyclopedias of the Soviet Union
4 The Creativity of Leonardo da Vinci in the Encyclopedias of Modern Russia
5 Conclusion
References
Astronomy of Shadows and Light: Athanasius Kircher's Sundials Between Geometry, Perspective and Science
Abstract
1 Introduction
2 Kircher's Sundials and the Epiphany of Physical Realities
3 Geometry, Conic Sections and Sundials
4 Conclusion
References
Design Method of Original Motifs and Decorative Patterns Using Geometric Baseline Derived from Japanese Crafts
Abstract
1 Introduction
2 Method
2.1 Participants
2.2 Design Process
3 Result
3.1 Images of Selected Works
4 Discussion
References
Material Models of Ruled Surfaces as Witnesses to the Development of Mathematical Teaching
1 Ruled Surfaces
1.1 Definition of Ruled Surfaces
1.2 Typical Examples
1.3 History of Ruled Surfaces
2 Material Mathematical Models
2.1 First Teaching Models at the École Polytechnique
2.2 Further Scattered Models
2.3 Series Productions of Material Mathematical Models
3 Application of Ruled Surface Models in Current Teaching Projects
4 Conclusion
References
The Masonry Domes Over the Centuries: The Important Role of Geometry
Abstract
1 Introduction
1.1 Historical Background
2 Parabola and Catenary
2.1 Mathematical Details
3 Masonry Domes
3.1 Pantheon in Rome
3.2 Santa Maria del Fiore in Florence
3.3 St. Paul's Cathedral in London
3.4 St. Peter's Dome in Rome and St. Gaudenzio's Dome in Novara
4 Catenary Monument
5 Conclusion
References
Theater and The Towns
Abstract
1 Introduction
2 Theme and Analysis
3 Objectives
4 Method
5 Process
6 Results
7 Conclusion
References
Digital Approach to Michelangelo's Design. The Inner Light of Neoplatonic Geometry
Abstract
1 Human Anthropometry and Animal Proportions
2 A Geometric Approach: Rationalism Versus Neoplatonism
3 Michelangelo's Works and Digital Shape
References
Abraham Bosse and the Perspective in Practice
Abstract
1 Introduction
2 Perspective in Theoretical Terms
3 Perspective in Practical Terms
4 Conclusions
References
The Triad of Vitruvius in the Modern World
Abstract
1 Elements of Architectural Language
2 Innovativeness of the Architectural Object
3 Stages of Innovative Architectural and Urban Planning Process
4 The Innovative Role of Information Technology in Solving Architectural-Urban Problems
5 The Role of Geometric Theory in the Creation of Innovative Architectural Object
6 Fractal Principles of Construction of Organized Space
7 Innovative Architectural-Urban Masterpieces of the Modern World
8 Conclusions
References
Geometry, Arithmetic, Architecture. Calculation Methods for Vault Surfaces in the Modo di Misurare le Fabriche by Guarini
Abstract
1 Introduction
2 Measuring the Vaults in the Modo di misurare le fabriche
3 Reconstructing Guarini's Vaults by Digital Models
3.1 Simple Vaults: Barrel and Conic Vaults, Pendentives and Domes
3.2 Composed Vaults: Cloister, Groin, and Lunettes Vaults
4 Conclusion
References
The Influence of the Discovery of Prehistoric Pile Dwellings Around the Alps on Architect Hannes Meyer
Abstract
1 Introduction
1.1 Research Background
1.2 Previous Studies
1.3 Aim, Method, and Research Materials
2 Reconstruction Plan of Prehistoric Pile Dwellings
2.1 The Sites of Pile Dwellings
2.2 Reconstruction of Pile Dwellings Around Alps by the 1920s
3 The Influence of Pile Dwellings on Hannes Meyer's Architectural Works
3.1 "Peters Schule" Competition Project (1926-27)
3.2 "League of Nations" Competition Project (1927)
3.3 The Concept of "Contemporary Pile Dwellings" in Teacher's Housing "ADGB Trade Union School" (1928-30)
4 Conclusion
References
Between Survey and Interpretation: The Ideal Shape of Flavian Amphitheater According to Carlo Lucangeli
Abstract
1 Introduction to the Research
2 The Wooden Model of the Flavian Amphitheater as an Instrument of Knowledge and Communication
2.1 The Subdivision of the Model
2.2 The Discretization of the Model
3 Carlo Lucangeli and the Definition of the Ideal Model Between Observation and Interpretation
Acknowledgements
References
Simulation of the Giant Wild Goose Pagoda in Immersive Virtual Reality Environment
Abstract
1 Introduction
2 Objectives
3 Use of Software Programs in Simulating Ancient Structures
4 Modeling Method
5 Simulation Process
5.1 3D Model and Static Rendering
5.2 Dynamic Rendering
5.3 Interactivity
6 Real-Time Rendering Techniques in Lumion
7 Conclusion
References
VIII Posters
The Golden Ratio and Jewelry Design
Abstract
1 Introduction
2 Golden Ratio
3 The Grid for Harmonic Proportions
4 Final Considerations
References
Federated Parametric Models for Seismic Risk Analysis in Existing Buildings
Abstract
1 Methodological Foreword
2 The Study Case: BIM Federated Models of the "G. Verdi" School Complex in Florence
3 Conclusions
References
Wallace-Simson Line in Four Cayley-Klein Planes
1 Introduction
2 Euclidean and Quasi-elliptic Plane
3 Pseudo-Euclidean and Quasi-hyperbolic Plane
References
Geometry of Conjugation of Curvilinear Channels of the Parts
Abstract
1 Introduction
1.1 Actuality
1.2 Problem of Research
1.3 Research Problems
2 Foundations
2.1 General Approach
2.2 Conclusions on a Geometrical Problem
References
Designing by Rules: Parametric Workflow Behind ICGG 2018 Conference Logo
Abstract
1 Input
2 Process
3 Output
4 Personal Thoughts and Conclusion
References
The Alexander Mosaic and the House of the Faun. The Iconic Light of Geometric Relationships
Abstract
1 The Gran Mosaico
1.1 The Art of Composition and Its Rules. Within the Symphony of the Alexander Mosaic
2 The House of the Faun
2.1 The Iconic Light of Geometric Relationships
References
MRT as a Testing Instrument in Research on a Singular Aptitude Among Architecture Students
Abstract
1 Research Aim and Methodology
2 Research Analysis and the Results
3 Comparison of the Results with the Earlier Research
4 Conclusions
References
Visual Simulation of Erosion Terrain Considering Different Materials
Abstract
1 Introduction
2 Outline of Erosion Process
2.1 Apply Material Parameters to Terrain
2.2 Particle-Based Erosion
2.3 Definition of Differential Erosion
3 Implementation and Results
4 Conclusion and Future Work
References
Study on Analysis Support of Lubrication Phenomenon by Three-Dimensional CAD Development of Auxiliary Analysis Tool for CAD
Abstract
1 Introduction
2 Method
2.1 Export and Import
2.2 Comparison with Conventional Analysis Method
3 Results
4 Consideration
5 Conclusions
Parametrizing 3-Webs of Circles on Darboux Cyclides
1 Introduction to Darboux Cyclides and 3-Webs
2 Parametrizations of 3-Webs
References
Representation of an Object as a Semiotic Sign in Engineering
Abstract
1 Composition of Drawings Through Communication Skills and Social/Material Interactions
2 From the Analysis of Peirce's Triadic Model to the Semiotic Activity of the Design Process
3 Conclusions
Acknowledgements
References
Luca Pacioli: A Friend of Leonardo da Vinci De Divina Proportione in Capital Letters
Abstract
References
Vilnius Cathedral Ceiling Interactive 3D Models-Exploration and Digitalization
Abstract
1 Introduction
2 Geometrical Analysis of Rosettes and 3D Modelling
3 Interactive Web-Based System Model
4 Conclusions
References
Comparison with Expression on "Rakuchu Rakugai-zu", Scenes in and Around the Capital of Kyoto
Abstract
1 Preface
2 Rakuchu Rakugai-zu
3 The Feature of Each Works
3.1 Rakuchu Rakugai-zu, Rekihaku a Version
3.2 Rakuchu Rakugai-zu, Funaki Version
4 Comparison of Depicted Objects
4.1 Expression by Oblique Projection
4.2 Depicted Purview on Rakuchu Rakugai-zu
5 Representation as a Request of the Times
References
Visual Art as Science
Abstract
1 Foundation
2 To Project
3 Methodology
4 Process of Combining
5 Propaedeutic
6 Levels
Spatial Analysis and 3D Modeling: Drawing the Cathedral of Brasilia in Different Software
Abstract
1 Introduction
2 The Cathedral of Brasília
2.1 Building History
2.2 Formal Analysis
3 Digital Modeling
4 Conclusion
References
Learning Creative, Learning MOOC
Abstract
1 Introduction
1.1 Development of Online Learning
1.2 MOOC in Europe: The European Multiple MOOC Aggregator EMMA
2 A MOOC as Support and Parallel Pathway to Traditional Teaching of Projective Geometry
2.1 A Sample in Graphic Education
2.2 Drawing Light
References
Projections: Applications from Geometric and Project Design Education
Abstract
1 Introduction, Teaching and Application of Design
2 Conclusion
References
Kinematical Ruled Surfaces Based on Interrelated Movements in Axoids' Triad "Torse-Cone-Cone"
Abstract
1 Introduction
2 Geometrical Model of Axoids' Triad "Torse-Cone-Cone"
3 Conclusions
References
Building Types and Narrative Development in Emaki-Comparing the Compositions of KASUGA GONGEN GENKI and Ishiyama-dera Engi Emaki
Abstract
1 Introduction
2 Pictorializing Stories
3 Methods
4 Results
5 Consideration
6 Conclusion
References
A Study on Automatic Generation of Heating Patterns of Contour Maps for 2.5D Printing
Abstract
1 Introduction
2 Method
3 Experiments
4 Summary
Acknowledgements
References
Quadratic Characteristics of Workspace Curves of Generalized Planar Cable-Driven Parallel Mechanisms
Abstract
1 Introduction
2 Description of Generalized Planar 4-Cable-Driven Mechanism
3 Workspace Curve Expression Deduction
4 Simulation Result
5 Conclusion
Acknowledgements
References
Getting the Smallest Sphere Which is Tangent to Four Non-parallel Unlimited Skew Lines in General Positions Based on MATLAB
Abstract
1 Introduction
2 Research Methodology
2.1 Building Function to Find the Minimum Value
2.2 VBA and MATLAB Mixed Programming
2.3 Program Flow and Result
3 Conclusion
References
Features of Teaching the Graphic Discipline Courses for Different Specialty Students
Abstract
1 Introduction
2 Syllabuses of Graphic Disciplines
2.1 Descriptive Geometry
2.2 Engineering Graphics
2.3 Computer Graphics
3 Conclusions
References
A Study on Monozukuri Education in Karakuri Doll Production
Abstract
1 Introduction
2 Karakuri Doll Production
3 Conclusions
Acknowledgements
References
Determining Features of Volumes of Interest of Medical Ultrasound Images
1 Introduction
2 Selection of Objects
3 Finding the Volume of Interest
4 Computing the Volume Using Subdivision
5 Results
6 Future Work
References
The Modeling for Numerical Simulation of a Benchmark Model Based on CAD System
Abstract
1 Introduce
2 The Description of BEAVRS and Modeling Procedure
3 Validation and Conclusion
References
Geometric Analysis and Engineering Application of Conic Section
Abstract
1 The General Situation of the Plane Truncated Cone
1.1 Projective Projection of Elliptic Short Axis End Point Trails
1.2 Projection of the Rest of the Trajectory of the Elliptic Short Axis Endpoint
1.3 Mathematical Analysis of Parabola
2 Elliptic Projection Is a Special Case of a Circle
2.1 Geometric Analysis
2.2 Mathematical Analysis
2.3 The Correspondence Between a and ß
3 Spherical Curved Surface Engineering Application
3.1 Ball Shift Surface
3.2 Ball Shift Surface Approximate Production
3.3 Bend Pipes in Hydraulic Structures
4 Conclusion
References
An Algorithm for Computing Geodesic Curve Based on Digital Experiment of Point Clouds
Abstract
1 Introduction
2 The Method of Point Clouds Digital Experiment
2.1 The Mathematical Model of the Line Orthographic Projected to the Conical Surface
2.2 The Principle of Orthographic Projected Curve Approaching the Geodesic
2.3 Algorithm Design for Geodesic Computing
2.4 The Correctness Verification of OPA Algorithm
3 The Generality of OPA Algorithm
3.1 Geodesics on Toroidal Surface
3.2 Geodesics on the Bspline Surface
4 Conclusions
References
Correction to: Geometrical Universality of Truss-Z System
Correction to: Chapter "Geometrical Universality of Truss-Z System" in: L. Cocchiarella (Ed.), ICGG 2018-Proceedings of the 18th International Conference on Geometry and Graphics, Advances in Intelligent Systems and Computing 809. https://doi.org/10.1007/978-3-319-95588-9_101
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ICGG 2018 - Proceedings of the 18th International Conference on Geometry and Graphics

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