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Table of Contents
Intro
Editor's Preface to the Proceedings of the 19th International Conference on Geometry and Graphics
Organization
Program Committee
Local Organizing Committee
Organizing Staff
Sponsor
Support
Contents
Theoretical Graphics and Geometry
String Constructions of Quadrics Revisited
1 Introduction
2 Confocal Central Quadrics
3 String Constructions of Central Quadrics
4 Paraboloids
References
Space Kinematics and Projective Differential Geometry over the Ring of Dual Numbers
1 Introduction
2 Preliminaries
2.1 Projective Geometry over Dual Numbers
2.2 Space Kinematics
2.3 Straight Lines
3 Osculating Lines
4 Osculating Conics
4.1 Bennett Motions
4.2 Motions Based on Osculating Circles of Elliptic Geometry
5 Conclusion
References
Examples of Isoptic Ruled Surfaces
1 Introduction
2 General Results, Elementary Surfaces
3 Helical and Spiral Developables
3.1 Helical Developables
3.2 Spiral Developables
4 Algebraic Isoptic Ruled Surfaces
4.1 Some Special Polynomial Curves
5 Conclusion, Future Work
References
A One-Parameter Family of Triangle Cubics
1 Introduction
2 Prerequsites
3 Some Properties of the Cubics
4 Cubics Determined by Triangle Centers
5 How to Find Triangle Centers on Such Curves?
6 Future Work
References
Vermeer's Specific Ratio
Abstract
1 Introduction
2 Analysis of "Milk Maid"
2.1 "Milk Maid" Plan View and Projection Drawing
2.2 "Milk Maid" Scene and View Angle
2.3 "Milk Maid" Canvas Angles and Depicted Models
3 Camera Obscura and Frame Composition
3.1 Light Form and Floor Depiction
3.2 Appearance of the Floor
3.3 Definition of Euclid
4 Considerations
5 Conclusions
2.2 Whole Compound 3-Models of the 3-, 6- and 9-Cube
3 Fractals and Fractal-Like Structures
4 Planar Patterns
5 Concluding Remarks
References
Geometry and Proportion: Materialization of an Architectural Carpentry Project
Abstract
1 Introduction
2 The Treatises
3 The Geometry of the carpintería de lazo
4 Formal Solutions
5 Future Developments: Digital Computational Design Tools
6 Conclusions
References
Factorization of Locus Polynomials Using DGS
1 Introduction
2 Example by Holfeld
2.1 Locus Equation
2.2 Decomposition
Editor's Preface to the Proceedings of the 19th International Conference on Geometry and Graphics
Organization
Program Committee
Local Organizing Committee
Organizing Staff
Sponsor
Support
Contents
Theoretical Graphics and Geometry
String Constructions of Quadrics Revisited
1 Introduction
2 Confocal Central Quadrics
3 String Constructions of Central Quadrics
4 Paraboloids
References
Space Kinematics and Projective Differential Geometry over the Ring of Dual Numbers
1 Introduction
2 Preliminaries
2.1 Projective Geometry over Dual Numbers
2.2 Space Kinematics
2.3 Straight Lines
3 Osculating Lines
4 Osculating Conics
4.1 Bennett Motions
4.2 Motions Based on Osculating Circles of Elliptic Geometry
5 Conclusion
References
Examples of Isoptic Ruled Surfaces
1 Introduction
2 General Results, Elementary Surfaces
3 Helical and Spiral Developables
3.1 Helical Developables
3.2 Spiral Developables
4 Algebraic Isoptic Ruled Surfaces
4.1 Some Special Polynomial Curves
5 Conclusion, Future Work
References
A One-Parameter Family of Triangle Cubics
1 Introduction
2 Prerequsites
3 Some Properties of the Cubics
4 Cubics Determined by Triangle Centers
5 How to Find Triangle Centers on Such Curves?
6 Future Work
References
Vermeer's Specific Ratio
Abstract
1 Introduction
2 Analysis of "Milk Maid"
2.1 "Milk Maid" Plan View and Projection Drawing
2.2 "Milk Maid" Scene and View Angle
2.3 "Milk Maid" Canvas Angles and Depicted Models
3 Camera Obscura and Frame Composition
3.1 Light Form and Floor Depiction
3.2 Appearance of the Floor
3.3 Definition of Euclid
4 Considerations
5 Conclusions
2.2 Whole Compound 3-Models of the 3-, 6- and 9-Cube
3 Fractals and Fractal-Like Structures
4 Planar Patterns
5 Concluding Remarks
References
Geometry and Proportion: Materialization of an Architectural Carpentry Project
Abstract
1 Introduction
2 The Treatises
3 The Geometry of the carpintería de lazo
4 Formal Solutions
5 Future Developments: Digital Computational Design Tools
6 Conclusions
References
Factorization of Locus Polynomials Using DGS
1 Introduction
2 Example by Holfeld
2.1 Locus Equation
2.2 Decomposition