The volume reports on interdisciplinary discussions and interactions between theoretical research and practical studies on geometric structures and their applications in architecture, the arts, design, education, engineering, and mathematics. These related fields of research can enrich each other and renew their mutual interest in these topics through networks of shared inspiration, and can ultimately enhance the quality of geometry and graphics education. Particular attention is dedicated to the contributions that women have made to the scientific community and especially mathematics. The book introduces engineers, architects and designers interested in computer applications, graphics and geometry to the latest advances in the field, with a particular focus on science, the arts and mathematics education.
Different Faces of Geometry - edited by the world renowned geometers S. Donaldson, Ya. Eliashberg, and M. Gromov - presents the current state, new results, original ideas and open questions from the following important topics in modern geometry: These apparently diverse topics have a common feature in that they are all areas of exciting current activity. The Editors have attracted an impressive array of leading specialists to author chapters for this volume: G. Mikhalkin (USA-Canada-Russia), V.D. Milman (Israel) and A.A. Giannopoulos (Greece), C. LeBrun (USA), Ko Honda (USA), P. Ozsvath (USA) and Z. Szabo (USA), C. Simpson (France), D. Joyce (UK) and P. Seidel (USA), and S. Bauer (Germany). One can distinguish various themes running through the different contributions. There is some emphasis on invariants defined by elliptic equations and their applications in low-dimensional topology, symplectic and contact geometry (Bauer, Seidel, Ozsvath and Szabo). These ideas enter, more tangentially, in the articles of Joyce, Honda and LeBrun.Here and elsewhere, as well as explaining the rapid advances that have been made, the articles convey a wonderful sense of the vast areas lying beyond our current understanding. Simpson's article emphasizes the need for interesting new constructions (in that case of Kahler and algebraic manifolds), a point which is also made by Bauer in the context of 4-manifolds and the 11/8 conjecture. LeBrun's article gives another perspective on 4-manifold theory, via Riemannian geometry, and the challenging open questions involving the geometry of even well-known 4-manifolds. There are also striking contrasts between the articles. The authors have taken different approaches: for example, the thoughtful essay of Simpson, the new research results of LeBrun and the thorough expositions with homework problems of Honda. One can also ponder the differences in the style of mathematics. In the articles of Honda, Giannopoulos and Milman, and Mikhalkin, the geometry is present in a very vivid and tangible way; combining respectively with topology, analysis and algebra.The papers of Bauer and Seidel, on the other hand, makes the point that algebraic and algebro-topological abstraction (triangulated categories, spectra) can play an important role in very unexpected ways in concrete geometric problems. - From the Preface by the Editors
Human faces are familiar to our visual systems. We easily recognize a person's face in arbitrary lighting conditions and in a variety of poses; detect small appearance changes; and notice subtle expression details. Can computer vision systems process face images as well as human vision systems can? Face image processing has potential applications in surveillance, image and video search, social networking, and other domains. A comprehensive guide to this fascinating topic, this book provides a systematic description of modeling face geometry and appearance from images, including information on mathematical tools, physical concepts, image processing and computer vision techniques, and concrete prototype systems. The book will be an excellent reference for researchers and graduate students in computer vision, computer graphics, and multimedia as well as application developers who would like to gain a better understanding of the state of the art.
The volume reports on interdisciplinary discussions and interactions between theoretical research and practical studies on geometric structures and their applications in architecture, the arts, design, education, engineering, and mathematics. These related fields of research can enrich each other and renew their mutual interest in these topics through networks of shared inspiration, and can ultimately enhance the quality of geometry and graphics education. Particular attention is dedicated to the contributions that women have made to the scientific community and especially mathematics. The book introduces engineers, architects and designers interested in computer applications, graphics and geometry to the latest advances in the field, with a particular focus on science, the arts and mathematics education.
Forensic art may be defined as 'portrait art minus a tangible subject.' The main objective of this book is to present a series of practical indices interrelating the key features of the human face that will provide a foundation for any exercise in forensic art from composite sketch to post-mortem 're-facing.' These indices are illustrated with a survey of the numerous and often surprising geometric forms that permeate facial design. The various triangles and rectangles, rhomboids and trapezoids, parallelograms and circles that define the human face (the theme) and give it individuality (variations on the theme) are examined. The chapters provide necessary information to define the cephalometric points, planes, areas and lines that demarcate the human face, including the detailed surface anatomy of the eye, nose, mouth and ear. The underlying geometry of the human facial plan is revealed, illustrating a selection of triangles, rectangles, and other polygons. The graphic facial analysis (GFA) of the frontal face is covered, with sixteen indices and triangles defining and illustrating their means and ranges of variation. The GFA details the lateral face by means of eight angles and indices with special attention given to the nose and ear. With 45 illustrations and two tables in this clear and comprehensive text, this book leaves little to the imagination and is truly a unique treatise and source of information.
New York Times bestselling author Danica McKellar makes it a breeze to excel in high school geometry! Hollywood actress and math whiz Danica McKellar has completely shattered the “math nerd” stereotype. For years, she’s been showing girls how to feel confident and ace their math classes—with style! With Girls Get Curves, she applies her winning techniques to high school geometry, giving readers the tools they need to feel great and totally “get” everything from congruent triangles to theorems, and more. Inside you’ll find: • Time-saving tips and tricks for homework and tests • Illuminating practice problems (and proofs!) with detailed solutions • Totally relateable real-world examples • True stories from Danica’s own life as an actress and math student • A Troubleshooting Guide, for getting unstuck during even the trickiest proofs! With Danica as a coach, girls everywhere can stop hiding from their homework and watch their scores rise!
Human faces are familiar to our visual systems. We easily recognize a person's face in arbitrary lighting conditions and in a variety of poses; detect small appearance changes; and notice subtle expression details. Can computer vision systems process face images as well as human vision systems can? Face image processing has potential applications in surveillance, image and video search, social networking and other domains. A comprehensive guide to this fascinating topic, this book provides a systematic description of modeling face geometry and appearance from images, including information on mathematical tools, physical concepts, image processing and computer vision techniques, and concrete prototype systems. The book will be an excellent reference for researchers and graduate students in computer vision, computer graphics and multimedia, as well as application developers who would like to gain a better understanding of the state of the art.
This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.
Build four projects using Blender for 3D Printing, giving you all the information that you need to know to create high-quality 3D printed objects. About This Book A project based guide that helps you design beautiful 3D printing objects in Blender Use mesh modeling and intersections to make a custom architectural model of a house Create a real world 3D printed prosthetic hand with organic modeling and texturing painting Who This Book Is For If you're a designer, artist, hobbyist and new to the world of 3D printing, this is the book for you. Some basic knowledge of Blender and geometry will help, but is not essential. What You Will Learn Using standard shapes and making custom shapes with Bezier Curves Working with the Boolean, Mirror, and Array Modifiers Practicing Mesh Modeling tools such as Loop Cut and Slide and Extrude Streamlining work with Proportional Editing and Snap During Transform Creating Organic Shapes with the Subdivision Surface Modifier Adding Color with Materials and UV Maps Troubleshooting and Repairing 3D Models Checking your finished model for 3D printability In Detail Blender is an open-source modeling and animation program popular in the 3D printing community. 3D printing brings along different considerations than animation and virtual reality. This book walks you through four projects to learn using Blender for 3D Printing, giving you information that you need to know to create high-quality 3D printed objects. The book starts with two jewelry projects-- a pendant of a silhouette and a bracelet with custom text. We then explore architectural modeling as you learn to makes a figurine from photos of a home. The final project, a human hand, illustrates how Blender can be used for organic models and how colors can be added to the design. You will learn modeling for 3D printing with the help of these projects. Whether you plan to print at-home or use a service bureau, you'll start by understanding design requirements. The book begins with simple projects to get you started with 3D modeling basics and the tools available in Blender. As the book progresses, you'll get exposed to more robust mesh modeling techniques, modifiers, and Blender shortcuts. By the time you reach your final project, you'll be ready for organic modeling and learning how to add colors. In the final section, you'll learn how to check for and correct common modeling issues to ensure the 3D printer can make your idea a reality! Style and approach The profile pendant teaches background images, Bezier Curves, and Boolean Union. The Mirror Modifier, Boolean Difference, and Text objects are introduced with the coordinate bracelet. Mesh modeling, importing SVG files, and Boolean Intersection help make the house figurine. The human hand illustrates using the Subdivision Surface Modifier for organic shapes and adding color to your designs.
