Mathematical algorithms are a fundamental component of Computer Aided Design and Manufacturing (CAD/CAM) systems. This book provides a bridge between algebraic geometry and geometric modelling algorithms, formulated within a computer science framework.

Apart from the algebraic geometry topics covered, the entire book is based on the unifying concept of using algebraic techniques properly specialized to solve geometric problems to seriously improve accuracy, robustness and efficiency of CAD-systems. It provides new approaches as well as industrial applications to deform surfaces when animating virtual characters, to automatically compare images of handwritten signatures and to improve control of NC machines.

This book further introduces a noteworthy representation based on 2D contours, which is essential to model the metal sheet in industrial processes. It additionally reviews applications of numerical algebraic geometry to differential equations systems with multiple solutions and bifurcations.

Future Vision and Trends on Shapes, Geometry and Algebra is aimed specialists in the area of mathematics and computer science on the one hand and on the other hand at those who want to become familiar with the practical application of algebraic geometry and geometric modelling such as students, researchers and doctorates.

Includes supplementary material: sn.pub/extras

Autorentext

Raffaele de Amicis is the Managing Director of Fondazione Graphitech, he holds a Ph.D. from University of Bologna, Italy. He has been research fellow at Fraunhofer Inst. for Computer Graphics Research (IGD) in Darmstadt, Germany and senior researcher at Technical Univ. of Darmstadt. He is coordinator of GEPSUS, BRISEIDE, i-SCOPE and VISION. His interests are in CAD, virtual reality, virtual engineering, geovisual analytics and science and technology policy. He has authored 3 books, contributed to 11 scientific texts and he is author or co-author of more than 120 scientific papers. He serves as cons. prof. in undergraduate courses related computer graphics, at the Dept. of ICT at the Univ. of Trento, Italy. He is currently member of the Experts Board of the Italian Committee for Evaluation of Research (CIVR).

Dr. Giuseppe Conti is currently CTO at Trilogis, an Italian SME focusing on geospatial technologies. Previously, he worked at Fondazione Graphitech as senior researcher since 2002. He received a M.Eng. in Civil Engineering and a Ph.D. degree at the University of Strathclyde, Glasgow (UK). In the past, he worked for a number of engineering firms including Ove Arup Scotland engineering consultants. He has been involved in several projects co-funded by the European Commission, as well as in industrial projects dealing with issues related to the use of Virtual Reality to planning, large terrain 3D visualization and in the context of geobrowsers. In the past, he was member of the board of AM/FM GIS Italy association and member of Technical Committee of the Open Geospatial Consortium. He has been invited speaker at a number of international events dealing with environmental protection and GIS. He is author or co-author of more than 80 publications in the field of geo-visual analytics and computer graphics.

Inhalt

Introduction.- Future Shape Modelling Scenarios.- A Hilbert-Driven Strategy for Signature-based Gröbner Basis Algorithms.- Numerical Algebraic Geometry and Differential Equations.- Sparse Discriminants and Applications.- Parametrization of the Bisector of Two Low Degree Surfaces.- Computer Aided Algebraic Geometry: Constructing Surfaces of Genus Zero.- Elastic Bone Transformation for Realistic Facial Animation in Web GL.- Geometric Features for Hand-Written Signatures.- Using 2D Contours to Model Metal Sheets in Industrial Machining Processes.- The Case for Scripted Process Design and Engineering.