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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.
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.
Access, distribution and processing of Geographic Information (GI)
are basic preconditions to support strategic environmental
decision-making. The heterogeneity of information on the
environment today available is driving a wide number of
initiatives, on both sides of the Atlantic, all advocating both the
strategic role of proper management and processing of environme-
related data as well as the importance of harmonized IT
infrastructures designed to better monitor and manage the
environment. The extremely wide range of often multidimensional
environmental information made available at the global scale poses
a great challenge to technologists and scientists to find extremely
sophisticated yet effective ways to provide access to relevant data
patterns within such a vast and highly dynamic information flow. In
the past years the domain of 3D scientific visualization has
developed several solutions designed for operators requiring to
access results of a simulation through the use of 3D visualization
that could support the understanding of an evolving phenomenon.
However 3D data visualization alone does not provide model and
hypothesis-making neither it provide tools to validate results. In
order overcome this shortcoming, in recent years scientists have
developed a discipline that combines the benefits of data mining
and information visualization, which is often referred to as Visual
Analytics (VA).
Access, distribution and processing of Geographic Information (GI)
are basic preconditions to support strategic environmental
decision-making. The heterogeneity of information on the
environment today available is driving a wide number of
initiatives, on both sides of the Atlantic, all advocating both the
strategic role of proper management and processing of environme-
related data as well as the importance of harmonized IT
infrastructures designed to better monitor and manage the
environment. The extremely wide range of often multidimensional
environmental information made available at the global scale poses
a great challenge to technologists and scientists to find extremely
sophisticated yet effective ways to provide access to relevant data
patterns within such a vast and highly dynamic information flow. In
the past years the domain of 3D scientific visualization has
developed several solutions designed for operators requiring to
access results of a simulation through the use of 3D visualization
that could support the understanding of an evolving phenomenon.
However 3D data visualization alone does not provide model and
hypothesis-making neither it provide tools to validate results. In
order overcome this shortcoming, in recent years scientists have
developed a discipline that combines the benefits of data mining
and information visualization, which is often referred to as Visual
Analytics (VA).
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