Huge variety of approaches and algorithms
Covers not only the core topics but also looks at all the related themes
Interweaves theory with applications in a way not previously attempted
Possibly the most comprehensive overview of computer graphics as seen in the context of geometric modelling, this two volume work covers implementation and theory in a thorough and systematic fashion.
Computer Graphics and Geometric Modelling: Mathematics, contains the mathematical background needed for the geometric modeling topics in computer graphics covered in the first volume. This volume begins with material from linear algebra and a discussion of the transformations in affine & projective geometry, followed by topics from advanced calculus & chapters on general topology, combinatorial topology, algebraic topology, differential topology, differential geometry, and finally algebraic geometry. Two important goals throughout were to explain the material thoroughly, and to make it self-contained. This volume by itself would make a good mathematics reference book, in particular for practitioners in the field of geometric modelling. Due to its broad coverage and emphasis on explanation it could be used as a text for introductory mathematics courses on some of the covered topics, such as topology (general, combinatorial, algebraic, and differential) and geometry (differential & algebraic). |This volume details the mathematical background needed for geometric modeling in computer graphics. It begins with material from linear algebra and a discussion of the transformations in affine and projective geometry followed by topics from advanced calculus and chapters on general topology, combinatorial topology, algebraic topology, differential topology, differential geometry, and algebraic geometry. A companion volume covers the implementation aspects of the topic in a thorough and systematic fashion.
Linear Algebra Topics Affine Geometry Projective Geometry Advanced Calculus Topics Point Set Topology Combinatorial Topology Algebraic Topology Differential Topology Differential Geometry Algebraic Geometry Appendices: Basic Algebra Basic Linear Algebra Basic Calculus & Analysis Basic Complex Analysis A Bit of Numerical Analysis
Possibly the most comprehensive overview of computer graphics as seen in the context of geometric modelling, this two volume work covers implementation and theory in a thorough and systematic fashion. Computer Graphics and Geometric Modelling: Mathematics , contains the mathematical background needed for the geometric modeling topics in computer graphics covered in the first volume. This volume begins with material from linear algebra and a discussion of the transformations in affine & projective geometry, followed by topics from advanced calculus & chapters on general topology, combinatorial topology, algebraic topology, differential topology, differential geometry, and finally algebraic geometry. Two important goals throughout were to explain the material thoroughly, and to make it self-contained. This volume by itself would make a good mathematics reference book, in particular for practitioners in the field of geometric modelling. Due to its broad coverage and emphasis on explanation it could be used as a text for introductory mathematics courses on some of the covered topics, such as topology (general, combinatorial, algebraic, and differential) and geometry (differential & algebraic).
Linear Algebra Topics
Affine Geometry
Projective Geometry
Advanced Calculus Topics
Point Set Topology
Combinatorial Topology
Algebraic Topology
Differential Topology
Differential Geometry
Algebraic Geometry
Appendices:
Basic Algebra
Basic Linear Algebra
Basic Calculus & Analysis
Basic Complex Analysis
A Bit of Numerical Analysis
Inhaltsverzeichnis
Linear Algebra Topics.- Affine Geometry.- Projective Geometry.- Advanced Calculus Topics.- Point Set Topology.- Combinatorial Topology.- Algebraic Topology.- Differential Topology.- Differential Geometry.- Algebraic Geometry.
Klappentext
Possibly the most comprehensive overview of computer graphics as seen in the context of geometric modelling, this two volume work covers implementation and theory in a thorough and systematic fashion. Computer Graphics and Geometric Modelling: Mathematics, contains the mathematical background needed for the geometric modeling topics in computer graphics covered in the first volume. This volume begins with material from linear algebra and a discussion of the transformations in affine & projective geometry, followed by topics from advanced calculus & chapters on general topology, combinatorial topology, algebraic topology, differential topology, differential geometry, and finally algebraic geometry. Two important goals throughout were to explain the material thoroughly, and to make it self-contained. This volume by itself would make a good mathematics reference book, in particular for practitioners in the field of geometric modelling. Due to its broad coverage and emphasis on explanation it could be used as a text for introductory mathematics courses on some of the covered topics, such as topology (general, combinatorial, algebraic, and differential) and geometry (differential & algebraic).
This volume details the mathematical background needed for geometric modeling in computer graphics. It begins with material from linear algebra and a discussion of the transformations in affine and projective geometry followed by topics from advanced calculus and chapters on general topology, combinatorial topology, algebraic topology, differential topology, differential geometry, and algebraic geometry. A companion volume covers the implementation aspects of the topic in a thorough and systematic fashion.
