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).
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First Sentence:
This chapter assumes a basic knowledge and familiarity of linear algebra that is roughly equivalent to what one would get from an introductory course in the subject. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
continuously varying choice, pure dimensional varieties, nonzero normal vector field, universal factorization property, deglex order, linear polyhedron, adapted frame field, qth homology group, regular parameterization, orientable pseudomanifold, alternating multilinear maps, principal normal curvatures, labeled polygon, combinatorial surface, ferentiable map, same homology groups, proper triangulation, bordered surface, nondegenerate conic, projective conic, nonzero vector field, moving trihedron, coordinate parameterization, abstract manifolds, signed curvature Key Phrases - Capitalized Phrases (CAPs): (learn more)
Prove Lemma, Hilbert Nullstellensatz, Prove Proposition, Solve Exercise, Linear Algebra Topics New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
This chapter assumes a basic knowledge and familiarity of linear algebra that is roughly equivalent to what one would get from an introductory course in the subject. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
continuously varying choice, pure dimensional varieties, nonzero normal vector field, universal factorization property, deglex order, linear polyhedron, adapted frame field, qth homology group, regular parameterization, orientable pseudomanifold, alternating multilinear maps, principal normal curvatures, labeled polygon, combinatorial surface, ferentiable map, same homology groups, proper triangulation, bordered surface, nondegenerate conic, projective conic, nonzero vector field, moving trihedron, coordinate parameterization, abstract manifolds, signed curvature Key Phrases - Capitalized Phrases (CAPs): (learn more)
Prove Lemma, Hilbert Nullstellensatz, Prove Proposition, Solve Exercise, Linear Algebra Topics New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 81
books:
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- Advanced Calculus by R. Creighton Buck on 6 pages
- Advanced Calculus, 3rd Edition by Angus E. Taylor on 6 pages
- Elements of Differential Geometry by Richard S. Millman in Back Matter
- A Panoramic View of Riemannian Geometry by Marcel Berger in Back Matter
- The Mathematics of Surfaces (The Institute of Mathematics and Its Applications Conference Series, New Ser., 6) (v. 1) by J. A. Gregory in Back Matter
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