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The geometry of lines occurs naturally in such different areas as sculptured surface machining, computation of offsets and medial axes, surface reconstruction for reverse engineering, geometrical optics, kinematics and motion design, and modeling of developable surfaces. This book covers line geometry from various viewpoints and aims towards computation and visualization. Besides applications, it contains a tutorial on projective geometry and an introduction into the theory of smooth and algebraic manifolds of lines. It will be useful to researchers, graduate students, and anyone interested either in the theory or in computational aspects in general, or in applications in particular.
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Advances in Architectural Geometry 2023
Kathrin Dörfler, Jan Knippers, Achim Menges, Stefana Parascho, Helmut Pottmann, …
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R1,811
R1,420
Discovery Miles 14 200
Save R391 (22%)
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Ships in 10 - 15 working days
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From the reviews: " A unique and fascinating blend, which is
shown to be useful for a variety of applications, including
robotics, geometrical optics, computer animation, and geometric
design. The contents of the book are visualized by a wealth of
carefully chosen illustrations, making the book a shear pleasure to
read, or even to just browse in." Mathematical Reviews
This textbook is a comprehensive and yet accessible introduction to
non-Euclidean Laguerre geometry, for which there exists no previous
systematic presentation in the literature. Moreover, we present new
results by demonstrating all essential features of Laguerre
geometry on the example of checkerboard incircular nets. Classical
(Euclidean) Laguerre geometry studies oriented hyperplanes,
oriented hyperspheres, and their oriented contact in Euclidean
space. We describe how this can be generalized to arbitrary
Cayley-Klein spaces, in particular hyperbolic and elliptic space,
and study the corresponding groups of Laguerre transformations. We
give an introduction to Lie geometry and describe how these
Laguerre geometries can be obtained as subgeometries. As an
application of two-dimensional Lie and Laguerre geometry we study
the properties of checkerboard incircular nets.
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