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This book is written for students, CAD system users and software developers who are interested in geometric continuity--a notion needed in everyday practice of Computer-Aided Design and also a hot subject of research. It contains a description of the classical geometric spline c…
Preface -- Notation -- 1. Introduction -- 2. Geometric continuity of curves: 2.1. Equations of geometric continuity; 2.2. Interpretation; 2.3. Geometric spline curves; 2.4. Tensor product geometric spline patches -- 3. Pairs of surface patches: 3.1. Geometric continuity at a com…
Dieses Buch ist eine Einführung in die Differentialgeometrie und ein passender Begleiter zum Differentialgeometrie-Modul (ein- und zwei-semestrig). Zunächst geht es um die klassischen Aspekte wie die Geometrie von Kurven und Flächen, bevor dann höherdimensionale Flächen sowie ab…
Given a curve C over a field K, the period of C is the g.c.d. of the degrees of Gal(K ̄/K)-invariant invertible sheaves on C, while the index of C is the g.c.d. of the degrees of Gal(K ̄/K)-invariant divisors. S. Lichtenbaum proved divisibility conditions between the genus, period…
Bezier polynomials are used frequently in computer graphics for interactive generation of smooth curves. As these polynomials have parametric equation forms, only a small number of guiding points are required to specify a desired curve. The inverse problem of finding an optimal …
