Geometric transformations for modeling of curves and surfaces

Autor*innen

• Georgi H. Georgiev

Parameter

• Mathematik

Mehr zum Buch

Geometric transformations, curves, and surfaces are fundamental in various mathematics branches and are crucial in modern computer science fields like computer-aided geometric design, graphics, and vision. This book demonstrates the close relationship between these concepts and provides direct constructions for geometric modeling. It presents several classes of curves and surfaces, including self-similar curves in Euclidean spaces, space-like Bézier curves and surfaces in Minkowski 3-space, and rational curves and surfaces in the 3-sphere. Divided into four parts, the first discusses shape spaces of similar triangles and tetrahedra, focusing on equivalence classes under direct similarities. The second part explores shape curvatures of Frenet curves, identifying differential-geometric invariants that locally define these curves up to direct similarity, with a complete classification of self-similar curves. The third part examines Bézier curves and surfaces, deriving formulas for their shape curvatures and establishing conditions for space-like Bézier surfaces in Minkowski 3-space. The final part addresses nonlinear transformations in projective and Euclidean spaces, utilizing three-dimensional geometric algebra to investigate plane quadratic transformations and rational ruled surfaces. It also explores special involutions in complex projective space. This book is aimed at graduate students and researchers in mathematics and

• Sprache: Englisch
• Erscheinungsdatum: 2012