Oriented projective geometry : a framework for geometric computations /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Stolfi, Jorge
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Boston : Academic Press, �1991.
Temas:
Geometry, Projective > Data processing.
G�eom�etrie projective > Informatique.
MATHEMATICS > Geometry > General.
Geometry, Projective > Data processing
Projektive Geometrie
Algorithmische Geometrie
Orientierung > Mathematik
Geometrische Modellierung
G�eom�etrie projective.
Projective geometry
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Front Cover; Oriented Projective Geometry: A Framework for Geometric Computations; Copyright Page; Table of Contents; Chapter 0. Introduction; Chapter 1. Projective geometry; 1. The classic projective plane; 2. Advantages of projective geometry; 3. Drawbacks of classical projective geometry; 4. Oriented projective geometry; 5. Related work; Chapter 2. Oriented projective spaces; 1. Models of two-sided space; 2. Central projection; Chapter 3. Flats; 1. Definition; 2. Points; 3. Lines; 4. Planes; 5. Three-spaces; 6. Ranks; 7. Incidence and independence; Chapter 4. Simplices and orientation
  • 1. Simplices2. Simplex equivalence; 3. Point location relative to a simplex; 4. The vector space model; Chapter 5. The join operation; 1. The join of two points; 2. The join of a point and a line; 3. The join of two arbitrary flats; 4. Properties of join; 5. Null objects; 6. Complementary flats; Chapter 6. The meet operation; 1. The meeting point of two lines; 2. The general meet operation; 3. Meet in three dimensions; 4. Properties of meet; Chapter 7. Relative orientation; 1. The two sides of a line; 2. Relative position of arbitrary flats; 3. The separation theorem
  • 4. The coefficients of a hyperplaneChapter 8. Projective maps; 1. Formal definition; 2. Examples; 3. Properties of projective maps; 4. The matrix of a map; Chapter 9. General two-sided spaces; 1. Formal definition; 2. Subspaces; Chapter 10. Duality; 1. Duomorphisms; 2. The polar complement; 3. Polar complements as duomorphisms; 4. Relative polar complements; 5. General duomorphisms; 6. The power of duality; Chapter 11. Generalized projective maps; 1. Projective functions; 2. Computer representation; Chapter 12. Projective frames; 1. Nature of projective frames; 2. Classification of frames
  • 3. Standard frames4. Coordinates relative to a frame; Chapter 13. Cross ratio; 1. Cross ratio in unoriented geometry; 2. Cross ratio in the oriented framework; Chapter 14. Convexity; 1. Convexity in classical projective space; 2. Convexity in oriented projective spaces; 3. Properties of convex sets; 4. The half-space property; 5. The convex hull; 6. Convexity and duality; Chapter 15. Affine geometry; 1. The Cartesian connection; 2. Two-sided affine spaces; Chapter 16. Vector algebra; 1. Two-sided vector spaces; 2. Translations; 3. Vector algebra; 4. The two-sided real line; 5. Linear maps
  • Chapter 17. Euclidean geometry on the two-sided plane1. Perpendicularity; 2. Two-sided Euclidean spaces; 3. Euclidean maps; 4. Length and distance; 5. Angular measure and congruence; 6. Non-Euclidean geometries; Chapter 18. Representing flats by simplices; 1. The simplex representation; 2. The dual simplex representation; 3. The reduced simplex representation; Chapter 19. Pl�ucker coordinates; 2. The canonical embedding; 3. Plucker coefficients; 4. Storage eff�iciency; 5. The Grassmann manifolds; Chapter 20. Formulas for Pl�ucker coordinates; 1. Algebraic formulas; 2. Formulas for computers

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