Oriented Projective Geometry: A Framework for Geometric Computations

摘要: Part 1 Projective geometry: the classic projective plane advantages of geometry drawbacks classical oriented related work. 2 Oriented spaces: models two-sided space central projection. 3 Flats: definition points lines planes three-spaces ranks incidence and dependence. 4 Simplices orientation: simplices simplex equivalence point location relative to a vector model. 5 The join operation: two line arbitrary flats properties null objects complementary flats. 6 meeting general meet operation in three dimensions meet. 7 Relative sides position separation theorem coefficients hyperplane. 8 maps: formal examples maps matrix map. 9 General: spaces - subspaces. 10 Duality: duomorphisms polar complement complements as power duality. 11 Generalized functions computer representation. 12 frames: nature frames classification standard coordinates frame. 13 Cross ratio: cross ratio unoriented framework. 14 Convexity: convexity convex sets half-space property hull 15 Affine geomerty: Cartesian connection affine spaces. 16 Vector albegra: translations algebra real linear maps. 17 Euclidean on plane: perpendicularity length distance angular measure congruence non-Euclidean geometries. 18 Representing by simplices: representation dual reduced 19 Plucker coordinates: canonical embedding storage efficiency Grassmann manifolds. 20 Formulas for algebraic formulas computers directions parallelism.