Oriented Projective Geometry: A Framework for Geometric ComputationsStolfi's book describes oriented projective geometry, a geometric model that combines the elegance and efficiency of classical projective geometry with the consistent handling of oriented lines and planes, signed angles, line segments, convex sets, and many other fundamental geometric computing concepts that classical theory does not support. |
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Oriented Projective Geometry: A Framework for Geometric Computations Jorge Stolfi Limited preview - 2014 |
Common terms and phrases
3-space affine frame affine geometry affine map affine space algorithms angle arbitrary back range canonical Cartesian central projection chapter closed convex sets compute consists contained convex set cross ratio defined definition denote determinant dimension direction dual duality duomorphism equation equivalent Euclidean geometry Euclidean map example flat of rank flat set formula frame ƒ front range homogeneous coordinates intersection inverse isomorphism join line at infinity linear map linear subspace main simplex matrix meet operation negative Note null object Null(F operands oriented projective geometry oriented projective space pair perpendicular Plücker coordinates points at infinity polar complement positive side projective function projective map PROOF proper simplex rank(a relative orientation result segment pq set of points signature simplex representation span sphere spherical model straight model subflats T₁ T₂ theorem three-space two-sided plane two-sided space unoriented v-dimensional vector space model vertices zero