Line-Based Affine Reasoning in Euclidean Plane
نویسندگان
چکیده
We consider the binary relations of parallelism and convergence between lines in a 2-dimensional affine space. Associating with parallelism and convergence the binary predicates P and C and the modal connectives [P ] and [C], we consider a first-order theory based on these predicates and a modal logic based on these modal connectives. We investigate the axiomatization/completeness and the decidability/complexity of this first-order theory and this modal logic.
منابع مشابه
Spatial Analysis in curved spaces with Non-Euclidean Geometry
The ultimate goal of spatial information, both as part of technology and as science, is to answer questions and issues related to space, place, and location. Therefore, geometry is widely used for description, storage, and analysis. Undoubtedly, one of the most essential features of spatial information is geometric features, and one of the most obvious types of analysis is the geometric type an...
متن کاملAffine Surface Reconstruction by Purposive Viewpoint Control
We present an approach for building an affine representation of an unknown curved object viewed under orthographic projection from images of its occluding contour. It is based on the observation that the projection of a point on a curved, featureless surface can be computed along a special viewing direction that does not belong to the point’s tangent plane. We show that by circumnavigating the ...
متن کاملOn the Affine Heat Equation for Non-convex Curves
In the past several years, there has been much research devoted to the study of evolutions of plane curves where the velocity of the evolving curve is given by the Euclidean curvature vector. This evolution appears in a number of different pure and applied areas such as differential geometry, crystal growth, and computer vision. See for example [4, 5, 6, 15, 16, 17, 19, 20, 35] and the referenc...
متن کاملClass Notes for Math 3400: Euclidean and Non-euclidean Geometry
We discuss aspects of Euclidean geometry including isometries of the plane, affine tranformations in the plane and symmetry groups. We then explore similar concepts in the sphere and projective space, and explore elliptic and hyperbolic geometry.
متن کاملAffine congruence by dissection of intervals
Tarski’s circle squaring problem (see [8]) has motivated the following question: Can a circular disc be dissected into finitely many topological discs such that images of these pieces under suitable Euclidean motions form a dissection of a square? Dubins, Hirsch, and Karush give a negative answer in [1]. However, one can get positive results if the group of Euclidean motions is replaced by suit...
متن کامل