(Résolution de systèmes bivariés et topologie de courbes planes) A fundamental problem in computational geometry is the computation of the topology of an algebraic plane curve given by its implicit equation, that is, the computation of a graph lines that approximates the curve while preserving ...
To start with, we describe a natural parameter space for all regular covers of a finite CW-complex , with group of deck transformations a fixed abelian group , which in the case of free abelian covers of rank coincides with the Grassmanian of -planes in (,[Special characters omitted.] )...
we map each point in theR33D space to a unit vector pointing towards the closest surface point. We mathematically demonstrate that the surface points can be recovered at the−1level set of the flux density of VF. The proposed
Plots show mean CV values as a function of the barrel and un-barrel factor β, for the different 2D planes along which the barrelling/un-barrelling was done (xy, yz, xz (rows)). All the transformations in a–c (scaling, shearing, barrelling) showed that distorting or un-distorting ...
The consideration is based on the role played by isoclinic 2-planes in the geometry of the real Clifford algebraC(3,0)which provide an invariant geometric frame for it. It can be generalized to larger Clifford algebras. 展开 关键词: Algebras Dirac equation ...
Additionally, modeling large-scale objects on a voxel grid can be resource-intensive, as it must considers all voxels in the space where the target geometry exists. One of the major types of volumetric representation is an occupancy map; this includes the 2D occupancy map, 3D occupancy map ...
We then tilted the lattice so that the three planes of movement all had the same relationship to gravity, and were thus all equally easy (or hard) to traverse. We found that the elongation of the axes followed the tilt of the maze, and the difference between horizontal and vertical place...
and the GIT quotient is isomorphic to the cotangent bundle of v-planes in \mathbb {C}^w in the case \theta <0 and to in the case \theta >0. The two varieties are isomorphic to each other, but we have the following different identifications of the points in the Grassmannian: \theta...
Many methods for creating hatching lines rely on the computation of curves that result from intersecting a model with a set of planes. Depending on how the actual computation of these curves is performed, intersection calculation can be very time consuming. We shall thus introduce an approach ...
Directly representing 3D contents in volumes is memory- and computation-intensive, as well as redundant since 3D con- tents are always sparse. Peng et al. [40] propose to project features of point cloud to multiple planes for 3D geometry reconstructio...