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Iterative Methods Based on Linearization for Nonlinear Elliptic Grid Systems
Published in Guri I. Marchuk, Numerical Methods and Applications, 2017
Each point Pi is a vertex of the simplex; for 1 ≤ k ≤ j − 1, k-dimensional faces of the simplex are k-dimensional simplexes with k + 1 different vertices, Pi1,..., Pik, from the given set of Pi. One-dimensional faces are called edges. We will be dealing with special d-dimensional simplexes, which may be referred to as regular parts of some cubes in Rd. More precisely, let us consider a cube
Automatic machining feature recognition from STEP files
Published in International Journal of Computer Integrated Manufacturing, 2023
V Naga Malleswari, P Gourav Pragvamsa
In a STEP AP 203 file, the faces indicate the second level of characterization. A face is a topological structure that specifies a loop-bounded portion of a surface that exchanges an edge with precisely one other face to create a CLOSED SHELL. Examine the cylinder’s four sides, as well as various other characteristics such as the edges and vertices. Two pointers can be applied to examine each face: bound and surface. The first pointer is often used for the bound, while the second pointer is used to represent the face’s surface. The ADVANCED FACE item concludes with a Boolean flag which determines whether the loop direction is parallel to or perpendicular to the surface baseline.
Procedural and relational understanding of pre-service mathematics teachers regarding spatial perception of angles in pyramids
Published in International Journal of Mathematical Education in Science and Technology, 2019
Item 7 (comprising two parts) referred to the relation between the pyramid height and the apex angle of a lateral face as well as to the relation between the pyramid height and the angle between two adjacent lateral faces. Item 8 (part 1) referred to the relation of the size of the apex angle of the lateral face and the angles (central angle or angle between edges) of the polygon in the base of a right and regular pyramid. Item 8 (part 2) referred to the relation of the boundaries of the angle between the adjacent faces in a right and regular pyramid and the angles (central angle and angle between edges) of the polygon which forms the base of the pyramid.
Design in the service of topology and the classification theorem
Published in International Journal of Mathematical Education in Science and Technology, 2023
In Figure 3(a), we can see lines of latitude and longitude, which define a map constructed by edges, vertices, and faces. Each intersection of two lines defines a vertex; an edge is a line between two vertices; and if a domain is bounded by edges, it defines a face. Figure 3(b) gives a triangulation of the surface, i.e. the map on the surface is a collection of triangles.