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Types of mesh. A mesh is a representation of a larger geometric domain by smaller discrete cells. Meshes are commonly used to compute solutions of partial differential equations and render computer graphics, and to analyze geographical and cartographic data. A mesh partitions space into elements (or cells or zones) over which the equations can ...
Example of a low poly triangle mesh representing a dolphin. In 3D computer graphics and solid modeling, a polygon mesh is a collection of vertices, edges and faces that defines the shape of a polyhedral object's surface. It simplifies rendering, as in a wire-frame model. The faces usually consist of triangles (triangle mesh), quadrilaterals ...
Consider a line segment AB as a shape in a 1-dimensional space (the 1-dimensional space is the line in which the segment lies). One can place a new point C somewhere off the line. The new shape, triangle ABC, requires two dimensions; it cannot fit in the original 1-dimensional space. The triangle is the 2-simplex, a simple shape that requires ...
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an -dimensional manifold, or -manifold for short, is a topological space with the property that each point has a neighborhood that is homeomorphic to an open subset of -dimensional Euclidean space.
e. A one-dimensional space (1D space) is a mathematical space in which location can be specified with a single coordinate. An example is the number line, each point of which is described by a single real number. [1] Any straight line or smooth curve is a one-dimensional space, regardless of the dimension of the ambient space in which the line ...
Lattice graph. In graph theory, a lattice graph, mesh graph, or grid graph is a graph whose drawing, embedded in some Euclidean space , forms a regular tiling. This implies that the group of bijective transformations that send the graph to itself is a lattice in the group-theoretical sense. Typically, no clear distinction is made between ...
Grid classification. In applied mathematics, a grid or mesh is defined as the set of smaller shapes formed after discretisation of a geometric domain. Meshing has applications in the fields of geography, designing, computational fluid dynamics, [1] and more generally in partial differential equations numerical solving.
Many examples of bounded convex polytopes can be found in the article "polyhedron".In the 2-dimensional case the full-dimensional examples are a half-plane, a strip between two parallel lines, an angle shape (the intersection of two non-parallel half-planes), a shape defined by a convex polygonal chain with two rays attached to its ends, and a convex polygon.