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The generation of a bicylinder Calculating the volume of a bicylinder. A bicylinder generated by two cylinders with radius r has the volume =, and the surface area [1] [6] =.. The upper half of a bicylinder is the square case of a domical vault, a dome-shaped solid based on any convex polygon whose cross-sections are similar copies of the polygon, and analogous formulas calculating the volume ...
In this case two-dimensional unstructured mesh uses triangle elements while three-dimensional uses tetrahedral elements. These are combination of small structured mesh arranged in unstructured pattern. In this type of grid each single cell is treated as a block. There is no structure of coordinate lines that is given by the grid.
Face-vertex meshes represent an object as a set of faces and a set of vertices. This is the most widely used mesh representation, being the input typically accepted by modern graphics hardware. Face-vertex meshes improve on VV mesh for modeling in that they allow explicit lookup of the vertices of a face, and the faces surrounding a vertex.
For such applications it can be interesting to convert already existing meshes to CSG trees. This problem of automatically converting meshes to CSG trees is called inverse CSG. A resulting CSG tree is required to occupy the same volume in 3D space as the input mesh while having a minimal number of nodes.
The basic object used in mesh modeling is a vertex, a point in three-dimensional space.Two vertices connected by a straight line become an edge.Three vertices, connected to each other by three edges, define a triangle, which is the simplest polygon in Euclidean space.
A coarse mesh may provide an accurate solution if the solution is a constant, so the precision depends on the particular problem instance. One can selectively refine the mesh in areas where the solution gradients are high, thus increasing fidelity there. Accuracy, including interpolated values within an element, depends on the element type and ...
Let be a metric space with distance function .Let be a set of indices and let () be a tuple (indexed collection) of nonempty subsets (the sites) in the space .The Voronoi cell, or Voronoi region, , associated with the site is the set of all points in whose distance to is not greater than their distance to the other sites , where is any index different from .
Alternatively, a Reuleaux triangle may be constructed from an equilateral triangle T by drawing three arcs of circles, each centered at one vertex of T and connecting the other two vertices. [9] Or, equivalently, it may be constructed as the intersection of three disks centered at the vertices of T, with radius equal to the side length of T. [10]