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When n = 3, a level set is called a level surface (or isosurface); so a level surface is the set of all real-valued roots of an equation in three variables x 1, x 2 and x 3. For higher values of n, the level set is a level hypersurface, the set of all real-valued roots of an equation in n > 3 variables. A level set is a special case of a fiber.
The Level-set method (LSM) is a conceptual framework for using level sets as a tool for numerical analysis of surfaces and shapes. LSM can perform numerical computations involving curves and surfaces on a fixed Cartesian grid without having to parameterize these objects. [ 1 ]
Example mechanical drawing. Here is an example of an engineering drawing (an isometric view of the same object is shown above). The different line types are colored for clarity. Black = object line and hatching; Red = hidden line; Blue = center line of piece or opening; Magenta = phantom line or cutting plane line
An example of a multiview orthographic drawing from a US Patent (1913), showing two views of the same object. Third angle projection is used. In third-angle projection , the object is conceptually located in quadrant III, i.e. it is positioned below and behind the viewing planes, the planes are transparent , and each view is pulled onto the ...
This is a list of surfaces in mathematics. They are divided into minimal surfaces , ruled surfaces , non-orientable surfaces , quadrics , pseudospherical surfaces , algebraic surfaces , and other types of surfaces.
The simplest type of parametric surfaces is given by the graphs of functions of two variables: = (,), (,) = (,, (,)). A rational surface is a surface that admits parameterizations by a rational function. A rational surface is an algebraic surface. Given an algebraic surface, it is commonly easier to decide if it is rational than to compute its ...
For these surfaces with second Chern class can be any integer from 3 to 11. Surfaces with all these values are known; a few of the many examples that have been studied are: c 2 = 3: Fake projective plane (Mumford surface). The first example was found by Mumford using p-adic geometry, and there are 50 examples altogether. They have the same ...
In computational fluid dynamics, free-surface modelling (FSM) refers to the numerical modelling of a free surface—a freely moving interface between immiscible fluids—in order to be able to track and locate it. Common methods used in free surface modelling include the level-set method and the volume of fluid method