Concepts inEnrichment textures for detailed cutting of shells
Texture mapping
Texture mapping is a method for adding detail, surface texture, or color to a computer-generated graphic or 3D model. Its application to 3D graphics was pioneered by Dr Edwin Catmull in his Ph.D. thesis of 1974.
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Harmonic function
In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f : U ¿ R (where U is an open subset of R) which satisfies Laplace's equation, i.e. everywhere on U. This is usually written as or
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Computer graphics (computer science)
Computer graphics is a sub-field of computer science which studies methods for digitally synthesizing and manipulating visual content. Although the term often refers to the study of three-dimensional computer graphics, it also encompasses two-dimensional graphics and image processing.
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Finite element method
The finite element method (FEM) (its practical application often known as finite element analysis) is a numerical technique for finding approximate solutions of partial differential equations (PDE) as well as integral equations.
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Computer simulation
A computer simulation, a computer model, or a computational model is a computer program, or network of computers, that attempts to simulate an abstract model of a particular system. Computer simulations have become a useful part of mathematical modeling of many natural systems in physics, astrophysics, chemistry and biology, human systems in economics, psychology, social science, and engineering. Simulation of a system is represented as the running of the system's model.
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Function (mathematics)
In mathematics, a function is a relation between a set of inputs and a set of potential outputs with the property that each input is related to exactly one output. An example of such a relation is defined by the rule f(x) = x, which relates an input x to its square, which are both real numbers. The output of the function f corresponding to an input x is denoted by f(x) (read "f of x"). If the input is ¿3, then the output is 9, and we may write f(¿3) = 9.
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Continuous function
In mathematics, a continuous function is a function for which, intuitively, "small" changes in the input result in "small" changes in the output. Otherwise, a function is said to be "discontinuous". A continuous function with a continuous inverse function is called "bicontinuous". Continuity of functions is one of the core concepts of topology, which is treated in full generality below.
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Extended finite element method
The extended finite element method (XFEM), also known as generalized finite element method (GFEM) or partition of unity method (PUM) is a numerical technique that extends the classical finite element method (FEM) approach by enriching the solution space for solutions to differential equations with discontinuous functions.
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