Titlebook: Level Set Methods and Dynamic Implicit Surfaces; Stanley Osher,Ronald Fedkiw Textbook 2003 Springer-Verlag New York, Inc. 2003 computer gr

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Stanley Osher,Ronald Fedkiwtels etwas anderer Art sind, erscheint es angebracht, schon vorher gewisse Betrachtungen anzustellen, welche Sinn und Tatsachenwert des Mitgeteilten gegen geläufige Einwände schützen. Dergleichen wäre nicht nötig, wenn es sich hier um Feststellungen einer hochentwickelten Erfahrungswissenschaft wie

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Signed Distance Functionse boundary ∂Ω. Little was said about . otherwise, except that smoothness is a desirable property especially in sampling the function or using numerical approximations. In this chapter we discuss signed distance functions, which are a subset of the implicit functions defined in the last chapter. We d

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Motion in an Externally Generated Velocity Field 0. Given this velocity field V↦ ., we wish to move all the points on the surface with this velocity. The simplest way to do this is to solve the ordinary differential equation (ODE) . for every point V↦ on the front, i.e., for all V↦ with .(V↦) = 0. This is the . formulation of the interface evolut

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Motion Involving Mean Curvaturemotion for a self-generated velocity field (x↦ that depends directly on the level set function .. As an example, we consider motion by mean curvature where the interface moves in the normal direction with a velocity proportional to its curvature; i.e., V↦ = -.N↦, where . > 0 is a constant and . is t

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Hamilton-Jacobi Equations three spatial dimensions, we can write . as an expanded version of equation (5.1). Convection in an externally generated velocity field (equation (3.2)) is an example of a Hamilton-Jacobi equation where .(∇..;↦ ·∇.. The level set equation (equation (4.4)) is another example of a Hamilton-Jacobi equ

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Extrapolation in the Normal Direction be used to propagate information in the direction of these characteristics. For example, . (8.1) is a Hamilton-Jacobi equation (in . that extrapolates . normal to the interface, i.e. so that . is constant on rays normal to the interface. Since ., we can solve this equation with the techniques prese