mitral-valve 发表于 2025-3-25 07:07:49
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http://reply.papertrans.cn/59/5854/585323/585323_22.png英寸 发表于 2025-3-25 12:20:02
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柳树;枯黄 发表于 2025-3-25 18:19:02
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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圆柱 发表于 2025-3-26 02:55:52
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 evolutDOTE 发表于 2025-3-26 06:25:18
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 tEntropion 发表于 2025-3-26 10:55:15
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 equVisual-Acuity 发表于 2025-3-26 16:43:18
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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