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Contour advection is a Lagrangian method of simulating the evolution of one or more contours or isolines of a tracer as it is stirred by a moving fluid. Consider a blob of dye injected into a river or stream: to first order it could be modelled by tracking only the motion of its outlines. It is an excellent method for studying chaotic mixing: even when advected by smooth or finitely-resolved velocity fields, through a continuous process of stretching and folding, these contours often develop into intricate fractals. The tracer is typically passive as in 〔 〕 but may also be active as in,〔 〕 representing a dynamical property of the fluid such as vorticity. At present, advection of contours is limited to two dimensions, but generalizations to three dimensions are possible. ==Method== First we need a set of points that accurately define the contour. These points are advected forward using a trajectory integration technique. To maintain its integrity, points must be added to or removed from the curve at regular intervals based on some criterion or metric. The most obvious criterion is to maintain the distance between adjacent points within a certain interval. A better method is to use curvature since fewer points are required for the same level of precision. The curvature of a two-dimensional, Cartesian curve is given as: : where is the radius of curvature and is the path. We need to keep the fraction of arc traced out between two adjacent points, , where is the path difference between them, roughly constant In,〔 〕 cubic spline fitting is used both to calculate the curvature and interpolate new points into the contour. The spline, which is fitted parametrically, returns a set of second-order derivatives. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Contour advection」の詳細全文を読む スポンサード リンク
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