Integration algorithm used in the function stream3?

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Ana Cadavid 2017-8-11

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https://ww2.mathworks.cn/matlabcentral/answers/352368-integration-algorithm-used-in-the-function-stream3

评论： Walter Roberson 2017-8-14

What is the integration algorithm used in the function stream3 to calculate the streamline coordinates (Euler ?, Runge-Kutta?, what order?). I need to report this in a paper for a description on how the results have been obtained.

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Ana Cadavid 2017-8-14

Thank you for your reply. Are you sure? The input is a 3d vector space which gives the direction in which the streamline will go. This implies some type of integration. Thanks again

Walter Roberson 2017-8-14

Using the definition from https://en.wikipedia.org/wiki/Streamlines,_streaklines,_and_pathlines that,

"Streamlines are a family of curves that are instantaneously tangent to the velocity vector of the flow. These show the direction in which a massless fluid element will travel at any point in time"

then given non-uniformly sampled 3D data and a sampling point, the processing could be to use interpolation on each of the U, V, W components, and calculate the surface normals. The interpolation from scattered coordinates could require Convex Hull or Delaunay Triangulation methods to figure out which are the influencing points for any one location to be interpolated at, but once those are known, probably a method such as bilinear interpolation would be used. I do not see any role for integration in this, unless you want to phrase linear interpolation in terms of integration.

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