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about signed distance function

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Hi All, This may sounds a stupid question. I have been working on the level set for some time. I have a basic question about it. I am defining level set function as signed distance on a regular MAC grid. The function itself is defined on the center of the voxel, as shown below in 2D. --------- | | | f | | | --------- Now I also need this function to be signed distance at the centers of faces(3D)/edges(2D), as shown by the question mark below. ----?--- | | | f | | | -------- My question is whether simply interpolating onto the point in question using signed distance values at voxel centers surrounding this point will satisfy the condition that the interpolated values are also signed distance. Thanks, merlin74

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