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To define the boundaries between layers, we use a signed distance
field which is a continuous scalar function defined throughout the
volume. Often the value of the function is simply the distance to the
nearest point on the primary surface, with opposite signs on opposite
sides of the surface.
We can efficiently compute the value of the function at each point on a uniform grid (shown in the top image) using the Level Sets Fast Marching Method developed by Sethian. All points with value v define the v-isosurface and we can extract this isosurface using Marching Cubes or similar techniques. The signed distance field prevents self-intersection problems, seamlessly handles changes in topology, and places no restrictions on layer thickness, as illustrated in the bottom image. | ||