[jira] [Created] (MATH-1091) compute signed distance with respect to any BSP tree

["Luc Maisonobe (JIRA)" <ji...@apache.org>]

Luc Maisonobe created MATH-1091:
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             Summary: compute signed distance with respect to any BSP tree
                 Key: MATH-1091
                 URL: https://issues.apache.org/jira/browse/MATH-1091
             Project: Commons Math
          Issue Type: Improvement
    Affects Versions: 3.2
         Environment: all
            Reporter: Luc Maisonobe


BSP tree allow modelling of various complex shapes in Euclidean 1D, 2D and 3D, and now also on the 1-sphere and the 2-sphere. The current API allow to check if a point is located inside the shape, outside the shape, or near the boundary. There is however no way to know if the point is close or far to the shape, there is no continuous value representing this.

It would be interesting to be extend the notion of signed distance (the offset) that is used within BSP trees at cut sub-hyperplane level, in order to have it available at the global shape level.

Users could therefore compute a global offset, and this offset should be positive if the point is outside, negative if the point is inside, and close to zero near the boundary. An important property is that it should be continuous around the boundary so the value can be used in root solvers to converge toward a boundary or to ODE event to detect when a trajectory enters a region.



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