BSP-fields: An exact representation of polygonal objects by differentiable scalar fields based on binary space partitioning

The problem considered in this work is to find a dimension independent algorithm for the generation of signed scalar fields exactly representing polygonal objects and satisfying the following requirements: the defining real function takes zero value exactly at the polygonal object boundary; no extra zero-value isosurfaces should be generated; C1C1 continuity of the function in the entire domain. The proposed algorithms are based on the binary space partitioning (BSP) of the object by the planes passing through the polygonal faces and are independent of the object genus, the number of disjoint components, and holes in the initial polygonal mesh. Several extensions to the basic algorithm are proposed to satisfy the selected optimization criteria. The generated BSP-fields allow for applying techniques of the function-based modeling to already existing legacy objects from CAD and computer animation areas, which is illustrated by several examples.

Research highlights
► A new algorithm for the construction of the well-formed set-theoretic representation for the given polygonal object.
► An algorithm for the procedural scalar field evaluation at the given point.
► Several extensions to the basic algorithms to satisfy the optimization criteria.