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Solving Spatial Constraints with Generalized Distance Geometry

In: Distance Geometry

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  • Lu Yang

    (East China Normal University, Shanghai Key Laboratory of Trustworthy Computing)

Abstract

This is a short survey about how to use a generalization of distance geometry to solve spatial constraints. Described first are definitions and some basic theorems in the generalized distance geometry, and a systematic approach for the solution of spatial constraints follows, making use of results of the previous section. An intrinsic coordinate system based on geometric invariants, named distance coordinate system, is established for simplification and algorithmization to the process of constraint solving. A short program is proposed, which implements the algorithm producing automatically a complete set of constraint equations for a given point-plane configuration, and the point-line-plane configurations are converted into point-plane ones beforehand. The so-called nontypical constraint problem is considered in the last section and illustrated by an example, which the previous method seems unable to help.

Suggested Citation

  • Lu Yang, 2013. "Solving Spatial Constraints with Generalized Distance Geometry," Springer Books, in: Antonio Mucherino & Carlile Lavor & Leo Liberti & Nelson Maculan (ed.), Distance Geometry, edition 127, chapter 0, pages 95-120, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-5128-0_6
    DOI: 10.1007/978-1-4614-5128-0_6
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