Abstract
A recurring problem in solid modeling, computer graphics, and molecular modeling is the computation of the intersection of two objects. A general solution to this problem is obtained by applying two ideas of algebraic topology: (1) a chain complex, and (2) a boundary formula for the intersection of two objects. A general data structure for a chain complex made up of piecewise polynomial cells is described, as are algorithms for connectivity, containment and intersection. The basic ideas of this work are abstract, topological, and for the most part, independent of the shape and dimensionality of the objects. An application to structural molecular biology is presented. The application identifies convex and concave features of protein surfaces.
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Connolly, M.L. An application of algebraic topology to solid modeling in molecular biology. The Visual Computer 3, 72–81 (1987). https://doi.org/10.1007/BF02153663
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DOI: https://doi.org/10.1007/BF02153663