Geometric relationships between toleranced features
Artificial Intelligence - Special issue on geometric reasoning
Minkowski addition of polytopes: computational complexity and applications to Gro¨bner bases
SIAM Journal on Discrete Mathematics
Algorithmic geometry
Accurate Minkowski sum approximation of polyhedral models
Graphical Models - Special issue on PG2004
Minkowski sum boundary surfaces of 3D-objects
Graphical Models
Exact and efficient construction of Minkowski sums of convex polyhedra with applications
Computer-Aided Design
Covering Minkowski sum boundary using points with applications
Computer Aided Geometric Design
Contributing vertices-based Minkowski sum computation of convex polyhedra
Computer-Aided Design
Discrete & Computational Geometry - 23rd Annual Symposium on Computational Geometry
On the Exact Maximum Complexity of Minkowski Sums of Polytopes
Discrete & Computational Geometry
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Prompted by the development of algorithms for analysing geometric tolerancing, this article describes a method to determine the Minkowski sum for 3-dimensional polytopes. This method is based exclusively on intersection operations on normal cones, using the properties of the normal fan of a Minkowski sum obtained by common refinement of the normal fans of the operands. It can be used to determine from which vertices of the operands the vertices of the Minkowski sum derive. It is also possible to determine to which facets of the operands each facet of the Minkowski sum is oriented. The basic properties of the algorithms can be applied to n-polytopes. First, the main properties of the duality of normal cones and primal cones associated with the vertices of a polytope are described. Next, the properties of normal fans are applied to define the vertices and facets of the Minkowski sum of two polytopes. An algorithm is proposed, which generalises the method. Lastly, there is a discussion of the features of this algorithm, developed using the OpenCascade environment.