Pawel Boguslawski

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This work presents new operators for construction of 3D cell complexes. Each cell in a complex is represented with the Augmented Quad-Edge (AQE) data structure. Cells are linked together by the dual structure and form a mesh. This structure stores information about the geometry and topology of a modelled object. Navigation in the mesh is possible using(More)
This work presents the Dual Half Edge (DHE) structure and the associated construction methods for 3D models. Three different concepts are developed and described with particular reference to the Euler operators. All of them allow for simultaneous maintenance of both the primal and dual graphs. They can be used to build cell complexes in 2D or 3D. They are(More)
Recent advances in theoretical methods combined with the advent of massively parallel supercomputers allow one to reliably simulate the properties of complex materials and device structures from first principles. We describe applications in two general areas: i) novel polymer composites for ultra-high-density capacitors, necessary for pulsed-power(More)
There is an increasing need for building models that permit interior navigation, e.g., for escape route analysis. This paper presents a non-manifold Computer-Aided Design (CAD) data structure, the dual half-edge based on the Poincaré duality that expresses both the geometric representations of individual rooms and their topological relationships. Volumes(More)
Buildings are often modelled as two-dimensional (2D) footprints which are extruded to simple cubes. Buildings are also represented as more complex objects with roofs, facades, etc. – in this case they are polyhedra, sometimes of a complex shape. These allow for visualisation and analysis of a wide area like a city, but micro-scale analysis of interiors is(More)
This work presents the new attitude towards the construction and manipulation of 3D cells complexes, stored in the augmented quad-edge (AQE) data structure. Each cell of a complex is constructed using the usual quad-edge structure, and the cells are then linked together by the dual edge that penetrates the face shared by two cells. We developed the new set(More)
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