Horea T. Ilies

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As an innnite union operation, sweep of a moving object through space is a powerful and natural addition to the Boolean set operations that incorporates motion-related information for the purposes of shaping, collision detection, and simulation of moving objects. Use of sweep has been hindered by limited computational support and by the fact that it is a(More)
The mathematical envelopes to families of both rigid and non-rigid moving shapes play a fundamental role in a variety of problems from very diverse application domains, from engineering design and manufacturing to computer graphics and computer assisted surgery. Geometric sin-gularities in these envelopes are known to induce malfunctions or unintended(More)
Shape skeletons are fundamental concepts for describing the shape of geometric objects, and have found a variety of applications in a number of areas where geometry plays an important role. Two types of skeletons commonly used in geometric computations are the straight skeleton of a (linear) polygon, and the medial axis of a bounded set of points in the(More)
We i n troduce and formally deene a new geometric mod-eling operation unsweep(EEM) which, given an arbitrary n-dimensional subset of Euclidean space E and a general motion M, returns the subset of E that remains inside E under M. This new operation is dual to the usual sweeping operation and has important applications in mechanical design. When M is a(More)
The rise of solid modeling as a principal medium for mechanical product description can be traced to the requirement of informational completeness of geometric representations. Unfortunately, traditional geometry-based systems do not contain important information needed for many engineering activities and tend to force costly iterations in a product(More)
The synthesis of functional molecular linkages is constrained by difficulties in fabricating nano-links of arbitrary shapes and sizes. Thus, the classical mechanism synthesis methods, which assume the ability to manufacture any designed links, cannot provide a systematic process for assembling such linkages. We propose a new approach to build functional(More)
• We propose a grid-free discretization scheme for analytic geometric modeling. • Solids are approximated with countable unions of 3D balls cut from 4D cones. • The unions turn into 3D slices of 4D Minkowski sums of knots and a template cone. • The Minkowski formulation embeds well into cross-correlations between solids. • The analytic formulation follows(More)