The six-dimensional space SE(3) is traditionally associated with the space of configurations of a rigid solid (a subset of Euclidean three-dimensional space R3). But a solid itself can be also considered to be a set of configurations, and therefore a subset of SE(3). This observation removes the artificial distinction between shapes and their configurations, and allows formulation and solution ...

We describe a configuration space visualization program for mechanical design. Configuration space is a geometric representation of mechanical function that encodes Quantitative information, such as part motions, and qualitative information, such as system failure modes. The program helps designers elucidate the qualitative information, which appears as geometric properties of the configuration...

We describe configuration space visualization methods for mechanical design. Configuration spaces are geometric representations of mechanical function that encode quantitative information, such as part motions, and qualitative information, such as system failure modes. Visualization tools help designers elucidate the qualitative information, which appears as geometric properties of the configur...

Given a configuration C of geometric objects in R2 (called the input configuration), a target configuration T of geometric objects in R1, and a class S of allowable sectioning lines we consider in this paper many variations on the following problem: ‘Is there a line S ∈ S such that the section S ∩ C is equivalent by rigid motion to the target T ?’ Mathematics Subject Classifications (2000): 68Q...

An implicit unsteady upwind solver including a mesh motion approach was applied to simulate a helicopter including body, main rotor and tail rotor in hover flight. The discretization was based on a second order finite volume approach with fluxes given by the Roeand#39;s scheme. Discretization of Geometric Conservation Laws (GCL) was devised in such a way that the three-dimensional flows on arbi...

An important problem in geometric reasoning is to find the configuration of a collection of geometric bodies so as to satisfy a set of given constraints. Recently, it has been suggested that this problem can be solved efficiently by symbolically reasoning about geometry using a degrees of f r e e d o m analysis. The approach employs a set of specialized routines called plan fragments that speci...

An (nk)-configuration is a set of n points and n lines in the projective plane such that their point – line incidence graph is k-regular. The configuration is geometric, topological, or combinatorial depending on whether lines are considered to be straight lines, pseudolines, or just combinatorial lines. We provide an algorithm for generating, for given n and k, all topological (nk)-configurati...