61 Rigidity and Scene
نویسندگان
چکیده
The rigidity of frameworks examines points constrained by fixed distances between pairs of points, using vocabulary and linear techniques drawn from structural engineering: bars and joints, first-order rigidity and first-order flexes, and static rigidity and static self-stresses (Section 61.1. Section 61.2 describes some extended structures and their applications. Scene analysis and the dual concept of parallel drawings are described in Section 61.3. Finally, Section 61.4 describes reciprocal diagrams which form a fundamental geometric connection between liftings of polyhedral pictures and self-stresses in frameworks which continue to be used in structural engineering. These core problems have a wide range of applications across many areas of applied geometry. The methods used and the results obtained for these problems serve as a model for what might be hoped for other sets of constraints (plane firstorder results) and as a warning of the complexity that does arise (higher dimensions and broader forms of rigidity). The subject has a rich history, stretching back into at least the middle of the 19th century, in structural and mechanical engineering. Other independent rediscoveries and connections have arisen in crystallography and scene analysis. The range of constraints and applications has continued to expand over the last two decades. For more general geometric reconstruction problems, see Chapter 34.
منابع مشابه
61 Rigidity and Scene Analysis
spherical polyhedron S = (V, F ;E): For a 2-connected planar graph GS = (V,ES), embedded on a sphere (or in the plane), we record the vertices as V and the regions as faces F , and rewrite the directed edges E as ordered 4-tuples e = 〈h, i; j, k〉, where the edge from vertex h to vertex i has face j on the right and face k on the left. (The reversed edge −e = 〈i, h; k, j〉 runs from i to h, with ...
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