Knots and Links As Form-Generating Structures
Practical modeling of spatial surfaces is more convenient by means of transformation of their flat developments made as topologically connected kinetic structures. Any surface in 3D space topologically consists of three types of elements: planar facets (F), linear edges (E) and point vertexes (V). It is possible to identify the first two types of these elements with structural units of two common types of transformable systems: folding structures and kinematic nets respectively.
In the paper a third possible type of flat transformable structures with vertexes as form-generative units is considered. In this case flat developments of surfaces are formed by arranged point sets given by contacting crossing points of some classes of periodic knots and links made of elastic-flexible material, so that their crossing points have real physical contacts. A fragment of plane point surface can be reversibly converted into a fragment of a spatial surface with positive, negative or combined Gaussian curvature by means of transformation which saves connectivity between the points, but not the distances and angles between them. It was proved experimentally that this new form-generative method can be applied to modeling of both oriented and non-oriented differentiable topological 2D manifolds. The method of form-generation based upon the developing properties of periodic structures of knots and links may be applied to many practical fields including art, design and architecture.
KeywordsGaussian Curvature Point Surface Nodus Structure Torus Surface Coil Turn
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