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A method of constructing phyllotaxically arranged modular models by partitioning the interior of a cylinder or a cone

Stępień C.

Machine Graphics and Vision

2014

Vol. 23, No. 1/2

21--36

The paper describes a method of partitioning a cylinder space into three-dimensional subspaces, congruent to each other, as well as partitioning a cone space into subspaces similar to each other. The way of partitioning is of such a nature that the intersection of any two subspaces is the empty set. Subspaces are arranged with regard to phyllotaxis. Phyllotaxis lets us distinguish privileged directions and observe parastichies trending these directions. The subspaces are created by sweeping a changing cross-section along a given path, which enables us to obtain not only simple shapes but also complicated ones. Having created these subspaces, we can put modules inside them, which do not need to be obligatorily congruent or similar. The method ensures that any module does not intersect another one. An example of plant model is given, consisting of modules phyllotaxically arranged inside a cylinder or a cone.