Articles you may be interested inOn the value of geometric algebra for spacetime analyses using an investigation of the form of the self-force on an accelerating charged particle as a case study Am. An extension of the classical theory of algebraic invariants to pseudo-Riemannian geometry and Hamiltonian mechanicsThe completely dual approach to Clifford algebra is used to enlarge the concept of the projective split and to develop a new geometric representation for the Pauli algebra ͑space and counterspace͒, for the momenta ͑planelike vectors͒, and for the phase space. The Pauli algebra appears in this context as the phase space extended by time ͑scalar͒ and energy ͑pseudoscalar͒. Lagrangian and Hamiltonian mechanics are embedded into the dual framework of space and counterspace. Several examples illustrate the new techniques. The dual approach to mechanics provides a new possibility to interpret symplectic geometry.Ϫ , it seems to complicate the presentation unnecessarily. But only on the base of the completely dual approach to geometric algebra and its plus-minus notation is it possible to introduce and express the con-6996
Photographs of mistletoe (Viscum album L.) berries taken by a permanently fixed camera during their development in autumn were subjected to an outline shape analysis by fitting path curves using a mathematical algorithm from projective geometry. During growth and maturation processes the shape of mistletoe berries can be described by a set of such path curves, making it possible to extract changes of shape using one parameter called Lambda. Lambda describes the outline shape of a path curve. Here we present methods and software to capture and measure these changes of form over time. The present paper describes the software used to automatize a number of tasks including contour recognition, optimization of fitting the contour via hill-climbing, derivation of the path curves, computation of Lambda and blinding the pictures for the operator. The validity of the program is demonstrated by results from three independent measurements showing circadian rhythm in mistletoe berries. The program is available as open source and will be applied in a project to analyze the chronobiology of shape in mistletoe berries and the buds of their host trees.
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