10 Extension of the Monogenic Phasor Method to Extract Displacements and Their Derivatives from 3-D Fringe Patterns 65 Fig. 10.3 (a) Displacement vector dp in the 3-D space; (b) projections of the displacement vector in the plane x1-x2, at successive times; (c) projections of the vector dp and corresponding angles Fig. 10.4 Large deformations of a vessel taken in a time sequence. Time t D0 corresponds to the reference configuration in this example, the time t corresponding to different recordings. Because the planes are fixed to the body’s material, the correspondence among volume elements can be obtained due to the parametrization of the planes with orders that are preserved in the deformation course. A matter of notation, we consider real- or complex-valued functions f(x) defined on<n, where n is an orderly list of integers. Ordinary case letters will represent scalar quantities, bold letters will represent vectorial quantities and we will write f(x) or f(x1,...,xn), the bold lower case indicating a vector quantity or we will list the low cases variables whichever is more convenient in context. The following notation will be utilized, fi(x) are functions of x and the index “i” will take the values, i D1,2,3.
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