Alternatively, a polar coordinate system
can be used for targeting, with the needle angled slightly upwards as opposed to perpendicular in the Cartesian coordinate system.
Similarly, in Table II, there are relative changes of parameters of the considered indices when SE is realized in the polar coordinate system
. The mentioned changes of the parameters of the considered indices characterizing properties of PSSE are calculated using formula: [DELTA][p.sub.X] = 100([p.sub.X,S] - [p.sub.X,S-])/ [p.sub.X,S-], where [p.sub.X,S], [p.sub.X,S-] are parameters of index X, when SE is performed for PS with or without PhS, respectively.
* polar coordinate system
[tau], [theta] in a two-dimensional space);
Polar coordinate transformation is similar to Cartesian coordinate transformation, it firstly establishes the polar coordinate system
with the center point as the midpoint and the direction of the center point as the positive direction, then divides the fingerprint image into many segments, and each segment is divided into many small blocks.
, as the original data is in the polar coordinate system
, an interpolation method was utilized to transform the polar coordinate system
into the three-dimensional Cartesian coordinate system.
Firstly, a transformation of the rectangular coordinate geometry into a series of local polar coordinate systems
is devised as depicted in Figure 2, in which the first local polar coordinate system
is set as in Figure 1; thus, every geometric center of machines is set as a local polar origin, and their local polar axes are directed as x-axis.
Bear  proved that if r = [K.sub.q.sup.1/2] or r = [K.sub.j.sup.-1/2] in the polar coordinate system
, mapping can form an ellipse (under the condition of three-dimensional ellipsoid), where r represents radius vector, [K.sub.q] represents permeability coefficient in the direction of the flow line, and [K.sub.j] represents permeability coefficient in the direction of the hydraulic gradient.
Then we turn to the polar coordinate system
such that [x.sup.*.sub.[phi]] = 0 (Figure 3) and we assume that values of all angles satisfy -[pi] < [a.sup.i.sub.[phi]] [less than or equal to] [pi] (the case [a.sup.i.sub.[phi]] = 0 is excluded since [x.sup.*.sub.[phi]] [not equal to] [a.sup.i.sub.[phi]]).
From the periodicity of limit cycle and the property of polar coordinate system
, we know that the conclusion of the lemma is true.
This block treats [[??].sub.pi,l(n)] as amplitude variation [alpha] and phase shift [DELTA][theta] in a polar coordinate system
in order to enable microvariations to be easily calculated.
The resulting coordinate values can be stored in a table and drawn in the plane equipped with the polar coordinate system
. GeoGebra is a very convenient tool with which to do so.
The radius e of the trajectory of centre [O.sub.2] of roundness measure and polar angle [alpha] in polar coordinate system
are described by the equations