Fig 1. Painting the 'sinus' grid by a virtual pen. The
mark of the pen is a circular disk
(symbolized by the circles) with D diameter. D is equal to the
width of the 'streets'
(or lines) of
the grid. The trace of the center of the virtual pen is a sine curve; this
is
the middle
line of the street. The distortion level is defined as the
amplitude of the
sine curve
( i.e. the maximal + or - swing from the straight). It can be seen that the
amplitude of
the (upper, lower or left, right) edges of the streets are equal to the
amplitude of the
middle line.
Therefore an equivalent definition: the distortion
level is the amplitude
of the
(upper, lower or right, left) edges of the streets.
N.B.1: The form of the edges is not sine wave; only the middle line
is sine wave.
N.B.2: If the amplitude of a sine wave is 1, then it swings between -1 to
+1.
Fig 2. Painting the 'wave' grid by a virtual pen. The
mark of the pen is a circular disk
(symbolized by the circles) with D diameter. D is equal to the
width of the 'streets' of
the grid. The trace of the center of the virtual pen (i.e. the middle line
of the street)
consists of two straight
lines and a sine curve with one period.
The distortion
level is defined as the amplitude of the sine curve (i.e. the
maximal + or - swing from
the straight). It can be seen that the amplitude of the (upper,
lower or left, right)
edges of the streets are equal to the amplitude of the middle line.
Therefore an
equivalent definition: the distortion level is the
amplitude of the (upper, lower or
right, left) edges of the streets.
Fig 3. Painting the 'hump' grid by a virtual pen. The
mark of the pen is a circular disk
(symbolized by the circles) with D diameter. D is equal to the
width of the 'streets' of
the grid. The trace of the center of the virtual pen (i.e.the
middle line of the street )
consists of two straight
lines and a 'hump'. The distortion
level is defined as
the amplitude of the middle line; i.e. the maximal + swing from the
straight).
It can be seen that the amplitude of the (upper or right) edges
of the streets are
equal to the amplitude of the middle line. Therefore an equivalent
definition: the
distortion level is the amplitude of the upper or right edges of the streets.
Fig 4. The "half hump'
grid. It was generated from the 'hump' grid (see Fig 3) by
replacing the lower (or left) curve by a straight edge segment.
The
distortion level is defined as the distortion level of the
original 'hump' grid.
Fig 5. The 'asymmetrical
hump' grid. It was generated from the 'hump' grid (see fig 3),
by mirroring its lower (or left) curve along the edge of the
street.
The distortion
level is defined as the distortion level of the original 'hump' grid.
Fig 6. Painting the 'knot' grid. There are painted
elliptical 'balls' in the middle part of
the street segments The distortion level is defined
as the amplitude of the
(upper, lower or right, left) edges of the streets. |