do Instituto Hidrográfico

70 ANAIS DO INSTITUTO HIDROGRÁFICO N.º 15
this computational environment, assessing data in a
point or along a random contour. From this reason it
was introduced as an output the number of points. If
this number is 1, for any point selected in the area is
provided the depth and as a comparison measure is
given also the location and the value of the maximum
depth in the field (figure 7). If this number is greater can
be generated a path in the field from these points and
can be visualized the bathymetric distribution along it.
In figure 8 is illustrated such a path created by 5 points
and the corresponding bathymetry. It is also available an
enlarged view of the bathymetric distribution where can
be seen in detail the variations along the lines which
compose the created path. For generating the path divisions
was used the solution of varying the steps length
and number on each line of the path. The reference step
will be considered constant for a given bathymetric
configuration and its value will be the minimum of the
grid steps:
d st r = min(DXC1, DYC1). (1)
The reason for this election was that even with a
smaller step the resolution would be the same because
all the interpolations are made anyway between the
points of the grid. Each line is defined by its endpoints
and the length of the j-line will be given by:
Llj = E (x 2j – x lj) 2
+ (y 2j – y lj) 2
, (2)
where (x lj, y lj) and respectively (x 2j, y 2j) are the line end
points. The number of the points on the line will be:
Npj = V (Llj / d st r), (3)
where V is the MATLAB ceil function which rounds the
argument to the nearest greater integer. The new step
for the j-line will be:
d st j = Llj / Npj. (4)
With this step the computational process will
advance in space from the first to the last point of the
line. If the distance between the line endpoints is less
than dst l than on that line this distance will be the step
dst j . The procedure is reinitialized for every line of the
given path.
Reshaping the configuration of the field is another
procedure available in this new computational environment.
The global variables that control the process of
reshaping are: XCO2- the x coordinate of the new origin,
YCO2- the y coordinate of the new origin, XLENC2- the
length of the new grid in x direction, YLENC2- the
length of the new grid in y direction, MXC2- the number
of meshes in x direction and MYC2- the number of
meshes in y direction. To illustrate this process it was
elected another area in the vicinity of the Pinheiro da
Cruz beach. Figure 9 shows the initial grid before
reshaping while in figure 10 is presented the reshaped
grid. In figure 11 can be seen the map of the area and
the location of the reshaped area.
Finally defining the mathematical isolines of the
bottom it is also a process that can be developed using
this interface. In this respect was created a special operator
denoted by:
C = C (wd, k sh, XoX, YoY, ZoZ) (5)
in which wd is the imposed water depth for which is
generated the isoline, k sh is the advanced shore coefficient
which gives the sense of the iteration, if k sh is
greater than wd this will be the positive sense of x axis
and if k sh is less than wd is reversed. For considering the
iteration along the y axis it was used a similar operator
denoted by C * . XoX, YoY and ZoZ are the matrices
giving the x coordinate, y coordinate and respectively
the depth in the grid points. From the way it was defined
is obvious that the above operators can be applied both
for the initial and the reshaped grids. Supposing that
the lines of the grid are parallel with the y axis, which is
also almost parallel to the shore, and the columns are
parallel with the x axis, the algorithm developed find for
any column the grid point with the closer value (of wd).
Then interpolates between the two successive grid
points on the column. In this way the isoline is built
with a single point in any column and will have the
same number of points as a regular line of the grid,
which is a great advantage for the MATLAB environment
where the dimension of vectors and matrices should
correspond.
If no value is found, means that the depth imposed
for the isoline is out of range and in this case the value
is zero if there is a coast side in the area or either zero
or maximum if there isn’t. If the coast is parallel with
the x axis then the iteration is made along the y axis and
it is used the operator C * . In the figures 11 and respectively
12 is presented the way in which can be generated
the isolines in the initial and respectively the reshaped
area, while in figure 13 could be seen the natural
isolines of the bottom. A further option available is to
design automatically an isomap, that is to set the colors
and the distance, in terms of depths, between them as it
showed in figure 14.
Another facility is to work in parallel, simultaneous
on two different windows, with the initial and with the
reshaped grid for both the processes of data assessment
and generating isolines. Although were used the same
programs for the initial and the reshaped grid this was
possible because the system works with two categories
of global variables (that have the index 1 for the initial
surface and the index 2 for the reshaped one). These are
changed alternatively from one case to another.