Introduction

Having digitized the outer limit line as described in the documentation Outer Limit Line Generation will normally result in a line that still can be optimized with regard to the delineation rules of the new boundary. All bays in the derived line can optionally be shortcutted with a new line up to 60 nautical mile length. These shortcut lines will increase the area between the baseline of the country and the new outer limit line. There are several ways to shortcut a bay in a legal way, but only one solution that maximizes the area. A set of algorithms have been developed to handle the maximizing procedure.

In this section:

Menu for maximizing the outer limit line

The outer limit line has schema Limit Line and a command Maximize outer limitis provided on this schema for doing the maximizing.

Menu for maximizing the area within the outer limit line

Cursor positions

The algorithms for maximizing the area is based on an interactive communication with the user. It is necessary for the user to decide which type of updating procedure is used for the different bays along the line.

The interactive control is through placing the cursor correctly at two or three positions and then push the corresponding button in the menu. The screen should preferably be in 2D mode for easy cursor use by just clicking with the left mouse button. In the following text we shall discuss the various cases of algorithms and the use of different cursor positions.

NB! Cursor positions used in this menu are always placed before any menu action. One can check the actual cursor positions by the appropriate buttons on the top of the menu.

One can also check the 60 nautical mile circle by marking a cursor position and then push Show. This should be used extensively throughout the task to get a visual orientation about which updating algorithm to be used.

Each algorithm has a brief explanation and a picture that can be activated in the menu. Use this to get familiar with the different cases and as a guide to select the right algorithm for the various bays in the curve. The process of updating the new outer limit line is in principle straight forward and easy to follow, but mistakes can be done. Only when correct steps and algorithms are applied that give the disired result one should update the line.

Starting procedure

The digitized line coming from digitizing the outer limit line is usually called Digitized outer limit. This line should be saved in its original form and kept as a backup. Then make a copy of the original dataset and start working on the copy by activating the command object on that dataset which then will be input to all calculations. All updates on the outer limit line will be to this copy, the backup dataset will be safe, and further input to the algorithms will be from the copy

Displaying and saving updates

After a calculation one can choose between three display and save options:

Options for display and saving of updates

New outer limit line
Maximum area gained
New line segment

Select the proper option and display the data. It is important to get a visual impression how the updating has performed before deciding to save the new outer limit line. If the updating is not satisfactory due to maybe improper settings of the cursor positions or the algorithm used was not fitted for this part of the curve, redo the calculation with different cursor settings or another algorithm.

When everything seems to be correct then take action to save the new generated line. Reset the combo box to the text New outer limit line and push Save data in project. The saving is always to the same dataset in the project so be sure to start any maximizing by using a copy of the original dataset as explained before.

Two types of bays

The definition of a bay is a part of the line that is enclosed by the tangent across the line and the curve under the tangent.

The maximizing menu differs between two type of bays:

Bays that are wider than 60 mile. This type of bays can be shortcutted with one or more lines of maximum length 60 mile.
Bays that are lower than 60 mile. This type of bay is always shortcutted with a line less than 60 mile.

The bay in the next picture is the large bay that is about 90 mile long, while the bay in the picture below is the small bay at the lower start point of the line to be maximized.

The large bay is longer than 60 mile and has to be drawn with two shortcut lines to maximize the area. It is just an illustration of the bay that a single line is drawn. The two lines solution is found further down in Large bay shortcutted with two lines.

A bay is the part of the line under the tangent. This bay is about 90 mile long.

This bay is less than 60 mile

Large bay shortcutted with one 60 mile line

The work task started in the lower part of the line. The first large bay to analyze (see picture at right) was seen to fit for one shortcut line. The 60 mile circle* was drawn in the middle of the bay for control. Two cursor positions was placed on each side of the bay. The Show button displayed the number 1 for the first position and 2 for the second position. To find the shortcut line that maximizes the area underneath the line indicated with two cursor positions, press button Calculate under the text Use two cursor positions to maximize the outer limit across a bay with a 60 NM line.

Large bay shortcutted with one line

The new line segment (the shortcut line) was displayed and also the area underneath. The size of the area is listed in the menu.

The picture to the right shows the same bay with the 60 mile circle to control the new line segment. It has a perfect match and this line is also the line that maximizes the area of the bay within all the possible shortcut lines. The algorithm for finding the optimized line is done between the two cursor positions. If looking fine do the saving as in Displaying and saving updates.

Large bay shortcutted with one line

Large bay shortcutted with two lines

The next major bay is so large that one visually may see that the optimized shortcut is done by two lines. Although one single line of 60 mile in the bottom of the bay could have been drawn, one sees immediately that a more optimized situation is to draw two lines as shown in the picture to the right.

The procedure this time is to first mark the cursor position for the 60 mile circle and push Show 60 NM circle at cursor position.

Large bay shortcutted with two lines

Then mark the curve with three cursor positions as indicated. Then visualize the cursor positions pushing Show last three cursor positions. When everything is correct do the maximizing by pushing Calculate under the text Maximizing outer limit line using three cursor positions. Then draw the new outer limit line, optionally the area underneath. Visualization and saving are explained in Displaying and saving updates.

The algorithm tries out various positions for the placement of the line into the middle of the bay. The position that maximizes the area is selected.

Large bay shortcutted with two lines

Large bay shortcutted with one line

The next large bay is a type of bay that one can see is optimized by one line. Mark the cursor position for the 60 mile circle and push Show 60 NM circle at cursor position to get a visual impression of the bay and which algorithm to use. Then mark the curve with two cursor positions as indicated. Then visualize the cursor positions pushing Show last two cursor positions.

arge bay shortcutted with one line

When everything is correct do the maximizing by pushing Calculate under the text Use two cursor positions to maximize the outer limit across a bay with a 60 NM line. Visualization and saving are explained in Displaying and saving updates.

Large bay shortcutted with one line

Large bay cut short with two lines

The next case is similar to to the case Large bay shortcutted with two lines. Three cursor positions have to be placed before pushing Calculate under the text Maximizing outer limit line using three cursor positions. Again the algorithm uses the middle point of the cursor positions (position 2) as a starting point for varying the middle point to each side for finding the position that gives maximum area gained. The curve at position 1 and 3 will always be the tangent to the curve.

Large bay shortcutted with two lines

One can manually try other positions and get the area underneath with no maximizing and variation to see it clearly by using the Calculate under the text Calculate outer limit line using three cursor positions. All positions should give an area size lower than the one calculated using the maximize algorithm.

Large bay shortcutted with two lines

Specifying the land side direction

If everything has gone fine until now and the new outer limit line is saved properly the next picture shows the original line together with the segments of the new line. Closer inspection of the line reveals many small bays less than 60 mile. All these bays can ideally be optimized with shortcut lines that are tangents to the curve. This optimization is done automatically by one algorithm found under the menu tab Maximize bays lt 60 NM.

Original and new outer limit line

For this algorithm to work it is necessary to specify the land side direction so it will cut small bays on the correct side. Place the first cursor position at the curve and the next at the land side as shown in the next picture. Push Show last two cursor positions to see that it is correct. Then push First cursor on curve and second on land side under the text Show land direction to the left or right of curve by using two cursor positions to set the land side direction.

Specifying land side direction

Tangent lines less than 60 mile

Having set the correct land side direction it is now time to calculate the shortcut line for all the smaller bays. The bays are shortcutted with tangent lines as shown in the next two pictures. The menu has two options for applying this algorithm, either for the whole line, or for part of the line determined by two cursor positions.

Detail of tangent line of small bay

In this case we apply the algorithm for the whole line and push Calculate under the text Maximizing outer limit for bays lower than 60 NM for the whole line. The result can be displayed and saved as usual in Displaying and saving updates.

With this operation the whole line is now optimized with respect to shortcut lines that maximize the area underneath the curve within the rules of delineation.

Detail of tangent line of small bay

Maximizing remarks

The detailed procedure for optimizing the outer limit line with respect to get a maximized area is an option to the users of Geocap. It is based on computer generated algorithms that has the digitized outer limit line as input.

The next picture shows what happens if one runs the automatic optimizing algorithm (the previous case) on the original line. It apparently creates a good optimization. However, the algorithm only analyzes bays less than 60 mile and creates the maximized solution for those bays. The picture below shows what happens in larger bays. This is a detailed study of the automatic optimized line versus the controlled optimized line which is the correct one.

Optimizing run on the original line

The picture to the right also shows that all new segments that have to be generated must start at a curve point. It can however end at a new generated point at maximum 60 mile length. But the message is that there shall be a fairly good resolution in the outer limit curve in order to have the maximization as correct as possible within practical limits.

A line can be resampled to a new resolution with the command mak lin dis new_distance exact. This will only interpolate between the original points and may be satisfactory when the resolution is already adequate and the points have been generated geodetic correct originally.

Automatic versus controlled optimizing

Maximizing western outer limit

The digitized outer limit for the western part was handled in two passes as shown in the two next pictures. Notice that the search for small bays in the second picture was done using two cursor positions in order to avoid the area where the outer limit curve had been generated by the outermost points of the 1% sediment thickness lines.

Although not directly visible the semi automatic routine for searching small bays found two places where the outer limit curve can be shortcutted by tangent lines.

Large bay maximized using three positions

Small bay at top maximized using two positions

The trimming of the eastern and western outer limit line is now finished in its first edition. It may not be the final solution because one may redo lines and resolution and work through the procedure over again. Eventually everything will look fine and the optimized new outer limit line is established.

Summary

The picture to the right shows the new outer limit area as a shaded display in the overview map. The process is explained in detail and will ultimately lead to the outer limit line as shown. To make everything correct along the work path is also a matter of training and practice to master the technical elements that is necessary for deriving at a good result.

It may happen that there are cases in other outer limit projects that will require special attention and traditional delineation. The algorithms presented here is just an offer to be used when suitable and appropriate. In general the described features should cover many typical projects that have bays in the outer limit line similar to the Atlantis project. To decide the best shortcut choice across a bay is a challenge and it is natural to look for program assistance for the calculations.

The final goal is to determine the new outer limit line and the algorithms for maximizing the area should be a helpful tool in the computational work.

Overview display of maximized area within the outer limit line

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