Abstract:
A system and method for label placement is disclosed that achieves the twin goals of practical efficiency and high labeling quality by employing cartographic heuristics. A caller defines map and label properties. Then labels are pulled within a map boundary. Labels are next ordered by priority in descending importance. The order of testing labels is determined. Attempts are made to move overlapping labels. This is an iterative process; therefore there must be criteria that halt the procedure. Upon reaching an acceptable solution, the label properties are adjusted to reflect the new label placements.

Description:
FIELD OF THE INVENTION  
         [0001]    The present invention relates to a computer-implemented method and apparatus for automatically labeling maps or graph layouts in accordance with predefined label criteria.  
         BACKGROUND OF THE INVENTION  
         [0002]    Maps include geographic drawings showing countries, cities, rivers, bodies of water, mountains, and other features of interest. Labeling cartographic features is a fundamental part of map-making. Placing each label optimally with respect to its corresponding feature invariably produces labels overlapping each other or too close to each other. As this results in confusion and unacceptable maps, methods to reposition labels or not draw them at all must be used to create a map that conveys as much information as possible.  
           [0003]    Tagging graphical objects with text labels is a fundamental task in the design of many types of informational graphics. This problem is seen in its most essential form in cartography, but it also arises frequently in the production of other informational graphics such as scatter plots. The quality of a labeling is determined essentially by the degree to which labels obscure other labels or features of the underlying graphic. The goal is to choose positions for the labels that do not give rise to label overlaps and that minimize obscuration of features. Construction of good labeling is thus a combinatorial optimization problem, which has been shown to be NP-hard (Marks and Shieber, 1991). As a hypothetical baseline algorithm, randomly choosing positions for each label generates poor labeling, both aesthetically, and as quantified using a metric that counts the number of conflicted labels, i.e., those that obscure point features or other labels.  
           [0004]    In addition to geographical and technical maps, there are many labeling applications relating to graph layouts and drawings. These applications include, but are not limited to, areas such as database design (e.g. entity relationship diagrams), software engineering including CASE, software debugging, complex web pages, CAD drafting, complex electrical diagrams, and telecommunications and communications networking. In fact, the labeling of the graphical features of any drawing is generally necessary because it conveys information essential to understanding the drawing. For complex and information rich drawings, computer aided labeling is increasingly employed.  
           [0005]    As used in the present specification, the term “map” is used to include both geographical and technical maps as well as graph layouts and drawings. The term “label” is used to refer to text or other indicia to be placed on a map.  
           [0006]    A system and method for labeling objects on maps while avoiding collisions with other labels has been sought after. Some apparently powerful algorithms for automatic label placement on maps use heuristics that capture considerable cartographic expertise but are hampered by provably inefficient methods of search and optimization.  
           [0007]    This patent discloses a system and method for label placement that achieves the twin goals of practical efficiency and high labeling quality by employing cartographic heuristics.  
         SUMMARY OF THE INVENTION  
         [0008]    The present invention provides a computer-implemented system and method of automatically labeling a map in accordance with predefined label location, placement, and priority criteria.  
           [0009]    Here, each label is represented as a convex polygon with any orientation on the map. Labels have various parameters associated with them such as location, size, shape, number and location of vertices, target feature, priority, movement constraints, and clearance. After finding the best position of a label for every feature without regard to other labels or features, higher priority label positions are compared to lower priority label positions two at a time. If the labels interfere, the lower priority label is moved within its movement constraint. Several candidate locations for the lower priority label position are found by moving it the shortest distance to avoid the higher priority label position. A new location is acceptable if the location does not collide with a label of higher priority. It can collide with a label of lower priority. If no candidate positions are acceptable, the label is not moved. This process continues until all labels are inspected, after which a deviation from the desired result function is calculated. This function is zero if the label interference for all labels is zero and greater than zero otherwise. The whole process is repeated until the evaluation function equals zero or the change in the evaluation function is less than a given percent (e.g., two percent) for a small number (e.g., four) of iterations or if it oscillates for a number (e.g., six) of iterations or if the number of iterations is greater than a set number (e.g., twenty). If any interference remains, then interfering labels with lower priorities are not drawn.  
           [0010]    The details of the present invention, both as to its structure and operation, can best be understood in reference to the accompanying drawings, in which like reference to the accompanying drawings, in which like reference numerals refer to like parts, and in which: 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0011]    [0011]FIG. 1 is a diagram of a computer hardware architecture compatible with the present system and method.  
         [0012]    [0012]FIG. 2 is a schematic diagram showing an exemplary computer program product.  
         [0013]    [0013]FIG. 3 is a flow chart showing the overall logic of the present system and method.  
         [0014]    [0014]FIGS. 4 a ,  4   b , and  4   c  is a flow chart showing the initialization of the anti-collision system and method.  
         [0015]    [0015]FIG. 5 is a flow chart of the sorting labels by priority.  
         [0016]    [0016]FIG. 6 is a flow chart showing the initialization of halting criteria variables.  
         [0017]    [0017]FIGS. 7 a  and  7   b  is a flow chart showing the test of whether each label has been tested.  
         [0018]    [0018]FIG. 8 is a flow chart showing the overlap test FIGS. 9 a ,  9   b , and  9   c  is a flow chart showing the movement procedure.  
         [0019]    [0019]FIG. 10 is a flow chart showing the initiation of collision scores and priority ranges.  
         [0020]    [0020]FIG. 11 is a flow chart showing the calculation of the evaluation function.  
         [0021]    [0021]FIG. 12 is a flow chart showing the halt routine.  
         [0022]    [0022]FIG. 13 is a flow chart showing the routine to adjust label properties.  
         [0023]    [0023]FIG. 14 is a flow chart showing the return to caller.  
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0024]    Referring initially to FIG. 1, a system is shown which includes a digital processing apparatus. This system is a general-purpose computer  1000 . The computer may include a graphics display, print hardware, and print software, or may be as simple as a generic personal computer. The example computer in FIG. 1 includes central processor  1010 , system memory  1015 , disk storage  1020  (e.g., hard drive, floppy drive, CD-ROM drive, or DVD drive), controller  1005 , and network adapter  1050 . Data input may be through one or more of the following agencies: keyboard  1035 , pointing device  1040 , disk storage  1020 , local area network  1060 , point to point communications  1065 , and wide area network  1070  (e.g., internet).  
         [0025]    One or more features of the computer as shown may be omitted while still permitting the practice of the invention. For example, printer  1045  is not necessary for maps intended to be displayed only on monitor  1055 . Likewise, network adapter  1050 , local area network  1060 , point to point communications  1065 , and wide area network  1070  are not necessary when the primary method of data input is via removable disk storage.  
         [0026]    The flow charts herein illustrate the structure of the logic of the present invention as embodied in computer program software. Those skilled in the art will appreciate that the flow charts illustrate the structures of logic elements, such as computer program code elements or electronic logic circuits, that function according to this invention. Manifestly, the invention is practiced in its essential embodiment by a machine component that renders the logic elements in a form that instructs a digital processing apparatus (that is, a computer) to perform a sequence of function steps corresponding to those shown.  
         [0027]    [0027]FIG. 2 shows a computer program product which includes a disk  1080  having a computer usable medium  1085  thereon for storing program modules a, b, c, and d. While  4  modules are shown in FIG. 2, it is to be understood that the number of modules into which the program is divided is arbitrary and may be in any particular embodiment a different number.  
         [0028]    Modules a, b, c, d may be a computer program that is executed by processor  1010  within the computer  1000  as a series of computer-executable instructions. In addition to the above-mentioned disk storage  1020 , these instructions may reside, for example in RAM or ROM of the computer  1000  or the instructions may be stored on a DASD array, magnetic tape, electronic read-only memory, or other appropriate data storage device. In an illustrative embodiment of the invention, the computer-executable instructions may be lines of compiled C++ code.  
         [0029]    [0029]FIG. 3 is an overview and summary of the label anti-collision procedure for maps. The caller of the procedure performs the first stage, routine  5 , and the second stage, routine  8 . Routine  5  involves locating each label on a map in the optimal position with respect to its target feature without regard to other labels or features. Routine  8  assigns properties to the map and the labels.  
         [0030]    To begin, the user must specify how to initially place labels on a map. That is, commencing at routine  5 , it is assumed that the user will assign positions that give the best label location with respect to its associated feature. For this procedure to work, the user places the labels in the best spots according to their criteria regardless of other labels and map features. For example, in the initial positions, labels may overlap each other and/or extend over the map boundary. Labels are assumed to be convex polygons while the map boundary is assumed to be a rectangle.  
         [0031]    Next, at routine  8 , the user must assign properties to the map and the labels. Map properties include its height and width. A label&#39;s properties include the associated map feature(s), initial location, size, shape, angular orientation, priority, movement constraints, and clearance. In addition, each label has an associated property that indicates the fraction of the label area that can extend outside the map boundary before it is not drawn. The procedure takes all of these properties into account to move labels to acceptable positions or to not draw the label.  
         [0032]    The following discussion concerns only those geometric objects in the plane of the map, of which the labels are a part. All labels are restricted to convex planar polygons in this plane. A planar polygon is convex if it contains all the line segments connecting any pair of its points. If two convex planar polygons overlap, this means that:  
         [0033]    1) at least one vertex of one polygon is inside the other polygon, or  
         [0034]    2) at least one edge of one polygon crosses or touches (i.e., intersects) an edge of the other polygon.  
         [0035]    To begin the anti-collision procedure, three initialization steps occur. First, labels lying partially inside the map boundary must either be moved completely inside the portrait or be excluded from being compared to other labels and excluded from being drawn. Each label has movement types and constraints that determine whether or not the label qualifies for movement completely onto the map. These movement types and constraints are explained below. Labels qualifying for movement to the inside of the map are moved regardless of the collision status with any other label.  
         [0036]    Second, the labels must be ordered in a list with respect to priority from highest priority to lowest priority. In general, many labels will have the same priority. Within any group of labels with the same priority, any particular label is randomly placed within that block.  
         [0037]    Third and last, variables that monitor the state of the procedure must be initialized.  
         [0038]    The purpose of routine  10  is to move labels within the map boundary. If too much of a label is outside the boundary, it will not be included in the map. Each label is tested to determine what fraction of its area is within the map boundary.  
         [0039]    At routine  20 , labels are sorted in order of descending priority. Halting criteria parameters are initialized at routine  30 .  
         [0040]    Every combination of two labels is tested for overlap in routine  40 . When comparing labels to determine if they overlap, it is important to choose the order of comparison properly to avoid excessive calculation and moving labels more times than necessary. The highest priority labels should be tested for overlap before labels of lower priority.  
         [0041]    The overlap test at routine  45  has three parts. First, it must be determined if any vertex of a first label is inside the second label. Second, it must be determined if any vertex of a second label is inside the first label. Third, it must determine if any edge of the first label intersects any edge of the second label. If at any point either label is determined to overlap the other label, then any remaining parts are bypassed.  
         [0042]    Labels are moved about the map at routine  50  to clear existing label collisions. After it is determined that two labels overlap, the routine finds several new locations for the lower priority of the two labels that eradicate the existing overlap. These locations are ranked by how far the label must be moved, shortest to longest. Then if appropriate, the lower priority is moved to a new location, and its location parameters are adjusted.  
         [0043]    The evaluation function, routine  60 , quantifies the extent of label collisions. Routines  40 ,  45 ,  50 , and  60  iterate until halt routine criteria  70  are satisfied. Labels may move several times before the iterations stop.  
         [0044]    After the iterations stop, all labels are examined for any overlap and label properties are adjusted at routine  80 . Finally, control is returned at routine  90  to the user to draw or view the map.  
         [0045]    [0045]FIGS. 4 a ,  4   b , and  4   c  display the logic of routine  10  in detail. The purpose of routine  10  is to make sure all of a label is within the map boundary. If too much of a label is outside the boundary, it will not be included in the map. Each label is tested to determine what fraction of its area is within the map boundary. A particular label is divided into a grid; 32 by 32 cells is a typical division that works well in practice. If the centroid of a cell is within the map boundary, the entire cell contributes to the fraction of the label within the boundary. The areas of each cell within the map are added to together. If this sum of cell areas, divided by the total label area, is greater than a predetermined value, then the label is moved entirely onto the map according to the movement procedure and the movement constraints described below. The only change to the procedure is that there is no test for overlap with other labels. The qualifying labels are moved onto the map at this time and tested later.  
         [0046]    Step  100  obtains a list of labels from data storage. Each label is tested for whether the entire label is inside the map boundary. First, step  108  initializes flags that will be used in routine  10 . Step  112  tests whether vertices of each label are outside the map boundary. If the vertices of a label are all inside the map boundary, then the next label is tested. If any vertices of a label are outside the map boundary, then, at step  116 , a circumscribing rectangle is placed around the label. Then the circumscribing rectangle is divided into a plurality of cells at step  120 . For example, the rectangle may be divided into 64 cells by 64 cells forming a total of 4096 cells.  
         [0047]    Each cell is tested, step  124 . The test includes finding the center point of each cell to find the number of cells inside the label, step  128 . Then, at step  132 , the center point of each cell used to find the number of cells both inside the label and inside the map.  
         [0048]    The fraction of the label inside the map boundary is determined at step  136 . Then the label is tested, step  144 , to determine if the fraction of the label inside the map boundary is high enough to qualify for attempted movement inside the map. There is one of two possible ways the label might move depending on its movement constraints. One movement, in both the x-axis and y-axis direction, is performed at step  168 . The other movement, restricted to a vector, is performed at step  188 . Once all labels have been tested, step  104  exits routine  10  and proceeds to routine  20 . Referring to FIG. 5, labels are sorted by priority at step  200  from the highest priority label to the lowest priority label and placed into a data structure map. In FIG. 6, step  300  initializes halting criteria variables.  
         [0049]    The above-described logic is further shown in the following pseudo-code with comments:  
                                     PULL IN THE LABELS FROM THE EDGES OF THE MAP ROUTINE                                //Pseudo-code for the Initialization of the Anti-collision Procedure       for Maps       //List of pseudo-code variables       previous_collision_score - the collision score from the previous       iteration       previous_previous_collision_score - the collision score from two       iterations ago       iteration_count - number of times the anti-collision procedure has       looped       slow_change_count - number of iterations of continuous slow change of       collision score       oscillation_count - number of iterations of continuous oscillation of       collision score       priority_of_most_important_label - numerical priority value of the most       important label       priority_range - the difference between the priority of the least and       the most important labels. This number is non-negative.       frac_inside - fraction of label inside the map boundaries       map_x_size - the number of x units in the map - map boundary is a       rectangle       map_y_size - the number of y units in the map - map boundary is a       rectangle       (xMove2D, yMove2D) - the label movement if the label qualifies for       movement completely inside the map boundary and the label parameters       specify 2D type movement       (xMoveVec[], yMoveVec[]) - an array of label movements if the label       qualifies for movement completely inside the map boundary and the label       parameters specify vector type movement       (xc, yc) - center point of a cell formed from a grid within the       circumscribing rectangle around the label       (x_IP, y_IP) - a point satisfying various conditions used to properly       move a label completely inside the map boundary       LABEL_TOO_MUCH_OUTSIDE_PORTRAIT - indicates       if the procedure has       determined that the label has much area outside the map boundary or can       not be properly moved to a new position completely inside the map       boundary. This is a flag of every label set by the procedure.       LABEL_OUTSIDE_PORTRAIT - Not used. This is       a flag of every label set by the procedure.       LABEL_MOVED_INTO_PORTRAIT - indicates       if the procedure has moved a       label that was originally partially outside the map boundary to a new       position completely inside the map boundary. This is a flag of every       label set by the procedure.       LABEL_MIN_FRACTION_INSIDE - minimum fraction       of the label that must be       inside the map boundary to attempt relocation completely inside the map       boundary. This is a parameter of every label set by caller.       LABEL_NEW_LOCATION - A vector (x, y)       which is added to all vertices of       a label if the procedure moves the label. This vector has an initial       value of (0, 0) . This is a parameter of every label determined by the       procedure.       // pseudo-code also has:       // a list of possible label movement candidates to pull the label       inside the map boundary       // a data structure map of labels and their properties sorted by       priority from the most       // important label to the least important label       ------------------------------------------------------------       // THIS IS THE START OF ROUTINE 10       // The labels are not in any particular order at this point.       // They are only in the order in which they are received from the       caller.       for i = first unordered label to last unordered label        set label i flag LABEL_OUTSIDE_PORTRAIT = FALSE        set label i flag        LABEL_TOO_MUCH_OUTSIDE_PORTRAIT = FALSE        set label i flag LABEL_MOVED_INTO_PORTRAIT = FALSE        set label i parameter LABEL_NEW_LOCATION = (0, 0)        // Determine if the label is inside or outside the map boundary.        // If all vertices are inside, then the entire label is inside.        // Here, a vertex on the map boundary is inside the boundary.        label_inside_map = TRUE        for j = first vertex of label i to last vertex of label i         if ( vertex j outside map boundary ) {          label_inside_map = FALSE         }        next j        if ( label_inside_map = FALSE ) {        // Below, find the approximate fraction of the label inside the map       boundary.        // The circumscribing rectangle has edges parallel to the map edges.        // Note that both the rectangle and the label are convex polygons.        Put a circumscribing rectangle around label i        Divide the circumscribing rectangle into 64 units by 64 units forming       4096 cells        in_label = 0        in_label_and_map = 0        for k = first cell to last cell         Find center point of cell k called (xc, yc)         // Here, a point on a label edge or map boundary is inside the label       or map.         // Use the “point inside convex polygon” procedure described in the         // labels overlap section.         if( (xc, yc) inside label ) {          in_label ≡ in_label + 1          if( (xc, yc) inside map boundary ) {           in_label_and_map = in_label_and_map + 1          }         }        next k        frac_inside = ( in_label_and_map )/( in_label )        // Move the label inside the map boundary if enough of the label is       inside.        // Some of the vertices below may be the same vertex.        (x_low, yL) = coordinates of vertex with lowest x coordinate        (x_high, yH) = coordinates of vertex with highest x coordinate        (xL, y_low) = coordinates of vertex with lowest y coordinate        (xH, y_high) = coordinates of vertex with highest y coordinate        // find the new location for the label        if ( frac_inside &gt; LABEL_MIN_FRACTION_INSIDE        parameter of label i ) {         if ( 2D type movement for label i ) {          (xMove2D, yMove2D) = (0, 0)          // If both conditions are true, the label will not fit into the       map.          if ( x_low &lt; 0 ) {           xMove2D = 0 − x_low          }          else if ( x_high &gt; map_x_size − 1 ) {           xMove2D = map_x_size − 1 − x_high          }          // If both conditions are true, the label will not fit into the       map.          if ( y_low &lt; 0 ) {           yMove2D = 0 − y_low          }          else if ( y_high &gt; map_y_size − 1 ) {           yMove2D = map_y_size − 1 − y_high          }          // Determine if the label is still within its movement parameters.          // This means has the label moved too far from its original       position.          // The original location parameter is never changed. It does not       change          // because it is always used for comparison to the new position.          if ( (xMove2D, yMove2D) within label i 2D          type movement parameters       ) {          // Determine if the label is still inside the map boundary after       movement.          // This is really a test to see if the label is too big to fit in       the map.          // Here, a vertex on the map boundary is not outside the map.          // This test works because both label and map are convex polygons.          for j = first vertex of label i to last vertex of label i           label_moved_outside_map = FALSE           if ( ( vertex j + (xMove2D, yMove2D) ) of label i is outside map       boundary ) {             label_moved_outside_map = TRUE           }          next j          if ( label_moved_outside_map = FALSE ) {           set label i flag LABEL_MOVED_INTO_PORTRAIT = TRUE           set label i parameter           LABEL_NEW_LOCATION = (xMove2D, yMove2D)          }         }        }        else { // vector type movement         count = 0         // If both conditions are true, the label will not fit into the       map.         if ( x_low &lt; 0 ) {          find a point (x_IP, y_IP) which meets the following requirements           contained by a line parallel to the vector type movement           contained by a the line x = 0           contained by a line also containing (x_low, yL)          if ( (x_IP, y_IP) exists ) {           xMoveVec[count] = x_IP − x_low           yMoveVec[count] = y_IP − yL           place in list of possible label movement candidates           count = count + 1          }         }         else if ( x_high &gt; map_x_size − 1 ) {          find a point (x_IP, y_IP) which meets the following requirements           contained by a line parallel to the vector type movement           contained by a the line x = map_x_size − 1           contained by a line also containing (x_high, yH)          if ( (x_IP, y_IP) exists ) {           xMoveVec[count] = x_IP − x_high           yMoveVec[count] = y_IP − yH           place in list of possible label movement candidates           count = count + 1          }         }        // If both conditions are true, the label will not fit into the map.         if ( y_low &lt; 0 ) {          find a point (x_IP, y_IP) which meets the following requirements           contained by a line parallel to the vector type movement           contained by a the line y = 0           contained by a line also containing (xL, y_low)          if ( (x_IP, y_IP) exists ) {           xMoveVec[count] = x_IP − xL           yMoveVec[count] = y_IP − y_low           place in list of possible label movement candidates           count = count + 1          }         }         else if ( y_high &gt; map_y_size − 1 ) {          find a point (x_IP, y_IP) which meets the following requirements           contained by a line parallel to the vector type movement           contained by a the line y = map_y_size − 1           contained by a line also containing (xH, y_high)          if ( (x_IP, y_IP) exists ) {           xMoveVec[count] = x_IP − xH           yMoveVec[count] = y_IP − y_high           place in list of possible label movement candidates           count = count + 1          }         }         // Can have zero, one, or two possible label movement candidates         for k = 0 to (count − 1)         // Determine if the label is still within its movement parameters.         // This means has the label moved too far from its original       position.         // The original location parameter is never changed. It does not       change         // because it is always used for comparison to the new position.         move_distance = magnitude of (xMoveVec[k], yMoveVec[k])         if ( move_distance within label i vector type movement parameters       ) {         // Determine if the label is still inside the map boundary after       movement.         // This is really a test to see if the label is too big to fit in       the map.         // Here, a vertex on the map boundary is not outside the map.         // This test works because both label and map are convex       polygons.         for j = first vertex of label i to last vertex of label i             label_moved_outside_map = FALSE             if(( vertex j + (xMoveVec[k], yMoveVec[k])) of label i is       outside map boundary) {              label_moved_outside_map = TRUE             }            next j            if ( label_moved_outside_map = FALSE ) {             set label i flag             LABEL_MOVED_INTO_PORTRAIT = TRUE             set label i parameter             LABEL_NEW_LOCATION = (xMoveVec[k],       yMoveVec[k])             break out of loop // go past next k            }            }           next k          } // end of vector type movement         }         if ( label i flag LABEL_MOVED_INTO_PORTRAIT = FALSE ) {          set label i flag          LABEL_TOO_MUCH_OUTSIDE_PORTRAIT = TRUE         }        } // end if label_inside_map = FALSE       next i       // THIS IS THE START OF ROUTINE 20       // Sort the labels by priority.       // The labels with the highest priorities have the lowest numbers.       // Priorities may be negative numbers.       // Labels may have the same priority.       // After this loop, assume all labels are ordered properly.       Sort labels by priority from the most important label to the least       important label        and place into a data structure map       // THIS IS THE START OF ROUTINE 30       // Initialize halting criteria variables       priority_range = priority_of_least_important_label −       priority_of_most_important_label       // initialize these two variables to large numbers       previous_collision_score = Very Large Number       previous_previous_collision_score = Very Large Number       iteration_count = 0       slow_change_count = 0       oscillation_count = 0                  
 
         [0050]    Referring to FIGS. 7 a  and  7   b , labels are compared to determine if they overlap. It is important to choose the order of comparison properly to avoid excessive calculation and moving labels more times than necessary. The highest priority labels should be tested for overlap before labels of lower priority. Labels are tested for overlap two at a time. For example, suppose there are three priorities, high, medium, and low. The labels ranked as high priority should be tested among themselves first. High priority labels are then tested against medium and low priority labels before medium priority labels are tested against other medium priority labels. At this stage of the anti-collision algorithm, the labels have been sorted in descending priority.  
         [0051]    The above-described logic is further shown in the following pseudo-code with comments:  
                                     Order of Comparison for the Label Overlap Test Routine                                // The n labels have already been sorted in priority order,       // from the most important, label 0, consecutively,       // to the least important, label (n − 1).       LABEL_TOO_MUCH_OUTSIDE_PORTRAIT - indicates if the procedure has       determined that the label has much area outside the map boundary or can       not be properly moved to a new position completely inside the map       boundary. This is a flag of every label set by the procedure.       LABEL_OUTSIDE_PORTRAIT - Not used. This is a flag of every label set by       the procedure.       LABEL_MOVED_INTO_PORTRAIT - indicates if the procedure has moved a       label that was originally partially outside the map boundary to a new       position completely inside the map boundary. This is a flag of every       label set by the procedure.       last_Label_Index = number_of_labels − 1; // zero based       // Zero based.       // The highest priority is zero and the lowest priority is a number       greater than zero.       // Note that there may be priorities which have no labels.       last_Pri = lowest priority − highest priority; // which equal the       lowest priority       // Below, if there are no labels with priority p,       // first_Pri[p] = −1 and last_Pri[p] = −1       // first_label[p] = first label index with priority p       // last_label[p] = last label index with priority p       for p = 0 to last_Pri; // highest priority to lowest priority        if labels with priority p exist         first_label[p] = most important label with priority p;         last_label[p] = least important label with priority p;        else         first_label[p] = −1;         last_label[p] = −1;       next p;       for i_pri = 0 to last_Pri; // highest priority to lowest priority        if first_label[i_pri] = −1, continue to next i_pri;        for j_pri = i_pri to last_Pri; // highest priority to lowest priority         if first_label[j_pri] = −1, continue to next j_pri;         for i_idx = first_label[i_pri] to last_label[i_pri];         if i_idx flag LABEL_TOO_MUCH_OUTSIDE_PORTRAIT = TRUE OR             LABEL_OUTSIDE_PORTRAIT = TRUE, continue to next i_idx          for j_idx = first_label[j_pri] to last_label[j_pri];           // Do not compare a label to itself or           // compare labels which have been previously compared,           // for this particular iteration of the entire algorithm.           if i_idx &lt;= j_idx, continue to next j_idx;           if j_idx flag LABEL_TOO_MUCH_OUTSIDE_PORTRAIT = TRUE OR             LABEL_OUTSIDE_PORTRAIT = TRUE, continue to next j_idx           if label i_idx overlaps label j_idx,            then perform the label movement procedure on label j_idx;          next j_idx;         next i_idx;        next j_pri;       next i_pri;                  
 
         [0052]    All labels are restricted to convex planar polygons in the plane of the map. A planar polygon is convex if it contains all the line segments connecting any pair of its points. If two convex planar polygons overlap, this means that  
         [0053]    1) at least one vertex of one polygon is inside the other polygon, or  
         [0054]    2) at least one edge of one polygon intersects an edge of the other polygon Routine  45 , shown in FIG. 8, is a label overlap test procedure. The overlap test has three parts. First, it determines if any vertex of the first polygon is inside the second polygon. Second, it determines if any vertex of the second polygon is inside the first polygon. Third, it determines if any edge of the first polygon intersects any edge of the second polygon. Once any vertex is found to be inside the other polygon, there is no need to test remaining vertices and edges. Once any edge is found to intersect any edge of the other polygon, there is no need to test remaining edges and vertices.  
         [0055]    [0055]FIG. 8 shows the test for whether a vertex of a polygon is inside another polygon. The method is shown in “Determining if a Point Lies on the Interior of a Polygon,” Paul Bourke, http://astronomy.swin.edu.au/˜pbourke/geometry/insidepoly/. Consider the standard right-handed two-dimensional Cartesian coordinate system with the positive y direction up and the positive x direction to the right. A first polygon&#39;s edges are chosen such that the perimeter is traversed in the counterclockwise (CCW) direction (the perimeter may be traversed in a clockwise direction so long as it is done consistently). At step  462 , if any vertex of a second polygon is to the left of all edges of the first polygon, then that vertex is inside the first polygon. Likewise, at step  466 , if any vertex of the first polygon is to the left of all edges of the second polygon then that vertex is inside the second polygon. If any vertex of a polygon is inside another polygon, then the polygons overlap. This is the test for a point being inside a convex planar polygon. Lines containing the edges that make up a polygon may be written,  
         ( y−Y 1)( X 2 −X 1)−( x−X 1)( Y 2 −Y 1)=0  
         [0056]    where  
         [0057]    (x,y) is any point on the line, and  
         [0058]    (X1,Y1) and (X2,Y2) are the endpoints of an edge of the polygon under test. Points lying on the polygon edges satisfy the line equations, while points not on the polygon edges do not satisfy those equations. If (x, y) is any point in the plane, the equation for a line containing an edge is:  
         ( y−Y 1)( X 2 −X 1)−( x−X 1)( Y 2− Y 1)= K    
         [0059]    where K is a real number constant.  
         [0060]    Then, for all points to the left of any edge, K&gt;0, and for all points to the right of any edge, K&lt;0. Note that point  2  in the above equation is at the head of the vector representing the edge and point  1  is at the tail of the vector representing edge. This is true because, for all edges pointing to the right, (X2−X1)&gt;0. For any point above the line containing the edge, (x_above, y_above), there exists a point, (x,y), on the line, such that:  
         x_above=x and y_above&gt;y  
         [0061]    Therefore:  
             (     y   -   Y1     )          (     X2   -   X1     )       -       (     x   -   X1     )          (     Y2   -   Y1     )         =         (     y   -   Y1     )          (     X2   -   X1     )       -       (     x   -   X1     )          (     Y2   -   Y1     )                       (     y_above   -   Y1     )          (     X2   -   X1     )       -       (     x   -   X1     )          (     Y2   -   Y1     )         &gt;         (     y   -   Y1     )          (     X2   -   X1     )       -       (     x   -   X1     )          (     Y2   -   Y1     )                       (     y_above   -   Y1     )          (     X2   -   X1     )       -       (     x_above   -   X1     )          (     Y2   -   Y1     )         &gt;         (     y   -   Y1     )          (     X2   -   X1     )       -       (     x   -   X1     )          (     Y2   -   Y1     )                               
 
         [0062]    A point that is above a line pointing to the right is a point that lies to the left of the line. Similar arguments show that any point on the left of lines pointing up, pointing down, or pointing left yields a positive value with substituted into the line equation. Step  470  tests whether the edges of one polygon intersect another polygon. Consider the equations of the lines that contain the edges of the first polygon and the equations of the lines that contain the edges of the second polygon. Determine the intersection point for every two-line combination, where one line is a line that contains an edge of the first polygon and the other line is a line that contains an edge of the second polygon. If the intersection point lies on or between the endpoints of the polygon edges, then the edge of one polygon intersects the edge of the other polygon and the polygons overlap. In cases where the lines are parallel, and not coincident, no intersection point exists for that pair of lines. If the lines are coincident, then the edges may or may not touch, but if the edges touch then the polygons overlap.  
         [0063]    The above-described logic is further shown in the following pseudo-code with comments:  
                                     Pseudo-code for the Overlap Test of Convex Planar Polygons                                List of pseudo-code variables        (x_2_i, y_2_i) - vertex i of polygon 2        (X1_j, Y1_j) - vertex 1 of edge j of polygon 1        (X2_j, Y2_j) - vertex 2 of edge j of polygon 1        (x_IP, y_IP) - intersection point of lines containing edges       x_max_i - max x of edge i       y_min_j - min y on edge j       find max x, max y, min x, min y on polygon 1 - each will be on a       vertex       find max x, max y, min x, min y on polygon 2 - each will be on a       vertex       // if any expression is true, the polygons do not overlap, so return       false       if (min x of polygon 1 &gt;= max x of polygon 2) RETURN NO_OVERLAP       if (min x of polygon 2 &gt;= max x of polygon 1) RETURN NO_OVERLAP       if (min y of polygon 1 &gt;= max y of polygon 2) RETURN NO_OVERLAP       if (min y of polygon 2 &gt;= max y of polygon 1) RETURN NO_OVERLAP       // if any vertex of polygon 2 is inside polygon 1, the result is       greater than zero.       // proceed around polygon 1 in the CCW direction for each vertex of       polygon 2       for i = first vertex of polygon 2 to last vertex of polygon 2        inside = TRUE        for j = first edge of polygon 1 to last edge of polygon 1 in CCW       direction         if((y_2_i − Y1_j) (X2_j − X1_j) − (x_2_i − X1_j)       (Y2_j − Y1_j) &lt;= 0)       inside = FALSE        next j        if (inside = TRUE), RETURN OVERLAP       next i       Repeat the above, except test polygon 1 vertices with polygon 2 edges       Return OVERLAP if appropriate       // perform the edge intersection test       for i = first edge of polygon 1 to last edge of polygon 1        of the two endpoints of edge i, get x_max_i, y_max_i,        x_min_i, y_min_i        for j = first edge of polygon 2 to last edge of polygon 2         of the two endpoints of edge j, get x_max_j, y_max_j, x_min_j,       y_min_j         solve for intersection point, (x_IP, y_IP), of lines containing edge       i and edge j         if intersection point exists          // An intersection at an endpoint is an overlap.          // These tests also take care vertical and horizontal edges.          if (x_IP &lt;= x_max_i and x_IP &gt;= x_min_i) and           (y_IP &lt;= y_max_i and y_IP &gt;= y_min _i) and           (x_IP &lt;= x_max_j and x_IP &gt;= x_min_j) and           (y_IP &lt;= y_max_j and y_IP &gt;= y_min_j),           RETURN OVERLAP        next j       next i       RETURN NO_OVERLAP                  
 
         [0064]    Labels must be moved about the map to clear existing label collisions. After it is determined that two labels overlap, routine  50  (FIGS. 9 a ,  9   b , and  9   c ) finds several new locations for the lower priority of the two labels that eradicate the existing overlap. The higher priority label is a first label while a lower priority label is a second label. These locations are ranked by how far the second label must be moved, shortest to longest. The actual location finally selected must meet the following criteria:  
         [0065]    1) the second label moves a shorter distance than other qualifying locations;  
         [0066]    2) the second label movement does not result in overlap with another label (or labels) of equal or higher priority than the first label;  
         [0067]    3) the second label movement does not exceed the maximum movement parameters for that particular label; and  
         [0068]    4) no part of the second label is moved outside the map boundary.  
         [0069]    If no candidate locations meet these criteria, the second label is not moved. During the process of fixing existing collisions, other collisions may be created. New collisions are only allowed if it reduces collisions among labels with priorities equal to or higher than the first label. As the procedure iterates, new collisions are handled like the original collisions. The procedure will minimize collisions.  
         [0070]    Labels may be moved in one of two ways. First, a label may move in any of the four directions in the map&#39;s coordinate system, +X, −X, +Y, −Y, up to a maximum distance from the original location. This is referred to as 2D type movement. Second, a label may move along a vector up to a maximum distance from the original location in the positive vector direction or the negative vector direction. This is referred to as vector type movement. Both the vector and the maximum distances are in the label&#39;s parameter list.  
         [0071]    Given two labels to compare, a first label&#39;s edges are traversed in a CCW direction. Step  512  tests whether each vertex of a second label is left of a line containing an edge of the first label. A vertex of the second label is said to be on an inside side of the line containing the edge of the first label if the vertex of the second label and the first label are on the same side of the line containing the edge of the first label. If step  515  specifies a 2D type movement, then step  518  finds an intersection of two lines. A first line is the line that contains one edge of the first label. A second line is perpendicular the first line and contains the vertex. If, instead, step  515  specifies a vector type movement, then step  518  finds an intersection of a line containing an edge and a line parallel to the vector type movement also containing the vertex.  
         [0072]    If in either the 2D type movement case or the vector type movement case, an intersection exists and the vertex is on the inside side, step  527  calculates a first vector from the vertex to the intersection. If the first vector is too small, then the routine calculates, in steps  533 ,  536 , and  539 , a second vector with desirable properties listed in steps  536  and  539 . In the case that the first vector is too small, the first vector is replaced by the second vector. Whichever vector remains, it is hereafter referred to as the vector.  
         [0073]    Step  542  tests whether the vector is within movement bounds from the original label location. If at step  545 , it is within bounds, the vector is placed on an end of a list of qualified vectors and a length of the vector is placed on an end of a length list. Once all vertices of the second label are tested, if there any qualified vectors (step  548 ), then, at step  551 :  
         [0074]    1) Find the maximum length in the length list and a corresponding qualified vector from the vector list;  
         [0075]    2) Insert the length and the qualified vector into a data structure map that is sorted by distance; and  
         [0076]    3) Empty the length list and vector list.  
         [0077]    After all the edges of the first label are checked, at step  554  the steps starting at step  512  are repeated using the edges of the second label and the vertices of the first label. For any qualifying vectors, a negative of the vector is taken and that vector and its length are inserted into the data structure map.  
         [0078]    Next, tests are performed to determine if proposed locations for the second label are acceptable. At step  560 , starting with a shortest vector in the data structure map, the second label is moved in both a direction and a length of the shortest vector to obtain a new location for the second label. Then, at step  563 , a test is performed to determine if part of the new location for the second label is outside the map boundary. If, the new location for the second label places part of the second label outside the map boundary, repeat steps  557 ,  560 , and  563 , using a next vector from the data structure map. Otherwise, at step  572 , a test is performed of whether the new location for the second label overlaps any label with greater or equal priority than that of the first label. If there is an overlap, repeat steps  557  through  572 . Otherwise, the second label is moved to the candidate location.  
         [0079]    The above-described logic is further shown in the following pseudo-code with comments:  
                                     Movement Procedure of Convex Planar Polygons                                // List of pseudo-code variables        (x_2_j, y_2_j) - vertex j of polygon 2        (X1_i, Y1_i) - vertex 1 of edge i of polygon 1        (X2_i, Y2_i) - vertex 2 of edge i of polygon 1        (x_IP, y_IP) - intersection point of lines containing edge and vertex        (X,Y) - vector from vertex to edge       pseudo-code also has:        a list of distances        a list of vectors        a data structure map of distances and vectors sorted by distance,       short to long       // Polygon 1 is the more important polygon and polygon 2 will move if       possible       // Here, the vertices in a polygon are on the left side of the edge       // of the other polygon when traversing it in the CCW direction,       // but the vertices are not necessarily inside the other polygon.       // That is why all possibilities are caught in the algorithm below -       // even where no vertex from either polygon is inside the other.       // Do not have to check specifically for the above case.       // If a vertex of polygon 2 is on left side a polygon 1 edge, the       result is greater than zero.       // proceed around polygon 1 in the CCW direction for each vertex of       polygon 2       // Note the the vertex in question does not have to be inside polygon 1       for i = first edge of polygon 1 to last edge of polygon 1 in CCW       direction        count_of_possible_vertices = 0        for j = first vertex of polygon 2 to last vertex of polygon 2         if((y_2_j − Y1_i)(X2_i − X1_i) − (x_2_j − X1_i)         (Y2_i − Y1_i) &gt; 0)          if (2D type movement for polygon 2)          // a solution will always exist for this case          solve for intersection point, (x_IP, y_IP), of a line containing       edge i          and a line perpendicular to edge i containing (x_2_j, y_2_j)         if (vector type movement for polygon 2)         // a solution might not exist for this case         solve for intersection point, (x_IP, y_IP), of a line containing       edge i         and a line parallel to the vector type movement containing (x_2_j,       y_2_j)         if ( solution exits for (x_IP, y_IP) )          // get vector from vertex to intersection point          (X,Y) = (x_IP − x_2_j, y_IP − y_2_j)          if ( (X,Y) length minute )           if ( 2D type movement for polygon 2 )            find a point (X,Y) which meets the following requirements             on right side of edge i (CCW)             contained by a line perpendicular to edge i             contained by a line also containing (x_IP, y_IP)             a minute distance from (x_IP, y_IP)           else // vector type movement for polygon 2            find a point (X,Y) which meets the following requirements             on right side of edge i (CCW)             contained by a line parallel to the vector type movement             contained by a line also containing (x_IP, y_IP)             a minute distance from (x_IP, y_IP)          // because polygon may move several times, keep the original       location of the label          if ( movement of (X,Y) leaves polygon with movement limit )          // Make vector just a bit larger that the distance to the edge          // so when polygon 2 is moved, it moves just outside the polygon 1          length_of_XY = length of (X, Y) * (1.0 + 1.0e−09)          X = X * (1.0 + 10e−09)          Y = Y * (1.0 + 10e−09)          append length_of_XY to end of distance list          append (X,Y) to end of vector list          count_of_possible_vertices = count_of_possible_vertices + 1        next j        if (count_of_possible_vertices &gt; 0)         find the maximum distance in the distance list         get the corresponding vector to this distance from the vector list         insert the distance and the vector into the data structure map sorted       by distance,         from the shortest distance to the longest distance         empty distance list and vector list       next i       Repeat the above, except use polygon 1 vertices and with polygon 2       edges       The vector for possible movement, (X,Y), is reversed       Insert the results into the same distance/vector data structure map       // the outer loop is just going thought the sorted data structure map       for i = first location candidate to last location candidate        get new location for polygon by adding vector (X,Y) to each vertex        if ( any part of label outside map boundary ) next i        for j = first label to last label whose priority &gt;= polygon 1         if ( polygon 1 is label j or polygon 2 is label j) next j         if ( polygon 2 in location candidate i overlaps label j ) next i         update polygon 2 location in its parameter list         break out of both for loops        next j       next i       clear the data structure map       get the next pair of labels to be tested for overlap                  
 
         [0080]    The Evaluation Function, the Halting Criteria, and the Adjustment of Label Properties  
         [0081]    The calculation of the evaluation function is represented by FIG. 11. All labels that overlap are known at this point. The procedure used to reduce label collisions is an iterative process. When using this technique, there must be some way to measure the extent of the remaining collisions after each iteration. In this anti-collision procedure for maps, the evaluation function at step  620  is:  
         [0082]    Collision Score= 
         ∑   ij                  (         (     label                 i                 adjusted                 priority     )     2     +       (     label                 j                 adjusted                 priority     )     2       )                           
 
         [0083]    where the score is the summation over every pair of overlapping labels. The result of this function is defined as zero if no collisions remain and greater than zero if any collisions remain. The function penalizes disproportionately for collisions involving high priority labels. For instance, a collision involving a high priority label and a low priority label gets a higher score (worse) than a collision involving two medium priority labels.  
         [0084]    Routine  70  as shown in FIG. 12 evaluates halting criteria. The iterative process must halt at some point. Example rules tested at step  735  to halt the procedure follow:  
         [0085]    1) the evaluation function is below a minimum value;  
         [0086]    2) the number of iterations is greater than a maximum value;  
         [0087]    3) the evaluation function changes less than a minimum percentage of the previous iteration for more than a set number of iterations; and  
         [0088]    4) the evaluation function oscillates for more than a set number of consecutive iterations.  
         [0089]    If none of these conditions are meet, the anti-collision algorithm is repeated, noting that labels may move several times before the iterations stop. A label&#39;s new position is stored in its parameter list at the time a label is moved. The original position is always available in the label&#39;s parameter list.  
         [0090]    Routine  80 , as shown in FIG. 13, adjusts label properties. After the halting criteria have been satisfied, all the labels are examined for any overlap at step  820  and the label properties are adjusted (steps  840  and  845 ). The result of this examination and the state of the MUST DRAW flag determines if the DRAW flag is true or false. These flags are in the label&#39;s parameter list. The MUST DRAW flag is set by the caller. If the DRAW flag is true, this procedure will draw the label. If the DRAW is false, this procedure will not draw the label. For any pair of overlapping labels, the following somewhat arbitrary rules determine the final state of a label&#39;s DRAW flag:  
         [0091]    1) If one label has MUST DRAW=TRUE, that label sets DRAW=TRUE, and the second label sets DRAW=FALSE.  
         [0092]    2) If both labels have MUST DRAW=TRUE, the label higher on the list of label priority sets DRAW=TRUE, and the other label sets DRAW=FALSE. Note that this will hold for labels of equal priority.  
         [0093]    3) If neither label has MUST DRAW=TRUE, the label higher on the list of label priority sets DRAW=TRUE, and the other label sets DRAW=FALSE. Note that this will hold for labels of equal priority.  
         [0094]    The label priority list and the overlap test are described in preceding sections of the description of the entire anti-collision procedure.  
         [0095]    After label properties are adjusted, control is returned to the caller, FIG. 14.  
         [0096]    The above-described logic is further shown in the following pseudo-code with comments.  
         [0097]    Pseudo-code for the Evaluation Function, the Halting Criteria, and the Adjustment of Label Properties  
                                   List of pseudo-code variables       collision_score - the sum of the evaluation function after each       iteration       previous_collision_score - the collision score from the previous       iteration       previous_previous_collision_score - the collision score from two       iterations ago       iteration_count - number of times the anti-collision procedure has       looped       slow_change_count - number of iterations of continuous slow change of       collision score       oscillation_count - number of iterations of continuous oscillation of       collision score       priority_of_most_important_label - numerical priority value of the most       important label       priority_range - the difference between the priority of the least and       the most important labels. This number is non-negative.       adjusted_priority_1 - the label 1 priority modified to make it work in       the evaluation function       // Initialize halting criteria variables       priority_range = priority_of_least_important_label −       priority_of_most_important_label       // initialize these two variables to large numbers       previous_collision_score = Very Large Number       previous_previous_collision_score = Very Large Number       iteration_count = 0       slow_change_count = 0       oscillation_count = 0       //------ The above must be done at the top of the procedure --------//       // Evaluation Function -----------------------------------------------       collision_score = 0       // these loops go thought label priority list       for i = first label to last label        if( label i flag LABEL_TOO_MUCH_OUTSIDE_PORTRAIT = TRUE OR         label i flag LABEL_OUTSIDE_PORTRAIT = TRUE ) next i        for j = label i+1 to last label        if( label j flag LABEL_TOO_MUCH_OUTSIDE_PORTRAIT = TRUE OR         label j flag LABEL_OUTSIDE_PORTRAIT = TRUE ) next j        if( label i and label j overlap )        {        // Adjust the label priorities to make the evaluation function work       properly.        // Note that the highest priority labels are assigned the lowest       numbers and        // priorities may be positive or negative.        adjusted_priority_1 = 1 + priority_range −             ( label_1_priority −       priority_of_most_important_label )        adjusted_priority_2 = 1 + priority_range −             ( label_2_priority −       priority_of_most_important_label )        collision_score = collision_score +             (adjusted_priority_1)*(adjusted_priority_1) +             (adjusted_priority_2)*(adjusted_priority_2)        }        next j       next i       // Halting Algorithm ---------------------------------------       // is there slow change ?       if(collision_score &lt;= previous_collision_score AND        collision_score &gt; 0.98*previous_collision_score)       {        slow_change_count = slow_change_count + 1       }       else       {        slow_change_count = 0       }       // is there oscillation ?       if( (collision_score &gt; previous_collision_score AND        previous_collision_score &lt; previous_previous_collision_score ) OR        (collision_score &lt; previous_collision_score AND        previous_collision_score &gt; previous_previous_collision_score ) )       {        oscillation_count = oscillation_count + 1       }       else       {        oscillation_count = 0       }       iteration_count = iteration_count + 1       previous_previous_collision_score = previous_collision_score       previous_collision_score = collision_score       if(collision_score = 0) goto ADJUST_LABEL_PARAMETERS       if(iteration_count &gt; 20) goto ADJUST_LABEL_PARAMETERS       if(slow_change_count &gt; 4) goto ADJUST_LABEL_PARAMETERS       if(oscillation_count &gt; 6) goto ADJUST_LABEL_PARAMETERS       goto Start of Next Iteration       ADJUST_LABEL_PARAMETERS: //-------------------------------------------       // set label flag DRAW = TRUE for all labels       for i = first label to last label        label_i_DRAW = TRUE        next i       // these loops go thought label priority list and set the draw flag       for i = first label to last label        if( label i flag LABEL_TOO_MUCH_OUTSIDE_PORTRAIT = TRUE OR         label i flag LABEL_OUTSIDE_PORTRAIT = TRUE )        {         label_i_DRAW = FALSE         next i        }        for j = label i+1 to last label         if( label j flag LABEL_TOO_MUCH_OUTSIDE_PORTRAIT = TRUE OR          label j flag LABEL_OUTSIDE_PORTRAIT = TRUE )         {          label_j_DRAW = FALSE          next j         }         if( label i and label j overlap )         {          if ( label_i_MUST_DRAW = TRUE AND label_j_MUST_DRAW = TRUE )          {           label_j_DRAW = FALSE          }          else if ( label_i_MUST_DRAW = TRUE )          {           label_j_DRAW = FALSE          }          else if ( label_j_MUST_DRAW = TRUE )          {           label_i_DRAW = FALSE          }          else          {           label_j_DRAW = FALSE          }          }         next j       next i       return to caller                  
 
         [0098]    While the particular SYSTEM AND METHOD FOR LABELING MAPS as herein shown and described in detail is fully capable of attaining the above-described objects of the invention, it is to be understood that it is the presently preferred embodiment of the present invention and is thus representative of the subject matter which is broadly contemplated by the present invention, that the scope of the present invention fully encompasses other embodiments which may become obvious to those skilled in the art, and that the scope of the present invention is accordingly to be limited by nothing other than the appended claims, in which reference to an element in the singular means “at least one”. All structural and functional equivalents to the elements of the above-described preferred embodiment that are known or later come to be known to those of ordinary skill in the art are expressly incorporated herein by reference and are intended to be encompassed by the present claims. Moreover, it is not necessary for a device or method to address each and every problem sought to be solved by the present invention, for it to be encompassed by the present claims. Furthermore, no element, component, or method step in the present disclosure is intended to be dedicated to the public regardless of whether the element, component, or method step is explicitly recited in the claims.