Geo-spatial datasets are captured using different methods, instruments, reference systems and geodetic datum that make datasets to vary. Thus, different operations and many algorithms exist for carrying out clipping and finding intersection between two datasets. Some focus on merging similar geometric objects [3] including exchange of attributes or for homogenizing geometry. This address semantics heterogeneity of spatial datasets, improvement of quality in case one dataset is captured to a higher quality, multi representation based on the matching of two datasets using Unified Modeling language (UML), selecting matching objects using Structured Query Language (SQL), and geo-spatial object geometry adjustment. For polygon overlays, many algorithms are explained by [2] and [4] that can work on different polygons like convex, rectangle, and concave polygons with some requiring complex and specific data structures and others computing Boolean operations on polygons that help to determine the intersection of segments [2] . Although these operations determine the spatial coincidence (if any) of two data layers, they do not guide the end user on how to implement them to update geo-spatial datasets through aligning features for same, adjacent, or complementary datasets.

For the approaches that handle combined primitives, we find a huge number of research efforts in this domain: 1) approaches dealing with geo-spatial object matching, and 2) methods for geo-spatial object intersection or database updating. Different schemes have been proposed: a) layer’s overlying approaches that use algorithms for different geo-spatial data merging tasks, and b) more specific ideas, using individual geo-spatial object adjustment strategies, to achieve full integrated solution. The latter is the focus of this work dealing with geometry alignment basing on current approaches like Boolean polygon matching [2] , alignment algorithms [5] , computational geometry [7] , and object adjustment in corresponding datasets [6] .

There are two common spatial data models for geo-spatial data storage—raster and vector. In the alignment method, we focus on vector, which is the use of directional lines to represent a geographic feature. Several different vector data models exist, however only two are commonly used in GIS data storage: computer-aided drafting (CAD) and topologic data structure. The focus is on topologic since it maintains spatial relationships among features. Three files types are considered: 1) shapefile as it has been around since the 1980s and remains one of the most common data transfer formats, 2) GML is text and is human readable, and 3) Spatialite as it uses one file and is able to store geometries and query them with spatial functions similar to what is found in geodatabase like PostGIS.

As we developed method, we link topological data structures to the requirement of geo-spatial framework:

1) The ideal method for improving data usability should be based on object-oriented data model [8] [9] . The geo-spatial data must be modeled as identifiable objects according to the geographic entities (features) existing in the real world, which helps to link spatial information with various social-economic and natural resource information.

2) Geo-spatial data from different sources with varying scales must be able to be mapped to the same standards, data model, projection, and representation [10] [11] so that the description of the same entity in different datasets is consistent.

3) The relationships among objects should be modeled and integration of different geo-spatial datasets must handle the three dimension 1) horizontal (adjacency), 2) vertical (overlay), and 3) temporal (time) integration [12] , for example, the relations among buildings and land plots, the relations between poles (point object) and electricity line (line object) [13] , etc.

The alignment method uses the three characteristics where objects forming features are used as the modeling unit basing on the primary spatial primitives (point, polylines, and polygons) to accomplish the geometrical inconsistency correction through updating and adjustment of objects so that they align in the three dimensions (horizontal, vertical, and temporal) of spatial data. This is done by putting into consideration the desirable characteristics of information systems—being true, up-to-date, standard, flexible, concise, in desired form and sufficient to the needs of users and their need to share [14] . For GIS, sharing provides avenues to distribute geographic information among many users which enhances decision-making and produces significant savings in data collection and merging by reducing the effort and money wasted as result of duplication [15] [16] , which is the aim of many initiatives like openstreepmap, googlemaps, OpenGIS, and SDI. The alignment method compliments these initiatives by making it easy to update, adjust, and align geometries of objects in dataset horizontally, vertically and over time in line with the second and third characteristics of geo-spatial framework.

The first task is reading the geo-spatial datasets involved in the alignment as layers—reference dataset (RD) that will provide alignment values and adjustment dataset (AD) that has objects to be aligned. The user specifies the AD and RD, also identifies the primary attribute (PA) which is the meaning of features. As the data is read in, the data structures are compared to check for geometry type of objects (points, lines, polygons) before storing them in matrices according to their geometry type. This is vital to ensure that same geometry type are used when comparing, updating, adjusting, and aligning datasets.

Data preparation involves putting the data into the same projection, cleaning and removing unnecessary geome-

tries, matching the corresponding object in the datasets, difference determination, and making sure that geometries being worked on are the same—point with point, line with line, and polygon with polygon. This is achieved by algorithms based either on geometric, topological, or semantic matching [3] . For the GIS data layers the difference is determined and parameters used in comparison are precision, resolution, and actual data values. Those steps are already available in the existing GIS applications like QGIS, ArcGIS, and Jump GIS.

If the difference obtained is zero, that means the layers are the same and objects do match. If the result is not zero, it could be positive or negative, that means the two datasets have variations. The positive or negative values indicate the direction, to either subtract or add during the geometrical adjustment. It helps also in identifying the objects that are causing the differences. For positive, it means the first dataset have bigger or more geometry components and vice versa for negative. Implying that for the positive, either geometry objects have to be reduced in the first dataset or more objects have to be added in the second dataset. For negative it means they are more or bigger objects in the second dataset thus the need to add in the adjustment dataset if requirement is only to update or to reduce in the second (reference dataset) in case of complementary.

To apply the above, the method takes advantage of the way geo-spatial datasets are organized according to meaning (themes). Each theme is stored independently in layers like road layer having types of roads (like highways, avenues), building layer having different buildings (like houses, plazas, gatehouse, arcades, etc.). This provides a natural way and technique to organize and visualize data from different sources making it an efficient way of data storage, manipulation, and analysis [1] . For gatehouse on a building layer, there are objects like window, door, etc. that are represented by spatial objects. The objects are defined by their shape, size, and location presented by primitives (points, lines, and polygons). The vertices define the shape of the polyline along its length. Polylines that connect to each other will share a common node. Polygons are formed by bounding polylines that keep track of the location of each polygon.

During the processing, the requirements vary from one dataset to another. That is why each algorithm is able to run and be called upon to act independently depending on the complementary situations and adjacent requirements.

The method translates and decodes the geometry shape into text by reading and creating the data structure followed by storing the text in a matrix. In MATLAB, the function “shaperead” handles the reading of layers and it populates matrixes, for example S = shaperead (“nakawa.shp”)—reads the nakawa layer and keeps the matrix in variable S. The alignment method creates a data structure if needed for example using “struct” function in MATLAB S = struct (“Geometry”, “Line”, “Bounding Box”, [0 0; 3 3], “X”, [1 2 2 1 1], “Y”, [1 1 2 2 1]). To reference and work on a particular spatial point in a matrix, the approach of specifying its row and column number is used, where in the matrix variable S, specify the row then column: S (row, column). The number of objects inside the structure is computed and is used to determine the number of iterations to perform on the structure during the alignment process. Since the x-y coordinates for points, vertices, and nodes of all objects forming features on a layer are read, geometry adjustment takes place by changing the x-y values that are handled in their respective indexes as variables to ensure the objects and shape can be reconstructed.

The method takes advantage of the geometries editing in a text form and the following capabilities are provided:

1) Creation of points, lines, and polygons;

2) Moving points, lines, and polygons;

3) Deleting points, lines, and polygons;

4) Inserting, moving, and deleting vertices;

5) Combining and exploding of geometries to and from datasets.

The alignment method runs in such a way that it loads the various adjustment algorithms in different combinations to provide the needed geometry alignment. Different functions in existing algorithms were extracted and grouped into the following sub-algorithms that form the alignment method:

1) Reading the datasets and identifying geometry type;

2) Carrying out dataset to dataset referencing and deciding on type of adjustment;

3) Making the number of objects the same in the two datasets;

4) Updating, adjusting, and aligning the geometries using coordinate values;

5) Writing the aligned dataset onto disk.

To put the method into action, we used Nakawa shapefiles having many but varying objects. The data sources were KCCA (Kampala City Council Authority) and UBOS (Uganda Bureau of Statistics) representing Nakawa division of Kampala City in Uganda as shown on Figure 2.

From the above figure, we are able to see the size and shape of objects but not their structure details (geometry type, location, number of objects, and attributes). KCCA dataset is used as RD (on left) has smaller sub-divi- sions called parishes and the one from UBOS used as AD (right) represents Nakawa as one solid object. Using MATLAB (or any data structure details viewer), we extracted the data structure (see Table 1 and Table 2) in order to have the parameters that are updated and adjusted.

In the tables above, we have the file name characters (Filename), types of geometry objects inside (ShapeType), the location extend of the dataset (Bounding Box), number of objects inside (NumFeatures), the number of attributes associated with each structure (Attributes). The dataset from KCCA (Table 1) had 23 objects that can observed by looking at the NumFeatures row and comparing it with Table 2 of UBOS that has only one object. In addition, the dataset from KCCA has more details that can be observed by looking at the attributes as it has 18 columns of attributes as compared to eight columns in the dataset from UBOS. It can also be observed that the two datasets although representing the same location (Nakawa division of Kampala City) lie in different locations according to the min and max values as per Bounding Box of each dataset (Table 1 and Table 2). Extracting the bounding box values and comparing them using Table 3, we observe variation in location.

From table, the two datasets are located between same latitudes as per their Easting (x-coordinates) readings, but in different longitudes (locations) along the northing (y-coordinates) readings. Putting that on the x-y axes, we get Figure 3 that shows relative location of the two bounding boxes for the two datasets.

Further analysis shows that two datasets occupy the same size of area of 9057 by 13755 meters on earth’s surface, although they are at different locations because of varying y-values, they have same x-values. This is common for datasets that have been capture and stored using different systems. That means for the two datasets to lie in the same location and to have the same size of boundary box for the two datasets, method carried out dataset to dataset referencing, that we termed “Dataset Referencing”. This is achieved by translating AD through 9,800,000 meters (difference between the y-values as computed in Table 3) along the y-axis to be at the same location as RD on the earth’s surface. This makes the AD to have the size of the bounding box and to be in the same location as RD.

The next step was to deal with the number objects in the datasets, from Table 1 and Table 2, dataset AD from UBOS had one object, therefore, the number of objects in AD had to be increased to match those of RD. The method accomplishes that by inserting more objects into AD using the coordinates details of the objects in RD.

This is done by handling one object in RD at a time and the process involves reading object’s details that are attached to points (in this case the vertices along the segments that make up the edges of polygons and transferring them into AD. This is done by inserting the x-y values and corresponding attributes into matrix having the AD data structure. The process continues until all objects in RD and their attributes are read and transferred. This makes AD to have the same numbers of objects as RD and its attribute matrix will increase as per number of copied objects. This alignment process accomplishes the updating and adjustment of AD.

We have shown that geo-spatial data integration can be effectively carried out by incorporating geometry alignment to update and adjust one dataset with changes from another dataset or a known source. This can be easily done by using spatial geometry objects that are manipulated to define all geo-spatial data elements. With this, we obtain a uniform alignment that avoids slivers and danglings that are always created during data merging due to overlaps, openings, and overshoots among geometries of features on layers as a result of variations in data capture, storage, and manipulation approaches. This supplements effective integration of data from a variety of sources that contributes to increased understanding and informed decision-making about actions taking place on earth through answering complex questions in geo-spatial information systems. The method was tested on actual geo-spatial datasets and an analysis of resultant datasets met requirements of topological vector GIS datasets.

To facilitate day-to-day use by GIS practitioners, we plan to convert the method into an application or extension using python that can be used as a plugin in QGIS. This will put all the functionalities into a QGIS menu like “Geometry Alignment” and different functions accessed by QGIS users by clicking on its submenus. The functionalities will come from the different independent algorithms that make up the method. QGIS plugin will have the help that links and explains all functionalities and a well-documented user guide detailing on how to implement all tasks on actual data.