GIS Lecture 7a Notes PDF

1. Spatial Calculations in GIS ​ Spatial vs. Attribute Data: Spatial data contains both geometry (spatial information) and attributes (non-spatial information). Unlike attribute calculations, which focus on non-spatial attributes, spatial calculations involve properties related to fe...

1. Spatial Calculations in GIS ​ Spatial vs. Attribute Data: Spatial data contains both geometry (spatial information) and attributes (non-spatial information). Unlike attribute calculations, which focus on non-spatial attributes, spatial calculations involve properties related to feature geometry based on X, Y coordinate vertices. ​ Spatial Operations: These include calculations like distance, perimeter, area, centroid, and minimum enclosing rectangle. These calculations involve arithmetic operations on spatial properties. 2. Euclidean Distance ​ Definition: The Euclidean distance is the straight-line distance between two points in space. ​ Formula: You can calculate it using the Pythagorean theorem. For example, the distance between points (−2,−3)(-2, -3)(−2,−3) and (−4,4)(-4, 4)(−4,4) can be calculated as: Distance=(x2−x1)2+(y2−y1)2\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}Distance=(x2​−x1​)2+(y2​−y1​)2​ ​ Application to other objects: When working with lines or polygons, you find the point on each object closest to the other and calculate the distance between those points. ​ Impact of Spatial Definition: The calculation method depends on how the spatial relationship is defined in GIS. For example, the distance between a polygon and a line could vary depending on whether the closest point is on the edge or the vertices of the objects. ​ Practical Considerations: When using tools like the "Near Tool" in GIS software, it will calculate the distance between objects using the closest edge or vertices. 3. Perimeter and Length ​ Polygon Perimeter: The perimeter of a polygon or the length of a polyline is the sum of all its edge lengths. Each edge is calculated using Euclidean distance (Pythagorean theorem). ​ Example: If a polygon has four edges of lengths 7, 7, 3, and 3 units, the total perimeter is 7+7+3+3=207 + 7 + 3 + 3 = 207+7+3+3=20 units. 4. Area Calculation Using the Trapezoid Algorithm ​ Trapezoid Algorithm: This method calculates the area of polygons by approximating the shape with trapezoids and summing their areas. ○​ Process: 1.​ The vertices of the polygon are numbered in order, starting from the leftmost point. 2.​ Trapezoids are formed by dropping lines from the vertices to the X-axis.  3.​ The area of each trapezoid is calculated and then summed. If a trapezoid is below the polygon, its area is subtracted. ​ Formula for a Trapezoid: Area=b1+b22×h\text{Area} = \frac{b_1 + b_2}{2} \times hArea=2b1​+b2​​×h where b1b_1b1​and b2b_2b2​are the lengths of the parallel sides, and hhh is the height. ​ Complex Shapes: This method works for non-rectangular shapes as well. ​ Example: The area of a polygon with several vertices can be computed by summing the areas of the trapezoids formed by each pair of vertices. 5. Centroid Calculation ​ Definition: The centroid is the center of mass (or geometric center) of a polygon and is calculated by averaging the X and Y coordinates of its vertices. ​ Calculation: ○​ The centroid’s X coordinate is the average of the X coordinates of all vertices. ○​ Similarly, the centroid’s Y coordinate is the average of the Y coordinates. ​ Example: For a polygon with vertices at (2,2),(4,1),(4,4),(6,6),(8,6)(2, 2), (4, 1), (4, 4), (6, 6), (8, 6)(2,2),(4,1),(4,4),(6,6),(8,6), the centroid is calculated as: Xcentroid=2+4+4+6+85=4.8X_{\text{centroid}} = \frac{2 + 4 + 4 + 6 + 8}{5} = 4.8Xcentroid​=52+4+4+6+8​=4.8 Ycentroid=2+1+4+6+65=3.8Y_{\text{centroid}} = \frac{2 + 1 + 4 + 6 + 6}{5} = 3.8Ycentroid​=52+1+4+6+6​=3.8 ​ Issues: The centroid may fall outside the polygon, especially for irregular shapes. This is common in GIS applications. ​ Uses: Centroids are used to reduce storage by representing polygons as points, calculate distances between objects, geocode locations, and determine site suitability (e.g., the center of a forest for a watchtower). 6. Minimum Enclosing Rectangle (MAR) ​ Definition: The minimum enclosing rectangle (MAR) is a rectangle that surrounds an object (point, line, or polygon), defined by the minimum and maximum X and Y values of the object. ​ Example: For a polygon with vertices at specific coordinates, the MAR is drawn based on the outermost points. ​ Uses: ○​ Computational Efficiency: MAR reduces computational effort when checking for intersections between objects. If the MARs do not overlap, the objects themselves do not intersect. ○​ Bounding Geometry: MAR is used for default extents in calculations and clipping background layers. ○​ GIS Tools: The MAR can be calculated using the "Minimum Bounding Geometry" tool, specifically the "Envelope" option. 7. Conclusion ​ Spatial Calculations Summary: Spatial calculations in GIS involve arithmetic operations that identify spatial properties of feature geometry. Common calculations include distance, perimeter, area, centroid, and the minimum enclosing rectangle. ​ Important Concepts: ○​ Understanding the definition of spatial relationships between objects (e.g., how distance is calculated). ○​ Knowing how geometries are recorded in GIS. ○​ Using the appropriate GIS tools for these spatial operations.