Spatial Calculations in GIS

Spatial Calculations in GIS

• Spatial data combines geometry (location) and attributes (non-spatial details)
• Spatial calculations focus on feature geometry, unlike attribute calculations that deal with non-spatial data
• Calculations include distance, perimeter, area, centroid, and minimum enclosing rectangles
• These involve arithmetic operations on spatial properties (e.g., coordinates)

Euclidean Distance

• Euclidean distance is the straight-line distance between two points
• Calculated using the Pythagorean theorem: √((x₂ - x₁)² + (y₂ - y₁)²), where (x₁, y₁) and (x₂, y₂) are the coordinates of the points.
• Applies to points, lines, and polygons: find closest points on objects when calculating distances between different objects
• Calculation method depends on GIS definition (e.g., closest point on a polygon's edge or vertex to a line)
• Tools like the "Near Tool" in GIS software use closest edges or vertices for calculations.

Perimeter and Length

• Polygon perimeter is the sum of all edge lengths calculated using Euclidean distance.
• Example: Perimeter of a quadrilateral with sides 7, 7, 3, 3 units = 20 units

Area Calculation (Trapezoid Algorithm)

• Approximates polygon area using trapezoids
• Vertices numbered consecutively starting from the leftmost
• Dropping lines from each vertex to the x-axis creates trapezoids
• Sum of trapezoid areas approximates the polygon area
• For trapezoids below the polygon, areas are subtracted

Centroid Calculation

• Centroid is the geometric center of a polygon
• Calculated by averaging X and Y coordinates of all vertices of the polygon
• Example: For points (2, 2), (4, 1), (4, 4), (6, 6), (8, 6), the centroid is (4.8, 3.8)
• Centroids may fall outside the polygon for irregular shapes.
• Used to represent polygons as points, calculate distances between objects, and for site suitability assessments

Minimum Enclosing Rectangle (MAR)

• MAR is the smallest rectangle completely containing a point, line, or polygon
• Defined by minimum and maximum X and Y coordinates
• Example: For specific coordinates, a rectangle is drawn based on the furthest outer points.
• Improves computational speed when checking for overlaps for complex objects
• Used in GIS tools for clipping or for bounding geometry