Geometric measurement functions

Geometry is a property of an object, just as is the thematic. With the appropriate measuring functions, queries can be performed. The general geometric queries are listed below:

Position – where (x, y)?

Vector model

Returns the position of each point from the map as x‐ and y‐coordinates.

Raster model

Example: Block encoding

Value	No. Cell	Location
1	8	4,2 5,2 6,2 4,3 5,3 4,4 5,4 5,5
2	7	7,2 6,3 7,3 6,4 7,4 6,5 7,5

Distance

Vector model

For vector data, the distance between two objects is calculated according to the Pythagorean Theorem and corresponds to the shortest distance.

Euclidean distance

Distance between point A and B

Example: The distance is 11,3 cm.

Raster model

In the raster model, there are three different approaches to measure the distance between points.

Euclidean distance	Straight line between point A and point B Beispiel: Mit einer Auflösung von 2 cm beträgt die Distanz 11,3 cm.
Manhattan distance	Distance along the cell boundary between points A and B. Example: Using a resolution of 2 cm, the distance is16 cm.
Neighborhood	Concentric zones with same distance around point A. Example: Using a resolution of 2 cm, the distance is 11,3 cm.

Practical examples

WHERE
In ArcInfo "Measuring Where" returns the x, y position of a selected point on a map.

LENGTH
In ArcInfo "Length" returns the length of a line section, which consists of two or more points.

WITHIN A CERTAIN DISTANCE
Two objects are lying "within a certain distance" if the distance between them is smaller than the given distance. Traditional GIS software offer pre‐programmed tools to answer these questions.

Question 1:
Select all mountain peaks that are less than 500m away from the cabins (planimetric).

Question 2:
Select all the trees that are less than 200m away from the collection point.

Size

Vector data model

PERIMETER
Sum of the length of all single sections.

AREA
Sum of the area of the simple geometric shapes (e.g. triangles and rectangles), into which the main object can be devided.

Raster data model

PERIMETER
Number of cell edges, which delimit the object, multiplied by the resolution of the cells.
Example:
Using a cell resolution of 2cm, the perimeter is 32 cm.

AREA
Number of cells, which define the object, mutliplied by the area of one cell..
Example:
Using a cell resolution of 2cm, the area is 60 cm².

Proximity analysis / buffering

Vector data model

A buffer is a spatial expansion around points, lines and polygons defined by a distance.

	Point buffer
	Line buffer
	Polygon buffer

Raster data model

In the raster data model, proximity is calculated for the entire raster. Then a certain distance is chosen. For in-depth look have a look at the lesson Accessibility.