Isochrone as Alphashape

GOAT allows you to calculate and visualize isochrones using alpha shapes. GOAT is using the function pgr_pointsAsPolygon from the library pgRouting to generate alpha shapes. The result of this function is an isochrone (polygon) representing the area from a set of points that can be reached in a dedicated time.

1. Alphashape

Alpha shapes or α-shapes are often used to generalize bounding polygons around a given sets of points. Depending on the chosen alpha parameter the precision of the isochrone can differ. The following example illustrates how alpha shapes are generated depending on the alpha-parameter.

1.1. Points from the network
1.2. Convex Hull

In the first case is the α-parameter=0. This mean the generated shape from the calculation resembles all the data points. This is called convex hull.

1.3. Concave Hull

By decreasing the alpha parameter value, generated polygon will fit better the sample data. A Concave hull describes better the shape of the point cloud than the convex hull.

2. Level of detail isochrones

GOAT allows you to choose the level of detail to calculate isochrones. The level of detail of the isochrone depends on the alpha-parameter. In the front-end of GOAT the level of detail of isochrones is categorized into six groups from 0 to 5 as following:

  • Level of detail 0: α-parameter = 0.00003
  • Level of detail 1: α-parameter = 0.000003
  • Level of detail 2: α-parameter = 0.0000025
  • Level of detail 3: α-parameter = 0.000002
  • Level of detail 4: α-parameter = 0.0000017
  • Level of detail 5: α-parameter = 0.0000015

The following example shows how the shape of the isochrone fits better to the network by increasing the level of detail.

Note: Using very high level of detail can generate errors.