# 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.