Problems with convex hulls

[EricChristiansen2]

We are using ArcGIS to examine the outline shapes of pits in lava flows. We have outlined most of the pits using the Freehand tool and some with a point to point (polygon) method. We have then calculated the convex hull. Many of the convex hulls drawn on the Freehand shapes lie WITHIN the shape. It appears that there are a few discrete points that are used on the Freehand outline, rather than every point that would appear to lie on the perimeter. Thus, in these cases the area of the convex hull is LESS than the area of the shape, when it should always be larger. This ratio is commonly used in morphometric studies, but will be incorrect in the Freehand tool is used to define the perimeter. 

We have not noticed this problem when the shape was digitized by the point to point method. 

Has anyone else noticed this? Is there any fix to the problem?

BTW, does anyone know what method ArcGIS uses to define the convex hull? 

[DanPatterson]

An image would help to address your situation.

esri doesn't specify which algorithm they use, but you can compare results to scipy's

from scipy.spatial import ConvexHull as CH

you just need an array of points (perimeter is fine).

[Dale_Honeycutt]

The Minimum Bounding Geometry tool calculates a convex hull (as well as other shapes) for features in a feature class. The help doesn't the say what method is used to define the convex hull.