Convex Hull

Use convex hull as a geometric outer-boundary overlay on grouped scatter data, and read it as an exploratory envelope rather than an automatic statement about group separation.

Figure purpose

Convex hull draws an outer boundary around grouped points in a two-dimensional scatter-like view. It can help the reader see the broad extent of each group at a glance.

In practice, the hull is the outer polygon formed by the most extreme visible points of a group in the plotted x-y space. The output is therefore an envelope of the group's displayed extent, not a model-based summary of where most points lie.

That convenience comes with limits. The boundary is geometric, not a proof of stability, confidence, or true cluster structure.

When to use or avoid

Use convex hull when you want a quick outer-envelope view around grouped point clouds. It can be helpful as an overlay when the main question is how far a group extends across the plotted space.

Avoid reading the hull as a robust group summary in small samples or outlier-heavy data. A few extreme points can pull the boundary outward and make a group look more spread out than its central mass suggests.

This is why the page stays conservative even though the current renderer exists.

Required columns

  • One numeric x variable
  • One numeric y variable
  • A grouping variable if multiple hulls are being compared

The current implementation is a two-dimensional grouped overlay. Docs should keep the scope there rather than broadening it into a general shape-analysis workflow.

Convex hull can help readers see one outer boundary, but it does not guarantee separation and does not prove that one group is internally cohesive. It is best treated as an exploratory geometry layer on top of a scatter-like view.

Licklider does not automatically determine from this hull whether the apparent group spread is stable, whether an extreme point is a meaningful observation or an outlier artifact, or whether one group is truly separated from another. Those are interpretation questions that need the underlying points and study context, not just the boundary.

Alternative figures

  • Use Scatter Plot when the points themselves are still the most important part of the story.
  • Use PCA Biplot when a reduced multivariate view is more useful than a direct grouped scatter overlay.
  • Use Confidence Ellipse when a smoother summary of central spread and orientation is easier to read than a strict outer boundary.

Stay with convex hull when the outer extent of each group is the main visual question. Prefer confidence ellipse when you want a less outlier-driven overlay that emphasizes broad orientation more than extreme boundary reach.

TODO (Phase02+)

  • Expand only if the public product surface later exposes clearer guidance on outlier sensitivity and boundary interpretation.