defining and controlling the elements

This chart defines the formal hierarchies for the different types of spaces.

The following charts provide two possible formal approaches for the spaces. The oval elements that define the spaces are cut into segments which work together to create a hierarchy of glamorous entrance, enclosure, and exit. Two different methods were employed to join the corresponding sets of curves.

1. The first set uses parallel tangency to create a connection between the curving elements. This creates a connection through a smooth point (mathematical inflection).

2. The second set uses a hierarchy of tangential angles to connect the elements. This creates a connection through a smooth or singular point (Cache's inflection).