### Input Shape Autoindexing

Since physical edge indexing is being abandoned, we introduce *logical edges* – groupings of the input region edges into geometrically (or otherwise) meaningful sets. Selection indexes shall correspond to that of these sets. Applied rules should preserve/propagate these edge sets.

Following shape classes could result in the following actions:

**Rectangular quad**– trivial case.**Quad**,**not axis-aligned**, we can try:- simple: determine index for the first edge, increment successive edges
- harder: compute
*Oriented Bounding Box*; translate longest edge of that to x-axis; edge to the left (W-edge) has index 0.

**|e| > 4, but roughly looks like a quad**:*Cardinal Directions*selection will create 4 groups of edges- …?

**|e| > 4, looks like a multi-polygon**- length/angle threshold.

### Grid-based Parks

Grid rule requires for input region to be a quad and ideally rectangular or close to rectangular or it will look strange. In other words we need to provide the following guarantee to Grid rule:

- |Vi| == 4, Vi are vertices of the input region – a quad
- All angles >= threshold1 (e.g. 70 degrees) – close to rectangular
- Min Area >= threshold2 – minimum area required to build a park, otherwise fail (no derivation or a alternative rule)
- Input region convex – otherwise results make no sense.

The following fixes apply to the appropriate points

- Oriented Rectangle (Box): 1, 2, 4
- Bounding Box
- Inscribed Box
- Linear Combination
- Optimised Box that occupies area sufficient for a park (harder problem)

- Axis-aligned box: certain design constraints
- Autoindexing: 1
- Cardinal directions when looks like a quad; Grid still requires a ‘corner shape’ which can be a quad with vertices corresponding to the
*meething points*

- Cardinal directions when looks like a quad; Grid still requires a ‘corner shape’ which can be a quad with vertices corresponding to the
- Autoindexing + Oriented Box,
- which vertices are at proximity (using a certain function) to the meeting points