# Curve Collections

A CurveCollection is a an abstract base class for various collection of curves.

There are 5 concrete derived types:

- Path - curve primitives joining head to tail
- Loop - curve primitives joining head to tail and closing to form a loop
- ParityRegion -
`Loop`

s that bound a planar area by parity rules. - UnionRegion - boolean union of areas of
`Loop`

s and/or`ParityRegion`

s

`Path`

and `Loop`

`Path`

and `Loop`

are collections for which

- All members of the collection must be derived from CurvePrimitive, i.e. be one of
- Successive
`CurvePrimitive`

members must match "head to tail". - In a
`Loop`

, the last member's head must match the first member's tail. - Throughout the library, a
`Loop`

is expected to be a "filled" planar region. - A
`Path`

is usually does*not*return to its start point.- If a
`Path`

*does*return to its start point, it is*not*interpreted as enclosing area. The path is still just a wire that happens to come back to its start.

- If a

The immediate base class for both `Path`

and `Loop`

is `CurveChain`

. The `CurveChain`

base class implements various methods that depend on the internal head-to-tail matching but *not* on the closure of a `Loop`

.

### Special `Loop`

properties

- The purpose of a
`Loop`

is to act as the boundary of a planar region.- Unless specifically indicated by names or comments for various methods that at on
`Loop`

s, The containing plane will be determine "on demand" using the`FrameBuilder`

class.

- Unless specifically indicated by names or comments for various methods that at on
- A point is "inside" a loop if a line (within the
`Loop`

's plane) from the point "to infinity" crosses the loop an odd number of times. - The crossing count rule may be applied (and mathematically always produces the same result) for:
- Any line direction -- horizontal, vertical, or any other direction.
- Any curved path that starts at the and gets to infinity.

`ParityRegion`

A `ParityRegion`

is a curve collection whose immediate children are

*all*of type`Loop`

(i.e. array of`CurvePrimitive`

joined head-to-tail both internally an from last to first.- all coplanar.

"Inside" and "Outside" of a parity region is determined by the rule commonly called "even/odd", "exclusive or" or "parity":

- A point is "inside" the parity region if and only if it is classified as "inside" of an odd number of its
`Loop`

s. - A point is "inside" if and only if performing "exclusive or" among the (boolean) "inside" classification of all of its
`Loop`

s.

In nearly all uses, the various loops in a `ParityRegion`

- have no intersections among any pair of loops.
- have exactly one that can be called
`outer`

- all other than the
`outer`

`UnionRegion`

A `UnionRegion`

is a curve collection whose immediate children are

- limited to the two types
`Loop`

and`ParityRegion`

. - all coplanar.

"Inside" and "Outside" of a parity region is determined by the boolean "union" or "OR" rule:

- A point is "inside" the union region if it is "inside"
*one or more*of the members. - A point is "inside" if and only if performing "union" among the (boolean) "inside" classification of all of its
`Loop`

and`ParityRegion`

.

## Tips for Processing `CurveCollection`

s

Processing all 5 subtypes of `CurveCollection`

initially appears quite complex. However, within each of the cases of a top level switch statement or sequence of `if`

tests, the number of possibilities drops quickly:

- A
`Path`

or`Loop`

can*only*contain true`CurvePrimitive`

. - A
`ParityRegion`

may only contain`Loop`

s. - A
`UnionRegion`

may contain only`Loop`

,`ParityRegion`

, or further`UnionRegion`

. - A
`BagOfCurves`

is the only one with free mixture of both`CurveCollection`

and`CurvePrimitive`

.

## IModelJson Examples

Last Updated: 02 February, 2022