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 - coplanar 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/orParityRegion
s. - BagOfCurves - a collection of
AnyCurve
with no implied structure.
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.
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 act on
Loop
s, the containing plane will be determine "on demand" using theFrameBuilder
class.
- Unless specifically indicated by names or comments for various methods that act 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 ofCurvePrimitive
joined head-to-tail both internally and 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" the parity region if and only if performing XOR (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
- are either the
outer
loop or inside theouter
loop
UnionRegion
A UnionRegion
is a curve collection whose immediate children are
- limited to the two types
Loop
andParityRegion
. - 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
andParityRegion
.
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
orLoop
can only contain trueCurvePrimitive
. - A
ParityRegion
may only containLoop
s. - A
UnionRegion
may contain onlyLoop
,ParityRegion
, or furtherUnionRegion
. - A
BagOfCurves
is the only one with free mixture of bothCurveCollection
andCurvePrimitive
.
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Last Updated: 15 May, 2024