geomotif.bases.polygon

Base for motifs that are an exact list of corners.

Distinct from :class:~geomotif.ParametricMotif for a reason that matters: a polygon fed through a parametric position(u) is measured by evaluating it at evenly spaced parameters, and a corner survives that only if a sample happens to land exactly on it. A pentagon measured at 512 samples has none of its five corners land on one, so every vertex comes out slightly cut. Listing the corners instead keeps them exact and costs five points rather than five hundred.

Anything whose shape is decided by its vertices belongs here: rectangles, regular polygons, stars, the whole {n/k} family, and open polylines such as the Theodorus spiral's chain of triangles.

Classes:

Name	Description
PolygonMotif	Base for a motif drawn as one or more exact corner sequences.

PolygonMotif dataclass

PolygonMotif()

Bases: Motif, ABC

Base for a motif drawn as one or more exact corner sequences.

Implement :meth:outlines; :meth:build turns each one into a :class:~geomotif.Path::

@register("rectangle", family="primitive")
@dataclass(frozen=True, slots=True)
class Rectangle(PolygonMotif):
    width: float = 1.0
    height: float = 1.0

    def outlines(self) -> Iterable[Sequence[Point]]:
        w, h = self.width / 2.0, self.height / 2.0
        yield ((-w, -h), (w, -h), (w, h), (-w, h))

:meth:outlines is plural because one shape is not always one loop: the star polygon {6/2} is two overlaid triangles, and drawing it as a single path would invent an edge between them that is not there.

Notes

Corners are emitted as given -- no deduplication, no collinear-point removal. A motif that wants a vertex repeated (to hold a pen, to mark a lattice site) is entitled to it, and guessing otherwise would silently change geometry the author chose.

Methods:

Name	Description
outlines	Return the corner sequences to draw, one per stroke. At least one.

outlines abstractmethod

outlines() -> Iterable[Sequence[Point]]

Return the corner sequences to draw, one per stroke. At least one.

Source code in src/geomotif/bases/polygon.py

@abstractmethod
def outlines(self) -> Iterable[Sequence[Point]]:
    """Return the corner sequences to draw, one per stroke. At least one."""