Polygon¶

detroit.polygon_area(polygon: list[tuple[float, float]]) → float¶

Returns the signed area of the specified polygon. If the vertices of the polygon are in counterclockwise order (assuming a coordinate system where the origin is in the top-left corner), the returned area is positive; otherwise it is negative, or zero.

Parameters:: polygon (list[Point2D]) – Polygon
Returns:: Signed area of the specified polygon
Return type:: float

Examples

>>> d3.polygon_area([[1, 1], [1.5, 0], [2, 1]])
-0.5

detroit.polygon_centroid(polygon: list[tuple[float, float]]) → tuple[float, float]¶

Returns the centroid of the specified polygon.

Parameters:: polygon (list[Point2D]) – Polygon
Returns:: Centroid point
Return type:: Point2D

Examples

>>> d3.polygon_centroid([[1, 1], [1.5, 0], [2, 1]])
[1.5, 0.6666666666666666]

detroit.polygon_contains(polygon: list[tuple[float, float]], point: tuple[float, float]) → bool¶

Returns True if and only if the specified point is inside the specified polygon.

Parameters:

polygon (list[Point2D]) – Polygon
point (Point2D) – 2D Point

Returns:

True if and only if the specified point is inside the specified polygon.

Return type:

bool

Examples

>>> d3.polygon_contains([[1, 1], [1.5, 0], [2, 1]], [1.5, 0.667])
True

detroit.polygon_hull(points: list[tuple[float, float]]) → list[tuple[float, float]] | None¶

Returns the convex hull of the specified points using Andrew’s monotone chain algorithm. The returned hull is represented as an array containing a subset of the input points arranged in counterclockwise order. Returns None if points has fewer than three elements.

Parameters:: points (list[Point2D]) – List of points
Returns:: Convex hull or None if points has fewer than three elements.
Return type:: list[Point2D] | None

Examples

>>> points = [
...     [2, 2],
...     [6, 8],
...     [10, 10],
...     [12, 10],
...     [14, 4],
...     [20, 4],
...     [24, 8],
...     [29, 6],
...     [32, 4],
...     [35, 5],
...     [38, 2],
... ]
>>> d3.polygon_hull(points)
[[38, 2], [2, 2], [6, 8], [10, 10], [12, 10], [24, 8], [35, 5]]

detroit.polygon_length(polygon: list[tuple[float, float]]) → float¶

Returns the length of the perimeter of the specified polygon.

Parameters:: polygon (list[Point2D]) – Polygon
Returns:: Length of the perimeter of the specified polygon.
Return type:: float

Examples

>>> d3.polygon_length([[1, 1], [1.5, 0], [2, 1]])
3.23606797749979