trimesh.path.polygons

trimesh.path.polygons.edges_to_polygons(edges, vertices)

Given an edge list of indices and associated vertices representing lines, generate a list of polygons.

Parameters:

  • edges ((n, 2) int) – Indexes of vertices which represent lines

  • vertices ((m, 2) float) – Vertices in 2D space

Returns:

polygons – Polygon objects with interiors

Return type:

(p,) shapely.geometry.Polygon

trimesh.path.polygons.enclosure_tree(polygons)

Given a list of shapely polygons with only exteriors, find which curves represent the exterior shell or root curve and which represent holes which penetrate the exterior.

This is done with an R-tree for rough overlap detection, and then exact polygon queries for a final result.

Parameters:

polygons ((n,) shapely.geometry.Polygon) – Polygons which only have exteriors and may overlap

Returns:

  • roots ((m,) int) – Index of polygons which are root

  • contains (networkx.DiGraph) – Edges indicate a polygon is contained by another polygon

trimesh.path.polygons.identifier(polygon: Polygon) → ndarray[Any, dtype[float64]]

Return a vector containing values representative of a particular polygon.

Parameters:

polygon (shapely.geometry.Polygon) – Input geometry

Returns:

identifier – Values which should be unique for this polygon.

Return type:

(8,) float

trimesh.path.polygons.medial_axis(polygon: Polygon, resolution: float | floating | int | integer | unsignedinteger | None = None, clip=None)

Given a shapely polygon, find the approximate medial axis using a voronoi diagram of evenly spaced points on the boundary of the polygon.

Parameters:

  • polygon (shapely.geometry.Polygon) – The source geometry

  • resolution (float) – Distance between each sample on the polygon boundary

  • clip (None, or (2,) int) – Clip sample count to min of clip[0] and max of clip[1]

Returns:

  • edges ((n, 2) int) – Vertex indices representing line segments on the polygon’s medial axis

  • vertices ((m, 2) float) – Vertex positions in space

trimesh.path.polygons.paths_to_polygons(paths, scale=None)

Given a sequence of connected points turn them into valid shapely Polygon objects.

Parameters:

  • paths ((n,) sequence) – Of (m, 2) float closed paths

  • scale (float) – Approximate scale of drawing for precision

Returns:

polys – Filled with Polygon or None

Return type:

(p,) list

trimesh.path.polygons.plot(polygon=None, show=True, axes=None, **kwargs)

Plot a shapely polygon using matplotlib.

Parameters:

  • polygon (shapely.geometry.Polygon) – Polygon to be plotted

  • show (bool) – If True will display immediately

  • **kwargs – Passed to plt.plot

trimesh.path.polygons.polygon_bounds(polygon, matrix=None)

Get the transformed axis aligned bounding box of a shapely Polygon object.

Parameters:

  • polygon (shapely.geometry.Polygon) – Polygon pre-transform

  • matrix ((3, 3) float or None.) – Homogeneous transform moving polygon in space

Returns:

bounds – Axis aligned bounding box of transformed polygon.

Return type:

(2, 2) float

trimesh.path.polygons.polygon_obb(polygon: Polygon | ndarray[Any, dtype[_ScalarType_co]])

Find the oriented bounding box of a Shapely polygon.

The OBB is always aligned with an edge of the convex hull of the polygon.

Parameters:

polygons (shapely.geometry.Polygon) – Input geometry

Returns:

  • transform ((3, 3) float) – Transformation matrix which will move input polygon from its original position to the first quadrant where the AABB is the OBB

  • extents ((2,) float) – Extents of transformed polygon

trimesh.path.polygons.polygon_scale(polygon)

For a Polygon object return the diagonal length of the AABB.

Parameters:

polygon (shapely.geometry.Polygon) – Source geometry

Returns:

scale – Length of AABB diagonal

Return type:

float

trimesh.path.polygons.polygons_obb(polygons: Iterable[Polygon])

Find the OBBs for a list of shapely.geometry.Polygons

trimesh.path.polygons.projected(mesh, normal, origin=None, ignore_sign=True, rpad=1e-05, apad=None, tol_dot=0.01, max_regions=200)

Project a mesh onto a plane and then extract the polygon that outlines the mesh projection on that plane.

Note that this will ignore back-faces, which is only relevant if the source mesh isn’t watertight.

Also padding: this generates a result by unioning the polygons of multiple connected regions, which requires the polygons be padded by a distance so that a polygon union produces a single coherent result. This distance is calculated as: apad + (rpad * scale)

Parameters:

  • mesh (trimesh.Trimesh) – Source geometry

  • check (bool) – If True make sure is flat

  • normal ((3,) float) – Normal to extract flat pattern along

  • origin (None or (3,) float) – Origin of plane to project mesh onto

  • ignore_sign (bool) – Allow a projection from the normal vector in either direction: this provides a substantial speedup on watertight meshes where the direction is irrelevant but if you have a triangle soup and want to discard backfaces you should set this to False.

  • rpad (float) – Proportion to pad polygons by before unioning and then de-padding result by to avoid zero-width gaps.

  • apad (float) – Absolute padding to pad polygons by before unioning and then de-padding result by to avoid zero-width gaps.

  • tol_dot (float) – Tolerance for discarding on-edge triangles.

  • max_regions (int) – Raise an exception if the mesh has more than this number of disconnected regions to fail quickly before unioning.

Returns:

projected – Outline of source mesh

Return type:

shapely.geometry.Polygon or None

Raises:

ValueError – If max_regions is exceeded

trimesh.path.polygons.random_polygon(segments=8, radius=1.0)

Generate a random polygon with a maximum number of sides and approximate radius.

Parameters:

  • segments (int) – The maximum number of sides the random polygon will have

  • radius (float) – The approximate radius of the polygon desired

Returns:

polygon – Geometry object with random exterior and no interiors.

Return type:

shapely.geometry.Polygon

trimesh.path.polygons.repair_invalid(polygon, scale=None, rtol=0.5)

Given a shapely.geometry.Polygon, attempt to return a valid version of the polygon through buffering tricks.

Parameters:

  • polygon (shapely.geometry.Polygon) – Source geometry

  • rtol (float) – How close does a perimeter have to be

  • scale (float or None) – For numerical precision reference

Returns:

repaired – Repaired polygon

Return type:

shapely.geometry.Polygon

Raises:

ValueError – If polygon can’t be repaired

trimesh.path.polygons.resample_boundaries(polygon: Polygon, resolution: float, clip=None)

Return a version of a polygon with boundaries re-sampled to a specified resolution.

Parameters:

  • polygon (shapely.geometry.Polygon) – Source geometry

  • resolution (float) – Desired distance between points on boundary

  • clip ((2,) int) – Upper and lower bounds to clip number of samples to avoid exploding count

Returns:

kwargs – Keyword args for a Polygon constructor Polygon(**kwargs)

Return type:

dict

trimesh.path.polygons.sample(polygon, count, factor=1.5, max_iter=10)

Use rejection sampling to generate random points inside a polygon.

Parameters:

  • polygon (shapely.geometry.Polygon) – Polygon that will contain points

  • count (int) – Number of points to return

  • factor (float) – How many points to test per loop

  • max_iter (int) – Maximum number of intersection checks is: > count * factor * max_iter

Returns:

hit – Random points inside polygon where n <= count

Return type:

(n, 2) float

trimesh.path.polygons.second_moments(polygon: Polygon, return_centered=False)

Calculate the second moments of area of a polygon from the boundary.

Parameters:

  • polygon (shapely.geometry.Polygon) – Closed polygon.

  • return_centered (bool) – Get second moments for a frame with origin at the centroid and perform a principal axis transformation.

Returns:

  • moments ((3,) float) – The values of [Ixx, Iyy, Ixy]

  • principal_moments ((2,) float) – Principal second moments of inertia: [Imax, Imin] Only returned if centered.

  • alpha (float) – Angle by which the polygon needs to be rotated, so the principal axis align with the X and Y axis. Only returned if centered.

  • transform ((3, 3) float) – Transformation matrix which rotates the polygon by alpha. Only returned if centered.

trimesh.path.polygons.stack_boundaries(boundaries)

Stack the boundaries of a polygon into a single (n, 2) list of vertices.

Parameters:

boundaries (dict) – With keys ‘shell’, ‘holes’

Returns:

stacked – Stacked vertices

Return type:

(n, 2) float

trimesh.path.polygons.transform_polygon(polygon, matrix)

Transform a polygon by a a 2D homogeneous transform.

Parameters:

  • polygon (shapely.geometry.Polygon) – 2D polygon to be transformed.

  • matrix ((3, 3) float) – 2D homogeneous transformation.

Returns:

result – Polygon transformed by matrix.

Return type:

shapely.geometry.Polygon