Error calling projected with very niche inputs

[MattTheCuber]

Hello,

We ran into an edge case in our software and tracked it down to the mesh.projected(precise=True) call. Now this is a long story, so I'm going to cut to the chase. We save our meshes as VTP files using PyVista, then read them later using PyVista and convert to a Trimesh object using trimesh.Trimesh(pv_mesh.points, pv_mesh.regular_faces). After this, we call mesh.projected with a set of very specific normals. With a very specific single mesh at a specific single normal, this fails. We have tried many thousands of other meshes with these normals before without any problems, so this is extremely niche. The mesh that fails is uploaded in the example below (54 vertices and 104 faces). The normal that fails with this mesh is also in the example below.

I am not sure if this a PyVista problem with the vertex positions array (see workarounds), if this is a problem with Trimesh, or a problem with shapely. I decided to start here and we can move the issue if desired.

Minimal Example

feature.zip (download and extract the single file it contains, GitHub won't let me upload a VTP file)

import trimesh
import pyvista as pv

pv_mesh: pv.PolyData = pv.read("feature.vtp")
mesh = trimesh.Trimesh(pv_mesh.points, pv_mesh.regular_faces)
mesh.projected([-0.7941530735495742, 0.5769859816799351, 0.19080899537654492], precise=True)  # Crashes

GEOSException: TopologyException: Ring edge missing at -1.5732562941774 7.904434391775184

Stack trace

---------------------------------------------------------------------------
GEOSException                             Traceback (most recent call last)
...

File .venv/lib/python3.13/site-packages/trimesh/base.py:2726, in Trimesh.projected(self, normal, **kwargs)
   2723 from .path import Path2D
   2724 from .path.polygons import projected
-> 2726 projection = projected(mesh=self, normal=normal, **kwargs)
   2727 if projection is None:
   2728     return Path2D()

File .venv/lib/python3.13/site-packages/trimesh/path/polygons.py:836, in projected(mesh, normal, origin, ignore_sign, rpad, apad, tol_dot, precise)
    833     faces = mesh.faces[side]
    834     # just union all the polygons
    835     return (
--> 836         ops.unary_union(
    837             [Polygon(f) for f in vertices_2D[np.column_stack((faces, faces[:, :1]))]]
    838         )
    839         .buffer(eps)
    840         .buffer(-eps)
    841     )
    843 # a sequence of face indexes that are connected
    844 face_groups = graph.connected_components(adjacency, nodes=np.nonzero(side)[0])

File .venv/lib/python3.13/site-packages/shapely/ops.py:117, in CollectionOperator.unary_union(self, geoms)
    111 def unary_union(self, geoms):
    112     """Return the union of a sequence of geometries.
    113 
    114     Usually used to convert a collection into the smallest set of polygons
    115     that cover the same area.
    116     """
--> 117     return shapely.union_all(geoms, axis=None)

File .venv/lib/python3.13/site-packages/shapely/decorators.py:173, in deprecate_positional.<locals>.decorator.<locals>.wrapper(*args, **kwargs)
    171 @wraps(func)
    172 def wrapper(*args, **kwargs):
--> 173     result = func(*args, **kwargs)
    175     n = len(args)
    176     if n > warn_from:

File .venv/lib/python3.13/site-packages/shapely/decorators.py:88, in multithreading_enabled.<locals>.wrapped(*args, **kwargs)
     86     for arr in array_args:
     87         arr.flags.writeable = False
---> 88     return func(*args, **kwargs)
     89 finally:
     90     for arr, old_flag in zip(array_args, old_flags):

File .venv/lib/python3.13/site-packages/shapely/set_operations.py:553, in union_all(geometries, grid_size, axis, **kwargs)
    549         raise ValueError("grid_size parameter only accepts scalar values")
    551     return lib.unary_union_prec(collections, grid_size, **kwargs)
--> 553 return lib.unary_union(collections, **kwargs)

GEOSException: TopologyException: Ring edge missing at -1.5732562941774 7.904434391775184

Workarounds

• Change pv_mesh.points to pv_mesh.points.astype(np.float32)
• Change pv_mesh.points to np.round(pv_mesh.points, 64)
• Saving as STL and load that instead

[mikedh]

Yeah getting a projection to work reliably is definitely a pain in the neck since it seems to come down to union-of-a-ton-of-triangles. If you're feeling ambitious we could probably reduce that error to the minimal geos error case by binary searching through the 2D triangles produced in trimesh.path.polygons.projected and then adding it as a test case upstream to either shapely or geos.

On the trimesh side the precise code path seems like it has room for improvement:

   if precise:
        eps = 1e-10
        faces = mesh.faces[side]
        # just union all the polygons
        return (
            ops.unary_union(
                [Polygon(f) for f in vertices_2D[np.column_stack((faces, faces[:, :1]))]]
            )
            .buffer(eps)
            .buffer(-eps)
        )

• eps should probably be passable, i.e. precise_eps
• since this is using already buffer twice (i.e. dilate-erode) to clean up the result, this should probably be using your round approach before the union? i.e. vertices_2D_rounded = np.round(vertices_2D, np.abs(np.round(np.log10(eps))) + 1)?
• a minimal cleanup of the triangles would probably help too, i.e. after the round discading any triangles that have two vertices that are floating-point identical, i.e.:

triangles = vertices_2D_rounded[faces]
valid = ~(triangles[:,[0,0,2]] == triangles[:,[1,2,1]]).all(axis=2).any(axis=1)
triangles = triangles[valid]

[MattTheCuber]

Thank you for the response. I tried binary searching and removing any single face allows the projected case to pass :/

still_failing_faces = []
for i in range(len(mesh.faces)):
    m = mesh.copy()
    m.faces = np.delete(m.faces, i, axis=0)
    m.remove_unreferenced_vertices()
    try:
        m.projected([-0.7941530735495742, 0.5769859816799351, 0.19080899537654492], precise=True)
    except:
        still_failing_faces.append(i)
still_failing_faces  # []

Trimesh object straight from NumPy arrays

import trimesh
import numpy as np

mesh = trimesh.Trimesh(
    np.array(
        [
            [-12.286852860721421, -76.31204392588535, -13.557952225023367],
            [-6.105210201226011, -74.47771388561483, -13.27954387369909],
            [-11.52427890711882, -60.95949902362122, -13.28876487059643],
            [-3.686413284421442, -55.60006516683082, -12.630405185312648],
            [-11.971314235392274, -75.9930300058383, -11.389943523706183],
            [-0.5510750131001787, -77.2633890088828, -10.283544560496484],
            [12.134738960151555, -74.52556597362188, -8.921217501876688],
            [-11.73171181184248, -53.34304168249797, -10.35276761436922],
            [1.5569204320106307, -50.41494963063758, -9.74914821362371],
            [14.740524633848228, -52.29827109434389, -8.344821483262283],
            [-11.526645587422683, -75.73383119580008, -7.322133082150471],
            [1.917922438825589, -85.06498835717619, -6.191166520906248],
            [15.535271731820945, -74.91635802567953, -5.934896574623886],
            [-11.990169221923704, -44.84359938410165, -6.19221822602723],
            [2.1993113251139524, -30.31422432910178, -6.832579439035292],
            [16.33857115763426, -38.6911880689086, -5.413406046828442],
            [-10.651164841184436, -12.748520356511232, -4.770471919361949],
            [2.234763451141956, -3.596808525161588, -4.7885549500702185],
            [15.041221337000948, -5.33144671541741, -3.8604612868621198],
            [-10.652780985036758, -73.04215124540312, -3.8206836619921503],
            [2.153676900822245, -74.77678943565894, -2.892589998784051],
            [15.039605193148628, -65.62507760430928, -2.9106730294923207],
            [-12.308417884126072, -39.80204011192957, -2.1918086226806963],
            [1.7710830357618557, -48.49801777178344, -0.7338870999226491],
            [16.331961966527043, -33.30782816811467, -1.5292641151984183],
            [-12.055387641136221, -2.4603214349939826, -1.6376232403347064],
            [1.944926161240967, 8.216675701580616, -1.469998238469419],
            [15.825878246135215, -1.692694189880779, -0.5539925856156565],
            [-31.1375659243754, -24.9508027983108, 3.6360957985799276],
            [-18.153391082401043, -26.200273985161726, 2.314101813390221],
            [1.4612417829374378, -31.53900991499668, 2.6834582378243432],
            [15.083587067630955, -17.784952619253996, 1.4417408211406202],
            [-31.046778377567243, -0.22722399466465149, 3.665242680647334],
            [-16.696718955466416, 13.988833817431885, 1.9130062614429226],
            [2.771608292357917, 7.062244078410391, 2.763023090374885],
            [15.864971783804851, -0.8054367247499208, 1.6378993369262935],
            [-29.931728520549317, 36.371647982732824, 3.9180982408871596],
            [-16.75063436109305, 45.302043907049836, 3.855985133873369],
            [-3.7955641655466934, 43.585350249796676, 4.843476168272797],
            [-30.304368793274755, -22.558198397957934, 5.108008055174938],
            [-17.19489258908911, -25.531863866967914, 6.410619282750714],
            [-2.6475107505874087, -23.844223263147594, 6.901570648815133],
            [-31.01433500016052, 9.702084266799705, 5.952218357722821],
            [-20.872344061241378, 11.057893426999645, 7.844704199466644],
            [0.7857059442991607, 11.965089262133436, 7.152688252769082],
            [-27.702087058988322, 43.16664447973494, 5.9133220979370185],
            [-15.016080264806007, 47.18621987232771, 7.162330620355704],
            [-2.99606350222958, 46.46843855222184, 8.120397879921402],
            [-12.282291984414229, -21.050857625735627, 9.385944676438108],
            [-3.650003862130613, -13.896970468680603, 9.899534444350873],
            [-12.48287322317642, 12.413702587199598, 10.125605375394477],
            [-2.8438655019240615, 22.642086398708035, 10.190714181261557],
            [-9.134698895134573, 44.67398525195722, 10.021711302888072],
            [-2.8439691008889536, 47.066589652310086, 10.251598043913472],
        ],
        dtype=np.float64,
    ),
    np.array(
        [
            [3, 1, 2],
            [0, 2, 1],
            [5, 4, 1],
            [0, 1, 4],
            [7, 2, 4],
            [0, 4, 2],
            [3, 7, 8],
            [7, 3, 2],
            [5, 3, 8],
            [3, 5, 1],
            [9, 6, 8],
            [5, 8, 6],
            [11, 10, 5],
            [4, 5, 10],
            [12, 11, 6],
            [5, 6, 11],
            [13, 7, 10],
            [4, 10, 7],
            [8, 13, 14],
            [13, 8, 7],
            [9, 14, 15],
            [14, 9, 8],
            [12, 9, 15],
            [9, 12, 6],
            [17, 14, 16],
            [13, 16, 14],
            [18, 15, 17],
            [14, 17, 15],
            [20, 19, 11],
            [10, 11, 19],
            [21, 20, 12],
            [11, 12, 20],
            [22, 13, 19],
            [10, 19, 13],
            [22, 20, 23],
            [20, 22, 19],
            [23, 21, 24],
            [21, 23, 20],
            [21, 15, 24],
            [15, 21, 12],
            [25, 16, 22],
            [13, 22, 16],
            [17, 25, 26],
            [25, 17, 16],
            [18, 26, 27],
            [26, 18, 17],
            [24, 18, 27],
            [18, 24, 15],
            [30, 29, 23],
            [22, 23, 29],
            [31, 30, 24],
            [23, 24, 30],
            [33, 29, 32],
            [28, 32, 29],
            [33, 25, 29],
            [22, 29, 25],
            [26, 33, 34],
            [33, 26, 25],
            [34, 31, 35],
            [31, 34, 30],
            [27, 34, 35],
            [34, 27, 26],
            [31, 27, 35],
            [27, 31, 24],
            [37, 33, 36],
            [32, 36, 33],
            [38, 34, 37],
            [33, 37, 34],
            [40, 39, 29],
            [28, 29, 39],
            [41, 40, 30],
            [29, 30, 40],
            [42, 32, 39],
            [28, 39, 32],
            [42, 40, 43],
            [40, 42, 39],
            [41, 34, 44],
            [34, 41, 30],
            [45, 36, 42],
            [32, 42, 36],
            [45, 43, 46],
            [43, 45, 42],
            [37, 45, 46],
            [45, 37, 36],
            [38, 46, 47],
            [46, 38, 37],
            [44, 38, 47],
            [38, 44, 34],
            [49, 48, 41],
            [40, 41, 48],
            [50, 43, 48],
            [40, 48, 43],
            [50, 49, 51],
            [49, 50, 48],
            [49, 44, 51],
            [44, 49, 41],
            [52, 46, 50],
            [43, 50, 46],
            [52, 51, 53],
            [51, 52, 50],
            [47, 52, 53],
            [52, 47, 46],
            [51, 47, 53],
            [47, 51, 44],
        ],
        dtype=np.int64,
    ),
)
mesh.projected([-0.7941530735495742, 0.5769859816799351, 0.19080899537654492], precise=True)

Changing the code in polygons.py to your description worked and gave me the same polygonal area as before. Should I open a PR with this change and the precise_eps parameter? Or should this be brought upstream to shapely/geos?

    if precise:
        eps = 1e-10
        faces = mesh.faces[side]
        # just union all the polygons
        vertices_2D_rounded = np.round(vertices_2D, int(np.abs(np.round(np.log10(eps))) + 1))
        triangles = vertices_2D_rounded[np.column_stack((faces, faces[:, :1]))]
        valid = ~(triangles[:,[0,0,2]] == triangles[:,[1,2,1]]).all(axis=2).any(axis=1)
        triangles = triangles[valid]
        return ops.unary_union([Polygon(f) for f in triangles]).buffer(eps).buffer(-eps)

[mikedh]

Yeah a PR with those changes for precise mode would be great!

If we can reduce it to a shapely-only example they may be able to help figuring out where in GEOS this is happening. I wasn't able to reproduce running the numpy-only example on my machine, it may need full f64 precision to reproduce? I'm on Python 3.14 with shapely=2.1.2 and numpy=2.3.5

Maybe add a np.save('err_union.npy', {'triangles': triangles, 'epsilon': eps}) in-line to try to extract a test case?

[MattTheCuber]

I can't even get numpy==2.3.5 to run on Python 3.14. I am using Python 3.13 with the latest versions to produce this. I will get the npy file tomorrow.

[MattTheCuber]

Ok, I did a bunch of testing and learned this bug only occurs with numpy<2.1 when using Trimesh. I worked on making a minimal example using shapely, and this example fails with the latest version of numpy.

Environment:

• Python 3.13
• Numpy 2.3.5
• Shapely 2.1.2

import numpy as np
from shapely import ops
from shapely.geometry import Polygon

polygons = np.array(
    [
        [
            [-9.107924729871753, -49.578770022602505],
            [-11.477396284004609, -55.48211427005445],
            [-8.779906989660152, -68.10055885244654],
            [-9.107924729871753, -49.578770022602505],
        ],
        [
            [-10.944553152533185, -68.40940481609661],
            [-8.779906989660152, -68.10055885244654],
            [-11.477396284004609, -55.48211427005445],
            [-10.944553152533185, -68.40940481609661],
        ],
        [
            [-9.665730626080167, -46.63520657856243],
            [-9.107924729871753, -49.578770022602505],
            [-6.1606394792661385, -39.56368325939373],
            [-9.665730626080167, -46.63520657856243],
        ],
        [
            [-9.107924729871753, -49.578770022602505],
            [-9.665730626080167, -46.63520657856243],
            [-11.477396284004609, -55.48211427005445],
            [-9.107924729871753, -49.578770022602505],
        ],
        [
            [-5.60266871361742, -43.06086475203977],
            [-9.107924729871753, -49.578770022602505],
            [-4.725701460041062, -67.88249984010983],
            [-5.60266871361742, -43.06086475203977],
        ],
        [
            [-8.779906989660152, -68.10055885244654],
            [-4.725701460041062, -67.88249984010983],
            [-9.107924729871753, -49.578770022602505],
            [-8.779906989660152, -68.10055885244654],
        ],
        [
            [-6.1606394792661385, -39.56368325939373],
            [-5.60266871361742, -43.06086475203977],
            [-4.414116785691194, -23.00105208875605],
            [-6.1606394792661385, -39.56368325939373],
        ],
        [
            [-5.60266871361742, -43.06086475203977],
            [-6.1606394792661385, -39.56368325939373],
            [-9.107924729871753, -49.578770022602505],
            [-5.60266871361742, -43.06086475203977],
        ],
        [
            [2.1655564768683804, -59.48149581506282],
            [-1.2937332149450005, -65.40092352724034],
            [-0.47975546014527914, -67.79429254345098],
            [2.1655564768683804, -59.48149581506282],
        ],
        [
            [-4.725701460041062, -67.88249984010983],
            [-0.47975546014527914, -67.79429254345098],
            [-1.2937332149450005, -65.40092352724034],
            [-4.725701460041062, -67.88249984010983],
        ],
        [
            [-2.053526421384758, -39.38388953414288],
            [-5.60266871361742, -43.06086475203977],
            [-1.2937332149450005, -65.40092352724034],
            [-2.053526421384758, -39.38388953414288],
        ],
        [
            [-4.725701460041062, -67.88249984010983],
            [-1.2937332149450005, -65.40092352724034],
            [-5.60266871361742, -43.06086475203977],
            [-4.725701460041062, -67.88249984010983],
        ],
        [
            [-2.053526421384758, -39.38388953414288],
            [2.1655564768683804, -59.48149581506282],
            [2.5949143307751905, -38.432078492985355],
            [-2.053526421384758, -39.38388953414288],
        ],
        [
            [2.1655564768683804, -59.48149581506282],
            [-2.053526421384758, -39.38388953414288],
            [-1.2937332149450005, -65.40092352724034],
            [2.1655564768683804, -59.48149581506282],
        ],
        [
            [2.5949143307751905, -38.432078492985355],
            [4.045017485226917, -44.591813884340915],
            [3.6619129070589773, -17.61026441148638],
            [2.5949143307751905, -38.432078492985355],
        ],
        [
            [4.045017485226917, -44.591813884340915],
            [2.5949143307751905, -38.432078492985355],
            [2.1655564768683804, -59.48149581506282],
            [4.045017485226917, -44.591813884340915],
        ],
        [
            [-3.7536959540663597, -8.859098859659706],
            [-5.923720686905879, -16.235821209122424],
            [-2.053526421384758, -39.38388953414288],
            [-3.7536959540663597, -8.859098859659706],
        ],
        [
            [-5.60266871361742, -43.06086475203977],
            [-2.053526421384758, -39.38388953414288],
            [-5.923720686905879, -16.235821209122424],
            [-5.60266871361742, -43.06086475203977],
        ],
        [
            [-4.04425967854734, -1.346139278400533],
            [-3.7536959540663597, -8.859098859659706],
            [-1.5732562941774, 7.904434391775184],
            [-4.04425967854734, -1.346139278400533],
        ],
        [
            [-3.7536959540663597, -8.859098859659706],
            [-4.04425967854734, -1.346139278400533],
            [-5.923720686905879, -16.235821209122424],
            [-3.7536959540663597, -8.859098859659706],
        ],
        [
            [4.843141390976509, -25.008359188703416],
            [0.4110324192521997, -31.95495216694697],
            [2.5949143307751905, -38.432078492985355],
            [4.843141390976509, -25.008359188703416],
        ],
        [
            [-2.053526421384758, -39.38388953414288],
            [2.5949143307751905, -38.432078492985355],
            [0.4110324192521997, -31.95495216694697],
            [-2.053526421384758, -39.38388953414288],
        ],
        [
            [-2.170090738900679, 1.6419854605789586],
            [-3.7536959540663597, -8.859098859659706],
            [0.4110324192521997, -31.95495216694697],
            [-2.170090738900679, 1.6419854605789586],
        ],
        [
            [-2.053526421384758, -39.38388953414288],
            [0.4110324192521997, -31.95495216694697],
            [-3.7536959540663597, -8.859098859659706],
            [-2.053526421384758, -39.38388953414288],
        ],
        [
            [-1.5732562941774, 7.904434391775184],
            [-2.170090738900679, 1.6419854605789586],
            [2.8024433800252715, 7.181446815562015],
            [-1.5732562941774, 7.904434391775184],
        ],
        [
            [-2.170090738900679, 1.6419854605789586],
            [-1.5732562941774, 7.904434391775184],
            [-3.7536959540663597, -8.859098859659706],
            [-2.170090738900679, 1.6419854605789586],
        ],
        [
            [2.8024433800252715, 7.181446815562015],
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)

ops.unary_union([Polygon(p) for p in polygons])