I have a TriangleMesh in open3d and I would like to crop it using a bounding box.
Open3d has the crop function, which removes triangles if they are fully or partially outside the bounding box.
Is there a function that slices triangles instead if are partially outside the bounding box?
Here is a simple 2D example (see plot below). Given the bounding box and the input triangle, the open3d crop function would simply remove the triangle. I would like a function that takes this triangle that overlaps with the bounding box and slices it. Is there such a function?
1 Answer
I build a solution that can crop AxisAlignedBoundingBoxes (which is what I need):
Input mesh: 
Clean crop with the below code:
Open3d crop:
import open3d as o3d import numpy as np def sliceplane(mesh, axis, value, direction): # axis can be 0,1,2 (which corresponds to x,y,z) # value where the plane is on that axis # direction can be True or False (True means remove everything that is # greater, False means less # than) vertices = np.asarray(mesh.vertices) triangles = np.asarray(mesh.triangles) new_vertices = list(vertices) new_triangles = [] # (a, b) -> c # c refers to index of new vertex that sits at the intersection between a,b # and the boundingbox edge # a is always inside and b is always outside intersection_edges = dict() # find axes to compute axes_compute = [0,1,2] # remove axis that the plane is on axes_compute.remove(axis) def compute_intersection(vertex_in_index, vertex_out_index): vertex_in = vertices[vertex_in_index] vertex_out = vertices[vertex_out_index] if (vertex_in_index, vertex_out_index) in intersection_edges: intersection_index = intersection_edges[(vertex_in_index, vertex_out_index)] intersection = new_vertices[intersection_index] else: intersection = [None, None, None] intersection[axis] = value const_1 = (value - vertex_in[axis])/(vertex_out[axis] - vertex_in[axis]) c = axes_compute[0] intersection[c] = (const_1 * (vertex_out[c] - vertex_in[c])) + vertex_in[c] c = axes_compute[1] intersection[c] = (const_1 * (vertex_out[c] - vertex_in[c])) + vertex_in[c] assert not (None in intersection) # save new vertice and remember that this intersection already added an edge new_vertices.append(intersection) intersection_index = len(new_vertices) - 1 intersection_edges[(vertex_in_index, vertex_out_index)] = intersection_index return intersection_index for t in triangles: v1, v2, v3 = t if direction: v1_out = vertices[v1][axis] > value v2_out = vertices[v2][axis] > value v3_out = vertices[v3][axis] > value else: v1_out = vertices[v1][axis] < value v2_out = vertices[v2][axis] < value v3_out = vertices[v3][axis] < value bool_sum = sum([v1_out, v2_out, v3_out]) # print(f"{v1_out=}, {v2_out=}, {v3_out=}, {bool_sum=}") if bool_sum == 0: # triangle completely inside --> add and continue new_triangles.append(t) elif bool_sum == 3: # triangle completely outside --> skip continue elif bool_sum == 2: # two vertices outside # add triangle using both intersections vertex_in_index = v1 if (not v1_out) else (v2 if (not v2_out) else v3) vertex_out_1_index = v1 if v1_out else (v2 if v2_out else v3) vertex_out_2_index = v3 if v3_out else (v2 if v2_out else v1) # print(f"{vertex_in_index=}, {vertex_out_1_index=}, {vertex_out_2_index=}") # small sanity check if indices sum matches assert sum([vertex_in_index, vertex_out_1_index, vertex_out_2_index]) == sum([v1,v2,v3]) # add new triangle new_triangles.append([vertex_in_index, compute_intersection(vertex_in_index, vertex_out_1_index), compute_intersection(vertex_in_index, vertex_out_2_index)]) elif bool_sum == 1: # one vertice outside # add three triangles vertex_out_index = v1 if v1_out else (v2 if v2_out else v3) vertex_in_1_index = v1 if (not v1_out) else (v2 if (not v2_out) else v3) vertex_in_2_index = v3 if (not v3_out) else (v2 if (not v2_out) else v1) # print(f"{vertex_out_index=}, {vertex_in_1_index=}, {vertex_in_2_index=}") # small sanity check if outdices sum matches assert sum([vertex_out_index, vertex_in_1_index, vertex_in_2_index]) == sum([v1,v2,v3]) new_triangles.append([vertex_in_1_index, compute_intersection(vertex_in_1_index, vertex_out_index), vertex_in_2_index]) new_triangles.append([compute_intersection(vertex_in_1_index, vertex_out_index), compute_intersection(vertex_in_2_index, vertex_out_index), vertex_in_2_index]) else: assert False # TODO remap indices and remove unused mesh = o3d.geometry.TriangleMesh() mesh.vertices = o3d.utility.Vector3dVector(np.array(new_vertices)) mesh.triangles = o3d.utility.Vector3iVector(np.array(new_triangles)) return mesh def clean_crop_xy(mesh, min_corner, max_corner): min_x = min(min_corner[0], max_corner[0]) min_y = min(min_corner[1], max_corner[1]) max_x = max(min_corner[0], max_corner[0]) max_y = max(min_corner[1], max_corner[1]) # mesh = sliceplane(mesh, 0, min_x, False) mesh_sliced = sliceplane(mesh, 0, max_x, True) mesh_sliced = sliceplane(mesh_sliced, 0, min_x, False) mesh_sliced = sliceplane(mesh_sliced, 1, max_y, True) mesh_sliced = sliceplane(mesh_sliced, 1, min_y, False) # mesh_sliced = mesh_sliced.paint_uniform_color([0,0,1]) return mesh_sliced knot_mesh = o3d.data.KnotMesh() mesh = o3d.io.read_triangle_mesh(knot_mesh.path) v = np.asarray(mesh.vertices) mesh_cropped = clean_crop_xy(mesh, (-200, 0), (0, -200)) bounding_box = o3d.geometry.AxisAlignedBoundingBox((-200, 0, -1000), (0,200,1000)) mesh_crop_bad = mesh.crop(bounding_box) o3d.visualization.draw_geometries([mesh], mesh_show_back_face=True, mesh_show_wireframe=True) o3d.visualization.draw_geometries([mesh_crop_bad], mesh_show_back_face=True, mesh_show_wireframe=True) o3d.visualization.draw_geometries([mesh_cropped], mesh_show_back_face=True, mesh_show_wireframe=True) 
