713 lines
26 KiB
Python
713 lines
26 KiB
Python
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"""
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intersections.py
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------------------
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Primarily mesh-plane intersections (slicing).
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"""
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import numpy as np
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from .constants import log, tol
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from . import util
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from . import geometry
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from . import grouping
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from . import transformations
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def mesh_plane(mesh,
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plane_normal,
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plane_origin,
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return_faces=False,
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cached_dots=None):
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"""
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Find a the intersections between a mesh and a plane,
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returning a set of line segments on that plane.
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Parameters
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---------
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mesh : Trimesh object
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Source mesh to slice
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plane_normal : (3,) float
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Normal vector of plane to intersect with mesh
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plane_origin: (3,) float
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Point on plane to intersect with mesh
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return_faces: bool
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If True return face index each line is from
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cached_dots : (n, 3) float
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If an external function has stored dot
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products pass them here to avoid recomputing
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Returns
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----------
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lines : (m, 2, 3) float
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List of 3D line segments in space
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face_index : (m,) int
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Index of mesh.faces for each line
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Only returned if return_faces was True
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"""
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def triangle_cases(signs):
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"""
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Figure out which faces correspond to which intersection
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case from the signs of the dot product of each vertex.
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Does this by bitbang each row of signs into an 8 bit
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integer.
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code : signs : intersects
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0 : [-1 -1 -1] : No
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2 : [-1 -1 0] : No
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4 : [-1 -1 1] : Yes; 2 on one side, 1 on the other
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6 : [-1 0 0] : Yes; one edge fully on plane
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8 : [-1 0 1] : Yes; one vertex on plane, 2 on different sides
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12 : [-1 1 1] : Yes; 2 on one side, 1 on the other
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14 : [0 0 0] : No (on plane fully)
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16 : [0 0 1] : Yes; one edge fully on plane
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20 : [0 1 1] : No
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28 : [1 1 1] : No
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Parameters
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----------
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signs: (n,3) int, all values are -1,0, or 1
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Each row contains the dot product of all three vertices
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in a face with respect to the plane
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Returns
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---------
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basic: (n,) bool, which faces are in the basic intersection case
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one_vertex: (n,) bool, which faces are in the one vertex case
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one_edge: (n,) bool, which faces are in the one edge case
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"""
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signs_sorted = np.sort(signs, axis=1)
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coded = np.zeros(len(signs_sorted), dtype=np.int8) + 14
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for i in range(3):
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coded += signs_sorted[:, i] << 3 - i
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# one edge fully on the plane
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# note that we are only accepting *one* of the on- edge cases,
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# where the other vertex has a positive dot product (16) instead
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# of both on- edge cases ([6,16])
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# this is so that for regions that are co-planar with the the section plane
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# we don't end up with an invalid boundary
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key = np.zeros(29, dtype=np.bool)
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key[16] = True
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one_edge = key[coded]
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# one vertex on plane, other two on different sides
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key[:] = False
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key[8] = True
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one_vertex = key[coded]
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# one vertex on one side of the plane, two on the other
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key[:] = False
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key[[4, 12]] = True
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basic = key[coded]
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return basic, one_vertex, one_edge
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def handle_on_vertex(signs, faces, vertices):
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# case where one vertex is on plane, two are on different sides
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vertex_plane = faces[signs == 0]
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edge_thru = faces[signs != 0].reshape((-1, 2))
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point_intersect, valid = plane_lines(plane_origin,
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plane_normal,
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vertices[edge_thru.T],
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line_segments=False)
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lines = np.column_stack((vertices[vertex_plane[valid]],
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point_intersect)).reshape((-1, 2, 3))
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return lines
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def handle_on_edge(signs, faces, vertices):
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# case where two vertices are on the plane and one is off
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edges = faces[signs == 0].reshape((-1, 2))
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points = vertices[edges]
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return points
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def handle_basic(signs, faces, vertices):
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# case where one vertex is on one side and two are on the other
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unique_element = grouping.unique_value_in_row(
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signs, unique=[-1, 1])
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edges = np.column_stack(
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(faces[unique_element],
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faces[np.roll(unique_element, 1, axis=1)],
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faces[unique_element],
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faces[np.roll(unique_element, 2, axis=1)])).reshape(
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(-1, 2))
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intersections, valid = plane_lines(plane_origin,
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plane_normal,
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vertices[edges.T],
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line_segments=False)
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# since the data has been pre- culled, any invalid intersections at all
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# means the culling was done incorrectly and thus things are
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# mega-fucked
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assert valid.all()
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return intersections.reshape((-1, 2, 3))
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# check input plane
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plane_normal = np.asanyarray(plane_normal,
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dtype=np.float64)
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plane_origin = np.asanyarray(plane_origin,
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dtype=np.float64)
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if plane_origin.shape != (3,) or plane_normal.shape != (3,):
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raise ValueError('Plane origin and normal must be (3,)!')
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if cached_dots is not None:
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dots = cached_dots
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else:
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# dot product of each vertex with the plane normal indexed by face
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# so for each face the dot product of each vertex is a row
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# shape is the same as mesh.faces (n,3)
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dots = np.einsum('i,ij->j', plane_normal,
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(mesh.vertices - plane_origin).T)[mesh.faces]
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# sign of the dot product is -1, 0, or 1
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# shape is the same as mesh.faces (n,3)
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signs = np.zeros(mesh.faces.shape, dtype=np.int8)
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signs[dots < -tol.merge] = -1
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signs[dots > tol.merge] = 1
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# figure out which triangles are in the cross section,
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# and which of the three intersection cases they are in
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cases = triangle_cases(signs)
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# handlers for each case
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handlers = (handle_basic,
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handle_on_vertex,
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handle_on_edge)
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# the (m, 2, 3) line segments
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lines = np.vstack([h(signs[c],
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mesh.faces[c],
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mesh.vertices)
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for c, h in zip(cases, handlers)])
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log.debug('mesh_cross_section found %i intersections',
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len(lines))
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if return_faces:
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face_index = np.hstack([np.nonzero(c)[0] for c in cases])
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return lines, face_index
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return lines
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def mesh_multiplane(mesh,
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plane_origin,
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plane_normal,
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heights):
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"""
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A utility function for slicing a mesh by multiple
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parallel planes, which caches the dot product operation.
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Parameters
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-------------
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mesh : trimesh.Trimesh
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Geometry to be sliced by planes
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plane_normal : (3,) float
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Normal vector of plane
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plane_origin : (3,) float
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Point on a plane
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heights : (m,) float
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Offset distances from plane to slice at
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Returns
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--------------
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lines : (m,) sequence of (n, 2, 2) float
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Lines in space for m planes
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to_3D : (m, 4, 4) float
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Transform to move each section back to 3D
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face_index : (m,) sequence of (n,) int
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Indexes of mesh.faces for each segment
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"""
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# check input plane
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plane_normal = util.unitize(plane_normal)
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plane_origin = np.asanyarray(plane_origin,
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dtype=np.float64)
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heights = np.asanyarray(heights, dtype=np.float64)
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# dot product of every vertex with plane
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vertex_dots = np.dot(plane_normal,
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(mesh.vertices - plane_origin).T)
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# reconstruct transforms for each 2D section
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base_transform = geometry.plane_transform(origin=plane_origin,
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normal=plane_normal)
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base_transform = np.linalg.inv(base_transform)
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# alter translation Z inside loop
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translation = np.eye(4)
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# store results
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transforms = []
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face_index = []
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segments = []
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# loop through user specified heights
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for height in heights:
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# offset the origin by the height
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new_origin = plane_origin + (plane_normal * height)
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# offset the dot products by height and index by faces
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new_dots = (vertex_dots - height)[mesh.faces]
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# run the intersection with the cached dot products
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lines, index = mesh_plane(mesh=mesh,
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plane_origin=new_origin,
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plane_normal=plane_normal,
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return_faces=True,
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cached_dots=new_dots)
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# get the transforms to 3D space and back
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translation[2, 3] = height
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to_3D = np.dot(base_transform, translation)
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to_2D = np.linalg.inv(to_3D)
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transforms.append(to_3D)
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# transform points to 2D frame
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lines_2D = transformations.transform_points(
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lines.reshape((-1, 3)),
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to_2D)
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# if we didn't screw up the transform all
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# of the Z values should be zero
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assert np.allclose(lines_2D[:, 2], 0.0)
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# reshape back in to lines and discard Z
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lines_2D = lines_2D[:, :2].reshape((-1, 2, 2))
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# store (n, 2, 2) float lines
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segments.append(lines_2D)
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# store (n,) int indexes of mesh.faces
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face_index.append(face_index)
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# (n, 4, 4) transforms from 2D to 3D
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transforms = np.array(transforms, dtype=np.float64)
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return segments, transforms, face_index
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def plane_lines(plane_origin,
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plane_normal,
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endpoints,
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line_segments=True):
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"""
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Calculate plane-line intersections
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Parameters
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---------
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plane_origin : (3,) float
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Point on plane
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plane_normal : (3,) float
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Plane normal vector
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endpoints : (2, n, 3) float
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Points defining lines to be tested
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line_segments : bool
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If True, only returns intersections as valid if
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vertices from endpoints are on different sides
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of the plane.
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Returns
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---------
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intersections : (m, 3) float
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Cartesian intersection points
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valid : (n, 3) bool
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Indicate whether a valid intersection exists
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for each input line segment
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"""
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endpoints = np.asanyarray(endpoints)
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plane_origin = np.asanyarray(plane_origin).reshape(3)
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line_dir = util.unitize(endpoints[1] - endpoints[0])
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plane_normal = util.unitize(np.asanyarray(plane_normal).reshape(3))
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t = np.dot(plane_normal, (plane_origin - endpoints[0]).T)
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b = np.dot(plane_normal, line_dir.T)
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# If the plane normal and line direction are perpendicular, it means
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# the vector is 'on plane', and there isn't a valid intersection.
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# We discard on-plane vectors by checking that the dot product is nonzero
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valid = np.abs(b) > tol.zero
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if line_segments:
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test = np.dot(plane_normal,
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np.transpose(plane_origin - endpoints[1]))
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different_sides = np.sign(t) != np.sign(test)
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nonzero = np.logical_or(np.abs(t) > tol.zero,
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np.abs(test) > tol.zero)
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valid = np.logical_and(valid, different_sides)
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valid = np.logical_and(valid, nonzero)
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d = np.divide(t[valid], b[valid])
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intersection = endpoints[0][valid]
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intersection = intersection + np.reshape(d, (-1, 1)) * line_dir[valid]
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return intersection, valid
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def planes_lines(plane_origins,
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plane_normals,
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line_origins,
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line_directions,
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return_distance=False,
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return_denom=False):
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"""
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Given one line per plane find the intersection points.
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Parameters
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-----------
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plane_origins : (n,3) float
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Point on each plane
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plane_normals : (n,3) float
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Normal vector of each plane
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line_origins : (n,3) float
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Point at origin of each line
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line_directions : (n,3) float
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Direction vector of each line
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return_distance : bool
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Return distance from origin to point also
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return_denom : bool
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Return denominator, so you can check for small values
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Returns
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----------
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on_plane : (n,3) float
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Points on specified planes
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valid : (n,) bool
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Did plane intersect line or not
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distance : (n,) float
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[OPTIONAL] Distance from point
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denom : (n,) float
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[OPTIONAL] Denominator
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"""
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# check input types
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plane_origins = np.asanyarray(plane_origins, dtype=np.float64)
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plane_normals = np.asanyarray(plane_normals, dtype=np.float64)
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line_origins = np.asanyarray(line_origins, dtype=np.float64)
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line_directions = np.asanyarray(line_directions, dtype=np.float64)
|
||
|
|
|
||
|
|
# vector from line to plane
|
||
|
|
origin_vectors = plane_origins - line_origins
|
||
|
|
|
||
|
|
projection_ori = util.diagonal_dot(origin_vectors, plane_normals)
|
||
|
|
projection_dir = util.diagonal_dot(line_directions, plane_normals)
|
||
|
|
|
||
|
|
valid = np.abs(projection_dir) > 1e-5
|
||
|
|
|
||
|
|
distance = np.divide(projection_ori[valid],
|
||
|
|
projection_dir[valid])
|
||
|
|
|
||
|
|
on_plane = line_directions[valid] * distance.reshape((-1, 1))
|
||
|
|
on_plane += line_origins[valid]
|
||
|
|
|
||
|
|
result = [on_plane, valid]
|
||
|
|
|
||
|
|
if return_distance:
|
||
|
|
result.append(distance)
|
||
|
|
if return_denom:
|
||
|
|
result.append(projection_dir)
|
||
|
|
|
||
|
|
return result
|
||
|
|
|
||
|
|
|
||
|
|
def slice_faces_plane(vertices,
|
||
|
|
faces,
|
||
|
|
plane_normal,
|
||
|
|
plane_origin,
|
||
|
|
cached_dots=None):
|
||
|
|
"""
|
||
|
|
Slice a mesh (given as a set of faces and vertices) with a plane, returning a
|
||
|
|
new mesh (again as a set of faces and vertices) that is the
|
||
|
|
portion of the original mesh to the positive normal side of the plane.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
---------
|
||
|
|
vertices : (n, 3) float
|
||
|
|
Vertices of source mesh to slice
|
||
|
|
faces : (n, 3) int
|
||
|
|
Faces of source mesh to slice
|
||
|
|
plane_normal : (3,) float
|
||
|
|
Normal vector of plane to intersect with mesh
|
||
|
|
plane_origin : (3,) float
|
||
|
|
Point on plane to intersect with mesh
|
||
|
|
cached_dots : (n, 3) float
|
||
|
|
If an external function has stored dot
|
||
|
|
products pass them here to avoid recomputing
|
||
|
|
|
||
|
|
Returns
|
||
|
|
----------
|
||
|
|
new_vertices : (n, 3) float
|
||
|
|
Vertices of sliced mesh
|
||
|
|
new_faces : (n, 3) int
|
||
|
|
Faces of sliced mesh
|
||
|
|
"""
|
||
|
|
|
||
|
|
if len(vertices) == 0:
|
||
|
|
return vertices, faces
|
||
|
|
|
||
|
|
if cached_dots is not None:
|
||
|
|
dots = cached_dots
|
||
|
|
else:
|
||
|
|
# dot product of each vertex with the plane normal indexed by face
|
||
|
|
# so for each face the dot product of each vertex is a row
|
||
|
|
# shape is the same as faces (n,3)
|
||
|
|
dots = np.einsum('i,ij->j', plane_normal,
|
||
|
|
(vertices - plane_origin).T)[faces]
|
||
|
|
|
||
|
|
# Find vertex orientations w.r.t. faces for all triangles:
|
||
|
|
# -1 -> vertex "inside" plane (positive normal direction)
|
||
|
|
# 0 -> vertex on plane
|
||
|
|
# 1 -> vertex "outside" plane (negative normal direction)
|
||
|
|
signs = np.zeros(faces.shape, dtype=np.int8)
|
||
|
|
signs[dots < -tol.merge] = 1
|
||
|
|
signs[dots > tol.merge] = -1
|
||
|
|
signs[np.logical_and(dots >= -tol.merge, dots <= tol.merge)] = 0
|
||
|
|
|
||
|
|
# Find all triangles that intersect this plane
|
||
|
|
# onedge <- indices of all triangles intersecting the plane
|
||
|
|
# inside <- indices of all triangles "inside" the plane (positive normal)
|
||
|
|
signs_sum = signs.sum(axis=1, dtype=np.int8)
|
||
|
|
signs_asum = np.abs(signs).sum(axis=1, dtype=np.int8)
|
||
|
|
|
||
|
|
# Cases:
|
||
|
|
# (0,0,0), (-1,0,0), (-1,-1,0), (-1,-1,-1) <- inside
|
||
|
|
# (1,0,0), (1,1,0), (1,1,1) <- outside
|
||
|
|
# (1,0,-1), (1,-1,-1), (1,1,-1) <- onedge
|
||
|
|
onedge = np.logical_and(signs_asum >= 2,
|
||
|
|
np.abs(signs_sum) <= 1)
|
||
|
|
inside = (signs_sum == -signs_asum)
|
||
|
|
|
||
|
|
# Automatically include all faces that are "inside"
|
||
|
|
new_faces = faces[inside]
|
||
|
|
|
||
|
|
# Separate faces on the edge into two cases: those which will become
|
||
|
|
# quads (two vertices inside plane) and those which will become triangles
|
||
|
|
# (one vertex inside plane)
|
||
|
|
triangles = vertices[faces]
|
||
|
|
cut_triangles = triangles[onedge]
|
||
|
|
cut_faces_quad = faces[np.logical_and(onedge, signs_sum < 0)]
|
||
|
|
cut_faces_tri = faces[np.logical_and(onedge, signs_sum >= 0)]
|
||
|
|
cut_signs_quad = signs[np.logical_and(onedge, signs_sum < 0)]
|
||
|
|
cut_signs_tri = signs[np.logical_and(onedge, signs_sum >= 0)]
|
||
|
|
|
||
|
|
# If no faces to cut, the surface is not in contact with this plane.
|
||
|
|
# Thus, return a mesh with only the inside faces
|
||
|
|
if len(cut_faces_quad) + len(cut_faces_tri) == 0:
|
||
|
|
|
||
|
|
if len(new_faces) == 0:
|
||
|
|
# if no new faces at all return empty arrays
|
||
|
|
empty = (np.zeros((0, 3), dtype=np.float64),
|
||
|
|
np.zeros((0, 3), dtype=np.int64))
|
||
|
|
return empty
|
||
|
|
|
||
|
|
# find the unique indices in the new faces
|
||
|
|
# using an integer-only unique function
|
||
|
|
unique, inverse = grouping.unique_bincount(new_faces.reshape(-1),
|
||
|
|
minlength=len(vertices),
|
||
|
|
return_inverse=True)
|
||
|
|
|
||
|
|
# use the unique indices for our final vertices and faces
|
||
|
|
final_vert = vertices[unique]
|
||
|
|
final_face = inverse.reshape((-1, 3))
|
||
|
|
|
||
|
|
return final_vert, final_face
|
||
|
|
|
||
|
|
# Extract the intersections of each triangle's edges with the plane
|
||
|
|
o = cut_triangles # origins
|
||
|
|
d = np.roll(o, -1, axis=1) - o # directions
|
||
|
|
num = (plane_origin - o).dot(plane_normal) # compute num/denom
|
||
|
|
denom = np.dot(d, plane_normal)
|
||
|
|
denom[denom == 0.0] = 1e-12 # prevent division by zero
|
||
|
|
dist = np.divide(num, denom)
|
||
|
|
# intersection points for each segment
|
||
|
|
int_points = np.einsum('ij,ijk->ijk', dist, d) + o
|
||
|
|
|
||
|
|
# Initialize the array of new vertices with the current vertices
|
||
|
|
new_vertices = vertices
|
||
|
|
|
||
|
|
# Handle the case where a new quad is formed by the intersection
|
||
|
|
# First, extract the intersection points belonging to a new quad
|
||
|
|
quad_int_points = int_points[(signs_sum < 0)[onedge], :, :]
|
||
|
|
num_quads = len(quad_int_points)
|
||
|
|
if num_quads > 0:
|
||
|
|
# Extract the vertex on the outside of the plane, then get the vertices
|
||
|
|
# (in CCW order of the inside vertices)
|
||
|
|
quad_int_inds = np.where(cut_signs_quad == 1)[1]
|
||
|
|
quad_int_verts = cut_faces_quad[
|
||
|
|
np.stack((range(num_quads), range(num_quads)), axis=1),
|
||
|
|
np.stack(((quad_int_inds + 1) % 3, (quad_int_inds + 2) % 3), axis=1)]
|
||
|
|
|
||
|
|
# Fill out new quad faces with the intersection points as vertices
|
||
|
|
new_quad_faces = np.append(
|
||
|
|
quad_int_verts,
|
||
|
|
np.arange(len(new_vertices),
|
||
|
|
len(new_vertices) +
|
||
|
|
2 * num_quads).reshape(num_quads, 2), axis=1)
|
||
|
|
|
||
|
|
# Extract correct intersection points from int_points and order them in
|
||
|
|
# the same way as they were added to faces
|
||
|
|
new_quad_vertices = quad_int_points[
|
||
|
|
np.stack((range(num_quads), range(num_quads)), axis=1),
|
||
|
|
np.stack((((quad_int_inds + 2) % 3).T, quad_int_inds.T),
|
||
|
|
axis=1), :].reshape(2 * num_quads, 3)
|
||
|
|
|
||
|
|
# Add new vertices to existing vertices, triangulate quads, and add the
|
||
|
|
# resulting triangles to the new faces
|
||
|
|
new_vertices = np.append(new_vertices, new_quad_vertices, axis=0)
|
||
|
|
new_tri_faces_from_quads = geometry.triangulate_quads(new_quad_faces)
|
||
|
|
new_faces = np.append(new_faces, new_tri_faces_from_quads, axis=0)
|
||
|
|
|
||
|
|
# Handle the case where a new triangle is formed by the intersection
|
||
|
|
# First, extract the intersection points belonging to a new triangle
|
||
|
|
tri_int_points = int_points[(signs_sum >= 0)[onedge], :, :]
|
||
|
|
num_tris = len(tri_int_points)
|
||
|
|
if num_tris > 0:
|
||
|
|
# Extract the single vertex for each triangle inside the plane and get the
|
||
|
|
# inside vertices (CCW order)
|
||
|
|
tri_int_inds = np.where(cut_signs_tri == -1)[1]
|
||
|
|
tri_int_verts = cut_faces_tri[range(
|
||
|
|
num_tris), tri_int_inds].reshape(num_tris, 1)
|
||
|
|
|
||
|
|
# Fill out new triangles with the intersection points as vertices
|
||
|
|
new_tri_faces = np.append(
|
||
|
|
tri_int_verts,
|
||
|
|
np.arange(len(new_vertices),
|
||
|
|
len(new_vertices) +
|
||
|
|
2 * num_tris).reshape(num_tris, 2),
|
||
|
|
axis=1)
|
||
|
|
|
||
|
|
# Extract correct intersection points and order them in the same way as
|
||
|
|
# the vertices were added to the faces
|
||
|
|
new_tri_vertices = tri_int_points[
|
||
|
|
np.stack((range(num_tris), range(num_tris)), axis=1),
|
||
|
|
np.stack((tri_int_inds.T, ((tri_int_inds + 2) % 3).T),
|
||
|
|
axis=1),
|
||
|
|
:].reshape(2 * num_tris, 3)
|
||
|
|
|
||
|
|
# Append new vertices and new faces
|
||
|
|
new_vertices = np.append(new_vertices, new_tri_vertices, axis=0)
|
||
|
|
new_faces = np.append(new_faces, new_tri_faces, axis=0)
|
||
|
|
|
||
|
|
# find the unique indices in the new faces
|
||
|
|
# using an integer-only unique function
|
||
|
|
unique, inverse = grouping.unique_bincount(new_faces.reshape(-1),
|
||
|
|
minlength=len(new_vertices),
|
||
|
|
return_inverse=True)
|
||
|
|
|
||
|
|
# use the unique indexes for our final vertex and faces
|
||
|
|
final_vert = new_vertices[unique]
|
||
|
|
final_face = inverse.reshape((-1, 3))
|
||
|
|
|
||
|
|
return final_vert, final_face
|
||
|
|
|
||
|
|
|
||
|
|
def slice_mesh_plane(mesh,
|
||
|
|
plane_normal,
|
||
|
|
plane_origin,
|
||
|
|
cap=False,
|
||
|
|
cached_dots=None,
|
||
|
|
**kwargs):
|
||
|
|
"""
|
||
|
|
Slice a mesh with a plane, returning a new mesh that is the
|
||
|
|
portion of the original mesh to the positive normal side of the plane
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
---------
|
||
|
|
mesh : Trimesh object
|
||
|
|
Source mesh to slice
|
||
|
|
plane_normal : (3,) float
|
||
|
|
Normal vector of plane to intersect with mesh
|
||
|
|
plane_origin : (3,) float
|
||
|
|
Point on plane to intersect with mesh
|
||
|
|
cap : bool
|
||
|
|
If True, cap the result with a triangulated polygon
|
||
|
|
cached_dots : (n, 3) float
|
||
|
|
If an external function has stored dot
|
||
|
|
products pass them here to avoid recomputing
|
||
|
|
|
||
|
|
Returns
|
||
|
|
----------
|
||
|
|
new_mesh : Trimesh object
|
||
|
|
Sliced mesh
|
||
|
|
"""
|
||
|
|
# check input for none
|
||
|
|
if mesh is None:
|
||
|
|
return None
|
||
|
|
|
||
|
|
# avoid circular import
|
||
|
|
from .base import Trimesh
|
||
|
|
from .creation import triangulate_polygon
|
||
|
|
|
||
|
|
# check input plane
|
||
|
|
plane_normal = np.asanyarray(plane_normal,
|
||
|
|
dtype=np.float64)
|
||
|
|
plane_origin = np.asanyarray(plane_origin,
|
||
|
|
dtype=np.float64)
|
||
|
|
|
||
|
|
# check to make sure origins and normals have acceptable shape
|
||
|
|
shape_ok = ((plane_origin.shape == (3,) or
|
||
|
|
util.is_shape(plane_origin, (-1, 3))) and
|
||
|
|
(plane_normal.shape == (3,) or
|
||
|
|
util.is_shape(plane_normal, (-1, 3))) and
|
||
|
|
plane_origin.shape == plane_normal.shape)
|
||
|
|
if not shape_ok:
|
||
|
|
raise ValueError('plane origins and normals must be (n, 3)!')
|
||
|
|
|
||
|
|
# start with copy of original mesh, faces, and vertices
|
||
|
|
sliced_mesh = mesh.copy()
|
||
|
|
vertices = mesh.vertices.copy()
|
||
|
|
faces = mesh.faces.copy()
|
||
|
|
|
||
|
|
# slice away specified planes
|
||
|
|
for origin, normal in zip(plane_origin.reshape((-1, 3)),
|
||
|
|
plane_normal.reshape((-1, 3))):
|
||
|
|
|
||
|
|
# calculate dots here if not passed in to save time
|
||
|
|
# in case of cap
|
||
|
|
if cached_dots is None:
|
||
|
|
# dot product of each vertex with the plane normal indexed by face
|
||
|
|
# so for each face the dot product of each vertex is a row
|
||
|
|
# shape is the same as faces (n,3)
|
||
|
|
dots = np.einsum('i,ij->j', normal,
|
||
|
|
(vertices - origin).T)[faces]
|
||
|
|
else:
|
||
|
|
dots = cached_dots
|
||
|
|
# save the new vertices and faces
|
||
|
|
vertices, faces = slice_faces_plane(vertices=vertices,
|
||
|
|
faces=faces,
|
||
|
|
plane_normal=normal,
|
||
|
|
plane_origin=origin,
|
||
|
|
cached_dots=dots)
|
||
|
|
|
||
|
|
# check if cap arg specified
|
||
|
|
if cap:
|
||
|
|
# check if mesh is watertight (can't cap if not)
|
||
|
|
if not sliced_mesh.is_watertight:
|
||
|
|
raise ValueError('Input mesh must be watertight to cap slice')
|
||
|
|
|
||
|
|
path = sliced_mesh.section(plane_normal=normal,
|
||
|
|
plane_origin=origin,
|
||
|
|
cached_dots=dots)
|
||
|
|
|
||
|
|
# transform Path3D onto XY plane for triangulation
|
||
|
|
on_plane, to_3D = path.to_planar()
|
||
|
|
|
||
|
|
# triangulate each closed region of 2D cap
|
||
|
|
# without adding any new vertices
|
||
|
|
v, f = [], []
|
||
|
|
for polygon in on_plane.polygons_full:
|
||
|
|
t = triangulate_polygon(
|
||
|
|
polygon, triangle_args='p', allow_boundary_steiner=False)
|
||
|
|
v.append(t[0])
|
||
|
|
f.append(t[1])
|
||
|
|
|
||
|
|
# append regions and reindex
|
||
|
|
vf, ff = util.append_faces(v, f)
|
||
|
|
|
||
|
|
# make vertices 3D and transform back to mesh frame
|
||
|
|
vf = np.column_stack((vf, np.zeros(len(vf))))
|
||
|
|
vf = transformations.transform_points(vf, to_3D)
|
||
|
|
|
||
|
|
# add cap vertices and faces and reindex
|
||
|
|
vertices, faces = util.append_faces([vertices, vf], [faces, ff])
|
||
|
|
|
||
|
|
# Update mesh with cap (processing needed to merge vertices)
|
||
|
|
sliced_mesh = Trimesh(vertices=vertices, faces=faces)
|
||
|
|
vertices, faces = sliced_mesh.vertices.copy(), sliced_mesh.faces.copy()
|
||
|
|
|
||
|
|
# return the sliced mesh
|
||
|
|
return Trimesh(vertices=vertices, faces=faces, process=False)
|