Distance

coxeter/shapes/convex_polyhedron.py

@@ -118,6 +118,14 @@ def __init__(self, vertices):
         self._sort_simplices()
         self.sort_faces()
 
+        # For shortest distance functions
+        self._edge_face_neighbors = None
+        self._vertex_zones = None
+        self._edge_zones = None
+        self._face_zones = None
+        self._vertex_normals = None
+        self._edge_normals = None
+
     def _consume_hull(self, hull):
         """Extract data from ConvexHull.
 

coxeter/shapes/convex_spheropolygon.py

@@ -9,6 +9,9 @@
 
 import numpy as np
 
+from ._distance2d import (
+    spheropolygon_shortest_displacement_to_surface,
+)
 from .base_classes import Shape2D
 from .convex_polygon import ConvexPolygon, _is_convex
 from .polygon import _align_points_by_normal
@@ -57,6 +60,10 @@ def __init__(self, vertices, radius, normal=None):
         if not _is_convex(self.vertices, self._polygon.normal):
             raise ValueError("The vertices do not define a convex polygon.")
 
+        self._vertex_zones = None
+        self._edge_zones = None
+        self._face_zones = None
+
     @property
     def polygon(self):
         """:class:`~coxeter.shapes.ConvexPolygon`: The underlying polygon."""
@@ -107,6 +114,9 @@ def _rescale(self, scale):
         """
         self.polygon._vertices *= scale
         self.radius *= scale
+        self._vertex_zones = None
+        self._edge_zones = None
+        self._face_zones = None
 
     @property
     def signed_area(self):
@@ -302,3 +312,70 @@ def to_hoomd(self):
 
         self._polygon.centroid = old_centroid
         return hoomd_dict
+
+    def shortest_distance_to_surface(self, points, translation_vector=None):
+        """
+        Solve for the shortest distance between points and surface of a polygon.
+
+        This function calculates the shortest distance (magnitude) by partitioning
+        the space around a polygon into zones: vertex, edge, and face.
+        Determining the zone(s) a point lies in, determines the distance
+        calculation(s) done. For a vertex zone,the distance is calculated
+        between a point and the vertex. For an edge zone, the distance is
+        calculated between a point and the edge. For a face zone, the
+        distance is calculated between a point and the face. Zones are
+        allowed to overlap, and points can be in more than one zone. By
+        taking the minimum of all the calculated distances, the shortest
+        distances are found.
+
+        Args:
+            points (list or :class:`numpy.ndarray`):
+                positions of the points [shape = (n_points,3) or (n_points,2)]
+            translation_vector (list or :class:`numpy.ndarray`):
+                translation vector of the polygon [shape = (3,) of (2,)]
+                (Default value: [0,0,0])
+
+        Returns
+        -------
+            :class:`numpy.ndarray`:
+                the shortest distance of each point to the surface
+                [shape = (n_points,)]
+        """
+        return np.linalg.norm(
+            spheropolygon_shortest_displacement_to_surface(
+                self._polygon, self.radius, points, translation_vector
+            ),
+            axis=1,
+        )
+
+    def shortest_displacement_to_surface(self, points, translation_vector=None):
+        """
+        Solve for the shortest displacement between points and surface of a polygon.
+
+        This function calculates the shortest displacement (vector) by partitioning
+        the space around a polygon into zones: vertex, edge, and face.
+        Determining the zone(s) a point lies in, determines the displacement
+        calculation(s) done. For a vertex zone, the displacement is
+        calculated between a point and the vertex. For an edge zone, the
+        displacement is calculated between a point and the edge. For a face
+        zone, the displacement is calculated between a point and the face.
+        Zones are allowed to overlap, and points can be in more than one
+        zone. By taking the minimum of all the distances of the calculated
+        displacements, the shortest displacements are found.
+
+        Args:
+            points (list or :class:`numpy.ndarray`):
+                positions of the points [shape = (n_points,3) or (n_points,2)]
+            translation_vector (list or :class:`numpy.ndarray`):
+                translation vector of the polygon [shape = (3,) or (2,)]
+                (Default value: [0,0,0])
+
+        Returns
+        -------
+            :class:`numpy.ndarray`:
+                the shortest displacement of each point to the surface
+                [shape = (n_points, 3)]
+        """
+        return spheropolygon_shortest_displacement_to_surface(
+            self._polygon, self.radius, points, translation_vector
+        )

coxeter/shapes/convex_spheropolyhedron.py

@@ -9,6 +9,10 @@
 
 import numpy as np
 
+from ._distance3d import (
+    shortest_distance_to_surface,
+    spheropolyhedron_shortest_displacement_to_surface,
+)
 from .base_classes import Shape3D
 from .convex_polyhedron import ConvexPolyhedron
 from .utils import _hoomd_dict_mapping, _map_dict_keys
@@ -69,6 +73,13 @@ def __init__(self, vertices, radius):
         self._polyhedron = ConvexPolyhedron(vertices)
         self.radius = radius
 
+        self._edge_face_neighbors = None
+        self._vertex_zones = None
+        self._edge_zones = None
+        self._face_zones = None
+        self._vertex_normals = None
+        self._edge_normals = None
+
     @property
     def gsd_shape_spec(self):
         """dict: Get a :ref:`complete GSD specification <gsd:shapes>`."""  # noqa: D401
@@ -97,6 +108,9 @@ def _rescale(self, scale):
         """
         self.polyhedron._rescale(scale)
         self.radius *= scale
+        self._vertex_zones = None
+        self._edge_zones = None
+        self._face_zones = None
 
     @property
     def volume(self):
@@ -364,3 +378,70 @@ def to_hoomd(self):
 
         self._polyhedron.centroid = old_centroid
         return hoomd_dict
+
+    def shortest_distance_to_surface(self, points, translation_vector=None):
+        """
+        Solve for the shortest distance between points and the surface.
+
+        If the point lies inside the spheropolyhedron, the distance is negative.
+
+        This function calculates the shortest distance (magnitude) by partitioning
+        the space around a spheropolyhedron into zones: vertex, edge, and face.
+        Determining the zone(s) a point lies in, determines the distance
+        calculation(s) done. For a vertex zone,the distance is calculated
+        between a point and the vertex. For an edge zone, the distance is
+        calculated between a point and the edge. For a face zone, the
+        distance is calculated between a point and the face. Zones are
+        allowed to overlap, and points can be in more than one zone. By
+        taking the minimum of all the calculated distances, the shortest
+        distances are found.
+
+        Args:
+            points (list or :class:`numpy.ndarray`):
+                positions of the points [shape = (n_points, 3)]
+            translation_vector (list or :class:`numpy.ndarray`):
+                translation vector of the spheropolyhedron [shape = (3,)]
+                (Default value: [0,0,0])
+
+        Returns
+        -------
+            :class:`numpy.ndarray`:
+                the shortest distance of each point to the surface
+                [shape = (n_points,)]
+        """
+        return (
+            shortest_distance_to_surface(self._polyhedron, points, translation_vector)
+            - self.radius
+        )
+
+    def shortest_displacement_to_surface(self, points, translation_vector=None):
+        """
+        Solve for the shortest displacement between points and the surface.
+
+        This function calculates the shortest displacement (vector) by partitioning
+        the space around a spheropolyhedron into zones: vertex, edge, and face.
+        Determining the zone(s) a point lies in, determines the displacement
+        calculation(s) done. For a vertex zone, the displacement is
+        calculated between a point and the vertex. For an edge zone, the
+        displacement is calculated between a point and the edge. For a face
+        zone, the displacement is calculated between a point and the face.
+        Zones are allowed to overlap, and points can be in more than one
+        zone. By taking the minimum of all the distances of the calculated
+        displacements, the shortest displacements are found.
+
+        Args:
+            points (list or :class:`numpy.ndarray`):
+                positions of the points [shape = (n_points, 3)]
+            translation_vector (list or :class:`numpy.ndarray`):
+                translation vector of the spheropolyhedron [shape = (3,)]
+                (Default value: [0,0,0])
+
+        Returns
+        -------
+            :class:`numpy.ndarray`:
+                the shortest displacement of each point to the surface
+                [shape = (n_points, 3)]
+        """
+        return spheropolyhedron_shortest_displacement_to_surface(
+            self._polyhedron, self.radius, points, translation_vector
+        )

coxeter/shapes/polygon.py

@@ -10,6 +10,13 @@
 
 from ..extern.bentley_ottmann import poly_point_isect
 from ..extern.polytri import polytri
+from ._distance2d import (
+    get_edge_zones,
+    get_face_zones,
+    get_vert_zones,
+    shortest_displacement_to_surface,
+    shortest_distance_to_surface,
+)
 from .base_classes import Shape2D
 from .circle import Circle
 from .utils import (
@@ -132,6 +139,10 @@ class Polygon(Shape2D):
     def __init__(self, vertices, normal=None, planar_tolerance=1e-5, test_simple=True):
         vertices = np.array(vertices, dtype=np.float64)
 
+        self._vertex_zones = None
+        self._edge_zones = None
+        self._face_zones = None
+
         if len(vertices.shape) != 2 or vertices.shape[1] not in (2, 3):
             raise ValueError("Vertices must be specified as an Nx2 or Nx3 array.")
         if len(vertices) < 3:
@@ -215,6 +226,9 @@ def _rescale(self, scale):
                 Scale factor.
         """
         self._vertices *= scale
+        self._vertex_zones = None
+        self._edge_zones = None
+        self._face_zones = None
 
     @property
     def perimeter(self):
@@ -418,6 +432,19 @@ def centroid(self):
     def centroid(self, value):
         self._vertices += np.asarray(value) - self.centroid
 
+        if self._vertex_zones is not None:
+            self._vertex_zones["bounds"] += self._vertex_zones["constraint"] @ (
+                np.asarray(value) - self.centroid
+            )
+        if self._edge_zones is not None:
+            self._edge_zones["bounds"] += self._edge_zones["constraint"] @ (
+                np.asarray(value) - self.centroid
+            )
+        if self._face_zones is not None:
+            self._face_zones["bounds"] += self._face_zones["constraint"] @ (
+                np.asarray(value) - self.centroid
+            )
+
     @property
     def edges(self):
         """:class:`numpy.ndarray`: Get the polygon's edges.
@@ -838,3 +865,102 @@ def to_hoomd(self):
 
         self.centroid = old_centroid
         return hoomd_dict
+
+    @property
+    def vertex_zones(self):
+        """dict: Get the constraints and bounds associated with the vertices.
+
+        The constraints and bounds are needed to partition the
+        volume surrounding a polygon into zones where the shortest
+        distance from any point that is within a vertex zone is the
+        distance between the point and the corresponding vertex.
+        """
+        if self._vertex_zones is None:
+            self._vertex_zones = get_vert_zones(self)
+        return self._vertex_zones
+
+    @property
+    def edge_zones(self):
+        """dict: Get the constraints and bounds associated with the edges.
+
+        The constraints and bounds are needed to partition
+        the volume surrounding a polygon into zones where the
+        shortest distance from any point that is within an edge zone
+        is the distance between the point and the corresponding edge.
+        """
+        if self._edge_zones is None:
+            self._edge_zones = get_edge_zones(self)
+        return self._edge_zones
+
+    @property
+    def face_zones(self):
+        """dict: Get the constraints and bounds associated with the faces.
+
+        The constraints and bounds are needed to partition
+        the volume surrounding a polygon into zones where the shortest
+        distance from any point that is within the face zone
+        is the distance between the point and the face of the polygon.
+        """
+        if self._face_zones is None:
+            self._face_zones = get_face_zones(self)
+        return self._face_zones
+
+    def shortest_distance_to_surface(self, points, translation_vector=None):
+        """
+        Solve for the shortest distance between points and surface of a polygon.
+
+        This function calculates the shortest distance (magnitude) by partitioning
+        the space around a polygon into zones: vertex, edge, and face.
+        Determining the zone(s) a point lies in, determines the distance
+        calculation(s) done. For a vertex zone,the distance is calculated
+        between a point and the vertex. For an edge zone, the distance is
+        calculated between a point and the edge. For a face zone, the
+        distance is calculated between a point and the face. Zones are
+        allowed to overlap, and points can be in more than one zone. By
+        taking the minimum of all the calculated distances, the shortest
+        distances are found.
+
+        Args:
+            points (list or :class:`numpy.ndarray`):
+                positions of the points [shape = (n_points,3) or (n_points,2)]
+            translation_vector (list or :class:`numpy.ndarray`):
+                translation vector of the polygon [shape = (3,) of (2,)]
+                (Default value: [0,0,0])
+
+        Returns
+        -------
+            :class:`numpy.ndarray`:
+                the shortest distance of each point to the surface
+                [shape = (n_points,)]
+        """
+        return shortest_distance_to_surface(self, points, translation_vector)
+
+    def shortest_displacement_to_surface(self, points, translation_vector=None):
+        """
+        Solve for the shortest displacement between points and surface of a polygon.
+
+        This function calculates the shortest displacement (vector) by partitioning
+        the space around a polygon into zones: vertex, edge, and face.
+        Determining the zone(s) a point lies in, determines the displacement
+        calculation(s) done. For a vertex zone, the displacement is
+        calculated between a point and the vertex. For an edge zone, the
+        displacement is calculated between a point and the edge. For a face
+        zone, the displacement is calculated between a point and the face.
+        Zones are allowed to overlap, and points can be in more than one
+        zone. By taking the minimum of all the distances of the calculated
+        displacements, the shortest displacements are found.
+
+        Args:
+            points (list or :class:`numpy.ndarray`):
+                positions of the points [shape = (n_points,3) or (n_points,2)]
+            translation_vector (list or :class:`numpy.ndarray`):
+                translation vector of the polygon [shape = (3,) or (2,)]
+                (Default value: [0,0,0])
+
+        Returns
+        -------
+            :class:`numpy.ndarray`:
+                the shortest displacement of each point to the surface
+                [shape = (n_points, 3)]
+        """
+        return shortest_displacement_to_surface(self, points, translation_vector)