def query(self, query_point, query_radius, curr_node):
# project a point onto its nearest triangles and find the nearest projection location
nearest = (None, float("inf"))
if type(curr_node) == Leaf:
if np.linalg.norm(query_point - curr_node.center) <= query_radius:
# project the point at the leaf node
proj_point = project_point_to_triangle(query_point, curr_node.triangle, thickness = self.thickness)
proj_dist = np.linalg.norm(query_point - proj_point)
nearest = (proj_point, proj_dist)
self.projection_count += 1
elif type(curr_node) == Node:
dist = np.linalg.norm(query_point - curr_node.center)
if dist > curr_node.radius_lo + query_radius: # query and partition spheres are completely not overlapping
nearest = self.query(query_point, query_radius, curr_node.outside_node)
elif dist < curr_node.radius_hi - query_radius: # query and partition spheres are completely overlapping
nearest = self.query(query_point, query_radius, curr_node.inside_node)
else:
# must examine both subtrees as the border of the query sphere overlaps the border of the partition sphere
nearest_inside = self.query(query_point, query_radius, curr_node.inside_node)
nearest_outside = self.query(query_point, query_radius, curr_node.outside_node)
if nearest_inside[1] < nearest_outside[1]:
nearest = nearest_inside
else:
nearest = nearest_outside
return nearest
def _query(query_point, query_radius, curr_node, thickness, center, radius_lo, radius_hi, inside_node, outside_node, triangle, is_leaf):
# project a point onto its nearest triangles and find the nearest projection location
nearest = (None, np.inf)
if is_leaf[curr_node]:
if np.linalg.norm(query_point - center[curr_node]) <= query_radius:
# project the point at the leaf node
proj_point = project_point_to_triangle(query_point, triangle[curr_node], thickness = thickness)
proj_dist = np.linalg.norm(query_point - proj_point)
nearest = (proj_point, proj_dist)
else:
dist = np.linalg.norm(query_point - center[curr_node])
if dist > radius_lo[curr_node] + query_radius: # query and partition spheres are completely not overlapping
nearest = _query(query_point, query_radius, outside_node[curr_node], thickness, center, radius_lo, radius_hi, inside_node, outside_node, triangle, is_leaf)
elif dist < radius_hi[curr_node] - query_radius: # query and partition spheres are completely overlapping
nearest = _query(query_point, query_radius, inside_node[curr_node], thickness, center, radius_lo, radius_hi, inside_node, outside_node, triangle, is_leaf)
else:
# must examine both subtrees as the border of the query sphere overlaps the border of the partition sphere
nearest_inside = _query(query_point, query_radius, inside_node[curr_node], thickness, center, radius_lo, radius_hi, inside_node, outside_node, triangle, is_leaf)
nearest_outside = _query(query_point, query_radius, outside_node[curr_node], thickness, center, radius_lo, radius_hi, inside_node, outside_node, triangle, is_leaf)
if nearest_inside[1] < nearest_outside[1]:
nearest = nearest_inside
else:
nearest = nearest_outside
return nearest
def visualize_projection():
tri = np.array([[0.0, 0.0, 0.0], [0.0, 1.0, 0.0], [1.0, 1.0, 0.0]])
p_perturb = np.array([1.5, 1.5, 0.5])
p_proj = project_point_to_triangle(p_perturb, tri, thickness=0.1)
plt.figure(figsize=(15, 15))
plt.subplot(111, projection="3d")
plt.gca().scatter(*np.vstack((p_perturb, p_proj)).T,
s=500,
depthshade=False,
c=["r", "g"])
plt.gca().plot_trisurf(*tri.T, triangles=((0, 1, 2)))
plt.show()
def _project_points_to_triangles(x, t):
x_proj = np.empty((len(x), 3))
for i in range(len(x)):
min_dist = np.inf
for j in range(len(t)):
p = project_point_to_triangle(x[i], t[j])
dist = np.linalg.norm(x[i] - p)
if dist < min_dist:
x_proj[i] = p
min_dist = dist
return x_proj
def query(self, query_point, query_radius, curr_node):
# project a point onto its nearest triangles and find the nearest projection location
nearest = (None, float("inf"))
if type(curr_node) == Leaf:
for tri in curr_node.bucket:
# go through each point in the bucket and project it
proj_point = project_point_to_triangle(
query_point, tri, thickness=self.thickness)
proj_dist = np.linalg.norm(query_point - proj_point)
if proj_dist < nearest[1]:
nearest = (proj_point, proj_dist)
self.projection_count += len(curr_node.bucket)
elif type(curr_node) == Node:
dist = np.linalg.norm(query_point - curr_node.center)
if dist > curr_node.radius + query_radius: # query and partition spheres are completely not overlapping
nearest = self.query(query_point, query_radius,
curr_node.outside_node)
elif dist <= curr_node.radius - query_radius: # query and partition spheres are completely overlapping
nearest = self.query(query_point, query_radius,
curr_node.inside_node)
else:
# must examine both subtrees as the border of the query sphere overlaps the border of the partition sphere
nearest_inside = self.query(query_point, query_radius,
curr_node.inside_node)
nearest_outside = self.query(query_point, query_radius,
curr_node.outside_node)
if nearest_inside[1] < nearest_outside[1]:
nearest = nearest_inside
else:
nearest = nearest_outside
return nearest
import numpy as np from matplotlib import pyplot as plt from mpl_toolkits.mplot3d import Axes3D from projection import project_point_to_triangle tri = np.array([[0.0, 0.0, 0.0], [0.0, 1.0, 0.0], [1.0, 1.0, 0.0]]) p_perturb = np.array([1.5, 1.5, 0.5]) p_proj = project_point_to_triangle(p_perturb, tri, thickness = 0.1) plt.figure(figsize = (15, 15)) plt.subplot(111, projection = "3d") plt.gca().scatter(*np.vstack((p_perturb, p_proj)).T, s = 500, depthshade = False, c = ["r", "g"]) plt.gca().plot_trisurf(*tri.T, triangles = ((0, 1, 2))) plt.show()