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"""
Math utilities
2015, Epic Games
"""
import math
import maya.api.OpenMaya as om
import maya.cmds as cmds
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# CLASSES
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
class KDTreeNode():
def __init__(self, point, left, right):
self.point = point
self.left = left
self.right = right
def is_leaf(self):
return (self.left is None and self.right is None)
class KDTreeNeighbours():
""" Internal structure used in nearest-neighbours search.
"""
def __init__(self, query_point, t):
self.query_point = query_point
self.t = t # neighbours wanted
self.largest_distance = 0 # squared
self.current_best = []
def calculate_largest(self):
if self.t >= len(self.current_best):
self.largest_distance = self.current_best[-1][1]
else:
self.largest_distance = self.current_best[self.t - 1][1]
def add(self, point):
sd = square_distance(point, self.query_point)
# run through current_best, try to find appropriate place
for i, e in enumerate(self.current_best):
if i == self.t:
return # enough neighbours, this one is farther, let's forget it
if e[1] > sd:
self.current_best.insert(i, [point, sd])
self.calculate_largest()
return
# append it to the end otherwise
self.current_best.append([point, sd])
self.calculate_largest()
def get_best(self):
return [element[0] for element in self.current_best[:self.t]]
class KDTree():
""" KDTree implementation built from http://en.wikipedia.org/wiki/K-d_tree as a starting point
Example usage:
from kdtree import KDTree
tree = KDTree.construct_from_data(data)
nearest = tree.query(point, t=4) # find nearest 4 points
"""
def __init__(self, data):
def build_kdtree(point_list, depth):
if not point_list:
return None
# check that all points share the same dimensions
dim = len(point_list[0])
for point in point_list:
if len(point) != dim:
print 'KDTREE: point', point, 'does not have', dim, 'dimensions.'
# select axis based on depth modulo tested dimension
axis = depth % dim
# sort point list
point_list.sort(key=lambda point: point[axis])
# choose the median
median = len(point_list) / 2
# create node and recursively construct subtrees
node = KDTreeNode(point=point_list[median],
left=build_kdtree(point_list[0:median], depth + 1),
right=build_kdtree(point_list[median + 1:], depth + 1))
return node
self.root_node = build_kdtree(data, depth=0)
@staticmethod
def construct_from_data(data):
tree = KDTree(data)
return tree
def query(self, query_point, t=1, debug=1):
stats = {'nodes_visited': 0, 'far_search': 0, 'leafs_reached': 0}
def nn_search(node, query_point, t, depth, best_neighbours):
if node is None:
return
stats['nodes_visited'] += 1
# if we have reached a leaf, let's add to current best neighbours,
# (if it's better than the worst one or if there is not enough neighbours)
if node.is_leaf():
# statistics['leafs_reached'] += 1
best_neighbours.add(node.point)
return
# this node is no leaf
# select dimension for comparison (based on current depth)
axis = depth % len(query_point)
# figure out which subtree to search
near_subtree = None # near subtree
far_subtree = None # far subtree (perhaps we'll have to traverse it as well)
# compare query_point and point of current node in selected dimension
# and figure out which subtree is farther than the other
if query_point[axis] < node.point[axis]:
near_subtree = node.left
far_subtree = node.right
else:
near_subtree = node.right
far_subtree = node.left
# recursively search through the tree until a leaf is found
nn_search(near_subtree, query_point, t, depth + 1, best_neighbours)
# while unwinding the recursion, check if the current node
# is closer to query point than the current best,
# also, until t points have been found, search radius is infinity
best_neighbours.add(node.point)
# check whether there could be any points on the other side of the
# splitting plane that are closer to the query point than the current best
if (node.point[axis] - query_point[axis]) ** 2 < best_neighbours.largest_distance:
# statistics['far_search'] += 1
nn_search(far_subtree, query_point, t, depth + 1, best_neighbours)
return
# if there's no tree, there's no neighbors
if self.root_node is not None:
neighbours = KDTreeNeighbours(query_point, t)
nn_search(self.root_node, query_point, t, depth=0, best_neighbours=neighbours)
result = neighbours.get_best()
else:
result = []
# print statistics
return result
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# METHODS
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
def square_distance(self, pointA, pointB):
# squared euclidean distance
distance = 0
dimensions = len(pointA) # assumes both points have the same dimensions
for dimension in range(dimensions):
distance += (pointA[dimension] - pointB[dimension]) ** 2
return distance
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
def getAngleBetween(object1, object2):
point1 = cmds.xform(object1, t=True, q=True, ws=True)
vector1 = om.MVector(point1)
point2 = cmds.xform(object2, t=True, q=True, ws=True)
vector2 = om.MVector(point2)
dotProduct = vector1.normal() * vector2.normal()
angle = math.acos(dotProduct) * 180 / math.pi
return angle
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
def returnPercentile(incomingRange, percent, key=lambda x: x):
floor = math.floor(percent)
ceil = math.ceil(percent)
if percent == 1:
return incomingRange[1]
if percent == 0:
return incomingRange[0]
d0 = key(incomingRange[int(floor)] * (ceil - percent))
d1 = key(incomingRange[int(ceil)] * (percent - floor))
return d0 + d1
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