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三维点云数据的哈希快速查找方法

对于三维空间中的浮点坐标点云数据，实现快速查找需要考虑浮点数的精度问题以及空间分布特性。以下是几种有效的哈希查找方法：

1. 网格哈希 (Grid Hashing)

原理：将三维空间划分为均匀的网格，每个点根据坐标分配到对应的网格单元。

import mathclass GridHash:def __init__(self, cell_size=0.1):self.cell_size = cell_sizeself.hash_table = {}def _get_cell_key(self, point):x, y, z = pointreturn (math.floor(x / self.cell_size),math.floor(y / self.cell_size),math.floor(z / self.cell_size))def insert(self, point):key = self._get_cell_key(point)if key not in self.hash_table:self.hash_table[key] = []self.hash_table[key].append(point)def query(self, point):key = self._get_cell_key(point)return self.hash_table.get(key, [])

2. 空间填充曲线哈希 (Z-order/Morton Code)

原理：使用空间填充曲线将三维坐标映射为一维哈希值。

def interleave_bits(x, y, z):# 将三个坐标的二进制位交错排列def spread_bits(n):n = (n | (n << 16)) & 0x030000FFn = (n | (n << 8)) & 0x0300F00Fn = (n | (n << 4)) & 0x030C30C3n = (n | (n << 2)) & 0x09249249return nreturn spread_bits(x) | (spread_bits(y) << 1) | (spread_bits(z) << 2)class MortonHash:def __init__(self, precision=1e-6):self.precision = precisionself.hash_table = {}def _quantize(self, coord):return int(coord / self.precision)def insert(self, point):x, y, z = [self._quantize(c) for c in point]key = interleave_bits(x, y, z)if key not in self.hash_table:self.hash_table[key] = []self.hash_table[key].append(point)def query(self, point):x, y, z = [self._quantize(c) for c in point]key = interleave_bits(x, y, z)return self.hash_table.get(key, [])

3. 近似最近邻哈希 (Locality Sensitive Hashing, LSH)

原理：使用随机投影将相近的点映射到相同哈希桶的概率更高。

import numpy as npclass LSHHash:def __init__(self, dim=3, num_tables=5, hash_size=10, w=4.0):self.num_tables = num_tablesself.hash_size = hash_sizeself.w = w# 生成随机投影向量self.hash_tables = []for _ in range(num_tables):table = {'projection': np.random.randn(dim, hash_size),'bias': np.random.uniform(0, w, size=hash_size),'table': {}}self.hash_tables.append(table)def _hash(self, point, table):projections = np.dot(point, table['projection']) + table['bias']hash_key = tuple(np.floor(projections / self.w).astype(int))return hash_keydef insert(self, point):point = np.array(point)for table in self.hash_tables:key = self._hash(point, table)if key not in table['table']:table['table'][key] = []table['table'][key].append(point)def query(self, point):point = np.array(point)results = set()for table in self.hash_tables:key = self._hash(point, table)if key in table['table']:for p in table['table'][key]:results.add(tuple(p))return list(results)

4. 八叉树 (Octree) 索引

虽然不是严格的哈希表，但八叉树也能提供快速的空间查找：

class OctreeNode:def __init__(self, center, size, capacity=10, max_depth=5):self.center = centerself.size = sizeself.capacity = capacityself.max_depth = max_depthself.points = []self.children = Nonedef insert(self, point, depth=0):if self.children is not None:index = self._get_child_index(point)self.children[index].insert(point, depth+1)else:self.points.append(point)if len(self.points) > self.capacity and depth < self.max_depth:self._split()def _get_child_index(self, point):x, y, z = pointcx, cy, cz = self.centerindex = 0if x > cx: index |= 1if y > cy: index |= 2if z > cz: index |= 4return indexdef _split(self):child_size = self.size / 2self.children = []for i in range(8):offset = [child_size if (i & 1) else -child_size,child_size if (i & 2) else -child_size,child_size if (i & 4) else -child_size]child_center = [self.center[j] + offset[j] for j in range(3)]self.children.append(OctreeNode(child_center, child_size, self.capacity, self.max_depth))for point in self.points:index = self._get_child_index(point)self.children[index].insert(point)self.points = []def query(self, point, radius):results = []if self.children is not None:index = self._get_child_index(point)results.extend(self.children[index].query(point, radius))# 检查相邻节点for i in range(8):if i != index and self._check_overlap(i, point, radius):results.extend(self.children[i].query(point, radius))else:for p in self.points:if np.linalg.norm(np.array(p) - np.array(point)) <= radius:results.append(p)return results

选择建议

1. 网格哈希：最简单直接，适合均匀分布的点云
2. Morton哈希：对空间局部性有更好保留，适合范围查询
3. LSH：适合高维数据和近似最近邻搜索
4. 八叉树：适合非均匀分布的点云，动态更新效率高

对于浮点坐标，关键是要处理好精度问题，通常需要将浮点数量化到适当的精度后再进行哈希。