為雙參數函數（點數據雲）構建網格並使用 Python 將其保存為 .ply 文件

Question

我正在嘗試為雙參數函數（點數據雲）構建網格，並使用 Python 將其另存為 .ply 文件。

輸入：3D 空間(x,y,z)中的百萬個數據點，其中z可被視為數學函數z=f(x,y) 的值

1. 如何構建表示該點雲的 3D 繪圖表面的網格？
2. 並將其導出為 3D 模型？

所需的輸出：包含網格的.PLY文件。

對於第 2 步，我具有以下功能：

def savePoly(filename, arrayOfXYZ):
    xyz = np.array(arrayOfXYZ)
    x_points = xyz[:, 0]
    y_points = xyz[:, 1]
    z_points = xyz[:, 2]
    # Write header of .ply file
    fid = open(filename, 'wb')
    fid.write(bytes('ply\n', 'utf-8'))
    fid.write(bytes('format binary_little_endian 1.0\n', 'utf-8'))
    fid.write(bytes('element vertex %d\n' % x_points.shape[0], 'utf-8'))
    fid.write(bytes('property float x\n', 'utf-8'))
    fid.write(bytes('property float y\n', 'utf-8'))
    fid.write(bytes('property float z\n', 'utf-8'))
    fid.write(bytes('property uchar red\n', 'utf-8'))
    fid.write(bytes('property uchar green\n', 'utf-8'))
    fid.write(bytes('property uchar blue\n', 'utf-8'))
    fid.write(bytes('end_header\n', 'utf-8'))

    rgb_points = np.ones(x_points.shape).astype(np.uint8) * 255

    # Write 3D points to .ply file
    for i in range(x_points.shape[0]):

        fid.write(bytearray(struct.pack("fffccc",
                                        x_points[i],
                                        y_points[i],
                                        z_points[i],
                                        rgb_points[i].tobytes(),
                                        rgb_points[i].tobytes(),
                                        rgb_points[i].tobytes()
                                        )))
    fid.close()

    print(fid)

但是那個只保存頂點，沒有表面。

以下代碼將三角形保存到 .ply 但我不確定什么是tris如何首先構建三角形：

"""
plyfun
@author:wronk
Write surface to a .ply (Stanford 3D mesh file) in a way that preserves
vertex order in the MNE sense. Extendable for colors or other vertex/face properties.
.ply format: https://en.wikipedia.org/wiki/PLY_(file_format)
"""

import mne
import numpy as np
from os import path as op
import os
from os import environ


def write_surf2ply(rr, tris, save_path):
    out_file = open(save_path, 'w')

    head_strs = ['ply\n', 'format ascii 1.0\n']
    ele_1 = ['element vertex ' + str(len(rr)) + '\n',
             'property float x\n',
             'property float y\n',
             'property float z\n']
    ele_2 = ['element face ' + str(len(tris)) + '\n',
             'property list uchar int vertex_index\n']
    tail_strs = ['end_header\n']

    # Write Header
    out_file.writelines(head_strs)
    out_file.writelines(ele_1)
    out_file.writelines(ele_2)
    out_file.writelines(tail_strs)

    ##############
    # Write output
    ##############
    # First, write vertex positions
    for vert in rr:
        out_file.write(str(vert[0]) + ' ')
        out_file.write(str(vert[1]) + ' ')
        out_file.write(str(vert[2]) + '\n')

    # Second, write faces using vertex indices
    for face in tris:
        out_file.write(str(3) + ' ')
        out_file.write(str(face[0]) + ' ')
        out_file.write(str(face[1]) + ' ')
        out_file.write(str(face[2]) + '\n')

    out_file.close()


if __name__ == '__main__':
    struct_dir = op.join(environ['SUBJECTS_DIR'])
    subject = 'AKCLEE_139'

    surf_fname = op.join(struct_dir, subject, 'surf', 'lh.pial')
    save_path = op.join('/media/Toshiba/Blender/Brains', subject,
                        'lh.pial_reindex.ply')

    rr, tris = mne.read_surface(surf_fname)
    write_surf2ply(rr, tris, save_path)

對於第 1 步：

下面的文章生成網格，但 (a) 它是一個通用點數據雲，而 z=f(x,y) 在這里就足夠了，(b) 它假設輸入中有一個法線數組： https:/ /towardsdatascience.com/5-step-guide-to-generate-3d-meshes-from-point-clouds-with-python-36bad397d8ba仍然需要構建。

所以總結一下：

有沒有一種簡單的方法可以使用 Python 為巨大的點雲數據構建網格，其中 z 坐標是 (x,y) 的函數，並將此網格導出到 .ply 文件？

Answer 1

解決方案：

1. 進口

import numpy as np
import scipy.spatial
import pandas as pd

2. 使用點雲數據加載 csv 文件：

df = pd.read_csv("data.csv")

print(df.columns)

x = df['column 0']
y = df['column 1']
z = df['column z values']

3. 如有必要，標准化數據以確保網格正確位於軸原點：

x0 = x[0]
y0 = y[0]
z0 = z[0]
pointslist = []
for i in range(len(x)):
    xi = (x[i] - x0) / 100
    yi = (y[i] - y0) / 4
    zi = (z[i] - z0) / 8
    pointslist.append([xi, yi, zi]) # array of triplets 
xyz = np.array(pointslist)

4. 由於z = f(x,y)我們不需要使用通用三角剖分，並且可以使用 Delaunay 算法來處理二維數據點集。

# xyz = np.random.random((12, 3))  # arbitrary 3D data set
# xyz = np.array([[0, 0,1], [0, 1,1], [1, 0.5,0], [1, 0,0]]) # smaller data set for testing 
# print(data)

mesh = scipy.spatial.Delaunay(xyz[:, :2])  # take the first two dimensions

# print(mesh.points)
# print(mesh.convex_hull)
# print(mesh.vertex_to_simplex)
#
# x = xyz[:, 0]
# y = xyz[:, 1]
# z = xyz[:, 2]

5. 網格已准備就緒，三角形作為頂點索引存儲在mesh.simplices 中。 使用以下函數將所有內容保存到.PLY文件：

writeSurface2PLY(xyz, mesh.simplices, "output.ply")

def writeSurface2PLY(vertices, meshanglesAsVertexIndices, save_path):
    out_file = open(save_path, 'w')

    head_strs = ['ply\n', 'format ascii 1.0\n']
    ele_1 = ['element vertex ' + str(len(vertices)) + '\n',
             'property float x\n',
             'property float y\n',
             'property float z\n']
    ele_2 = ['element face ' + str(len(meshanglesAsVertexIndices)) + '\n',
             'property list uchar int vertex_index\n']
    tail_strs = ['end_header\n']

    # Write Header
    out_file.writelines(head_strs)
    out_file.writelines(ele_1)
    out_file.writelines(ele_2)
    out_file.writelines(tail_strs)

    ##############
    # Write output
    ##############
    # First, write vertex positions
    for vert in vertices:
        out_file.write(str(vert[0]) + ' ')
        out_file.write(str(vert[1]) + ' ')
        out_file.write(str(vert[2]) + '\n')

    # Second, write faces using vertex indices
    for face in meshanglesAsVertexIndices:
        out_file.write(str(3) + ' ')
        out_file.write(str(face[0]) + ' ')
        out_file.write(str(face[1]) + ' ')
        out_file.write(str(face[2]) + '\n')

    out_file.close()