为两个参数的函数点数据云构建一个网格，然后使用Python将其另存为.ply文件

问题描述

我正在尝试为两个参数的函数（点数据云）构建网格，并使用Python将其另存为.ply文件。

输入：3D空间中的数百万个数据点（x，y，z） 其中 z 可被视为数学函数的值 z = f（x，y）

1. 如何构建表示该点云的3D绘图表面的网格？
2. 并将其导出为3D模型？

所需的输出：包含网格的 .PLY 文件。

对于步骤2，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()
                                        )))
    fid.close()

    print(fid)

但是那个只保存顶点，没有曲面。

以下代码将三角形保存为.ply，但我不确定 tris 是什么首先如何构建三角形：

"""
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','lh.pial_reindex.ply')

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

对于步骤1：

以下文章生成了网格，但（a）它是通用点数据云，而z = f（x，y）此处就足够了，（b）假设输入中包含法线数组： https://towardsdatascience.com/5-step-guide-to-generate-3d-meshes-from-point-clouds-with-python-36bad397d8ba，仍然需要构建。

总而言之：

是否有一种简单的方法可以使用Python为庞大的点云数据构建网格，其中z坐标是（x，y）的函数，然后将此网格导出到.ply文件？

解决方法

解决方案：

1. 进口

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

1. 使用点云数据加载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']

1. 如有必要，对数据进行归一化以确保网格正确位于轴原点中：

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)

1. 由于 z = f（x，y），因此我们无需使用通用三角剖分，并且可以将Delaunay算法用于2D数据点集。

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

1. 网格已准备好，三角形作为顶点索引存储在 mesh.simplices 中。使用以下功能将所有内容保存到 .PLY 文件中：

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()