一、写在前面
①配套文件：根据剖面对三维坐标点（X,Y,Z）分类资源-CSDN文库
②脱敏处理：蚀变数据已采用随机数生成覆盖
③剖面坐标按顺序排列在"剖面坐标点.xlsx"文件中
二、3点确定空间中平面方程
原理：
设3点A，B，C
计算向量AB和AC
法向量n = AB × AC （叉乘 ）
得到n（ni，nj，nk）后，设方程为
ni * X + nj * Y + nk * Z = D
代入A,B,C任意一点的坐标得出D值后就可以得到平面方程
代码：
输入：p1、p2、p3为平面上的3个点
输出：Ax+By+Cz+D=0平面方程中的系数
python
def plane_from_points(p1, p2, p3):
# 将点转换为numpy数组，如果已经是数组则不转换
a = np.array(p1)
b = np.array(p2)
c = np.array(p3)
# 计算法向量
normal = np.cross(b - a, c - a)
# 归一化法向量并计算d
d = -np.dot(normal, a)
print("平面方程: {}x + {}y + {}z + {} = 0".format(normal[0],normal[1],normal[2],d))
return normal[0], normal[1], normal[2], d三、确定空间中一点到平面的距离
代码：
输入：①平面方程中的4个系数；②待求与平面方程距离的点
输出：点到平面距离
python
def point2area_distance(Ax, By, Cz, D,p):
mod_d = Ax * p[0] + By * p[1] + Cz * p[2] + D
mod_area = np.sqrt(np.sum(np.square([Ax, By, Cz])))
d = abs(mod_d) / mod_area
return d四、完整代码
python
dataSample = pd.read_excel(r"C:\Users\zsllsz2022\Desktop\坐标分类.xlsx")
import numpy as np
def plane_from_points(p1, p2, p3):
# 将点转换为numpy数组，如果已经是数组则不转换
a = np.array(p1)
b = np.array(p2)
c = np.array(p3)
# 计算法向量
normal = np.cross(b - a, c - a)
# 归一化法向量并计算d
d = -np.dot(normal, a)
print("平面方程: {}x + {}y + {}z + {} = 0".format(normal[0],normal[1],normal[2],d))
return normal[0], normal[1], normal[2], d
def point2area_distance(Ax, By, Cz, D,p):
mod_d = Ax * p[0] + By * p[1] + Cz * p[2] + D
mod_area = np.sqrt(np.sum(np.square([Ax, By, Cz])))
d = abs(mod_d) / mod_area
return d
pointData = data = pd.read_excel(r"C:\Users\zsllsz2022\Desktop\剖面坐标点.xlsx")
point = []
for index in range(63):
x = pointData["X"].iloc[index]
y = pointData["Y"].iloc[index]
z = pointData["Z"].iloc[index]
point.append([x,y,z])
fileIndex = 1
for x in [3*x for x in range(3,4)]: #range21
p1 = point[x]
p2 = point[x+1]
p3 = point[x+2]
a,b,c,d = plane_from_points(p1, p2, p3)
dataSample = pd.read_excel(r"C:\Users\zsllsz2022\Desktop\坐标分类.xlsx")
classifyIndex = []
for index in range(len(dataSample)):
xTo = dataSample["Xto"].iloc[index]
yTo = dataSample["Yto"].iloc[index]
zTo = dataSample["Zto"].iloc[index]
toPoint = [xTo,yTo,zTo]
xFrom = dataSample["Xfrom"].iloc[index]
yFrom = dataSample["Yfrom"].iloc[index]
zFrom = dataSample["Zfrom"].iloc[index]
fromPoint = [xFrom,yFrom,zFrom]
if point2area_distance(a,b,c,d,toPoint) < 5:
classifyIndex.append(index)
if point2area_distance(a,b,c,d,fromPoint) < 5:
classifyIndex.append(index)
dataSample = dataSample.iloc[classifyIndex]
list_to_append = [np.nan,np.nan,np.nan,np.nan,np.nan,np.nan,np.nan,np.nan,
dataSample["Dep2200"].mean(),dataSample["IC"].mean(),dataSample["Pos2200"].mean(),
dataSample["Dep2250"].mean(),dataSample["Pos2250"].mean(),dataSample["Dep1900"].mean()]
new_row = pd.DataFrame([list_to_append], columns=list(dataSample.columns))
dataSample = dataSample.append(new_row,ignore_index=True)
print("剖面完成:",fileIndex)
dataSample.to_excel(r"C:\Users\zsllsz2022\Desktop\剖面{}.xlsx".format(fileIndex))
fileIndex += 1