如何在点云中获取立方体的对角线？

Question

我有一个立方体的点云。我用random（）创建了它，所以所有的x，y，z点都在0和1之间。我这样创建了多维数据集。

import numpy as np
import open3d
import random

listPoints = []

for i in range(10000):
    x = random.random()
    y = random.random()
    z = random.random()
    listPoints.append([x,y,z])

arrayPoints = np.asarray(listPoints) 

point_cloud = open3d.PointCloud()
point_cloud.points = open3d.Vector3dVector(arrayPoints)
open3d.draw_geometries([point_cloud])

现在，我想获得对角线上的点。我现在如何获取与点垂直的点。我需要将一些度数乘以度，但是我不知道该怎么做。我用来垂直于立方体中间的代码：（Y为0.5，因此我将其保持静态并检查所有具有0.5 Y值的点）

listPoints2 = []

minimumY = 0.5 - 0.02
maximumY = 0.5 + 0.02

for i in range(10000):
    if(listPoints[i][1] < maximumY and listPoints[i][1] > minimumY):
        listPoints2.append([listPoints[i][0],listPoints[i][1],listPoints[i][2]])

arrayPoints2 = np.asarray(listPoints2) 

point_cloud2 = open3d.PointCloud()
point_cloud2.points = open3d.Vector3dVector(arrayPoints2)
open3d.draw_geometries([point_cloud2])

我的最终输出带有垂直点。我希望它像对角线一样倾斜。

我应该将我的值乘以什么以获得对角线？

Answer 1

您需要的是计算点到轴的垂直距离，请参见：

• perpendicular distance of point to line/axis

由此，您只需测试所有点是否足够接近立方体的4个对角线。在 C ++ （抱歉，不是Python编码器）中，它看起来像这样：

import { PortalInjector } from '@angular/cdk/portal';
...
const tokens = new WeakMap();
tokens.set(MULTI_SELECT_OVERLAY_DATA, {
  options: this.listOptions,
});
const injector = new PortalInjector(this.injector, tokens);

...

const multiSelectPortal = new ComponentPortal(MultiSelectOverlayComponent, null, injector);

所以我声明了4个轴//--------------------------------------------------------------------------- const int n=10000; // points const int n3=n+n+n; // points*dimensions double pnt[n3]; // points x,y,z ... DWORD col[n]; // colors rgba, ... //--------------------------------------------------------------------------- double distance_point_axis(double *p,double *p0,double *dp) { int i; double l,d,q[3]; for (i=0;i<3;i++) q[i]=p[i]-p0[i]; // q = p-p0 for (l=0.0,i=0;i<3;i++) l+=dp[i]*dp[i]; // l = |dp|^2 for (d=0.0,i=0;i<3;i++) d+=q[i]*dp[i]; // d = dot(q,dp) if (l<1e-10) d=0.0; else d/=l; // d = dot(q,dp)/|dp|^2 for (i=0;i<3;i++) q[i]-=dp[i]*d; // q=q-dp*dot(q,dp)/|dp|^2 for (l=0.0,i=0;i<3;i++) l+=q[i]*q[i]; l=sqrt(l); // l = |q| return l; } //--------------------------------------------------------------------------- void pnt_init() { Randomize(); int i,i3,j; double r=0.1; // radius of diagonals cylinders double diag[4*6]= { // p0 dp 0.0,0.0,0.0, +1.0,+1.0,+1.0, // diagonal 1 0.0,1.0,0.0, +1.0,-1.0,+1.0, // diagonal 2 1.0,0.0,0.0, -1.0,+1.0,+1.0, // diagonal 3 1.0,1.0,0.0, -1.0,-1.0,+1.0, // diagonal 4 }; // compute some uniformly random points <0,1> for (i3=0;i3<n3;i3++) pnt[i3]=Random(); // compute color for (i=0,i3=0;i<n;i++,i3+=3) { // graysh col[i]=0x00303030; // diagonals j=0; if (distance_point_axis(pnt+i3,diag+j+0,diag+j+3)<r) col[i]|=0x00FF0000; j+=6; if (distance_point_axis(pnt+i3,diag+j+0,diag+j+3)<r) col[i]|=0x0000FF00; j+=6; if (distance_point_axis(pnt+i3,diag+j+0,diag+j+3)<r) col[i]|=0x000000FF; j+=6; if (distance_point_axis(pnt+i3,diag+j+0,diag+j+3)<r) col[i]|=0x00FF00FF; j+=6; } } //--------------------------------------------------------------------------- void gl_draw() { int i,i3; static double ang=0.0; ang+=2.5; if (ang>360.0) ang-=360.0; glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT); glEnable(GL_DEPTH_TEST); glDisable(GL_TEXTURE_2D); glMatrixMode(GL_MODELVIEW); glLoadIdentity(); glTranslatef(-0.5,-0.5,-5.0); glRotatef(ang,0.5,0.5,0.5); // render points froma list glBegin(GL_POINTS); for (i=0,i3=0;i<n;i++,i3+=3) { glColor4ubv((BYTE*)(col+i)); glVertex3dv(pnt+i3); } glEnd(); // glFlush(); glFinish(); SwapBuffers(hdc); } //--------------------------------------------------------------------------- （起点和方向向量），然后设置每个点的颜色，使其接近预定义的RGB颜色...

此处预览：

和GIF动画：

如果您想要更简单的东西，那么立方体的主对角线就是

diag[4*6]

只需测试

x = y = z

对于每个点...其他对角线仅是镜像，因此只需将镜像的fabs(x-y)+fabs(x-z)+fabs(y-z) <= 1e-2 替换为coordinate