Create planar TriangleMesh from points in border

Question

I'm using Python, Scipy and Open3D.

Problem:

I have N points (say, ~2000) that roughly correspond to a noisy plane. I managed to find all the Nv points corresponding to the points at the border of the plane. How can I quickly generate a TriangleMesh using these border points?

Here is my work so far:

Since I have a model for this plane, I flatten the whole pointcloud to make it fit the model.

After that, I can compute the convex hull directly using Open3D, but it's annoying because I cannot turn off the warnings. Instead, what I did is: using the model of the plane, I calculated the rotation matrix to align it with the XY plane, then used Scipy's ConvexHull implementation on the X and Y elements of these rotated points.

Using this, I find the indexes of all the original flattened points that are in the border. So far, so good.

Question:

How can I use this to automatically create a mesh now, though?

I know that I need the points array, of course, but also a vertices array showing how to connect the points to create a full triangle mesh. Is there any kind of algorithm I can directly apply in my case?

Answer 1

Alright, saurabheights said, I can use triangulation. Here's the code I came up with on Python, for future reference:

import numpy as np
from scipy.spatial import ConvexHull, Delaunay
from open3d.geometry import TriangleMesh, PointCloud
from open3d.utility import Vector3iVector, Vector3dVector

def get_mesh(plane_normal, plane_distance, points):
    
    points = np.asarray(points)

    # needs signed distance
    distances = points.dot(plane_normal) + plane_distance
    points -= (distances * plane_normal[..., np.newaxis]).T
    
    rot = get_rotation_from_axis(plane_normal)
    projection = (rot @ points.T).T[:, :2]
    
    chull = ConvexHull(projection)
    borders = projection[chull.vertices]
    
    triangles = Delaunay(borders).simplices
    
    # needed to make plane visible from both sides
    triangles = np.vstack([triangles, triangles[:, ::-1]]) 
    
    mesh = TriangleMesh()
    mesh.vertices = Vector3dVector(points[chull.vertices])
    mesh.triangles = Vector3iVector(triangles)
    
    return mesh

Where rotation is just a convenience function that gives the rotation matrix that aligns the axis z with the plane's normal vector.