Question

我想在3D空间中绘制船体的“横截面”，船体与平面的交点。

空间由轴X, Y, Z定义，交叉平面 平行于XZ 由Y = 50

定义

首先，我在points中加载了一片3D np.array：

#loading colors

points = np.array([(GEO.XYZRGB(rank, name, X, Y, Z))
                  for rank, name, X, Y, Z in csv.reader(open('colors.csv'))])

点结构为rank, name, X, Y, Z, R, G, B
每个点都在X, Y, Z

一些例子：

['2' 'Y2    ' '77.89506204' '87.46909733' '42.72168896' '254' '244' '21']
['3' 'Y4    ' '76.95634543' '83.94271933' '39.48573173' '255' '234' '0']
['4' 'PINKwA' '64.93353667' '59.00840333' '84.71839733' '218' '154' '225']
...

现在，我对点进行了scipy.Delaunay四面体化：

# Delaunay triangulation    
tri = scipy.spatial.Delaunay(points[:,[2,3,4]], furthest_site=False)

所以我可以获得所有vertices（即船体的每个奇异四面体）：

# indices of vertices
indices = tri.simplices

# the vertices for each tetrahedron
vertices = points[indices]

print vertices

我的问题：从这里开始，我有顶点，如何找到飞机和船体之间的所有交点？

由于

Answer 1

下面，我给出python代码，给定一组3d点和一个平面（由其法向矢量和平面上的一个点定义），计算3d Delaunay三角剖分（镶嵌）以及Delaunay边与飞机。

下图以单位立方体中与x=0平面相交的二十个随机点（交点为蓝色）的示例显示了结果。用于可视化的代码是从代码in this answer修改而来的。

要实际计算平面相交点，我使用以下代码。基本功能plane_delaunay_intersection使用两个辅助功能-collect_edges收集Delaunay三角剖分的边缘（每个线段只有一个副本），而plane_seg_intersection则将线段与平面相交

代码如下：

from scipy.spatial import Delaunay
import numpy as np

def plane_delaunay_intersection(pts, pln_pt, pln_normal):
    """ 
    Returns the 3d Delaunay triangulation tri of pts and an array of nx3 points that are the intersection
    of tri with the plane defined by the point pln_pt and the normal vector pln_normal.
    """
    tri = Delaunay(points)
    edges = collect_edges(tri)
    res_lst = []
    for (i,j) in edges:
        p0 = pts[i,:]
        p1 = pts[j,:]
        p = plane_seg_intersection(pln_pt, pln_normal, p0, p1)
        if not np.any(np.isnan(p)):
            res_lst.append(p)
    res = np.vstack(res_lst)
    return res, tri 


def collect_edges(tri):
    edges = set()

    def sorted_tuple(a,b):
        return (a,b) if a < b else (b,a)
    # Add edges of tetrahedron (sorted so we don't add an edge twice, even if it comes in reverse order).
    for (i0, i1, i2, i3) in tri.simplices:
        edges.add(sorted_tuple(i0,i1))
        edges.add(sorted_tuple(i0,i2))
        edges.add(sorted_tuple(i0,i3))
        edges.add(sorted_tuple(i1,i2))
        edges.add(sorted_tuple(i1,i3))
        edges.add(sorted_tuple(i2,i3))
    return edges


def plane_seg_intersection(pln_pt, pln_normal, p0, p1):
    t0 = np.dot(p0 - pln_pt, pln_normal)
    t1 = np.dot(p1 - pln_pt, pln_normal)
    if t0*t1 > 0.0:
        return np.array([np.nan, np.nan, np.nan])  # both points on same side of plane

    # Interpolate the points to get the intersection point p.
    denom = (np.abs(t0) + np.abs(t1))
    p = p0 * (np.abs(t1) / denom) + p1 * (np.abs(t0) / denom)
    return p

以下代码用于生成上图示例的输入：

np.random.seed(0)
x = 2.0 * np.random.rand(20) - 1.0
y = 2.0 * np.random.rand(20) - 1.0
z = 2.0 * np.random.rand(20) - 1.0

points = np.vstack([x, y, z]).T
pln_pt = np.array([0,0,0])  # point on plane
pln_normal = np.array([1,0,0])  # normal to plane
inter_pts, tri = plane_delaunay_intersection(points, pln_pt, pln_normal)

Python，四面体（scipy.Delaunay）3D云点的一部分

1 个答案: