如何从线创建 3D 平面

Question

我正在将 Helix Toolkit 与 WPF 结合使用，我想将一堆线条变成一个曲面。澄清一下，我有一组 3 维曲线，我想得到由所有这些线产生的弯曲刀片。 （这些线代表穿过刀片的线）。

在某种程度上，我想做与this question 所要求的相反的事情（使用线条作为线框将其变成模型）。

到目前为止，我有这个 XAML：

<Window x:Class="_3D_Geometry_Test.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    xmlns:helix="clr-namespace:HelixToolkit.Wpf;assembly=HelixToolkit.Wpf"
    xmlns:local="clr-namespace:_3D_Geometry_Test">
    <Grid>
        <helix:HelixViewport3D x:Name="view1">
            <helix:DefaultLights/>               
            <helix:MeshGeometryVisual3D x:Name="bladesMeshGeo" />    
        </helix:HelixViewport3D>
    </Grid>
</Window>

以及代码隐藏的相关部分（我不包括 GetSplines() 和 GetSpars() 的内容，因为它们完全由我在每个列表中添加大量 Point3D 对象组成）：

using HelixToolkit.Wpf;
using System.Collections.Generic;
using System.Windows;
using System.Windows.Media;
using System.Windows.Media.Media3D;
namespace _3D_Geometry_Test
{
    public partial class MainWindow : Window
    {
        const int NUM_SPLINES = 11;
        const int NUM_SPARS = 10;
        public MainWindow()
        {
            InitializeComponent();

            List<Point3D>[] splines = GetSplines();
            List<Point3D>[] spars = GetSpars();

            for (int i = 0; i < NUM_SPLINES; i++)
            {
                bladesMeshGeo.Children.Add(new LinesVisual3D
                {
                    Points = new Point3DCollection(splines[i]),
                    Color = Colors.Red
                });
            }

            for (int i = 0; i < NUM_SPARS; i++)
            {
                bladesMeshGeo.Children.Add(new LinesVisual3D
                {
                    Points = new Point3DCollection(spars[i]),
                    Color = Colors.Blue
                });
            }
        }
    }
}

结果是这样的：

但我想要这样的东西：

编辑：我不喜欢 Helix Toolkit，所以如果有人知道可以完成此任务的另一个库，我将不胜感激！

Answer 1

好的，所以我想出的最好的方法是制作很多很多连接所有点的小三角形，就像这样（XAML 保持不变）：

using HelixToolkit.Wpf;
using System;
using System.Collections.Generic;
using System.Windows;
using System.Windows.Media;
using System.Windows.Media.Media3D;

namespace _3D_Geometry_Test
{
    /// <summary>
    /// Interaction logic for MainWindow.xaml
    /// </summary>
    public partial class MainWindow : Window
    {
        const int NUM_SPLINES = 11;
        const int NUM_SPARS = 10;
        static Vector3D xAxis = new Vector3D(1, 0, 0);

        /// <summary>
        /// Creates the window.
        /// </summary>
        public MainWindow()
        {
            InitializeComponent();
            MakeBlades3();
        }

        /// <summary>
        /// Makes the blades.
        /// </summary>
        public void MakeBlades3()
        {
            var splines = GetSplines();
            var spars = GetSpars();

            MeshBuilder builder = new MeshBuilder(true, true);

            for (int i = 0; i < splines.Length; i++)
            {
                var currSpline = splines[i];
                if (i < splines.Length - 1)
                {
                    var nextSpline = splines[i + 1];
                    for (int j = 0; j < currSpline.Count; j++)
                    {
                        Point3D currPoint = currSpline[j];
                        Point3D pt1, pt2;
                        Find2NN(currPoint, nextSpline, out pt1, out pt2);
                        builder.AddTriangle(currPoint, pt1, pt2);

                        if (j > 0)
                        {
                            Point3D prevPoint = currSpline[j - 1];
                            Point3D pt3 = FindNN(currPoint, prevPoint, nextSpline);
                            builder.AddTriangle(currPoint, prevPoint, pt3);
                        }

                        if (j < currSpline.Count - 1)
                        {
                            Point3D nextPoint = currSpline[j + 1];
                            Point3D pt3 = FindNN(currPoint, nextPoint, nextSpline);
                            builder.AddTriangle(currPoint, nextPoint, pt3);
                        }
                    }
                }
                if (i > 0)
                {
                    var prevSpline = splines[i - 1];
                    for (int j = 0; j < currSpline.Count; j++)
                    {
                        Point3D currPoint = currSpline[j];
                        Point3D pt1, pt2;
                        Find2NN(currPoint, prevSpline, out pt1, out pt2);
                        builder.AddTriangle(currPoint, pt1, pt2);

                        if (j > 0)
                        {
                            Point3D prevPoint = currSpline[j - 1];
                            Point3D pt3 = FindNN(currPoint, prevPoint, prevSpline);
                            builder.AddTriangle(currPoint, prevPoint, pt3);
                        }
                        if (j < currSpline.Count - 1)
                        {
                            Point3D nextPoint = currSpline[j + 1];
                            Point3D pt3 = FindNN(currPoint, nextPoint, prevSpline);
                            builder.AddTriangle(currPoint, nextPoint, pt3);
                        }
                    }
                }
            }
            bladePlot.MeshGeometry = builder.ToMesh();
        }

        /// <summary>
        /// Finds the point in the input list of points that is closest to the two input points (Euclidean distance).
        /// </summary>
        /// <param name="origPoint1">The first point.</param>
        /// <param name="origPoint2">The second point.</param>
        /// <param name="listOfPoints">The list of points to find the nearest one in <note type="note">For the sake of speed, this should be a DISTINCT list (no duplicates).</note>.</param>
        /// <returns>The point in <paramref name="listOfPoints"/> that is closest to <paramref name="origPoint1"/> and <paramref name="origPoint2"/> (Euclidean distance).</returns>
        private Point3D FindNN(Point3D origPoint1, Point3D origPoint2, List<Point3D> listOfPoints)
        {
            Point3D result = listOfPoints[0];
            var dist = EuclidDist(origPoint1, result) + EuclidDist(origPoint2, result);
            for (int i = 1; i < listOfPoints.Count;i++)
            {
                var dist2 = EuclidDist(origPoint1, listOfPoints[i]) + EuclidDist(origPoint2, listOfPoints[i]);
                if (dist2 < dist)
                {
                    dist = dist2;
                    result = listOfPoints[i];
                }
            }
            return result;
        }

        /// <summary>
        /// Find the 2 nearest neighbors of the specified point (based on Euclidean distance).
        /// </summary>
        /// <param name="origPoint">The original point.</param>
        /// <param name="listOfPoints">A list of points to find the two nearest-neighbors from. <note type="note">For the sake of speed, this should be a DISTINCT list (no duplicates).</note></param>
        /// <param name="pt1">First nearest neighboring point (output).</param>
        /// <param name="pt2">Second nearest neighboring point (output).</param>
        private void Find2NN(Point3D origPoint, List<Point3D> listOfPoints, out Point3D pt1, out Point3D pt2)
        {
            pt1 = new Point3D();
            pt2 = new Point3D();

            List<Point3D> temp = new List<Point3D>(listOfPoints);

            pt1 = temp[0];
            var dist = EuclidDist(origPoint, pt1);
            for (int i = 1; i < temp.Count; i++)
            {
                var dist2 = EuclidDist(origPoint, temp[i]);
                if (dist2 < dist)
                {
                    dist = dist2;
                    pt1 = temp[i];
                }
            }
            temp.Remove(pt1);

            pt2 = temp[0];
            dist = EuclidDist(origPoint, pt2);
            for (int i = 1; i < temp.Count; i++)
            {
                var dist2 = EuclidDist(origPoint, temp[i]);
                if (dist2 < dist)
                {
                    dist = dist2;
                    pt2 = temp[i];
                }
            }
        }

        /// <summary>
        /// Calculates the Euclidean distance between the two input points.
        /// </summary>
        /// <param name="pt1">The first point.</param>
        /// <param name="pt2">The second point.</param>
        /// <returns>The Euclidean distance between <paramref name="pt1"/> and <paramref name="pt2"/>.</returns>
        private double EuclidDist(Point3D pt1, Point3D pt2)
        {
            double deltaX = pt1.X - pt2.X;
            double deltaY = pt1.Y - pt2.Y;
            double deltaZ = pt1.Z - pt2.Z;
            return Math.Sqrt(deltaX * deltaX + deltaY * deltaY + deltaZ * deltaZ);
        }
    }
}

生成的图像如下所示：

这绝对是对线框的改进，但它仍然不是很流畅（不确定这是否显示在我发布的图像上），我相信必须有更好的解决方案，所以我会离开这暂时没有答案。只是发布我的（临时）解决方案，以防它帮助任何人。