


How can I identify and polygonize convex holes within a 2D point cloud using C#?
This code demonstrates an approach to finding convex holes in a set of 2d points. The approach involves creating a bitmap of the point cloud, computing the data density for each cell in the bitmap, creating a list of unused areas (map[][] = 0 or map[][] <= treshold), segmenting the list of unused areas into groups of connected components, and polygonizing each group of connected components to obtain the convex polygons representing the holes.
Here's the C# implementation of the algorithm provided:
using System; using System.Collections.Generic; using System.Linq; using System.Drawing; namespace HoleFinder { class Program { // Define a cell structure for the bitmap public struct Cell { public double x0, x1, y0, y1; // Bounding box of points inside the cell public int count; // Number of points inside the cell } // Define a line structure for representing hole boundaries public struct Line { public double x0, y0, x1, y1; // Line edge points public int id; // Id of the hole to which the line belongs for segmentation/polygonization public int i0, i1, j0, j1; // Index in map[][] } // Compute the bounding box of the point cloud public static (double x0, double x1, double y0, double y1) ComputeBoundingBox(Listpoints) { double x0 = points[0].X; double x1 = points[0].X; double y0 = points[0].Y; double y1 = points[0].Y; foreach (var point in points) { if (point.X < x0) x0 = point.X; if (point.X > x1) x1 = point.X; if (point.Y < y0) y0 = point.Y; if (point.Y > y1) y1 = point.Y; } return (x0, x1, y0, y1); } // Create a bitmap of the point cloud public static int[,] CreateBitmap(List points, (double x0, double x1, double y0, double y1) boundingBox, int N) { // Create a 2D array to represent the bitmap int[,] bitmap = new int[N, N]; // Compute the scale factors for converting point coordinates to bitmap indices double mx = N / (boundingBox.x1 - boundingBox.x0); double my = N / (boundingBox.y1 - boundingBox.y0); // Iterate over the points and increment the corresponding cells in the bitmap foreach (var point in points) { int i = (int)Math.Round((point.X - boundingBox.x0) * mx); int j = (int)Math.Round((point.Y - boundingBox.y0) * my); if (i >= 0 && i < N && j >= 0 && j < N) bitmap[i, j]++; } return bitmap; } // Compute the data density for each cell in the bitmap public static void ComputeDataDensity(int[,] bitmap, Cell[] map) { for (int i = 0; i < map.Length; i++) { map[i].count = 0; } for (int i = 0; i < bitmap.GetLength(0); i++) { for (int j = 0; j < bitmap.GetLength(1); j++) { map[i * bitmap.GetLength(1) + j].count += bitmap[i, j]; } } } // Create a list of unused areas (map[][] = 0 or map[][] <= treshold) public static List<(int i0, int i1, int j0, int j1)> FindUnusedAreasHorizontalVertical(Cell[] map, int N, int treshold = 0) { List<(int i0, int i1, int j0, int j1)> unusedAreas = new List<(int, int, int, int)>(); // Scan horizontally for (int j = 0; j < N; j++) { int i0 = -1; int i1 = -1; for (int i = 0; i < N; i++) { if (map[i * N + j].count == 0 || map[i * N + j].count <= treshold) { if (i0 < 0) i0 = i; } else { if (i0 >= 0) { unusedAreas.Add((i0, i1, j, j)); i0 = -1; i1 = -1; } } } if (i0 >= 0) unusedAreas.Add((i0, i1, j, j)); } // Scan vertically for (int i = 0; i < N; i++) { int j0 = -1; int j1 = -1; for (int j = 0; j < N; j++) { if (map[i * N + j].count == 0 || map[i * N + j].count <= treshold) { if (j0 < 0) j0 = j; } else { if (j0 >= 0) { unusedAreas.Add((i, i, j0, j1)); j0 = -1; j1 = -1; } } } if (j0 >= 0) unusedAreas.Add((i, i, j0, j1)); } return unusedAreas; } // Segment the list of unused areas into groups of connected components public static List > SegmentUnusedAreas(List<(int i0, int i1, int j0, int j1)> unusedAreas) { // Initialize each unused area as a separate group List
> segments = new List
>(); foreach (var unusedArea in unusedAreas) { segments.Add(new List<(int i0, int i1, int j0, int j1)> { unusedArea }); } // Iterate until no more segments can be joined bool joined = true; while (joined) { joined = false; // Check if any two segments intersect or are adjacent for (int i = 0; i < segments.Count; i++) { for (int j = i + 1; j < segments.Count; j++) { // Check for intersection bool intersects = false; foreach (var unusedArea1 in segments[i]) { foreach (var unusedArea2 in segments[j]) { if (unusedArea1.i0 <= unusedArea2.i1 && unusedArea1.i1 >= unusedArea2.i0 && unusedArea1.j0 <= unusedArea2.j1 && unusedArea1.j1 >= unusedArea2.j0) { intersects = true; break; } } if (intersects) break; } // Check for adjacency bool adjacent = false; if (!intersects) { foreach (var unusedArea1 in segments[i]) { foreach (var unusedArea2 in segments[j]) { if (unusedArea1.i0 == unusedArea2.i0 && unusedArea1.i1 == unusedArea2.i1 && ((unusedArea1.j1 == unusedArea2.j0 && Math.Abs(unusedArea1.j0 - unusedArea2.j1) == 1) || (unusedArea1.j0 == unusedArea2.j1 && Math.Abs(unusedArea1.j1 - unusedArea2.j0) == 1))) { adjacent = true; break; } if (unusedArea1.j0 == unusedArea2.j0 && unusedArea1.j1 == unusedArea2.j1
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