Home Backend Development C++ How can I identify and polygonize convex holes within a 2D point cloud using C#?

How can I identify and polygonize convex holes within a 2D point cloud using C#?

Jan 18, 2025 am 07:22 AM

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:

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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(List<point> points)

        {

            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<point> 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<list<(int i0,="" int="" i1,="" j0,="" j1)="">> SegmentUnusedAreas(List<(int i0, int i1, int j0, int j1)> unusedAreas)

        {

            // Initialize each unused area as a separate group

            List<list<(int i0,="" int="" i1,="" j0,="" j1)="">> segments = new List<list<(int i0,="" int="" i1,="" j0,="" j1)="">>();

            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<p></p><p>The above is the detailed content of How can I identify and polygonize convex holes within a 2D point cloud using C#?. For more information, please follow other related articles on the PHP Chinese website!</p>

 

 

                        </list<(int></list<(int></list<(int></point></point>

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