periphery beams searching algorithms Sanjoy Nath's Geometrifying Trigonometry
Solution 1
To solve the problem of finding
anticlockwise green lines from a set of given 2D line segments forming the
outer boundary of a polygon, including concave sections with reentrant notches,
we can implement a C# program. This solution involves several steps:
1. Read line segment data from a
CSV file.
2. Determine outer boundary
segments.
3. Identify and sort segments in
anticlockwise order.
4. Filter green segments based on
criteria.
Below is the C# program to perform
these tasks:
### C# Code Implementation
```csharp
using System;
using System.Collections.Generic;
using System.Globalization;
using System.IO;
using System.Linq;
namespace PolygonBoundaryFinder
{
public class
LineSegment
{
public int RowNumber { get; set; }
public int SegmentId { get; set; }
public double X1 { get; set; }
public double Y1 { get; set; }
public double X2 { get; set; }
public double Y2 { get; set; }
public
LineSegment(int rowNumber, int segmentId, double x1, double y1, double x2,
double y2)
{
RowNumber = rowNumber;
SegmentId = segmentId;
X1 = x1;
Y1 = y1;
X2 = x2;
Y2 = y2;
}
public override string ToString()
{
return $"{RowNumber},{SegmentId},{X1}
}
}
public class
Program
{
static void Main(string[] args)
{
// Read line segments from CSV file
var lineSegments = ReadLineSegmentsFromCsv("
// Find outer boundary segments
var outerBoundarySegments = FindOuterBoundary(
// Identify anticlockwise green segments
var anticlockwiseGreenSegments = GetAnticlockwiseGreenSegments(
// Write output to CSV file
WriteSegmentsToCsv("output.
}
static List<LineSegment> ReadLineSegmentsFromCsv(string filePath)
{
var lineSegments = new List<LineSegment>();
foreach (var line in File.ReadLines(filePath))
{
var parts = line.Split(',');
var rowNumber = int.Parse(parts[0]);
var segmentId = int.Parse(parts[1]);
var x1 = double.Parse(parts[2],
CultureInfo.InvariantCulture);
var y1 = double.Parse(parts[3],
CultureInfo.InvariantCulture);
var x2 = double.Parse(parts[4],
CultureInfo.InvariantCulture);
var y2 = double.Parse(parts[5],
CultureInfo.InvariantCulture);
lineSegments.Add(new LineSegment(rowNumber,
segmentId, x1, y1, x2, y2));
}
return lineSegments;
}
static List<LineSegment> FindOuterBoundary(List<
{
// Placeholder for actual boundary finding algorithm
// Implement boundary finding logic here (Gift Wrapping, Convex
Hull, etc.)
var boundarySegments = new List<LineSegment>();
// Temporary simplistic approach to demonstrate
// Use Gift Wrapping or other algorithm for actual implementation
boundarySegments = GiftWrappingAlgorithm(
return boundarySegments;
}
static List<LineSegment> GiftWrappingAlgorithm(List<
{
// Placeholder for Gift Wrapping Algorithm implementation
// Assuming we get the boundary segments correctly using the
algorithm
// Replace this with actual Gift Wrapping logic
return lineSegments; // This needs to be replaced with actual
boundary detection logic
}
static List<LineSegment> GetAnticlockwiseGreenSegments(
{
var greenSegments = boundarySegments.Where(
// Sort segments in anticlockwise order
// This is a placeholder and needs to be implemented properly
greenSegments = greenSegments.OrderBy(s => Math.Atan2(s.Y2 -
s.Y1, s.X2 - s.X1)).ToList();
return greenSegments;
}
static bool IsGreenSegment(LineSegment segment)
{
// Placeholder for actual green segment criteria
// Assuming all segments are green for now
return true;
}
static void WriteSegmentsToCsv(string filePath, List<LineSegment>
segments)
{
using (var writer = new StreamWriter(filePath))
{
foreach (var segment in segments)
{
writer.WriteLine(segment.
}
}
}
}
}
```
### Explanation:
1. **LineSegment Class:**
Represents a 2D line segment with properties for row number, segment ID, and
coordinates.
2. **Main Method:**
- Reads line
segments from an input CSV file.
- Identifies outer
boundary segments using a placeholder algorithm (to be replaced with a proper
algorithm like Gift Wrapping).
- Filters and sorts
anticlockwise green segments.
- Writes the sorted
segments to an output CSV file.
3. **ReadLineSegmentsFromCsv
Method:** Reads and parses the line segment data from a CSV file.
4. **FindOuterBoundary Method:**
Placeholder method to find the outer boundary segments using an appropriate
algorithm (e.g., Gift Wrapping, Convex Hull).
5. **GiftWrappingAlgorithm
Method:** Placeholder for the Gift Wrapping algorithm to find boundary
segments. Replace with the actual algorithm.
6. **
7. **IsGreenSegment Method:**
Placeholder for the criteria to determine if a segment is green.
8. **WriteSegmentsToCsv Method:**
Writes the line segments to an output CSV file.
### Next Steps:
- Implement a proper boundary
finding algorithm in the `GiftWrappingAlgorithm` method.
- Define and implement the
criteria for green segments in the `IsGreenSegment` method.
- Ensure the sorting in `
This program provides a
structured approach to solving the problem based on the given requirements.
Replace the placeholder methods with actual implementations to achieve the
desired functionality.
Solution 2
To achieve the task of finding
the anticlockwise boundary line segments from a given set of 2D line segments
without constructing additional line segments, we can use the following steps:
1. Read the line segment data
from a CSV file.
2. Determine the outer boundary
segments by checking if endpoints of the line segments are shared with other
segments.
3. Identify and sort the boundary
segments in anticlockwise order.
4. Handle the detection of
reentrant notches where necessary.
5. Write the sorted boundary
segments to an output CSV file.
Here is a C# program to implement
these steps:
### C# Code Implementation
```csharp
using System;
using System.Collections.Generic;
using System.Globalization;
using System.IO;
using System.Linq;
namespace PolygonBoundaryFinder
{
public class
LineSegment
{
public int RowNumber { get; set; }
public int SegmentId { get; set; }
public double X1 { get; set; }
public double Y1 { get; set; }
public double X2 { get; set; }
public double Y2 { get; set; }
public LineSegment(int rowNumber, int segmentId, double x1, double y1, double
x2, double y2)
{
RowNumber = rowNumber;
SegmentId = segmentId;
X1 = x1;
Y1 = y1;
X2 = x2;
Y2 = y2;
}
public override string ToString()
{
return $"{RowNumber},{SegmentId},{X1}
}
public bool SharesEndpointWith(LineSegment other)
{
return (X1 == other.X1 && Y1 == other.Y1) || (X1 ==
other.X2 && Y1 == other.Y2) ||
(X2 == other.X1 && Y2 ==
other.Y1) || (X2 == other.X2 && Y2 == other.Y2);
}
}
public class
Program
{
static void Main(string[] args)
{
// Read line segments from CSV file
var lineSegments = ReadLineSegmentsFromCsv("
// Find outer boundary segments
var outerBoundarySegments = FindOuterBoundary(
// Identify anticlockwise segments
var anticlockwiseSegments = SortAnticlockwise(
// Write output to CSV file
WriteSegmentsToCsv("output.
}
static List<LineSegment> ReadLineSegmentsFromCsv(string filePath)
{
var lineSegments = new List<LineSegment>();
foreach (var line in File.ReadLines(filePath))
{
var parts = line.Split(',');
var rowNumber = int.Parse(parts[0]);
var segmentId = int.Parse(parts[1]);
var x1 = double.Parse(parts[2],
CultureInfo.InvariantCulture);
var y1 = double.Parse(parts[3],
CultureInfo.InvariantCulture);
var x2 = double.Parse(parts[4],
CultureInfo.InvariantCulture);
var y2 = double.Parse(parts[5],
CultureInfo.InvariantCulture);
lineSegments.Add(new LineSegment(rowNumber,
segmentId, x1, y1, x2, y2));
}
return lineSegments;
}
static List<LineSegment> FindOuterBoundary(List<
{
var boundarySegments = new List<LineSegment>();
var segmentDict = new Dictionary<Tuple<double, double>,
List<LineSegment>>();
foreach (var segment in lineSegments)
{
var start = Tuple.Create(segment.X1, segment.Y1);
var end = Tuple.Create(segment.X2, segment.Y2);
if (!segmentDict.ContainsKey(
{
segmentDict[start] = new
List<LineSegment>();
}
if (!segmentDict.ContainsKey(end)
{
segmentDict[end] = new
List<LineSegment>();
}
segmentDict[start].Add(
segmentDict[end].Add(segment);
}
var visited = new HashSet<LineSegment>();
var currentSegment = lineSegments[0];
var currentPoint = Tuple.Create(currentSegment.
while (true)
{
boundarySegments.Add(
visited.Add(currentSegment);
var nextSegments = segmentDict[currentPoint].
if (nextSegments.Count == 0)
{
break;
}
currentSegment = nextSegments.First();
currentPoint = currentSegment.
Tuple.Create(currentSegment.
Tuple.Create(currentSegment.
}
return boundarySegments;
}
static List<LineSegment> SortAnticlockwise(List<
{
var center = new Tuple<double, double>(
boundarySegments.Average(seg => (seg.X1 +
seg.X2) / 2),
boundarySegments.Average(seg => (seg.Y1 +
seg.Y2) / 2));
return boundarySegments.OrderBy(seg =>
{
var angle = Math.Atan2((seg.Y1 + seg.Y2) / 2 -
center.Item2, (seg.X1 + seg.X2) / 2 - center.Item1);
return (angle >= 0 ? angle : (2 * Math.PI +
angle));
}).ToList();
}
static void WriteSegmentsToCsv(string filePath, List<LineSegment>
segments)
{
using (var writer = new StreamWriter(filePath))
{
foreach (var segment in segments)
{
writer.WriteLine(segment.
}
}
}
}
}
```
### Explanation:
1. **LineSegment Class:**
Represents a 2D line segment with properties for row number, segment ID, and
coordinates. It includes a method to check if two segments share an endpoint.
2. **Main Method:**
- Reads line
segments from an input CSV file.
- Identifies outer
boundary segments.
- Sorts the boundary
segments in anticlockwise order.
- Writes the sorted
segments to an output CSV file.
3. **ReadLineSegmentsFromCsv
Method:** Reads and parses the line segment data from a CSV file.
4. **FindOuterBoundary Method:**
Uses a dictionary to group line segments by their endpoints and then traverses
through them to find the boundary segments.
5. **SortAnticlockwise Method:**
Sorts the boundary segments in anticlockwise order based on the center of the
boundary polygon.
6. **WriteSegmentsToCsv Method:**
Writes the line segments to an output CSV file.
This program finds the outer
boundary by checking if endpoints of the line segments are shared with other
segments, ensuring no new segments are created. The boundary segments are then
sorted in anticlockwise order and written to a CSV file.
---------- Forwarded message
---------
From: Sanjoy Nath <geometrifyingtrigonometry.
Date: Thu, 16 May 2024, 05:55
Subject: more powerful prompt with more restricted clarity
To: Sanjoy NathGeometrifyingTrigonometryS
Strict note 1 : Normal
Triangulations work where polygons boundary are given. Here Polygons Boundary
are to search (from the given sets of 2D Line segments only and obviously one
of the the end points of the boundary Line segments are obviously
overlapping with only one end point of next line segment in the given line
segment set (no additional convexity point construction allowed no additional
convexity line segment construction allowed)) Strict note 2: that the outer
boundary finding is to do from the existing supplied line segments set only.
Strict Note 3: The Outer boundary are concave or convex or having kinks that
means reentrants are present in the outer boundaries formed from the existing
sets of given line segments and also the fact is that we cannot accumulate any
point from the endpoints of any line segments to construct additional line
segments. If any line segments part is outside the best fit boundary then let
that part get trimmed and reports that case.Algorithms don't have permission to
construct any new line segment to make the boundary look good. Now think How
many triangulations Algorithms are available in Computational Geometry where
(loose points are not given instead Line segments data are given on 2D
only).Outer boundary clue is not there in the input set at all. We have to find
that through the algorithms only. After Visual Checking we can see that some
non boundary Line segments cuts the Real Boundary lines partially. Our motive
is that we need to find the largest Area (concave and irregular or convex or
whatever ...shaped) boundary wall (from the existing set of given line segments
as architectural walls planning) such that if a point sized nano robot is
placed inside the jungle of given line segments then it can cover the
maximum area on 2D )
I tried with the algorithms systems like this. I read a text file (or csv
file)having the long list in rows representing set or randomized list of only
2D line segments data that is visually looking like triangulated space
(row_number_as_integer,Line_
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