Skip to content

Commit

Permalink
Circle2D intersection with Line(Segment)2D (#237)
Browse files Browse the repository at this point in the history 
* Feat: Line2D.DistanceTo(point)

* feat: Circle2D.IntersectWith(Line2D)

* doc: fix xml comment

* refactor: extract the private method findParameterTs(Line2D)

Aleady existing test cases must be changed because of the implementation of FindRoots.Polynomial(coeffs), that is, the order of the solutions.

* feat: Circle2D.IntersectWith(LineSegment2D)

* doc: fix the variable-name list in comment

* fix: a typo

* change: use the fact that dot-product of the unit vector is always 1.0

* Revert "Feat: Line2D.DistanceTo(point)"

This reverts commit 0a2521d.

* remove: src/Spatial/Extensions/DoubleExtensions.cs

* doc: revise xml comments

* fix a typo

* test: fix testcases to test number of intersections

* fix: IntersectionWith() to return a single point when a line tangent to the circle

* test: Add tests for intersection of Circle and LineSegment2D

for the case where LineSegment contains some of obtained intersections.

* test: add TODO comment

* refactor: rename line to segment

* fix: type declaration (from 1d to 1.0)

* test: fix testcases to use expected points

* test: fix testcases to use expected points

* test: add testcases where the line is parallel to the Y-axis

* test: add testcases parallel to Y-axis and general cases

* test: add testcases for Intersection of Circle2D with LIneSegment2D

- parallel to X-axis
- parallel to Y-axis
- general cases (eg. x-y+c=0)

test: rename method's name

* test: replace +01 to +1

* Minor changes in test

---------

Co-authored-by: jkaliak <[email protected]>
  • Loading branch information
@f-frhs @jkalias
f-frhs and jkalias authored Dec 9, 2023
1 parent 8cae855 commit 9a40b9f
Show file tree
Hide file tree
Showing 3 changed files with 189 additions and 1 deletion.
123 changes: 122 additions & 1 deletion src/Spatial.Tests/Euclidean/Circle2DTests.cs
View file
Original file line number Diff line number Diff line change
@@ -1,4 +1,5 @@
using System;
using System;
using System.Linq;
using MathNet.Spatial.Euclidean;
using NUnit.Framework;

Expand Down Expand Up @@ -58,5 +59,125 @@ public void CircleFromThreePointsArgumentException()

Assert.Throws<ArgumentException>(() => { Circle2D.FromPoints(p1, p2, p3); });
}

//parallel to the X-axis
[TestCase("0,0", 1, "-10,-10", "+10,-10", null)]
[TestCase("0,0", 1, "-10,-1", "+10,-1", "0,-1")]
[TestCase("0,0", 1, "-10,0", "+10,0", "+1,0;-1,0")]
[TestCase("0,0", 1, "-10,+1", "+10,+1", "0,+1")]
[TestCase("0,0", 1, "-10,+10", "+10,+10", null)]
//parallel to the Y-axis
[TestCase("0,0", 1, "-10,-10", "-10,+10", null)]
[TestCase("0,0", 1, "-1,-10", "-1,+10", "-1,0")]
[TestCase("0,0", 1, "0,-10", "0,+10", "0,+1;0,-1")]
[TestCase("0,0", 1, "+1,-10", "+1,+10", "+1,0")]
[TestCase("0,0", 1, "+10,-10", "+10,+10", null)]
//general cases
[TestCase("0,0", 1, "-10,+10", "+10,+10", null)]
[TestCase("0,0", 1, "-1.414213562373095,0", "0,+1.414213562373095", "-0.707,0.707")]
[TestCase("0,0", 1, "-10,-10", "+10,+10", "+0.707,+0.707;-0.707,-0.707")]
[TestCase("0,0", 1, "0,-1.41421356", "+1.41421356,0", "+0.707,-0.707")]
[TestCase("0,0", 1, "0,-10", "+10,0", null)]
public void CircleIntersectWithLine2D(string sc, double radius, string sps, string spe, string intersections)
{
var circle = new Circle2D(Point2D.Parse(sc), radius);
var line = new Line2D(Point2D.Parse(sps), Point2D.Parse(spe));

var actual = circle.IntersectWith(line);

var expected = parseToPointsArray(intersections);
for (int i = 0; i < Math.Min(actual.Length, expected.Length); i++)
{
var a = actual[i];
var e = expected[i];
AssertGeometry.AreEqual(a, e, 1e-3); //needs to fix for the default tolerance
}
}
//parallel to X-axis
////segment contains the all intersections(same to the cases of circle and line)
[TestCase("0,0", 1, "-10,+10", "+10,+10", null)]
[TestCase("0,0", 1, "-10,+1", "+10,+1", "0,+1")]
[TestCase("0,0", 1, "-10,0", "+10,0", "+1,0;-1,0")]
[TestCase("0,0", 1, "-10,-1", "+10,-1", "0,-1")]
[TestCase("0,0", 1, "-10,-10", "+10,-10", null)]
////segments cross the circle's contour just 1 time
[TestCase("0,0", 1, "+0,+10", "+10,+10", null)]
[TestCase("0,0", 1, "+0,+1", "+10,+1", "0,1")]
[TestCase("0,0", 1, "+0,+0", "+10,+0", "1,0")]
[TestCase("0,0", 1, "+0,-1", "+10,-1", "0,-1")]
[TestCase("0,0", 1, "+0,-10", "+10,-10", null)]
////segment contains no intersections(px of the startingPoint is too big to intersect with the circle)
[TestCase("0,0", 1, "+10,+10", "+100,+10", null)]
[TestCase("0,0", 1, "+10,+1", "+100,+1", null)]
[TestCase("0,0", 1, "+10,+0", "+100,0", null)]
[TestCase("0,0", 1, "+10,-1", "+100,-1", null)]
[TestCase("0,0", 1, "+10,-10", "+100,-10", null)]
//parallel to Y-axis
////segment contains the all intersections(same to the cases of circle and line)
[TestCase("0,0", 1, "-10,-10", "-10,+10", null)]
[TestCase("0,0", 1, "-1,-10", "-1,+10", "-1,0")]
[TestCase("0,0", 1, "+0,-10", "+0,+10", "0,+1;0,-1")]
[TestCase("0,0", 1, "+1,-10", "+1,+10", "+1,0")]
[TestCase("0,0", 1, "+10,-10", "+10,+10", null)]
////segments cross the circle's contour just 1 time
[TestCase("0,0", 1, "+10,0", "+10,+10", null)]
[TestCase("0,0", 1, "+1,0", "+1,+10", "+1,0")]
[TestCase("0,0", 1, "+0,0", "+0,+10", "0,+1")]
[TestCase("0,0", 1, "-1,0", "-1,+10", "-1,0")]
[TestCase("0,0", 1, "-10,0", "-10,+10", null)]
////segment contains no intersections(py of the startingPoint is too big to intersect with the circle)
[TestCase("0,0", 1, "+10,+10", "+10,+100", null)]
[TestCase("0,0", 1, "+1,+10", "+1,+100", null)]
[TestCase("0,0", 1, "+0,+10", "+0,+100", null)]
[TestCase("0,0", 1, "-1,+10", "-1,+100", null)]
[TestCase("0,0", 1, "-10,+10", "-10,+100", null)]
//general cases
////segment contains the all intersections(same to the cases of circle and line)
[TestCase("0,0", 1, "-10,+10", "+10,+10", null)]
[TestCase("0,0", 1, "-1.414213562373095,0", "0,+1.414213562373095", "-0.707,0.707")]
[TestCase("0,0", 1, "-10,-10", "+10,+10", "+0.707,+0.707;-0.707,-0.707")]
[TestCase("0,0", 1, "0,-1.41421356", "+1.41421356,0", "+0.707,-0.707")]
[TestCase("0,0", 1, "0,-10", "+10,0", null)]
////segments cross the circle's contour just 1 time
[TestCase("0,0", 1, "+10,0", "+10,+10", null)]
[TestCase("0,0", 1, "+1,0", "+1,+10", "+1,0")]
[TestCase("0,0", 1, "+0,0", "+0,+10", "0,+1")]
[TestCase("0,0", 1, "-1,0", "-1,+10", "-1,0")]
[TestCase("0,0", 1, "-10,0", "-10,+10", null)]
////segment contains no intersections(py of the startingPoint is too big to intersect with the circle)
[TestCase("0,0", 1, "+10,+10", "+10,+100", null)]
[TestCase("0,0", 1, "+1,+10", "+1,+100", null)]
[TestCase("0,0", 1, "+0,+10", "+0,+100", null)]
[TestCase("0,0", 1, "-1,+10", "-1,+100", null)]
[TestCase("0,0", 1, "-10,+10", "-10,+100", null)]
public void CircleIntersectWithLineSegment2D(string sCenter, double radius, string sStart, string sEnd, string intersections)
{
var circle = new Circle2D(Point2D.Parse(sCenter), radius);
var segment = new LineSegment2D(Point2D.Parse(sStart), Point2D.Parse(sEnd));

var actual = circle.IntersectWith(segment);

var expected = parseToPointsArray(intersections);
for (int i = 0; i < Math.Min(actual.Length, expected.Length); i++)
{
var a = actual[i];
var e = expected[i];
AssertGeometry.AreEqual(a, e, 1e-3); //FIXME!
}
}

private Point2D[] parseToPointsArray(string input)
{
if (input == null)
{
return new Point2D[] { };
}

var result = input.Split(';')
.Select(s => Point2D.Parse(s))
.ToArray();

return result;
}
}
}
63 changes: 63 additions & 0 deletions src/Spatial/Euclidean/Circle2D.cs
View file
Original file line number Diff line number Diff line change
@@ -1,9 +1,11 @@
using MathNet.Spatial.Internals;
using System;
using System.Diagnostics.Contracts;
using System.Linq;
using System.Xml;
using System.Xml.Schema;
using System.Xml.Serialization;
using MathNet.Numerics;
using HashCode = MathNet.Spatial.Internals.HashCode;

namespace MathNet.Spatial.Euclidean
Expand Down Expand Up @@ -131,6 +133,67 @@ public static Circle2D FromPoints(Point2D pointA, Point2D pointB, Point2D pointC
return new Circle2D(center, radius);
}

/// <summary>
/// Returns the intersections of this circle with the given line.
/// </summary>
/// <param name="line">the given line</param>
/// <returns>intersections as a Point2D Array, depending on the count.</returns>
public Point2D[] IntersectWith(Line2D line)
{
var ts = this.findParameterTs(line);
var result = ts
.Select(t => line.StartPoint + t * line.Direction)
.ToArray();
return result;
}

private double[] findParameterTs(Line2D line)
{
// These 2 equations in vector form can be described
// (p-cc)^2=r^2 (eq1)
// p=s+t*d (eq2)
// , where p is the point on the line and/or circle,
// cc is the center of the circle,
// r is the radius of the circle,
// s is the starting point of the line,
// t is the parameter and
// d is the line direction.
// Substituting (eq2) into (eq1) yields:
// ((s+t*d)-cc)^2=r^2 (eq3)
// (eq3) reduces to the following quadratic equation: a*t^2 + b*t + c==0

var cc = this.Center.ToVector2D(); //center of circle
var s = line.StartPoint.ToVector2D();
var d = line.Direction;
var r = this.Radius;

var a = 1.0;
var b = 2 * (s.DotProduct(d) - d.DotProduct(cc));
var c = (s - cc).DotProduct(s - cc) - r * r;

var solutions = FindRoots.Polynomial(new[] { c, b, a });
var ts = solutions
.Where(z => z.IsReal())
.Select(z => z.Real)
.Distinct()
.ToArray();
return ts;
}

/// <summary>
/// Returns the intersections of this circle with the given line segment, which lie within the segment.
/// </summary>
/// <param name="segment">the given line-segment</param>
/// <returns>intersections as a Point2D Array, depending on the count.</returns>
public Point2D[] IntersectWith(LineSegment2D segment)
{
var ts = findParameterTs(segment.ToLine2D())
.Where(t => 0 <= t && t <= segment.Length);
var result = ts.Select(t => segment.StartPoint + t * segment.Direction).ToArray();
return result;
}


/// <summary>
/// Returns a value to indicate if a pair of circles are equal
/// </summary>
Expand Down
4 changes: 4 additions & 0 deletions src/Spatial/Euclidean/LineSegment2D.cs
View file
Original file line number Diff line number Diff line change
Expand Up @@ -236,5 +236,9 @@ void IXmlSerializable.WriteXml(XmlWriter writer)
writer.WriteElement("StartPoint", StartPoint);
writer.WriteElement("EndPoint", EndPoint);
}

/// <summary>convert this to Line2D </summary>
/// <returns>converted Line2D object</returns>
public Line2D ToLine2D() => new Line2D(StartPoint, EndPoint);
}
}

0 comments on commit 9a40b9f

Please sign in to comment.