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Circle2D intersection with Line(Segment)2D (#237)
* 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]>
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‎src/Spatial.Tests/Euclidean/Circle2DTests.cs‎

Lines changed: 122 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -1,4 +1,5 @@
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using System;
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using System;
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using System.Linq;
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using MathNet.Spatial.Euclidean;
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using NUnit.Framework;
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@@ -58,5 +59,125 @@ public void CircleFromThreePointsArgumentException()
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Assert.Throws<ArgumentException>(() => { Circle2D.FromPoints(p1, p2, p3); });
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}
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//parallel to the X-axis
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[TestCase("0,0", 1, "-10,-10", "+10,-10", null)]
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[TestCase("0,0", 1, "-10,-1", "+10,-1", "0,-1")]
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[TestCase("0,0", 1, "-10,0", "+10,0", "+1,0;-1,0")]
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[TestCase("0,0", 1, "-10,+1", "+10,+1", "0,+1")]
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[TestCase("0,0", 1, "-10,+10", "+10,+10", null)]
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//parallel to the Y-axis
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[TestCase("0,0", 1, "-10,-10", "-10,+10", null)]
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[TestCase("0,0", 1, "-1,-10", "-1,+10", "-1,0")]
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[TestCase("0,0", 1, "0,-10", "0,+10", "0,+1;0,-1")]
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[TestCase("0,0", 1, "+1,-10", "+1,+10", "+1,0")]
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[TestCase("0,0", 1, "+10,-10", "+10,+10", null)]
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//general cases
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[TestCase("0,0", 1, "-10,+10", "+10,+10", null)]
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[TestCase("0,0", 1, "-1.414213562373095,0", "0,+1.414213562373095", "-0.707,0.707")]
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[TestCase("0,0", 1, "-10,-10", "+10,+10", "+0.707,+0.707;-0.707,-0.707")]
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[TestCase("0,0", 1, "0,-1.41421356", "+1.41421356,0", "+0.707,-0.707")]
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[TestCase("0,0", 1, "0,-10", "+10,0", null)]
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public void CircleIntersectWithLine2D(string sc, double radius, string sps, string spe, string intersections)
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{
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var circle = new Circle2D(Point2D.Parse(sc), radius);
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var line = new Line2D(Point2D.Parse(sps), Point2D.Parse(spe));
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var actual = circle.IntersectWith(line);
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var expected = parseToPointsArray(intersections);
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for (int i = 0; i < Math.Min(actual.Length, expected.Length); i++)
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{
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var a = actual[i];
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var e = expected[i];
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AssertGeometry.AreEqual(a, e, 1e-3); //needs to fix for the default tolerance
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}
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}
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//parallel to X-axis
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////segment contains the all intersections(same to the cases of circle and line)
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[TestCase("0,0", 1, "-10,+10", "+10,+10", null)]
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[TestCase("0,0", 1, "-10,+1", "+10,+1", "0,+1")]
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[TestCase("0,0", 1, "-10,0", "+10,0", "+1,0;-1,0")]
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[TestCase("0,0", 1, "-10,-1", "+10,-1", "0,-1")]
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[TestCase("0,0", 1, "-10,-10", "+10,-10", null)]
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////segments cross the circle's contour just 1 time
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[TestCase("0,0", 1, "+0,+10", "+10,+10", null)]
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[TestCase("0,0", 1, "+0,+1", "+10,+1", "0,1")]
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[TestCase("0,0", 1, "+0,+0", "+10,+0", "1,0")]
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[TestCase("0,0", 1, "+0,-1", "+10,-1", "0,-1")]
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[TestCase("0,0", 1, "+0,-10", "+10,-10", null)]
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////segment contains no intersections(px of the startingPoint is too big to intersect with the circle)
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[TestCase("0,0", 1, "+10,+10", "+100,+10", null)]
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[TestCase("0,0", 1, "+10,+1", "+100,+1", null)]
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[TestCase("0,0", 1, "+10,+0", "+100,0", null)]
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[TestCase("0,0", 1, "+10,-1", "+100,-1", null)]
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[TestCase("0,0", 1, "+10,-10", "+100,-10", null)]
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//parallel to Y-axis
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////segment contains the all intersections(same to the cases of circle and line)
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[TestCase("0,0", 1, "-10,-10", "-10,+10", null)]
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[TestCase("0,0", 1, "-1,-10", "-1,+10", "-1,0")]
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[TestCase("0,0", 1, "+0,-10", "+0,+10", "0,+1;0,-1")]
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[TestCase("0,0", 1, "+1,-10", "+1,+10", "+1,0")]
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[TestCase("0,0", 1, "+10,-10", "+10,+10", null)]
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////segments cross the circle's contour just 1 time
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[TestCase("0,0", 1, "+10,0", "+10,+10", null)]
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[TestCase("0,0", 1, "+1,0", "+1,+10", "+1,0")]
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[TestCase("0,0", 1, "+0,0", "+0,+10", "0,+1")]
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[TestCase("0,0", 1, "-1,0", "-1,+10", "-1,0")]
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[TestCase("0,0", 1, "-10,0", "-10,+10", null)]
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////segment contains no intersections(py of the startingPoint is too big to intersect with the circle)
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[TestCase("0,0", 1, "+10,+10", "+10,+100", null)]
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[TestCase("0,0", 1, "+1,+10", "+1,+100", null)]
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[TestCase("0,0", 1, "+0,+10", "+0,+100", null)]
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[TestCase("0,0", 1, "-1,+10", "-1,+100", null)]
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[TestCase("0,0", 1, "-10,+10", "-10,+100", null)]
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//general cases
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////segment contains the all intersections(same to the cases of circle and line)
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[TestCase("0,0", 1, "-10,+10", "+10,+10", null)]
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[TestCase("0,0", 1, "-1.414213562373095,0", "0,+1.414213562373095", "-0.707,0.707")]
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[TestCase("0,0", 1, "-10,-10", "+10,+10", "+0.707,+0.707;-0.707,-0.707")]
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[TestCase("0,0", 1, "0,-1.41421356", "+1.41421356,0", "+0.707,-0.707")]
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[TestCase("0,0", 1, "0,-10", "+10,0", null)]
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////segments cross the circle's contour just 1 time
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[TestCase("0,0", 1, "+10,0", "+10,+10", null)]
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[TestCase("0,0", 1, "+1,0", "+1,+10", "+1,0")]
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[TestCase("0,0", 1, "+0,0", "+0,+10", "0,+1")]
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[TestCase("0,0", 1, "-1,0", "-1,+10", "-1,0")]
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[TestCase("0,0", 1, "-10,0", "-10,+10", null)]
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////segment contains no intersections(py of the startingPoint is too big to intersect with the circle)
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[TestCase("0,0", 1, "+10,+10", "+10,+100", null)]
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[TestCase("0,0", 1, "+1,+10", "+1,+100", null)]
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[TestCase("0,0", 1, "+0,+10", "+0,+100", null)]
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[TestCase("0,0", 1, "-1,+10", "-1,+100", null)]
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[TestCase("0,0", 1, "-10,+10", "-10,+100", null)]
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public void CircleIntersectWithLineSegment2D(string sCenter, double radius, string sStart, string sEnd, string intersections)
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{
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var circle = new Circle2D(Point2D.Parse(sCenter), radius);
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var segment = new LineSegment2D(Point2D.Parse(sStart), Point2D.Parse(sEnd));
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var actual = circle.IntersectWith(segment);
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var expected = parseToPointsArray(intersections);
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for (int i = 0; i < Math.Min(actual.Length, expected.Length); i++)
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{
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var a = actual[i];
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var e = expected[i];
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AssertGeometry.AreEqual(a, e, 1e-3); //FIXME!
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}
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}
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private Point2D[] parseToPointsArray(string input)
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{
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if (input == null)
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{
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return new Point2D[] { };
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}
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var result = input.Split(';')
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.Select(s => Point2D.Parse(s))
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.ToArray();
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return result;
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}
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}
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}

‎src/Spatial/Euclidean/Circle2D.cs‎

Lines changed: 63 additions & 0 deletions
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@@ -1,9 +1,11 @@
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using MathNet.Spatial.Internals;
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using System;
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using System.Diagnostics.Contracts;
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using System.Linq;
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using System.Xml;
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using System.Xml.Schema;
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using System.Xml.Serialization;
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using MathNet.Numerics;
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using HashCode = MathNet.Spatial.Internals.HashCode;
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namespace MathNet.Spatial.Euclidean
@@ -131,6 +133,67 @@ public static Circle2D FromPoints(Point2D pointA, Point2D pointB, Point2D pointC
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return new Circle2D(center, radius);
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}
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/// <summary>
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/// Returns the intersections of this circle with the given line.
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/// </summary>
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/// <param name="line">the given line</param>
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/// <returns>intersections as a Point2D Array, depending on the count.</returns>
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public Point2D[] IntersectWith(Line2D line)
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{
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var ts = this.findParameterTs(line);
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var result = ts
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.Select(t => line.StartPoint + t * line.Direction)
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.ToArray();
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return result;
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}
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private double[] findParameterTs(Line2D line)
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{
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// These 2 equations in vector form can be described
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// (p-cc)^2=r^2 (eq1)
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// p=s+t*d (eq2)
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// , where p is the point on the line and/or circle,
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// cc is the center of the circle,
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// r is the radius of the circle,
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// s is the starting point of the line,
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// t is the parameter and
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// d is the line direction.
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// Substituting (eq2) into (eq1) yields:
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// ((s+t*d)-cc)^2=r^2 (eq3)
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// (eq3) reduces to the following quadratic equation: a*t^2 + b*t + c==0
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var cc = this.Center.ToVector2D(); //center of circle
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var s = line.StartPoint.ToVector2D();
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var d = line.Direction;
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var r = this.Radius;
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var a = 1.0;
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var b = 2 * (s.DotProduct(d) - d.DotProduct(cc));
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var c = (s - cc).DotProduct(s - cc) - r * r;
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var solutions = FindRoots.Polynomial(new[] { c, b, a });
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var ts = solutions
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.Where(z => z.IsReal())
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.Select(z => z.Real)
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.Distinct()
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.ToArray();
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return ts;
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}
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/// <summary>
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/// Returns the intersections of this circle with the given line segment, which lie within the segment.
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/// </summary>
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/// <param name="segment">the given line-segment</param>
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/// <returns>intersections as a Point2D Array, depending on the count.</returns>
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public Point2D[] IntersectWith(LineSegment2D segment)
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{
190+
var ts = findParameterTs(segment.ToLine2D())
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.Where(t => 0 <= t && t <= segment.Length);
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var result = ts.Select(t => segment.StartPoint + t * segment.Direction).ToArray();
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return result;
194+
}
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134197
/// <summary>
135198
/// Returns a value to indicate if a pair of circles are equal
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/// </summary>

‎src/Spatial/Euclidean/LineSegment2D.cs‎

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Original file line numberDiff line numberDiff line change
@@ -236,5 +236,9 @@ void IXmlSerializable.WriteXml(XmlWriter writer)
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writer.WriteElement("StartPoint", StartPoint);
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writer.WriteElement("EndPoint", EndPoint);
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}
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/// <summary>convert this to Line2D </summary>
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/// <returns>converted Line2D object</returns>
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public Line2D ToLine2D() => new Line2D(StartPoint, EndPoint);
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}
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}

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