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Fix Polygon2D convex hull winding direction #249

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Fix Polygon2D convex hull winding direction #249

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64 changes: 46 additions & 18 deletions src/Spatial.Tests/Euclidean/Polygon2DTests.cs
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Original file line number Diff line number Diff line change
Expand Up @@ -95,7 +95,7 @@ public void IsPointInPolygonTest2(double x, double y, bool outcome)
Assert.AreEqual(outcome, testPoly.EnclosesPoint(testPoint));
}

// These test cases were generated using scipy.spatial's ConvexHull method
// These counter-clockwise test cases were generated using scipy.spatial's ConvexHull method
[TestCase("0.27,0.41;0.87,0.67;0.7,0.33;0.5,0.61;0.04,0.23;0.73,0.14;0.84,0.02;0.25,0.23;0.12,0.2;0.37,0.78", "0.87,0.67;0.37,0.78;0.04,0.23;0.12,0.2;0.84,0.02")]
[TestCase("0.81,0.25;0.77,0.15;0.17,0.48;0.4,0.58;0.29,0.92;0.37,0.26;0.7,0.91;0.04,0.1;0.39,0.73;0.7,0.12", "0.7,0.91;0.29,0.92;0.04,0.1;0.7,0.12;0.77,0.15;0.81,0.25")]
[TestCase("0.87,0.39;0.83,0.42;0.75,0.62;0.91,0.49;0.18,0.63;0.17,0.95;0.22,0.5;0.93,0.41;0.66,0.79;0.32,0.42", "0.66,0.79;0.17,0.95;0.18,0.63;0.22,0.5;0.32,0.42;0.87,0.39;0.93,0.41;0.91,0.49")]
Expand All @@ -107,27 +107,19 @@ public void ConvexHullTest(string points, string expected)
var testPoints = (from x in points.Split(';') select Point2D.Parse(x)).ToList();
var expectedPoints = (from x in expected.Split(';') select Point2D.Parse(x)).ToList();

var hullClockwise = Polygon2D.GetConvexHullFromPoints(testPoints, true);
var hullCounterClockwise = Polygon2D.GetConvexHullFromPoints(testPoints, false);
var counterClockwiseVertices = hullCounterClockwise.Vertices;
CollectionAssert.AreEqual(expectedPoints, counterClockwiseVertices);
Assert.That(SignedArea(hullCounterClockwise), Is.GreaterThan(0));

var hullClockwise = Polygon2D.GetConvexHullFromPoints(testPoints, true);
var clockwiseVertices = hullClockwise.Vertices;
expectedPoints.Reverse();
CollectionAssert.AreEqual(expectedPoints, clockwiseVertices);
/*
for (var i = 0; i < hullClockwise.VertexCount; i++)
{
Assert.That(ClockwiseVerticies[i], Is.EqualTo(expectedPoints[i]));
}
*/
Assert.That(SignedArea(hullClockwise), Is.LessThan(0));

var hullCounterClockwise = Polygon2D.GetConvexHullFromPoints(testPoints, false);
var counterClockwiseVertices = hullCounterClockwise.Vertices;
expectedPoints.Reverse();
CollectionAssert.AreEqual(expectedPoints, counterClockwiseVertices);
/*
for (var i = 0; i < hullCounterClockwise.VertexCount; i++)
{
Assert.That(counterClockwiseVerticies[i], Is.EqualTo(expectedPoints[hullCounterClockwise.VertexCount - 1 - i]));
}
*/
var defaultHull = Polygon2D.GetConvexHullFromPoints(testPoints);
CollectionAssert.AreEqual(clockwiseVertices, defaultHull.Vertices);

var pointsNotOnConvexHull = testPoints.Except(hullCounterClockwise.Vertices);
foreach (var pointNotOnConvexHull in pointsNotOnConvexHull)
Expand All @@ -148,6 +140,28 @@ public void ConvexHullTest(string points, string expected)
}
}

[Test]
public void ConvexHullHonorsDirectionForTriangle()
{
var points = new[]
{
new Point2D(0, 0),
new Point2D(1, 0),
new Point2D(0, 1)
};

var defaultHull = Polygon2D.GetConvexHullFromPoints(points);
var clockwiseHull = Polygon2D.GetConvexHullFromPoints(points, true);
var counterClockwiseHull = Polygon2D.GetConvexHullFromPoints(points, false);

CollectionAssert.AreEquivalent(points, defaultHull.Vertices);
CollectionAssert.AreEquivalent(points, clockwiseHull.Vertices);
CollectionAssert.AreEquivalent(points, counterClockwiseHull.Vertices);
Assert.That(SignedArea(defaultHull), Is.LessThan(0));
Assert.That(SignedArea(clockwiseHull), Is.LessThan(0));
Assert.That(SignedArea(counterClockwiseHull), Is.GreaterThan(0));
}

[TestCase("0,0;0.4,0;0.5,0;0.6,0;1,0;1,.25;1,.75;1,1;0,1;0,0.5", "1,0;1,1;0,1;0,0")]
public void ReduceComplexity(string points, string reduced)
{
Expand All @@ -166,6 +180,20 @@ private static Polygon2D TestPolygon1()
return new Polygon2D(points);
}

private static double SignedArea(Polygon2D polygon)
{
var vertices = polygon.Vertices.ToList();
double twiceArea = 0;
for (var i = 0; i < vertices.Count; i++)
{
var current = vertices[i];
var next = vertices[(i + 1) % vertices.Count];
twiceArea += (current.X * next.Y) - (next.X * current.Y);
}

return twiceArea / 2;
}

private static Polygon2D TestPolygon2()
{
var points = from x in new[] { "0,0", "0.25,0.5", "1,1", "-1,1", "0.5,-0.5", "0,0" } select Point2D.Parse(x);
Expand Down
7 changes: 1 addition & 6 deletions src/Spatial/Euclidean/Polygon2D.cs
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Original file line number Diff line number Diff line change
Expand Up @@ -163,19 +163,14 @@ public static Polygon2D GetConvexHullFromPoints(IEnumerable<Point2D> pointList,
throw new ArgumentException("Must have at least 3 points in the polygon to compute the convex hull");
}

if (count <= 3)
{
return new Polygon2D(pointList);
}

var chull = new ConvexHull(pointList, false);
chull.CalcConvexHull();
var hullPoints = chull.GetResultsAsArrayOfPoint();

// Order the hull points by angle to the centroid
var centroid = Point2D.Centroid(hullPoints);
var xAxis = new Vector2D(1, 0);
var results = (from x in hullPoints select new Tuple<Angle, Point2D>(centroid.VectorTo(x).SignedAngleTo(xAxis, clockWise), x)).ToList();
var results = (from x in hullPoints select new Tuple<Angle, Point2D>(centroid.VectorTo(x).SignedAngleTo(xAxis, !clockWise), x)).ToList();
results.Sort((a, b) => a.Item1.CompareTo(b.Item1));

return new Polygon2D(from x in results select x.Item2);
Expand Down