/// <summary>
/// Checks whether the specified line segment intersects the passed one.
/// </summary>
/// <remarks>
/// See http://www.wyrmtale.com/blog/2013/115/2d-line-intersection-in-c for details.
/// </remarks>
/// <param name="first">Line segment to check.</param>
/// <param name="second">Line segment to check.</param>
/// <param name="intersectionPoint">Intersection point, if found.</param>
/// <returns>
/// <c>true</c>, if both line segments intersect each other, and <c>false</c> otherwise.
/// </returns>
public static bool Intersects(this LineSegment2F first, LineSegment2F second, out Vector2F intersectionPoint)
{
// Get A,B,C of first line - points ps1 to pe1.
var a1 = first.Q.Y - first.P.Y;
var b1 = first.P.X - first.Q.X;
var c1 = a1 * first.P.X + b1 * first.P.Y;
// Get A,B,C of second line - points ps2 to pe2.
var a2 = second.Q.Y - second.P.Y;
var b2 = second.P.X - second.Q.X;
var c2 = a2 * second.P.X + b2 * second.P.Y;
// Get delta and check if the lines are parallel.
var delta = a1 * b2 - a2 * b1;
if (Math.Abs(delta) < float.Epsilon)
{
intersectionPoint = Vector2F.Zero;
return false;
}
// Return intersection point.
intersectionPoint = new Vector2F((b2 * c1 - b1 * c2) / delta, (a1 * c2 - a2 * c1) / delta);
return first.Contains(intersectionPoint) && second.Contains(intersectionPoint);
}
/// <summary>
/// Checks whether the specified line segment intersects the passed one.
/// </summary>
/// <remarks>
/// See http://jeffe.cs.illinois.edu/teaching/373/notes/x06-sweepline.pdf for details.
/// </remarks>
/// <param name="first">Line segment to check.</param>
/// <param name="second">Line segment to check.</param>
/// <returns>
/// <c>true</c>, if both line segments intersect each other, and <c>false</c> otherwise.
/// </returns>
public static bool Intersects(this LineSegment2F first, LineSegment2F second)
{
// By definition, line segments that share a point can't intersect.
if (first.P == second.P || first.P == second.Q || first.Q == second.P || first.Q == second.Q)
{
return false;
}
var a = first.P;
var b = first.Q;
var c = second.P;
var d = second.Q;
if (Vector2F.CounterClockwise(a, c, d) == Vector2F.CounterClockwise(b, c, d))
{
return false;
}
if (Vector2F.CounterClockwise(a, b, c) == Vector2F.CounterClockwise(a, b, d))
{
return false;
}
return true;
}
public void TestPolygonDoesNotContainIntersectingLineSegment()
{
// ARRANGE.
var line = new LineSegment2F(new Vector2F(2, 3), new Vector2F(6, 3));
// ASSERT.
Assert.IsFalse(this.polygon.Contains(line));
}
public void TestPolygonContainsLineSegment()
{
// ARRANGE.
var line = new LineSegment2F(new Vector2F(2, 3), new Vector2F(4, 3));
// ASSERT.
Assert.IsTrue(this.polygon.Contains(line));
}
public void GetLength()
{
var s = new LineSegment2F
{
Point1 = new Vector2F(1, 2),
Point2 = new Vector2F(-1, 9),
};
Assert.IsTrue(Numeric.AreEqual((s.Point2 - s.Point1).Length, s.GetLength(0, 1, 100, Numeric.EpsilonF)));
Assert.IsTrue(Numeric.AreEqual((s.Point2 - s.Point1).Length * 0.3f, s.GetLength(0.6f, 0.3f, 100, Numeric.EpsilonF)));
Assert.IsTrue(Numeric.AreEqual((s.Point2 - s.Point1).Length * 0.3f, s.GetLength(0.1f, 0.4f, 100, Numeric.EpsilonF)));
}
public void GetTangent()
{
var s = new LineSegment2F
{
Point1 = new Vector2F(1, 2),
Point2 = new Vector2F(-1, 9),
};
Assert.IsTrue(Vector2F.AreNumericallyEqual(s.Point2 - s.Point1, s.GetTangent(0)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(s.Point2 - s.Point1, s.GetTangent(0.3f)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(s.Point2 - s.Point1, s.GetTangent(1)));
}
public void Test()
{
var s = new LineSegment2F
{
Point1 = new Vector2F(1, 2),
Point2 = new Vector2F(-1, 9),
};
Assert.IsTrue(Vector2F.AreNumericallyEqual(s.Point1, s.GetPoint(0)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(s.Point2, s.GetPoint(1)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(s.Point1 * 0.7f + s.Point2 * 0.3f, s.GetPoint(0.3f)));
}
public void GetLength()
{
var s = new LineSegment2F
{
Point1 = new Vector2F(1, 2),
Point2 = new Vector2F(-1, 9),
};
Assert.IsTrue(Numeric.AreEqual((s.Point2 - s.Point1).Length, s.GetLength(0, 1, 100, Numeric.EpsilonF)));
Assert.IsTrue(Numeric.AreEqual((s.Point2 - s.Point1).Length * 0.3f, s.GetLength(0.6f, 0.3f, 100, Numeric.EpsilonF)));
Assert.IsTrue(Numeric.AreEqual((s.Point2 - s.Point1).Length * 0.3f, s.GetLength(0.1f, 0.4f, 100, Numeric.EpsilonF)));
}
public void Flatten()
{
var s = new LineSegment2F
{
Point1 = new Vector2F(1, 2),
Point2 = new Vector2F(-1, 9),
};
var points = new List<Vector2F>();
s.Flatten(points, 1, 1);
Assert.AreEqual(2, points.Count);
Assert.IsTrue(points.Contains(s.Point1));
Assert.IsTrue(points.Contains(s.Point2));
}
public void Flatten()
{
var s = new LineSegment2F
{
Point1 = new Vector2F(1, 2),
Point2 = new Vector2F(-1, 9),
};
var points = new List <Vector2F>();
s.Flatten(points, 1, 1);
Assert.AreEqual(2, points.Count);
Assert.IsTrue(points.Contains(s.Point1));
Assert.IsTrue(points.Contains(s.Point2));
}
public void TestLineIntersectsCircle()
{
// ARRANGE.
var line = new LineSegment2F(new Vector2F(-2.0f, 0.0f), new Vector2F(2.0f, 0.0f));
var circle = CircleF.UnitCircle;
Vector2F?first;
Vector2F?second;
// ACT.
var intersects = line.Intersects(circle, out first, out second);
// ASSERT.
Assert.IsTrue(intersects);
Assert.IsNotNull(first);
Assert.IsNotNull(second);
Assert.AreEqual(new Vector2F(1.0f, 0.0f), first);
Assert.AreEqual(new Vector2F(-1.0f, 0.0f), second);
}
public void TestLineIntersectsCircle()
{
// ARRANGE.
var line = new LineSegment2F(new Vector2F(-2.0f, 0.0f), new Vector2F(2.0f, 0.0f));
var circle = CircleF.UnitCircle;
Vector2F? first;
Vector2F? second;
// ACT.
var intersects = line.Intersects(circle, out first, out second);
// ASSERT.
Assert.IsTrue(intersects);
Assert.IsNotNull(first);
Assert.IsNotNull(second);
Assert.AreEqual(new Vector2F(1.0f, 0.0f), first);
Assert.AreEqual(new Vector2F(-1.0f, 0.0f), second);
}
/// <summary>
/// Checks whether the specified rectangle intersects the passed circle.
/// </summary>
/// <param name="rectangle">
/// Rectangle to check.
/// </param>
/// <param name="circle">
/// Circle to check.
/// </param>
/// <returns>
/// <c>true</c>, if rectangle and circle intersect each other, and <c>false</c> otherwise.
/// </returns>
public static bool Intersects(this RectangleF rectangle, CircleF circle)
{
// Check if rectangle contains center.
if (rectangle.Contains(circle.Center))
{
return true;
}
// Check each edge.
var topLeft = new Vector2F(rectangle.X, rectangle.Y);
var bottomLeft = new Vector2F(rectangle.X, rectangle.MaxY);
var topRight = new Vector2F(rectangle.MaxX, rectangle.Y);
var bottomRight = new Vector2F(rectangle.MaxX, rectangle.MaxY);
var left = new LineSegment2F(topLeft, bottomLeft);
var right = new LineSegment2F(topRight, bottomRight);
var top = new LineSegment2F(topLeft, topRight);
var bottom = new LineSegment2F(bottomLeft, bottomRight);
return left.Intersects(circle) || right.Intersects(circle) || top.Intersects(circle)
|| bottom.Intersects(circle);
}
public void TestPolygonDoesNotContainOutsideLineSegment()
{
// ARRANGE.
var line = new LineSegment2F(new Vector2F(2, 7), new Vector2F(4, 7));
// ASSERT.
Assert.IsFalse(this.polygon.Contains(line));
}
