/// <summary>
/// Checks whether the specified circle intersects the passed line.
/// </summary>
/// <param name="circle">
/// Circle to check.
/// </param>
/// <param name="line">
/// Line to check.
/// </param>
/// <param name="first">
/// First intersection point, if found.
/// </param>
/// <param name="second">
/// Second intersection point, if found.
/// </param>
/// <returns>
/// <c>true</c>, if circle and line intersect each other, and <c>false</c> otherwise.
/// </returns>
public static bool Intersects(
this CircleF circle,
LineSegment2F line,
out Vector2F?first,
out Vector2F?second)
{
return(line.Intersects(circle, out first, out second));
}
/// <summary>
/// Checks whether this polygon fully contains the passed line segment.
/// </summary>
/// <param name="lineSegment">Line segment to check.</param>
/// <returns>
/// <c>true</c>, if this polygon fully contains <paramref name="lineSegment" />, and
/// <c>false</c> otherwise.
/// </returns>
public bool Contains(LineSegment2F lineSegment)
{
// Check whether any of the edges intersect with the line.
if (this.Edges.Any(edge => lineSegment.Intersects(edge)))
{
return(false);
}
// Check whether the line endpoints are inside the polygon.
return(this.Contains(lineSegment.P) && this.Contains(lineSegment.Q));
}
/// <summary>
/// Checks whether the specified line intersects the passed circle.
/// </summary>
/// <remarks>
/// See http://devmag.org.za/2009/04/17/basic-collision-detection-in-2d-part-2/ for details.
/// </remarks>
/// <param name="line">
/// Line to check.
/// </param>
/// <param name="circle">
/// Circle to check.
/// </param>
/// <param name="first">
/// First intersection point, if found.
/// </param>
/// <param name="second">
/// Second intersection point, if found.
/// </param>
/// <returns>
/// <c>true</c>, if line and circle intersect each other, and <c>false</c> otherwise.
/// </returns>
public static bool Intersects(
this LineSegment2F line,
CircleF circle,
out Vector2F?first,
out Vector2F?second)
{
// Transform to local coordinates.
var localPointA = line.P - circle.Center;
var localPointB = line.Q - circle.Center;
// Precalculate this value. We use it often.
var localPointBMinusA = localPointB - localPointA;
var a = (localPointBMinusA.X) * (localPointBMinusA.X) + (localPointBMinusA.Y) * (localPointBMinusA.Y);
var b = 2 * ((localPointBMinusA.X * localPointA.X) + (localPointBMinusA.Y * localPointA.Y));
var c = (localPointA.X * localPointA.X) + (localPointA.Y * localPointA.Y) - (circle.Radius * circle.Radius);
var delta = b * b - (4 * a * c);
if (delta < 0)
{
// No intersection.
first = null;
second = null;
return(false);
}
if (delta > 0)
{
// Two intersections.
var squareRootDelta = MathF.Sqrt(delta);
var u1 = (-b + squareRootDelta) / (2 * a);
var u2 = (-b - squareRootDelta) / (2 * a);
// Use line point instead of local point because we want our answer in global space, not the circle's local space.
first = line.P + (u1 * localPointBMinusA);
second = line.P + (u2 * localPointBMinusA);
return(true);
}
// One intersection.
var u = -b / (2 * a);
first = line.P + (u * localPointBMinusA);
second = null;
return(true);
}
/// <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));
}
/// <summary>
/// Constructs a new polygon with the specified points.
/// </summary>
/// <param name="points">Points making up the new polygon.</param>
/// <exception cref="ArgumentNullException">
/// <paramref name="points"/> is <c>null</c>.
/// </exception>
/// <exception cref="ArgumentException">
/// <paramref name="points"/> contains two or less elements.
/// </exception>
public Polygon2F(IList <Vector2F> points)
{
if (points == null)
{
throw new ArgumentNullException("points");
}
if (points.Count < 3)
{
throw new ArgumentException("Polygon must consist of at least three points.", "points");
}
this.points = points;
// Build edges.
this.edges = new List <LineSegment2F>();
for (var i = 0; i < this.points.Count; i++)
{
var edge = new LineSegment2F(this.points[i], this.points[(i + 1) % this.points.Count]);
this.edges.Add(edge);
}
}
/// <summary>
/// Checks whether the specified line intersects the passed circle.
/// </summary>
/// <param name="line">
/// Line to check.
/// </param>
/// <param name="circle">
/// Circle to check.
/// </param>
/// <returns>
/// <c>true</c>, if line and circle intersect each other, and <c>false</c> otherwise.
/// </returns>
public static bool Intersects(this LineSegment2F line, CircleF circle)
{
return(line.GetDistance(circle.Center) < circle.Radius);
}
/// <summary>
/// Decomposes this polygon into triangles.
/// </summary>
/// <remarks>
/// See http://www.geometrictools.com/Documentation/TriangulationByEarClipping.pdf for details.
/// </remarks>
/// <returns>Triangles composing this polygon.</returns>
public List <Polygon2F> Triangulate()
{
var triangles = new List <Polygon2F>();
var vertices = new List <Vector2F>(this.points);
if (this.IsClockwise())
{
vertices.Reverse();
}
// Remove ears one by one.
var index = 0;
while (vertices.Count > 3)
{
var remainingPolygon = new Polygon2F(vertices);
// Get three consecutive vertices.
var u = vertices[(index - 1 + vertices.Count) % vertices.Count];
var v = vertices[index % vertices.Count];
var w = vertices[(index + 1) % vertices.Count];
// Check if middle vertex is convex.
var vu = u - v;
var vw = w - v;
var angle = Angle.Between(vw, vu);
var convex = angle < Math.PI;
if (!convex)
{
++index;
continue;
}
// Check if line segment lies completely inside the polygon.
var uw = new LineSegment2F(u, w);
if (!remainingPolygon.Contains(uw))
{
++index;
continue;
}
// Check if no other vertices of the polygon are contained in the triangle.
var triangle =
new Polygon2F(new[] { new Vector2F(u.X, u.Y), new Vector2F(v.X, v.Y), new Vector2F(w.X, w.Y) });
var containsOtherVertex =
vertices.Where(other => other != u && other != v && other != w)
.Any(other => triangle.Contains(other));
if (containsOtherVertex)
{
++index;
continue;
}
// Remove ear.
vertices.Remove(v);
triangles.Add(triangle);
}
// Add last triangle.
triangles.Add(new Polygon2F(vertices));
return(triangles);
}
/// <summary>
/// Checks whether the specified circle intersects the passed line.
/// </summary>
/// <param name="circle">
/// Circle to check.
/// </param>
/// <param name="line">
/// Line to check.
/// </param>
/// <returns>
/// <c>true</c>, if circle and line intersect each other, and <c>false</c> otherwise.
/// </returns>
public static bool Intersects(this CircleF circle, LineSegment2F line)
{
return(line.Intersects(circle));
}