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MEC.cs
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MEC.cs
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namespace LeagueSharp.Common
{
using System;
using System.Collections.Generic;
using System.Linq;
using SharpDX;
/// <summary>
/// Provides method to calculate the minimum enclosing circle.
/// </summary>
public static class MEC
{
#region Static Fields
/// <summary>
/// The minimum maximum box
/// </summary>
public static RectangleF g_MinMaxBox;
// For debugging.
/// <summary>
/// The minimum maximum corners
/// </summary>
public static Vector2[] g_MinMaxCorners;
/// <summary>
/// The non culled points
/// </summary>
public static Vector2[] g_NonCulledPoints;
#endregion
#region Public Methods and Operators
/// <summary>
/// Finds the minimal bounding circle.
/// </summary>
/// <param name="points">The points.</param>
/// <param name="center">The center.</param>
/// <param name="radius">The radius.</param>
public static void FindMinimalBoundingCircle(List<Vector2> points, out Vector2 center, out float radius)
{
// Find the convex hull.
var hull = MakeConvexHull(points);
// The best solution so far.
var best_center = points[0];
var best_radius2 = float.MaxValue;
// Look at pairs of hull points.
for (var i = 0; i < hull.Count - 1; i++)
{
for (var j = i + 1; j < hull.Count; j++)
{
// Find the circle through these two points.
var test_center = new Vector2((hull[i].X + hull[j].X) / 2f, (hull[i].Y + hull[j].Y) / 2f);
var dx = test_center.X - hull[i].X;
var dy = test_center.Y - hull[i].Y;
var test_radius2 = dx * dx + dy * dy;
// See if this circle would be an improvement.
if (test_radius2 < best_radius2)
{
// See if this circle encloses all of the points.
if (CircleEnclosesPoints(test_center, test_radius2, points, i, j, -1))
{
// Save this solution.
best_center = test_center;
best_radius2 = test_radius2;
}
}
} // for i
} // for j
// Look at triples of hull points.
for (var i = 0; i < hull.Count - 2; i++)
{
for (var j = i + 1; j < hull.Count - 1; j++)
{
for (var k = j + 1; k < hull.Count; k++)
{
// Find the circle through these three points.
Vector2 test_center;
float test_radius2;
FindCircle(hull[i], hull[j], hull[k], out test_center, out test_radius2);
// See if this circle would be an improvement.
if (test_radius2 < best_radius2)
{
// See if this circle encloses all of the points.
if (CircleEnclosesPoints(test_center, test_radius2, points, i, j, k))
{
// Save this solution.
best_center = test_center;
best_radius2 = test_radius2;
}
}
} // for k
} // for i
} // for j
center = best_center;
if (best_radius2 == float.MaxValue)
{
radius = 0;
}
else
{
radius = (float)Math.Sqrt(best_radius2);
}
}
/// <summary>
/// Returns the mininimum enclosing circle from a list of points.
/// </summary>
/// <param name="points">The points.</param>
/// <returns>MecCircle.</returns>
public static MecCircle GetMec(List<Vector2> points)
{
var center = new Vector2();
float radius;
var ConvexHull = MakeConvexHull(points);
FindMinimalBoundingCircle(ConvexHull, out center, out radius);
return new MecCircle(center, radius);
}
/// <summary>
/// Makes the convex hull.
/// </summary>
/// <param name="points">The points.</param>
/// <returns>Points that make up a polygon's convex hull..</returns>
public static List<Vector2> MakeConvexHull(List<Vector2> points)
{
// Cull.
points = HullCull(points);
// Find the remaining point with the smallest Y value.
// if (there's a tie, take the one with the smaller X value.
Vector2[] best_pt = { points[0] };
foreach (
var pt in points.Where(pt => (pt.Y < best_pt[0].Y) || ((pt.Y == best_pt[0].Y) && (pt.X < best_pt[0].X)))
)
{
best_pt[0] = pt;
}
// Move this point to the convex hull.
var hull = new List<Vector2> { best_pt[0] };
points.Remove(best_pt[0]);
// Start wrapping up the other points.
float sweep_angle = 0;
for (;;)
{
// If all of the points are on the hull, we're done.
if (points.Count == 0)
{
break;
}
// Find the point with smallest AngleValue
// from the last point.
var X = hull[hull.Count - 1].X;
var Y = hull[hull.Count - 1].Y;
best_pt[0] = points[0];
float best_angle = 3600;
// Search the rest of the points.
foreach (var pt in points)
{
var test_angle = AngleValue(X, Y, pt.X, pt.Y);
if ((test_angle >= sweep_angle) && (best_angle > test_angle))
{
best_angle = test_angle;
best_pt[0] = pt;
}
}
// See if the first point is better.
// If so, we are done.
var first_angle = AngleValue(X, Y, hull[0].X, hull[0].Y);
if ((first_angle >= sweep_angle) && (best_angle >= first_angle))
{
// The first point is better. We're done.
break;
}
// Add the best point to the convex hull.
hull.Add(best_pt[0]);
points.Remove(best_pt[0]);
sweep_angle = best_angle;
}
return hull;
}
#endregion
#region Methods
/// <summary>
/// Return a number that gives the ordering of angles
/// WRST horizontal from the point(x1, y1) to(x2, y2).
/// In other words, AngleValue(x1, y1, x2, y2) is not
/// the angle, but if:
/// Angle(x1, y1, x2, y2) > Angle(x1, y1, x2, y2)
/// then
/// AngleValue(x1, y1, x2, y2) > AngleValue(x1, y1, x2, y2)
/// this angle is greater than the angle for another set
/// of points,) this number for
/// This function is dy / (dy + dx).
/// </summary>
/// <param name="x1">The x1.</param>
/// <param name="y1">The y1.</param>
/// <param name="x2">The x2.</param>
/// <param name="y2">The y2.</param>
/// <returns>A number that gives the ordering of angles</returns>
private static float AngleValue(float x1, float y1, float x2, float y2)
{
float t;
var dx = x2 - x1;
var ax = Math.Abs(dx);
var dy = y2 - y1;
var ay = Math.Abs(dy);
if (ax + ay == 0)
{
// if (the two points are the same, return 360.
t = 360f / 9f;
}
else
{
t = dy / (ax + ay);
}
if (dx < 0)
{
t = 2 - t;
}
else if (dy < 0)
{
t = 4 + t;
}
return t * 90;
}
/// <summary>
/// Encloses the points in a circle.
/// </summary>
/// <param name="center">The center.</param>
/// <param name="radius2">The radius2.</param>
/// <param name="points">The points.</param>
/// <param name="skip1">The skip1.</param>
/// <param name="skip2">The skip2.</param>
/// <param name="skip3">The skip3.</param>
/// <returns><c>true</c> if the indicated circle encloses all of the points, <c>false</c> otherwise.</returns>
private static bool CircleEnclosesPoints(
Vector2 center,
float radius2,
List<Vector2> points,
int skip1,
int skip2,
int skip3)
{
return (from point in points.Where((t, i) => (i != skip1) && (i != skip2) && (i != skip3))
let dx = center.X - point.X
let dy = center.Y - point.Y
select dx * dx + dy * dy).All(test_radius2 => !(test_radius2 > radius2));
}
/// <summary>
/// Finds the circle through the three points.
/// </summary>
/// <param name="a">a.</param>
/// <param name="b">The b.</param>
/// <param name="c">The c.</param>
/// <param name="center">The center.</param>
/// <param name="radius2">The radius2.</param>
private static void FindCircle(Vector2 a, Vector2 b, Vector2 c, out Vector2 center, out float radius2)
{
// Get the perpendicular bisector of (x1, y1) and (x2, y2).
var x1 = (b.X + a.X) / 2;
var y1 = (b.Y + a.Y) / 2;
var dy1 = b.X - a.X;
var dx1 = -(b.Y - a.Y);
// Get the perpendicular bisector of (x2, y2) and (x3, y3).
var x2 = (c.X + b.X) / 2;
var y2 = (c.Y + b.Y) / 2;
var dy2 = c.X - b.X;
var dx2 = -(c.Y - b.Y);
// See where the lines intersect.
var cx = (y1 * dx1 * dx2 + x2 * dx1 * dy2 - x1 * dy1 * dx2 - y2 * dx1 * dx2) / (dx1 * dy2 - dy1 * dx2);
var cy = (cx - x1) * dy1 / dx1 + y1;
center = new Vector2(cx, cy);
var dx = cx - a.X;
var dy = cy - a.Y;
radius2 = dx * dx + dy * dy;
}
// Find a box that fits inside the MinMax quadrilateral.
/// <summary>
/// Gets the minimum maximum box.
/// </summary>
/// <param name="points">The points.</param>
/// <returns>RectangleF.</returns>
private static RectangleF GetMinMaxBox(List<Vector2> points)
{
// Find the MinMax quadrilateral.
Vector2 ul = new Vector2(0, 0), ur = ul, ll = ul, lr = ul;
GetMinMaxCorners(points, ref ul, ref ur, ref ll, ref lr);
// Get the coordinates of a box that lies inside this quadrilateral.
var xmin = ul.X;
var ymin = ul.Y;
var xmax = ur.X;
if (ymin < ur.Y)
{
ymin = ur.Y;
}
if (xmax > lr.X)
{
xmax = lr.X;
}
var ymax = lr.Y;
if (xmin < ll.X)
{
xmin = ll.X;
}
if (ymax > ll.Y)
{
ymax = ll.Y;
}
var result = new RectangleF(xmin, ymin, xmax - xmin, ymax - ymin);
g_MinMaxBox = result; // For debugging.
return result;
}
// Find the points nearest the upper left, upper right,
// lower left, and lower right corners.
/// <summary>
/// Gets the minimum maximum corners.
/// </summary>
/// <param name="points">The points.</param>
/// <param name="ul">The ul.</param>
/// <param name="ur">The ur.</param>
/// <param name="ll">The ll.</param>
/// <param name="lr">The lr.</param>
private static void GetMinMaxCorners(
List<Vector2> points,
ref Vector2 ul,
ref Vector2 ur,
ref Vector2 ll,
ref Vector2 lr)
{
// Start with the first point as the solution.
ul = points[0];
ur = ul;
ll = ul;
lr = ul;
// Search the other points.
foreach (var pt in points)
{
if (-pt.X - pt.Y > -ul.X - ul.Y)
{
ul = pt;
}
if (pt.X - pt.Y > ur.X - ur.Y)
{
ur = pt;
}
if (-pt.X + pt.Y > -ll.X + ll.Y)
{
ll = pt;
}
if (pt.X + pt.Y > lr.X + lr.Y)
{
lr = pt;
}
}
g_MinMaxCorners = new[] { ul, ur, lr, ll }; // For debugging.
}
/// <summary>
/// Culls points out of the convex hull that lie inside the trapezoid defined by the vertices with smallest and largest
/// X and Y coordinates.
/// </summary>
/// <param name="points">The points.</param>
/// <returns>Points that are not culled.</returns>
private static List<Vector2> HullCull(List<Vector2> points)
{
// Find a culling box.
var culling_box = GetMinMaxBox(points);
// Cull the points.
var results =
points.Where(
pt =>
pt.X <= culling_box.Left || pt.X >= culling_box.Right || pt.Y <= culling_box.Top
|| pt.Y >= culling_box.Bottom).ToList();
g_NonCulledPoints = new Vector2[results.Count]; // For debugging.
results.CopyTo(g_NonCulledPoints); // For debugging.
return results;
}
#endregion
/// <summary>
/// Represetns a MecCircle
/// </summary>
public struct MecCircle
{
#region Fields
/// <summary>
/// The center
/// </summary>
public Vector2 Center;
/// <summary>
/// The radius
/// </summary>
public float Radius;
#endregion
#region Constructors and Destructors
/// <summary>
/// Initializes a new instance of the <see cref="MecCircle" /> struct.
/// </summary>
/// <param name="center">The center.</param>
/// <param name="radius">The radius.</param>
public MecCircle(Vector2 center, float radius)
{
this.Center = center;
this.Radius = radius;
}
#endregion
}
}
}