/// <summary>
/// Checks if this triangle contains the given point. This is
/// never strict.
/// </summary>
/// <param name="tri">The triangle</param>
/// <param name="pos">The position of the triangle</param>
/// <param name="pt">The point to check</param>
/// <returns>true if this triangle contains the point or the point
/// is along an edge of this polygon</returns>
public static bool Contains(Triangle2 tri, Vector2 pos, Vector2 pt)
{
Vector2 relPt = pt - pos - tri.Vertices[0];
float r = tri.InvContainsBasis[0] * relPt.X + tri.InvContainsBasis[1] * relPt.Y;
if (r < -Math2.DEFAULT_EPSILON)
{
return(false);
}
float t = tri.InvContainsBasis[2] * relPt.X + tri.InvContainsBasis[3] * relPt.Y;
if (t < -Math2.DEFAULT_EPSILON)
{
return(false);
}
return((r + t) < 1 + Math2.DEFAULT_EPSILON);
}
/// <summary>
/// Determines if the specified polygon at the specified position and rotation contains the specified point
/// </summary>
/// <param name="poly">The polygon</param>
/// <param name="pos">Origin of the polygon</param>
/// <param name="rot">Rotation of the polygon</param>
/// <param name="point">Point to check</param>
/// <param name="strict">True if the edges do not count as inside</param>
/// <returns>If the polygon at pos with rotation rot about its center contains point</returns>
public static bool Contains(Polygon2 poly, Vector2 pos, Rotation2 rot, Vector2 point, bool strict)
{
// The point is contained in the polygon iff it is contained in one of the triangles
// which partition this polygon. Due to how we constructed the triangles, it will
// be on the edge of the polygon if its on the first 2 edges of the triangle.
for (int i = 0, len = poly.TrianglePartition.Length; i < len; i++)
{
var tri = poly.TrianglePartition[i];
if (Triangle2.Contains(tri, pos, point))
{
if (strict && (Line2.Contains(tri.Edges[0], pos, point) || Line2.Contains(tri.Edges[1], pos, point)))
{
return(false);
}
return(true);
}
}
return(false);
}
/// <summary>
/// Initializes a polygon with the specified vertices
/// </summary>
/// <param name="vertices">Vertices</param>
/// <exception cref="ArgumentNullException">If vertices is null</exception>
public Polygon2(Vector2[] vertices)
{
Vertices = vertices ?? throw new ArgumentNullException(nameof(vertices));
Normals = new List <Vector2>();
Vector2 tmp;
for (int i = 1; i < vertices.Length; i++)
{
tmp = Math2.MakeStandardNormal(Vector2.Normalize(Math2.Perpendicular(vertices[i] - vertices[i - 1])));
if (!Normals.Contains(tmp))
{
Normals.Add(tmp);
}
}
tmp = Math2.MakeStandardNormal(Vector2.Normalize(Math2.Perpendicular(vertices[0] - vertices[vertices.Length - 1])));
if (!Normals.Contains(tmp))
{
Normals.Add(tmp);
}
var min = new Vector2(vertices[0].X, vertices[0].Y);
var max = new Vector2(min.X, min.Y);
for (int i = 1; i < vertices.Length; i++)
{
min.X = Math.Min(min.X, vertices[i].X);
min.Y = Math.Min(min.Y, vertices[i].Y);
max.X = Math.Max(max.X, vertices[i].X);
max.Y = Math.Max(max.Y, vertices[i].Y);
}
AABB = new Rect2(min, max);
_LongestAxisLength = -1;
// Center, area, and lines
TrianglePartition = new Triangle2[Vertices.Length - 2];
float[] triangleSortKeys = new float[TrianglePartition.Length];
float area = 0;
Lines = new Line2[Vertices.Length];
Lines[0] = new Line2(Vertices[Vertices.Length - 1], Vertices[0]);
var last = Vertices[0];
Center = new Vector2(0, 0);
for (int i = 1; i < Vertices.Length - 1; i++)
{
var next = Vertices[i];
var next2 = Vertices[i + 1];
Lines[i] = new Line2(last, next);
var tri = new Triangle2(new Vector2[] { Vertices[0], next, next2 });
TrianglePartition[i - 1] = tri;
triangleSortKeys[i - 1] = -tri.Area;
area += tri.Area;
Center += tri.Center * tri.Area;
last = next;
}
Lines[Vertices.Length - 1] = new Line2(Vertices[Vertices.Length - 2], Vertices[Vertices.Length - 1]);
Array.Sort(triangleSortKeys, TrianglePartition);
Area = area;
Center /= area;
last = Vertices[Vertices.Length - 1];
var centToLast = (last - Center);
var angLast = Rotation2.Standardize((float)Math.Atan2(centToLast.Y, centToLast.X));
var cwCounter = 0;
var ccwCounter = 0;
var foundDefinitiveResult = false;
for (int i = 0; i < Vertices.Length; i++)
{
var curr = Vertices[i];
var centToCurr = (curr - Center);
var angCurr = Rotation2.Standardize((float)Math.Atan2(centToCurr.Y, centToCurr.X));
var clockwise = (angCurr < angLast && (angCurr - angLast) < Math.PI) || (angCurr - angLast) > Math.PI;
if (clockwise)
{
cwCounter++;
}
else
{
ccwCounter++;
}
Clockwise = clockwise;
if (Math.Abs(angLast - angCurr) > Math2.DEFAULT_EPSILON)
{
foundDefinitiveResult = true;
break;
}
last = curr;
centToLast = centToCurr;
angLast = angCurr;
}
if (!foundDefinitiveResult)
{
Clockwise = cwCounter > ccwCounter;
}
}
