public Polygon RectangleInside()
{
var p1 = Vector2.zero;
var p2 = Vector2.zero;
var maxLength = float.MinValue;
ForEachEdge((a, b, i) =>
{
var len = (a - b).magnitude;
if (len > maxLength)
{
p1 = a;
p2 = b;
maxLength = len;
}
});
var rotated = Rotate(GeometryHelpers.Angle(p1 - p2));
var minY = rotated.Vertices.Min(v => v.y);
var greatestDistance = rotated.Vertices.Max(v => v.y - minY);
var normal = GeometryHelpers.Rotate90(p2 - p1).normalized;
var newHouse = new Polygon(p1, p2, p2 - GeometryHelpers.Scale(normal, greatestDistance),
p1 - GeometryHelpers.Scale(normal, greatestDistance)).ZoomShrink(0.2f);
newHouse = newHouse.Translate(newHouse.Center - Center);
return(newHouse);
}
public float AngleAtVertex(int index)
{
var pt = Vertices[index];
var prev = GetPreviousVertex(index);
var next = GetNextVertex(index);
return(GeometryHelpers.AngleThreePoints(prev, pt, next));
}
public Polygon Peel(Vector2 v1, float amount)
{
var v2 = GetNextVertex(v1);
var n = GeometryHelpers.Scale(GeometryHelpers.Normalize(GeometryHelpers.Rotate90(v2 - v1)), amount);
return(Cut(v1 + n, v2 + n, 0).First());
}
public Vector2 GetCenter()
{
var sum = new Vector2();
Vertices.ForEach(v => sum += v);
sum = GeometryHelpers.Scale(sum, 1f / Vertices.Count);
return(sum);
}
public static float AngleThreePoints(Vector2 a, Vector2 b, Vector2 c)
{
var v1 = b - a;
var v2 = c - b;
var cross = GeometryHelpers.Cross(v1, v2);
var dot = Vector2.Dot(v1, v2);
return((float)Math.Atan2(cross, dot));
}
public Polygon ZoomShrink(float amount)
{
var newVertices = Vertices.Select(v =>
{
var d = Center - v;
return(v + GeometryHelpers.Scale(d, amount));
}).ToList();
return(new Polygon(newVertices));
}
public Vector2 Center()
{
var c = new Vector2();
foreach (var v in Vertices)
{
c = c + v.C;
}
return(GeometryHelpers.Scale(c, 1f / Vertices.Count));
}
public IEnumerable <Polygon> Bisect(Vector2 vertex, float ratio = 0.5f, float angle = 0.0f, float gap = 0.0f)
{
var next = GetNextVertex(vertex);
var p1 = GeometryHelpers.Interpolate(vertex, next, ratio);
var d = next - vertex;
var cosB = Math.Cos(angle);
var sinB = Math.Sin(angle);
var vx = d.x * cosB - d.y * sinB;
var vy = d.y * cosB + d.x * sinB;
var p2 = new Vector2((float)(p1.x - vy), (float)(p1.y + vx));
return(Cut(p1, p2, gap));
}
public Polygon Shrink(IList <float> shrinkAmounts)
{
var newPoly = new Polygon(this);
ForEachEdge((p1, p2, index) =>
{
var amount = shrinkAmounts[index];
if (amount > 0)
{
var n = GeometryHelpers.Scale(GeometryHelpers.Normalize(GeometryHelpers.Rotate90(p2 - p1)), amount);
newPoly = newPoly.Cut(p1 + n, p2 + n, 0).First();
}
});
return(newPoly);
}
public Polygon SmoothVertices(float amount = 1f)
{
var len = Vertices.Count;
var v1 = Vertices[len - 1];
var v2 = Vertices[0];
var newVertices = new List <Vector2> ();
for (var v = 0; v < Vertices.Count; v++)
{
var v0 = v1;
v1 = v2;
v2 = Vertices[(v + 1) % len];
newVertices.Add(GeometryHelpers.SmoothVertex(v1, v0, v2));
}
return(new Polygon(newVertices));
}
public static float Cross(Vector2 a, Vector2 b)
{
return(GeometryHelpers.CrossProduct(a.x, a.y, b.x, b.y));
}
public Polygon SortPointsClockwise()
{
var sortedVertices = Vertices.OrderBy(v => GeometryHelpers.Angle(v - Center)).ToList();
return(new Polygon(sortedVertices));
}
public Polygon Rotate(float angle)
{
return(new Polygon(Vertices.Select(vertex => GeometryHelpers.RotateAoundPoint(vertex, Center, angle))));
}
public IEnumerable <Polygon> Cut(Vector2 p1, Vector2 p2, float gap)
{
var x1 = p1.x;
var y1 = p1.y;
var dx1 = p2.x - x1;
var dy1 = p2.y - y1;
var len = Vertices.Count;
var edge1 = 0;
var ratio1 = 0.0f;
var edge2 = 0;
var ratio2 = 0.0f;
var count = 0;
for (var i = 0; i < len; i++)
{
var v0 = Vertices[i];
var v1 = Vertices[(i + 1) % len];
var x2 = v0.x;
var y2 = v0.y;
var dx2 = v1.x - x2;
var dy2 = v1.y - y2;
var t = GeometryHelpers.IntersectLines(x1, y1, dx1, dy1, x2, y2, dx2, dy2);
if (t.y >= 0 && t.y <= 1)
{
switch (count)
{
case 0:
edge1 = i;
ratio1 = t.x;
break;
case 1:
edge2 = i;
ratio2 = t.x;
break;
}
count++;
}
}
if (count == 2)
{
var point1 = p1 + GeometryHelpers.Scale(p2 - p1, ratio1);
var point2 = p1 + GeometryHelpers.Scale(p2 - p1, ratio2);
var half1 = new Polygon(Vertices.GetRange(edge1 + 1, edge2 - edge1));
half1.Vertices.Insert(0, point1);
half1.Vertices.Add(point2);
var half2 = new Polygon(Vertices.GetRange(edge2 + 1, Vertices.Count - edge2 - 1).Concat(Vertices.GetRange(0, edge1 + 1)));
half2.Vertices.Insert(0, point2);
half2.Vertices.Add(point1);
if (gap > 0)
{
half1 = half1.Peel(point2, gap / 2);
half2 = half2.Peel(point1, gap / 2);
}
var v = VectorI(edge1);
return(GeometryHelpers.CrossProduct(dx1, dy1, v.x, v.y) > 0 ?
new [] { half1, half2 } :
new [] { half2, half1 });
}
return(new [] { new Polygon(this) });
}
public Polygon Buffer(IList <float> shrinkAmounts)
{
var newPoly = new Polygon();
ForEachEdge((p1, p2, index) =>
{
var amount = shrinkAmounts[index];
if (amount <= 0.01)
{
newPoly.Vertices.Add(p1);
newPoly.Vertices.Add(p2);
}
else
{
var n = GeometryHelpers.Scale(GeometryHelpers.Normalize(GeometryHelpers.Rotate90(p2 - p1)), amount);
newPoly.Vertices.Add(p1 + n);
newPoly.Vertices.Add(p2 + n);
}
});
bool wasCut;
var lastEdge = 0;
do
{
wasCut = false;
var n = newPoly.Vertices.Count;
for (var i = lastEdge; i < n - 2; i++)
{
lastEdge = i;
var p11 = newPoly.Vertices[i];
var p12 = newPoly.Vertices[i + 1];
var x1 = p11.x;
var y1 = p11.y;
var dx1 = p12.x - x1;
var dy1 = p12.y - y1;
var maxJ = i > 0 ? n : n - 1;
for (var j = i + 2; j < maxJ; j++)
{
var p21 = newPoly.Vertices[j];
var p22 = j < n - 1 ? newPoly.Vertices[j + 1] : newPoly.Vertices[0];
var x2 = p21.x;
var y2 = p21.y;
var dx2 = p22.x - x2;
var dy2 = p22.y - y2;
var intersect = GeometryHelpers.IntersectLines(x1, y1, dx1, dy1, x2, y2, dx2, dy2);
if (intersect.x > Delta && intersect.x < (1 - Delta) && intersect.y > Delta && intersect.y < (1 - Delta))
{
var pn = new Vector2(x1 + dx1 * intersect.x, y1 + dy1 * intersect.x);
newPoly.Vertices.Insert(j + 1, pn);
newPoly.Vertices.Insert(i + 1, pn);
wasCut = true;
break;
}
}
}
} while (wasCut);
var regular = Enumerable.Range(0, newPoly.Vertices.Count).ToList();
Polygon bestPart = null;
var bestPartSq = float.MinValue;
while (regular.Count > 0)
{
var indices = new List <int> ();
var start = regular[0];
var i = start;
do
{
indices.Add(i);
regular.Remove(i);
var next = (i + 1) % newPoly.Vertices.Count;
var v = newPoly.Vertices[next];
var next1 = newPoly.Vertices.IndexOf(v);
if (next1 == next)
{
next1 = newPoly.Vertices.LastIndexOf(v);
}
i = next1 == -1 ? next : next1;
} while (i != start && indices.Count < 1000);
if (indices.Count >= 999)
{
indices = indices.Take(4).ToList();
}
var poly = new Polygon(indices.Select(v => newPoly.Vertices[v]));
var s = poly.Area();
if (s > bestPartSq)
{
bestPart = poly;
bestPartSq = s;
}
}
return(bestPart);
}