private static IEnumerable <Vector2> GetExtraMinDistanceVecsPolyPoly(Polygon2 poly1, Polygon2 poly2, Vector2 pos1, Vector2 pos2)
{
foreach (var vert in poly1.Vertices)
{
foreach (var vert2 in poly2.Vertices)
{
var roughAxis = ((vert2 + pos2) - (vert + pos1));
roughAxis.Normalize();
yield return(Math2.MakeStandardNormal(roughAxis));
}
}
}
/// <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;
}
}
/// <summary>
/// Determines the minimum translation vector to be applied to the circle to
/// prevent overlap with the rectangle, when they are at their given positions.
/// </summary>
/// <param name="circle">The circle</param>
/// <param name="rect">The rectangle</param>
/// <param name="pos1">The top-left of the circles bounding box</param>
/// <param name="pos2">The rectangles origin</param>
/// <returns>MTV for circle at pos1 to prevent overlap with rect at pos2</returns>
public static Tuple <Vector2, float> IntersectMTV(Circle2 circle, Rect2 rect, Vector2 pos1, Vector2 pos2)
{
// Same as polygon rect, just converted to rects points
HashSet <Vector2> checkedAxis = new HashSet <Vector2>();
Vector2 bestAxis = Vector2.Zero;
float shortestOverlap = float.MaxValue;
Func <Vector2, bool> checkAxis = (axis) =>
{
var standard = Math2.MakeStandardNormal(axis);
if (!checkedAxis.Contains(standard))
{
checkedAxis.Add(standard);
var circleProj = Circle2.ProjectAlongAxis(circle, pos1, axis);
var rectProj = Rect2.ProjectAlongAxis(rect, pos2, axis);
var mtv = AxisAlignedLine2.IntersectMTV(circleProj, rectProj);
if (!mtv.HasValue)
{
return(false);
}
if (Math.Abs(mtv.Value) < Math.Abs(shortestOverlap))
{
bestAxis = axis;
shortestOverlap = mtv.Value;
}
}
return(true);
};
var circleCenter = new Vector2(pos1.X + circle.Radius, pos1.Y + circle.Radius);
int last = 4;
var lastVec = rect.UpperRight + pos2;
for (int curr = 0; curr < 4; curr++)
{
Vector2 currVec = Vector2.Zero;
switch (curr)
{
case 0:
currVec = rect.Min + pos2;
break;
case 1:
currVec = rect.LowerLeft + pos2;
break;
case 2:
currVec = rect.Max + pos2;
break;
case 3:
currVec = rect.UpperRight + pos2;
break;
}
// Test along circle center -> vector
if (!checkAxis(Vector2.Normalize(currVec - circleCenter)))
{
return(null);
}
// Test along line normal
if (!checkAxis(Vector2.Normalize(Math2.Perpendicular(currVec - lastVec))))
{
return(null);
}
last = curr;
lastVec = currVec;
}
return(Tuple.Create(bestAxis, shortestOverlap));
}
/// <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)
{
if (vertices == null)
{
throw new ArgumentNullException(nameof(vertices));
}
Vertices = 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);
Center = new Vector2(0, 0);
foreach (var vert in Vertices)
{
Center += vert;
}
Center *= (1.0f / Vertices.Length);
// Find longest axis
float longestAxisLenSq = -1;
for (int i = 1; i < vertices.Length; i++)
{
var vec = vertices[i] - vertices[i - 1];
longestAxisLenSq = Math.Max(longestAxisLenSq, vec.LengthSquared());
}
longestAxisLenSq = Math.Max(longestAxisLenSq, (vertices[0] - vertices[vertices.Length - 1]).LengthSquared());
LongestAxisLength = (float)Math.Sqrt(longestAxisLenSq);
// Area and lines
float area = 0;
Lines = new Line2[Vertices.Length];
var last = Vertices[Vertices.Length - 1];
for (int i = 0; i < Vertices.Length; i++)
{
var next = Vertices[i];
Lines[i] = new Line2(last, next);
area += Math2.AreaOfTriangle(last, next, Center);
last = next;
}
Area = area;
last = Vertices[Vertices.Length - 1];
var centToLast = (last - Center);
var angLast = 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 = Math.Atan2(centToCurr.Y, centToCurr.X);
var clockwise = angCurr < angLast;
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;
}
}
/// <summary>
/// Determines the minimum translation that must be applied the specified polygon (at the given position
/// and rotation) to prevent intersection with the circle (at its given rotation). If the two are not overlapping,
/// returns null.
///
/// Returns a tuple of the axis to move the polygon in (unit vector) and the distance to move the polygon.
/// </summary>
/// <param name="poly">The polygon</param>
/// <param name="circle">The circle</param>
/// <param name="pos1">The origin of the polygon</param>
/// <param name="pos2">The top-left of the circles bounding box</param>
/// <param name="rot1">The rotation of the polygon</param>
/// <returns></returns>
public static Tuple <Vector2, float> IntersectMTV(Polygon2 poly, Circle2 circle, Vector2 pos1, Vector2 pos2, Rotation2 rot1)
{
// We have two situations, either the circle is not strictly intersecting the polygon, or
// there exists at least one shortest line that you could push the polygon to prevent
// intersection with the circle.
// That line will either go from a vertix of the polygon to a point on the edge of the circle,
// or it will go from a point on a line of the polygon to the edge of the circle.
// If the line comes from a vertix of the polygon, the MTV will be along the line produced
// by going from the center of the circle to the vertix, and the distance can be found by
// projecting the cirle on that axis and the polygon on that axis and doing 1D overlap.
// If the line comes from a point on the edge of the polygon, the MTV will be along the
// normal of that line, and the distance can be found by projecting the circle on that axis
// and the polygon on that axis and doing 1D overlap.
// As with all SAT, if we find any axis that the circle and polygon do not overlap, we've
// proven they do not intersect.
// The worst case performance is related to 2x the number of vertices of the polygon, the same speed
// as for 2 polygons of equal number of vertices.
HashSet <Vector2> checkedAxis = new HashSet <Vector2>();
Vector2 bestAxis = Vector2.Zero;
float shortestOverlap = float.MaxValue;
Func <Vector2, bool> checkAxis = (axis) =>
{
var standard = Math2.MakeStandardNormal(axis);
if (!checkedAxis.Contains(standard))
{
checkedAxis.Add(standard);
var polyProj = Polygon2.ProjectAlongAxis(poly, pos1, rot1, axis);
var circleProj = Circle2.ProjectAlongAxis(circle, pos2, axis);
var mtv = AxisAlignedLine2.IntersectMTV(polyProj, circleProj);
if (!mtv.HasValue)
{
return(false);
}
if (Math.Abs(mtv.Value) < Math.Abs(shortestOverlap))
{
bestAxis = axis;
shortestOverlap = mtv.Value;
}
}
return(true);
};
var circleCenter = new Vector2(pos2.X + circle.Radius, pos2.Y + circle.Radius);
int last = poly.Vertices.Length - 1;
var lastVec = Math2.Rotate(poly.Vertices[last], poly.Center, rot1) + pos1;
for (int curr = 0; curr < poly.Vertices.Length; curr++)
{
var currVec = Math2.Rotate(poly.Vertices[curr], poly.Center, rot1) + pos1;
// Test along circle center -> vector
if (!checkAxis(Vector2.Normalize(currVec - circleCenter)))
{
return(null);
}
// Test along line normal
if (!checkAxis(Vector2.Normalize(Math2.Perpendicular(currVec - lastVec))))
{
return(null);
}
last = curr;
lastVec = currVec;
}
return(Tuple.Create(bestAxis, shortestOverlap));
}
