/// <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>
/// 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 if the specified rectangle at pos1 intersects the specified polygon at pos2 with
/// no rotation.
/// </summary>
/// <param name="rect">The rectangle</param>
/// <param name="poly">The polygon</param>
/// <param name="pos1">Origin of rectangle</param>
/// <param name="pos2">Origin of polygon</param>
/// <param name="strict">If overlap is required for intersection</param>
/// <returns>If rect at pos1 no rotation intersects poly at pos2</returns>
public static bool Intersects(Rect2 rect, Polygon2 poly, Vector2 pos1, Vector2 pos2, bool strict)
{
return(Intersects(rect, poly, pos1, pos2, Rotation2.Zero, strict));
}
/// <summary>
/// Determines the minimum translation vector to be applied to the rect to prevent
/// intersection with the specified polygon, when they are at the given positions.
/// </summary>
/// <param name="rect">The rect</param>
/// <param name="poly">The polygon</param>
/// <param name="pos1">The origin of the rect</param>
/// <param name="pos2">The origin of the polygon</param>
/// <returns>MTV to move rect at pos1 to prevent overlap with poly at pos2</returns>
public static Tuple <Vector2, float> IntersectMTV(Rect2 rect, Polygon2 poly, Vector2 pos1, Vector2 pos2)
{
return(IntersectMTV(rect, poly, pos1, pos2, Rotation2.Zero));
}
/// <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>
/// Determines the vector, if any, to move poly at pos1 rotated rot1 to prevent intersection of rect
/// at pos2.
/// </summary>
/// <param name="poly">Polygon</param>
/// <param name="rect">Rectangle</param>
/// <param name="pos1">Origin of polygon</param>
/// <param name="pos2">Origin of rectangle</param>
/// <param name="rot1">Rotation of the polygon.</param>
/// <returns>The vector to move pos1 by or null</returns>
public static Tuple <Vector2, float> IntersectMTV(Polygon2 poly, Rect2 rect, Vector2 pos1, Vector2 pos2, Rotation2 rot1)
{
bool checkedX = false, checkedY = false;
Vector2 bestAxis = Vector2.Zero;
float bestMagn = float.MaxValue;
for (int i = 0; i < poly.Normals.Count; i++)
{
var norm = Math2.Rotate(poly.Normals[i], Vector2.Zero, rot1);
var mtv = IntersectMTVAlongAxis(poly, rect, pos1, pos2, rot1, norm);
if (!mtv.HasValue)
{
return(null);
}
if (Math.Abs(mtv.Value) < Math.Abs(bestMagn))
{
bestAxis = norm;
bestMagn = mtv.Value;
}
if (norm.X == 0)
{
checkedY = true;
}
if (norm.Y == 0)
{
checkedX = true;
}
}
if (!checkedX)
{
var mtv = IntersectMTVAlongAxis(poly, rect, pos1, pos2, rot1, Vector2.UnitX);
if (!mtv.HasValue)
{
return(null);
}
if (Math.Abs(mtv.Value) < Math.Abs(bestMagn))
{
bestAxis = Vector2.UnitX;
bestMagn = mtv.Value;
}
}
if (!checkedY)
{
var mtv = IntersectMTVAlongAxis(poly, rect, pos1, pos2, rot1, Vector2.UnitY);
if (!mtv.HasValue)
{
return(null);
}
if (Math.Abs(mtv.Value) < Math.Abs(bestMagn))
{
bestAxis = Vector2.UnitY;
bestMagn = mtv.Value;
}
}
return(Tuple.Create(bestAxis, bestMagn));
}
/// <summary>
/// Determines if the specified rectangle and polygon where rect is at pos1 and poly is at pos2 intersect
/// along the specified axis.
/// </summary>
/// <param name="rect">Rectangle</param>
/// <param name="poly">Polygon</param>
/// <param name="pos1">Origin of rectangle</param>
/// <param name="pos2">Origin of polygon</param>
/// <param name="rot2">Rotation of polygon</param>
/// <param name="strict"></param>
/// <param name="axis"></param>
/// <returns></returns>
public static bool IntersectsAlongAxis(Rect2 rect, Polygon2 poly, Vector2 pos1, Vector2 pos2, Rotation2 rot2, bool strict, Vector2 axis)
{
return(IntersectsAlongAxis(poly, rect, pos2, pos1, rot2, strict, axis));
}
/// <summary>
/// Determines if the specified rectangle and circle intersect at their given positions.
/// </summary>
/// <param name="rect">The rectangle</param>
/// <param name="circle">The circle</param>
/// <param name="pos1">The origin of the rectangle</param>
/// <param name="pos2">The top-left of the circles bounding box</param>
/// <param name="strict">If overlap is required for intersection</param>
/// <returns></returns>
public static bool Intersects(Rect2 rect, Circle2 circle, Vector2 pos1, Vector2 pos2, bool strict)
{
return(Intersects(circle, rect, pos2, pos1, strict));
}
/// <summary>
/// Multiply our min with original min and our max with original max and return
/// as a rect
/// </summary>
/// <param name="original">the original</param>
/// <returns>scaled rect</returns>
public Rect2 ToRect(Rect2 original)
{
return(new Rect2(original.Min * Min, original.Max * Max));
}
/// <summary>
/// Determines the vector to move pos1 to get rect not to intersect poly at pos2 rotated
/// by rot2 radians.
/// </summary>
/// <param name="rect">The rectangle</param>
/// <param name="poly">The polygon</param>
/// <param name="pos1">Origin of rectangle</param>
/// <param name="pos2">Origin of </param>
/// <param name="rot2">Rotation of the polygon</param>
/// <returns>Offset of pos1 to get rect not to intersect poly</returns>
public static Tuple <Vector2, float> IntersectMTV(Rect2 rect, Polygon2 poly, Vector2 pos1, Vector2 pos2, Rotation2 rot2)
{
var res = IntersectMTV(poly, rect, pos2, pos1, rot2);
return(res != null?Tuple.Create(-res.Item1, res.Item2) : res);
}
/// <summary>
/// Determines if the box when at pos contains point.
/// </summary>
/// <param name="box">The box</param>
/// <param name="pos">Origin of box</param>
/// <param name="point">Point to check</param>
/// <param name="strict">true if the edges do not count</param>
/// <returns>If the box at pos contains point</returns>
public static bool Contains(Rect2 box, Vector2 pos, Vector2 point, bool strict)
{
return(AxisAlignedLine2.Contains(box.Min.X + pos.X, box.Max.X + pos.X, point.X, strict, false) &&
AxisAlignedLine2.Contains(box.Min.Y + pos.Y, box.Max.Y + pos.Y, point.Y, strict, false));
}
/// <summary>
/// Determines if box1 with origin pos1 intersects box2 with origin pos2.
/// </summary>
/// <param name="box1">Box 1</param>
/// <param name="box2">Box 2</param>
/// <param name="pos1">Origin of box 1</param>
/// <param name="pos2">Origin of box 2</param>
/// <param name="strict">If overlap is required for intersection</param>
/// <returns>If box1 intersects box2 when box1 is at pos1 and box2 is at pos2</returns>
public static bool Intersects(Rect2 box1, Rect2 box2, Vector2 pos1, Vector2 pos2, bool strict)
{
return(AxisAlignedLine2.Intersects(box1.Min.X + pos1.X, box1.Max.X + pos1.X, box2.Min.X + pos2.X, box2.Max.X + pos2.X, strict, false) &&
AxisAlignedLine2.Intersects(box1.Min.Y + pos1.Y, box1.Max.Y + pos1.Y, box2.Min.Y + pos2.Y, box2.Max.Y + pos2.Y, strict, false));
}
/// <summary>
/// Projects the rectangle at pos along axis.
/// </summary>
/// <param name="rect">The rectangle to project</param>
/// <param name="pos">The origin of the rectangle</param>
/// <param name="axis">The axis to project on</param>
/// <returns>The projection of rect at pos along axis</returns>
public static AxisAlignedLine2 ProjectAlongAxis(Rect2 rect, Vector2 pos, Vector2 axis)
{
return(ProjectAlongAxis(axis, pos, Rotation2.Zero, rect.Center, rect.Min, rect.UpperRight, rect.LowerLeft, rect.Max));
}
/// <summary>
/// Deterimines in the box contains the specified polygon
/// </summary>
/// <param name="box">The box</param>
/// <param name="poly">The polygon</param>
/// <param name="boxPos">Where the box is located</param>
/// <param name="polyPos">Where the polygon is located</param>
/// <param name="strict">true if we return false if the any part of the polygon is on the edge, false otherwise</param>
/// <returns>true if the poly is contained in box, false otherwise</returns>
public static bool Contains(Rect2 box, Polygon2 poly, Vector2 boxPos, Vector2 polyPos, bool strict)
{
return(Contains(box, poly.AABB, boxPos, polyPos, strict));
}
/// <summary>
/// Determines if innerBox is contained entirely in outerBox
/// </summary>
/// <param name="outerBox">the (bigger) box that you want to check contains the inner box</param>
/// <param name="innerBox">the (smaller) box that you want to check is contained in the outer box</param>
/// <param name="posOuter">where the outer box is located</param>
/// <param name="posInner">where the inner box is located</param>
/// <param name="strict">true to return false if innerBox touches an edge of outerBox, false otherwise</param>
/// <returns>true if innerBox is contained in outerBox, false otherwise</returns>
public static bool Contains(Rect2 outerBox, Rect2 innerBox, Vector2 posOuter, Vector2 posInner, bool strict)
{
return(Contains(outerBox, posOuter, innerBox.Min + posInner, strict) && Contains(outerBox, posOuter, innerBox.Max + posInner, strict));
}
