/// <summary>
/// Determines if line1 intersects line2, when line1 is offset by pos1 and line2
/// is offset by pos2.
/// </summary>
/// <param name="line1">Line 1</param>
/// <param name="line2">Line 2</param>
/// <param name="pos1">Origin of line 1</param>
/// <param name="pos2">Origin of line 2</param>
/// <param name="strict">If overlap is required for intersection</param>
/// <returns>If line1 intersects line2</returns>
public static bool Intersects(Line2 line1, Line2 line2, Vector2 pos1, Vector2 pos2, bool strict)
{
if (line1.Horizontal && line2.Horizontal)
{
return(AxisAlignedLine2.Intersects(line1.MinX + pos1.X, line1.MaxX + pos1.X, line2.MinX + pos2.X, line2.MaxX + pos2.X, strict, false));
}
else if (line1.Vertical && line2.Vertical)
{
return(AxisAlignedLine2.Intersects(line1.MinY + pos1.Y, line1.MaxY + pos1.Y, line2.MinY + pos2.Y, line2.MaxY + pos2.Y, strict, false));
}
else if (line1.Horizontal || line2.Horizontal)
{
if (line2.Horizontal)
{
// swap line 1 and 2 to prevent duplicating everything
var tmp = line1;
var tmpp = pos1;
line1 = line2;
pos1 = pos2;
line2 = tmp;
pos2 = tmpp;
}
if (line2.Vertical)
{
return(AxisAlignedLine2.Contains(line1.MinX + pos1.X, line1.MaxX + pos1.X, line2.Start.X + pos2.X, strict, false) &&
AxisAlignedLine2.Contains(line2.MinY + pos2.Y, line2.MaxY + pos2.Y, line1.Start.Y + pos1.Y, strict, false));
}
else
{
// recalculate line2 y intercept
// y = mx + b
// b = y - mx
var line2YIntInner = line2.Start.Y + pos2.Y - line2.Slope * (line2.Start.X + pos2.X);
// check line2.x at line1.y
// line2.y = line2.slope * line2.x + line2.yintercept
// line1.y = line2.slope * line2.x + line2.yintercept
// line1.y - line2.yintercept = line2.slope * line2.x
// (line1.y - line2.yintercept) / line2.slope = line2.x
var line2XAtLine1Y = (line1.Start.Y + pos1.Y - line2YIntInner) / line2.Slope;
return(AxisAlignedLine2.Contains(line1.MinX + pos1.X, line1.MaxX + pos1.X, line2XAtLine1Y, strict, false) &&
AxisAlignedLine2.Contains(line2.MinX + pos2.X, line2.MaxX + pos2.X, line2XAtLine1Y, strict, false));
}
}
else if (line1.Vertical)
{
// vertical line with regular line
var line2YIntInner = line2.Start.Y + pos2.Y - line2.Slope * (line2.Start.X + pos2.X);
var line2YAtLine1X = line2.Slope * (line1.Start.X + pos1.X) + line2YIntInner;
return(AxisAlignedLine2.Contains(line1.MinY + pos1.Y, line1.MaxY + pos1.Y, line2YAtLine1X, strict, false) &&
AxisAlignedLine2.Contains(line2.MinY + pos2.Y, line2.MaxY + pos2.Y, line2YAtLine1X, strict, false));
}
// two non-vertical, non-horizontal lines
var line1YInt = line1.Start.Y + pos1.Y - line1.Slope * (line1.Start.X + pos1.X);
var line2YInt = line2.Start.Y + pos2.Y - line2.Slope * (line2.Start.X + pos2.X);
if (Math.Abs(line1.Slope - line2.Slope) <= Math2.DEFAULT_EPSILON)
{
// parallel lines
if (line1YInt != line2YInt)
{
return(false); // infinite lines don't intersect
}
// parallel lines with equal y intercept. Intersect if ever at same X coordinate.
return(AxisAlignedLine2.Intersects(line1.MinX + pos1.X, line1.MaxX + pos1.X, line2.MinX + pos2.X, line2.MaxX + pos2.X, strict, false));
}
else
{
// two non-parallel lines. Only one possible intersection point
// y1 = y2
// line1.Slope * x + line1.YIntercept = line2.Slope * x + line2.YIntercept
// line1.Slope * x - line2.Slope * x = line2.YIntercept - line1.YIntercept
// x (line1.Slope - line2.Slope) = line2.YIntercept - line1.YIntercept
// x = (line2.YIntercept - line1.YIntercept) / (line1.Slope - line2.Slope)
var x = (line2YInt - line1YInt) / (line1.Slope - line2.Slope);
return(AxisAlignedLine2.Contains(line1.MinX + pos1.X, line1.MaxX + pos1.X, x, strict, false) &&
AxisAlignedLine2.Contains(line2.MinX + pos1.X, line2.MaxX + pos2.X, x, strict, false));
}
}
/// <summary>
/// Finds the line of overlap between the the two lines if there is
/// one. If the two lines are not coincident (i.e., if the infinite
/// lines are not the same) then they don't share a line of points.
/// If they are coincident, they may still share no points (two
/// seperate but coincident line segments), one point (they share
/// an edge), or infinitely many points (the share a coincident
/// line segment). In all but the last case, this returns false
/// and overlap is set to null. In the last case this returns true
/// and overlap is set to the line of overlap.
/// </summary>
/// <param name="a">The first line</param>
/// <param name="b">The second line</param>
/// <param name="pos1">The position of the first line</param>
/// <param name="pos2">the position of the second line</param>
/// <param name="overlap">Set to null or the line of overlap</param>
/// <returns>True if a and b overlap at infinitely many points,
/// false otherwise</returns>
public static unsafe bool LineOverlap(Line2 a, Line2 b, Vector2 pos1, Vector2 pos2, out Line2 overlap)
{
if (!Parallel(a, b))
{
overlap = null;
return(false);
}
if (!AlongInfiniteLine(a, pos1, b.Start + pos2))
{
overlap = null;
return(false);
}
Vector2 relOrigin = a.Start + pos1;
float *projs = stackalloc float[4] {
0,
a.Magnitude,
Math2.Dot((b.Start + pos2) - relOrigin, a.Axis),
Math2.Dot((b.End + pos2) - relOrigin, a.Axis)
};
bool *isFromLine1 = stackalloc bool[4] {
true,
true,
false,
false
};
FindSortedOverlap(projs, isFromLine1);
if (isFromLine1[0] == isFromLine1[1])
{
// at best we overlap at one point, most likely no overlap
overlap = null;
return(false);
}
if (Math2.Approximately(projs[1], projs[2]))
{
// Overlap at one point
overlap = null;
return(false);
}
overlap = new Line2(
relOrigin + projs[1] * a.Axis,
relOrigin + projs[2] * a.Axis
);
return(true);
}
/// <summary>
/// Determines if the given point is along the infinite line described
/// by the given line shifted the given amount.
/// </summary>
/// <param name="line">The line</param>
/// <param name="pos">The shift for the line</param>
/// <param name="pt">The point</param>
/// <returns>True if pt is on the infinite line extension of the segment</returns>
public static bool AlongInfiniteLine(Line2 line, Vector2 pos, Vector2 pt)
{
float normalPart = Vector2.Dot(pt - pos - line.Start, line.Normal);
return(Math2.Approximately(normalPart, 0));
}
/// <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);
_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;
}
}