public static bool Contains(ref IntVector2 p1, ref IntVector2 p2, ref IntVector2 q)
{
var p1p2 = p1.To(p2);
var p1q = p1.To(q);
// not on line between p1 p2
if (GeometryOperations.Clockness(p1p2, p1q) != Clockness.Neither)
{
return(false);
}
var a = p1p2.Dot(p1q);
var b = p1p2.SquaredNorm2();
// outside segment p1-p2 on the side of p1
if (a < 0)
{
return(false);
}
// outside segment p1-p2 on the side of p2
if (a > b)
{
return(false);
}
return(true);
}
public static bool Contains(cInt p1x, cInt p1y, cInt p2x, cInt p2y, cInt qx, cInt qy)
{
var p1p2x = p2x - p1x;
var p1p2y = p2y - p1y;
var p1qx = qx - p1x;
var p1qy = qy - p1y;
// not on line between p1 p2
if (GeometryOperations.Clockness(p1p2x, p1p2y, p1qx, p1qy) != Clockness.Neither)
{
return(false);
}
var a = (long)p1p2x * p1qx + (long)p1p2y * p1qy; //p1p2.Dot(p1q);
var b = (long)p1p2x * p1p2x + (long)p1p2y * p1p2y; //p1p2.SquaredNorm2();
// outside segment p1-p2 on the side of p1
if (a < 0)
{
return(false);
}
// outside segment p1-p2 on the side of p2
if (a > b)
{
return(false);
}
return(true);
}
public static bool Intersects(cInt ax, cInt ay, cInt bx, cInt by, cInt cx, cInt cy, cInt dx, cInt dy)
{
// https://www.cdn.geeksforgeeks.org/check-if-two-given-line-segments-intersect/
// Note, didn't do SO variant because not robust to collinear segments
// http://stackoverflow.com/questions/3838329/how-can-i-check-if-two-segments-intersect
var o1 = GeometryOperations.Clockness(ax, ay, bx, by, cx, cy);
var o2 = GeometryOperations.Clockness(ax, ay, bx, by, dx, dy);
var o3 = GeometryOperations.Clockness(cx, cy, dx, dy, ax, ay);
var o4 = GeometryOperations.Clockness(cx, cy, dx, dy, bx, by);
if (o1 != o2 && o3 != o4)
{
return(true);
}
// handle endpoint containment.
if (o1 == 0 && Contains(ax, ay, bx, by, cx, cy))
{
return(true);
}
if (o2 == 0 && Contains(ax, ay, bx, by, dx, dy))
{
return(true);
}
if (o3 == 0 && Contains(cx, cy, dx, dy, ax, ay))
{
return(true);
}
if (o4 == 0 && Contains(cx, cy, dx, dy, bx, by))
{
return(true);
}
return(false);
}
public static int Compare(IntVector2 p, IntLineSegment2 a, IntLineSegment2 b)
{
#if DEBUG
if (GeometryOperations.Clockness(p.X, p.Y, a.X1, a.Y1, a.X2, a.Y2) != Clockness.Clockwise)
{
throw new InvalidStateException();
}
if (GeometryOperations.Clockness(p.X, p.Y, b.X1, b.Y1, b.X2, b.Y2) != Clockness.Clockwise)
{
throw new InvalidStateException();
}
#endif
var clk = GeometryOperations.Clockness(p.X, p.Y, a.X1, a.Y1, b.X1, b.Y1);
if (clk != Clockness.Clockwise)
{
// b before a; b \' a *origin
var res = (int)GeometryOperations.Clockness(b.First, b.Second, a.First);
if (res != 0)
{
return(res);
}
// just need something to resolve ambiguity. b1 b2 a1 is collinear.
// a1 must be within the angle b1 p b2 (see visibility polygon building algorithm)
// so a1 is BETWEEN b1 b2. a2 cannot be collinear with b1 b2 (disallow segments intersecting
// other than at endpoint), but still, a2 is either 'in front of' or 'behind' b.
res = (int)GeometryOperations.Clockness(b.First, b.Second, a.Second);
#if DEBUG
if (res == 0 && a != b)
{
throw new BadInputException();
}
#endif
return(res);
}
else
{
// a before b; a \' b *origin
var res = -(int)GeometryOperations.Clockness(a.First, a.Second, b.First);
if (res != 0)
{
return(res);
}
// just need something to resolve ambiguity. a1 a2 b1 is collinear.
res = -(int)GeometryOperations.Clockness(a.First, a.Second, b.Second);
#if DEBUG
if (res == 0 && a != b)
{
throw new BadInputException();
}
#endif
return(res);
}
}
/// <summary>
/// https://en.wikipedia.org/wiki/Sutherland%E2%80%93Hodgman_algorithm#Pseudo_code
/// Fails if result would be empty
/// </summary>
public static bool TryConvexClip(Polygon2 subject, Polygon2 clip, out Polygon2 result)
{
bool Inside(IntVector2 p, IntLineSegment2 edge) => GeometryOperations.Clockness(edge.First, edge.Second, p) != Clockness.CounterClockwise;
List <IntVector2> outputList = subject.Points;
for (var i = 0; i < clip.Points.Count - 1; i++)
{
var clipEdge = new IntLineSegment2(clip.Points[i], clip.Points[i + 1]);
List <IntVector2> inputList = outputList;
outputList = new List <IntVector2>();
var S = inputList[inputList.Count - 2];
for (var j = 0; j < inputList.Count - 1; j++)
{
var E = inputList[j];
if (Inside(E, clipEdge))
{
if (!Inside(S, clipEdge))
{
var SE = new IntLineSegment2(S, E);
if (!GeometryOperations.TryFindLineLineIntersection(SE, clipEdge, out var intersection))
{
throw new NotImplementedException();
}
outputList.Add(intersection.LossyToIntVector2());
}
outputList.Add(E);
}
else if (Inside(S, clipEdge))
{
var SE = new IntLineSegment2(S, E);
if (!GeometryOperations.TryFindLineLineIntersection(SE, clipEdge, out var intersection))
{
throw new NotImplementedException();
}
outputList.Add(intersection.LossyToIntVector2());
}
S = E;
}
if (outputList.Count == 0)
{
result = null;
return(false);
}
outputList.Add(outputList[0]);
}
result = new Polygon2(outputList);
return(true);
}