/// Union
///
/// Sets the rectangle to the union of two rectangles r1 and r2.
/// If either rect is empty, it is ignored. If both are empty, the rectangle
/// is set to r1.
/// Either of the input rectangle references may refer to the destination rectangle.
///
public void Union(Rect2D r1, Rect2D r2)
{
if ((r2.Right == r2.Left) || (r2.Bottom == r2.Top))
{
Set(r1);
}
else if ((r1.Right == r1.Left) || (r1.Bottom == r1.Top))
{
Set(r2);
}
else
{
Left = (r1.Left < r2.Left) ? r1.Left : r2.Left;
Top = (r1.Top > r2.Top) ? r1.Top : r2.Top;
Right = (r1.Right > r2.Right) ? r1.Right : r2.Right;
Bottom = (r1.Bottom < r2.Bottom) ? r1.Bottom : r2.Bottom;
}
}
public bool Equals(Rect2D r, double epsilon)
{
if (!MathUtil.AreValuesEqual(MinX, r.MinX, epsilon))
{
return(false);
}
if (!MathUtil.AreValuesEqual(MaxX, r.MaxX))
{
return(false);
}
if (!MathUtil.AreValuesEqual(MinY, r.MinY, epsilon))
{
return(false);
}
if (!MathUtil.AreValuesEqual(MaxY, r.MaxY, epsilon))
{
return(false);
}
return(true);
}
public bool Intersects(Rect2D r)
{
return (Right > r.Left) &&
(Left < r.Right) &&
(Bottom < r.Top) &&
(Top > r.Bottom);
}
public bool ContainsInclusive(Rect2D r, double epsilon)
{
return ((Left - epsilon) <= r.Left) && ((Right + epsilon) >= r.Right) && ((Top - epsilon) <= r.Top) && ((Bottom + epsilon) >= r.Bottom);
}
public bool ContainsInclusive(Rect2D r)
{
return (Left <= r.Left) && (Right >= r.Right) && (Top <= r.Top) && (Bottom >= r.Bottom);
}
public bool Contains(Rect2D r)
{
return (Left < r.Left) && (Right > r.Right) && (Top < r.Top) && (Bottom > r.Bottom);
}
public void Set(Rect2D b)
{
MinX = b.MinX;
MaxX = b.MaxX;
MinY = b.MinY;
MaxY = b.MaxY;
}
public bool Equals(Rect2D r)
{
return(Equals(r, MathUtil.EPSILON));
}
public bool Equals(Rect2D r)
{
return Equals(r, MathUtil.EPSILON);
}
// Given two polygons and their bounding rects, returns true if the two polygons intersect.
// This test will NOT determine if one of the two polygons is contained within the other or if the
// two polygons are similar - it will return false in all those cases. The only case it will return
// true for is if the two polygons actually intersect.
public static bool PolygonsIntersect2D( IList<Point2D> poly1, Rect2D boundRect1,
IList<Point2D> poly2, Rect2D boundRect2)
{
// do some quick tests first before doing any real work
if (poly1 == null || poly1.Count < 3 || boundRect1 == null || poly2 == null || poly2.Count < 3 || boundRect2 == null)
{
return false;
}
if (!boundRect1.Intersects(boundRect2))
{
return false;
}
// We first check whether any edge of one poly intersects any edge of the other poly. If they do,
// then the two polys intersect.
// Make the epsilon a function of the size of the polys. We could take the heights of the rects
// also into consideration here if needed; but, that should not usually be necessary.
double epsilon = Math.Max(Math.Min(boundRect1.Width, boundRect2.Width) * 0.001f, MathUtil.EPSILON);
int numVerts1 = poly1.Count;
int numVerts2 = poly2.Count;
for (int i = 0; i < numVerts1; ++i)
{
int lineEndVert1 = i + 1;
if (lineEndVert1 == numVerts1)
{
lineEndVert1 = 0;
}
for (int j = 0; j < numVerts2; ++j)
{
int lineEndVert2 = j + 1;
if (lineEndVert2 == numVerts2)
{
lineEndVert2 = 0;
}
Point2D tmp = null;
if (TriangulationUtil.LinesIntersect2D(poly1[i], poly1[lineEndVert1], poly2[j], poly2[lineEndVert2], ref tmp, epsilon))
{
return true;
}
}
}
return false;
}
public bool ContainsInclusive(Rect2D r, double epsilon)
{
return(((Left - epsilon) <= r.Left) && ((Right + epsilon) >= r.Right) && ((Top - epsilon) <= r.Top) && ((Bottom + epsilon) >= r.Bottom));
}
public bool ContainsInclusive(Rect2D r)
{
return((Left <= r.Left) && (Right >= r.Right) && (Top <= r.Top) && (Bottom >= r.Bottom));
}
public bool Contains(Rect2D r)
{
return((Left < r.Left) && (Right > r.Right) && (Top < r.Top) && (Bottom > r.Bottom));
}
/// Intersection
///
/// Sets the rectangle to the intersection of two rectangles.
/// Returns true if there is any intersection between the two rectangles.
/// If there is no intersection, the rectangle is set to 0, 0, 0, 0.
/// Either of the input rectangles may be the same as destination rectangle.
///
public bool Intersection(Rect2D r1, Rect2D r2)
{
if (!TriangulationUtil.RectsIntersect(r1, r2))
{
Left = Right = Top = Bottom = 0.0;
return false;
}
Left = (r1.Left > r2.Left) ? r1.Left : r2.Left;
Top = (r1.Top < r2.Top ) ? r1.Top : r2.Top;
Right = (r1.Right < r2.Right) ? r1.Right : r2.Right;
Bottom = (r1.Bottom > r2.Bottom) ? r1.Bottom : r2.Bottom;
return true;
}
public bool PolygonContainsPolygon(IList<Point2D> poly1, Rect2D boundRect1,
IList<Point2D> poly2, Rect2D boundRect2)
{
return PolygonContainsPolygon(poly1, boundRect1, poly2, boundRect2, true);
}
/// Union
///
/// Sets the rectangle to the union of two rectangles r1 and r2.
/// If either rect is empty, it is ignored. If both are empty, the rectangle
/// is set to r1.
/// Either of the input rectangle references may refer to the destination rectangle.
///
public void Union(Rect2D r1, Rect2D r2)
{
if ((r2.Right == r2.Left) || (r2.Bottom == r2.Top))
{
Set(r1);
}
else if ((r1.Right == r1.Left) || (r1.Bottom == r1.Top))
{
Set(r2);
}
else
{
Left = (r1.Left < r2.Left) ? r1.Left : r2.Left;
Top = (r1.Top > r2.Top) ? r1.Top : r2.Top;
Right = (r1.Right > r2.Right) ? r1.Right : r2.Right;
Bottom = (r1.Bottom < r2.Bottom) ? r1.Bottom : r2.Bottom;
}
}
/// <summary>
/// Checks to see if poly1 contains poly2. return true if so, false otherwise.
///
/// If the polygons intersect, then poly1 cannot contain poly2 (or vice-versa for that matter)
/// Since the poly intersection test can be somewhat expensive, we'll only run it if the user
/// requests it. If runIntersectionTest is false, then it is assumed that the user has already
/// verified that the polygons do not intersect. If the polygons DO intersect and runIntersectionTest
/// is false, then the return value is meaningless. Caveat emptor.
///
/// As an added bonus, just to cause more user-carnage, if runIntersectionTest is false, then the
/// boundRects are not used and can safely be passed in as nulls. However, if runIntersectionTest
/// is true and you pass nulls for boundRect1 or boundRect2, you will cause a program crash.
///
/// Finally, the polygon points are assumed to be passed in Clockwise winding order. It is possible
/// that CounterClockwise ordering would work, but I have not verified the behavior in that case.
///
/// </summary>
/// <param name="poly1">points of polygon1</param>
/// <param name="boundRect1">bounding rect of polygon1. Only used if runIntersectionTest is true</param>
/// <param name="poly2">points of polygon2</param>
/// <param name="boundRect2">bounding rect of polygon2. Only used if runIntersectionTest is true</param>
/// <param name="runIntersectionTest">see summary above</param>
/// <returns>true if poly1 fully contains poly2</returns>
public static bool PolygonContainsPolygon(IList<Point2D> poly1, Rect2D boundRect1,
IList<Point2D> poly2, Rect2D boundRect2,
bool runIntersectionTest)
{
// quick early-out tests
if (poly1 == null || poly1.Count < 3 || poly2 == null || poly2.Count < 3)
{
return false;
}
if (runIntersectionTest)
{
// make sure the polygons are not actually the same...
if (poly1.Count == poly2.Count)
{
// Check if the polys are similar to within a tolerance (Doesn't include reflections,
// but allows for the points to be numbered differently)
if (PolygonUtil.PolygonsAreSame2D(poly1, poly2))
{
return false;
}
}
bool bIntersect = PolygonUtil.PolygonsIntersect2D(poly1, boundRect1, poly2, boundRect2);
if (bIntersect)
{
return false;
}
}
// Since we (now) know that the polygons don't intersect and they are not the same, we can just do a
// single check to see if ANY point in poly2 is inside poly1. If so, then all points of poly2
// are inside poly1. If not, then ALL points of poly2 are outside poly1.
if (PolygonUtil.PointInPolygon2D(poly1, poly2[0]))
{
return true;
}
return false;
}
public bool Equals(Rect2D r, double epsilon)
{
if (!MathUtil.AreValuesEqual(MinX, r.MinX, epsilon))
{
return false;
}
if (!MathUtil.AreValuesEqual(MaxX, r.MaxX))
{
return false;
}
if (!MathUtil.AreValuesEqual(MinY, r.MinY, epsilon))
{
return false;
}
if (!MathUtil.AreValuesEqual(MaxY, r.MaxY, epsilon))
{
return false;
}
return true;
}
public static bool RectsIntersect(Rect2D r1, Rect2D r2)
{
return (r1.Right > r2.Left) &&
(r1.Left < r2.Right) &&
(r1.Bottom > r2.Top) &&
(r1.Top < r2.Bottom);
}