/// <summary>
/// Determines if polygon 1 and polygon 2 at position 1 and position 2, respectively, intersect along axis.
/// </summary>
/// <param name="poly1">polygon 1</param>
/// <param name="poly2">polygon 2</param>
/// <param name="pos1">Origin of polygon 1</param>
/// <param name="pos2">Origin of polygon 2</param>
/// <param name="rot1">Rotation of the first polygon</param>
/// <param name="rot2">Rotation of the second polygon</param>
/// <param name="strict">If overlapping is required for intersection</param>
/// <param name="axis">The axis to check</param>
/// <returns>If poly1 at pos1 intersects poly2 at pos2 along axis</returns>
public static bool IntersectsAlongAxis(Polygon2 poly1, Polygon2 poly2, Vector2 pos1, Vector2 pos2, Rotation2 rot1, Rotation2 rot2, bool strict, Vector2 axis)
{
var proj1 = ProjectAlongAxis(poly1, pos1, rot1, axis);
var proj2 = ProjectAlongAxis(poly2, pos2, rot2, axis);
return(AxisAlignedLine2.Intersects(proj1, proj2, strict));
}
/// <summary>
/// Determines the distance along axis, if any, that polygon 1 should be shifted by
/// to prevent intersection with polygon 2. Null if no intersection along axis.
/// </summary>
/// <param name="poly1">polygon 1</param>
/// <param name="poly2">polygon 2</param>
/// <param name="pos1">polygon 1 origin</param>
/// <param name="pos2">polygon 2 origin</param>
/// <param name="rot1">polygon 1 rotation</param>
/// <param name="rot2">polygon 2 rotation</param>
/// <param name="axis">Axis to check</param>
/// <returns>a number to shift pos1 along axis by to prevent poly1 at pos1 from intersecting poly2 at pos2, or null if no int. along axis</returns>
public static float?IntersectMTVAlongAxis(Polygon2 poly1, Polygon2 poly2, Vector2 pos1, Vector2 pos2, Rotation2 rot1, Rotation2 rot2, Vector2 axis)
{
var proj1 = ProjectAlongAxis(poly1, pos1, rot1, axis);
var proj2 = ProjectAlongAxis(poly2, pos2, rot2, axis);
return(AxisAlignedLine2.IntersectMTV(proj1, proj2));
}
/// <summary>
/// Determines if the circle at the specified position intersects the line,
/// which is at its true position and rotation, when the line is assumed to be horizontal.
/// </summary>
/// <param name="circle">The circle</param>
/// <param name="line">The line</param>
/// <param name="circleCenter">The center of the circle</param>
/// <param name="strict">If overlap is required for intersection</param>
/// <returns>If the circle with center circleCenter intersects the horizontal line</returns>
protected static bool CircleIntersectsHorizontalLine(Circle2 circle, Line2 line, Vector2 circleCenter, bool strict)
{
// This is exactly the same process as CircleIntersectsLine, except the projetions are easier
var lineY = line.Start.Y;
// Step 1 - Find closest distance
var vecCircleCenterToLine1D = lineY - circleCenter.Y;
var closestDistance = Math.Abs(vecCircleCenterToLine1D);
// Step 1a
if (strict)
{
if (closestDistance >= circle.Radius)
{
return(false);
}
}
else
{
if (closestDistance > circle.Radius)
{
return(false);
}
}
// Step 2 - Find closest point
var closestPointX = circleCenter.X;
// Step 3 - Is closest point on line
if (AxisAlignedLine2.Contains(line.Start.X, line.End.X, closestPointX, false, true))
{
return(true);
}
// Step 4 - Find edgeClosest
float edgeClosestX;
if (line.Start.X < line.End.X)
{
edgeClosestX = (closestPointX <= line.Start.X) ? line.Start.X : line.End.X;
}
else
{
edgeClosestX = (closestPointX >= line.Start.X) ? line.Start.X : line.End.X;
}
// Step 5 - Circle-point intersection on closest point
var distClosestEdgeToCircleSq = new Vector2(circleCenter.X - edgeClosestX, circleCenter.Y - lineY).LengthSquared();
if (strict)
{
return(distClosestEdgeToCircleSq < circle.Radius * circle.Radius);
}
else
{
return(distClosestEdgeToCircleSq <= circle.Radius * circle.Radius);
}
}
/// <summary>
/// Determines if the circle at the specified position intersects the line, which
/// is at its true position and rotation, when the line is assumed to be vertical
/// </summary>
/// <param name="circle">The circle</param>
/// <param name="line">The line</param>
/// <param name="circleCenter">The center of the circle</param>
/// <param name="strict">If overlap is required for intersection</param>
/// <returns>If the circle with center circleCenter intersects the line</returns>
protected static bool CircleIntersectsVerticalLine(Circle2 circle, Line2 line, Vector2 circleCenter, bool strict)
{
// Same process as horizontal, but axis flipped
var lineX = line.Start.X;
// Step 1 - Find closest distance
var vecCircleCenterToLine1D = lineX - circleCenter.X;
var closestDistance = Math.Abs(vecCircleCenterToLine1D);
// Step 1a
if (strict)
{
if (closestDistance >= circle.Radius)
{
return(false);
}
}
else
{
if (closestDistance > circle.Radius)
{
return(false);
}
}
// Step 2 - Find closest point
var closestPointY = circleCenter.Y;
// Step 3 - Is closest point on line
if (AxisAlignedLine2.Contains(line.Start.Y, line.End.Y, closestPointY, false, true))
{
return(true);
}
// Step 4 - Find edgeClosest
float edgeClosestY;
if (line.Start.Y < line.End.Y)
{
edgeClosestY = (closestPointY <= line.Start.Y) ? line.Start.Y : line.End.Y;
}
else
{
edgeClosestY = (closestPointY >= line.Start.Y) ? line.Start.Y : line.End.Y;
}
// Step 5 - Circle-point intersection on closest point
var distClosestEdgeToCircleSq = new Vector2(circleCenter.X - lineX, circleCenter.Y - edgeClosestY).LengthSquared();
if (strict)
{
return(distClosestEdgeToCircleSq < circle.Radius * circle.Radius);
}
else
{
return(distClosestEdgeToCircleSq <= circle.Radius * circle.Radius);
}
}
/// <summary>
/// Determines the best way for line1 to move to prevent intersection with line2
/// </summary>
/// <param name="line1">Line1</param>
/// <param name="line2">Line2</param>
/// <returns>MTV for line1</returns>
public static float?IntersectMTV(AxisAlignedLine2 line1, AxisAlignedLine2 line2)
{
if (line1.Axis != line2.Axis)
{
throw new ArgumentException($"Lines {line1} and {line2} are not aligned - you will need to convert to Line2 to check intersection.");
}
return(IntersectMTV(line1.Min, line1.Max, line2.Min, line2.Max, false));
}
/// <summary>
/// Determines if the two polygons intersect using the Separating Axis Theorem.
/// The performance of this function depends on the number of unique normals
/// between the two polygons.
/// </summary>
/// <param name="poly1">First polygon</param>
/// <param name="poly2">Second polygon</param>
/// <param name="pos1">Offset for the vertices of the first polygon</param>
/// <param name="pos2">Offset for the vertices of the second polygon</param>
/// <param name="rot1">Rotation of the first polygon</param>
/// <param name="rot2">Rotation of the second polygon</param>
/// <param name="strict">
/// True if the two polygons must overlap a non-zero area for intersection,
/// false if they must overlap on at least one point for intersection.
/// </param>
/// <returns>True if the polygons overlap, false if they do not</returns>
public static bool IntersectsSat(Polygon2 poly1, Polygon2 poly2, Vector2 pos1, Vector2 pos2, Rotation2 rot1, Rotation2 rot2, bool strict)
{
if (rot1 == Rotation2.Zero && rot2 == Rotation2.Zero)
{
// This was a serious performance bottleneck so we speed up the fast case
HashSet <Vector2> seen = new HashSet <Vector2>();
Vector2[] poly1Verts = poly1.Vertices;
Vector2[] poly2Verts = poly2.Vertices;
for (int i = 0, len = poly1.Normals.Count; i < len; i++)
{
var axis = poly1.Normals[i];
var proj1 = ProjectAlongAxis(axis, pos1, poly1Verts);
var proj2 = ProjectAlongAxis(axis, pos2, poly2Verts);
if (!AxisAlignedLine2.Intersects(proj1, proj2, strict))
{
return(false);
}
seen.Add(axis);
}
for (int i = 0, len = poly2.Normals.Count; i < len; i++)
{
var axis = poly2.Normals[i];
if (seen.Contains(axis))
{
continue;
}
var proj1 = ProjectAlongAxis(axis, pos1, poly1Verts);
var proj2 = ProjectAlongAxis(axis, pos2, poly2Verts);
if (!AxisAlignedLine2.Intersects(proj1, proj2, strict))
{
return(false);
}
}
return(true);
}
foreach (var norm in poly1.Normals.Select((v) => Tuple.Create(v, rot1)).Union(poly2.Normals.Select((v) => Tuple.Create(v, rot2))))
{
var axis = Math2.Rotate(norm.Item1, Vector2.Zero, norm.Item2);
if (!IntersectsAlongAxis(poly1, poly2, pos1, pos2, rot1, rot2, strict, axis))
{
return(false);
}
}
return(true);
}
/// <summary>
/// Determines if the given line contains the given point.
/// </summary>
/// <param name="line">The line to check</param>
/// <param name="pos">The offset for the line</param>
/// <param name="pt">The point to check</param>
/// <returns>True if pt is on the line, false otherwise</returns>
public static bool Contains(Line2 line, Vector2 pos, Vector2 pt)
{
// The horizontal/vertical checks are not required but are
// very fast to calculate and short-circuit the common case
// (false) very quickly
if (line.Horizontal)
{
return(Math2.Approximately(line.Start.Y + pos.Y, pt.Y) &&
AxisAlignedLine2.Contains(line.MinX, line.MaxX, pt.X - pos.X, false, false));
}
if (line.Vertical)
{
return(Math2.Approximately(line.Start.X + pos.X, pt.X) &&
AxisAlignedLine2.Contains(line.MinY, line.MaxY, pt.Y - pos.Y, false, false));
}
// Our line is not necessarily a linear space, but if we shift
// our line to the origin and adjust the point correspondingly
// then we have a linear space and the problem remains the same.
// Our line at the origin is just the infinite line with slope
// Axis. We can form an orthonormal basis of R2 as (Axis, Normal).
// Hence we can write pt = line_part * Axis + normal_part * Normal.
// where line_part and normal_part are floats. If the normal_part
// is 0, then pt = line_part * Axis, hence the point is on the
// infinite line.
// Since we are working with an orthonormal basis, we can find
// components with dot products.
// To check the finite line, we consider the start of the line
// the origin. Then the end of the line is line.Magnitude * line.Axis.
Vector2 lineStart = pos + line.Start;
float normalPart = Math2.Dot(pt - lineStart, line.Normal);
if (!Math2.Approximately(normalPart, 0))
{
return(false);
}
float axisPart = Math2.Dot(pt - lineStart, line.Axis);
return(axisPart > -Math2.DEFAULT_EPSILON &&
axisPart < line.Magnitude + Math2.DEFAULT_EPSILON);
}
/// <summary>
/// Calculates the shortest distance and direction to go from poly1 at pos1 to poly2 at pos2. Returns null
/// if the polygons intersect.
/// </summary>
/// <returns>The distance.</returns>
/// <param name="poly1">First polygon</param>
/// <param name="poly2">Second polygon</param>
/// <param name="pos1">Origin of first polygon</param>
/// <param name="pos2">Origin of second polygon</param>
/// <param name="rot1">Rotation of first polygon</param>
/// <param name="rot2">Rotation of second polygon</param>
public static Tuple <Vector2, float> MinDistance(Polygon2 poly1, Polygon2 poly2, Vector2 pos1, Vector2 pos2, Rotation2 rot1, Rotation2 rot2)
{
if (rot1.Theta != 0 || rot2.Theta != 0)
{
throw new NotSupportedException("Finding the minimum distance between polygons requires calculating the rotated polygons. This operation is expensive and should be cached. " +
"Create the rotated polygons with Polygon2#GetRotated and call this function with Rotation2.Zero for both rotations.");
}
var axises = poly1.Normals.Union(poly2.Normals).Union(GetExtraMinDistanceVecsPolyPoly(poly1, poly2, pos1, pos2));
Vector2?bestAxis = null; // note this is the one with the longest distance
float bestDist = 0;
foreach (var norm in axises)
{
var proj1 = ProjectAlongAxis(poly1, pos1, rot1, norm);
var proj2 = ProjectAlongAxis(poly2, pos2, rot2, norm);
var dist = AxisAlignedLine2.MinDistance(proj1, proj2);
if (dist.HasValue && (bestAxis == null || dist.Value > bestDist))
{
bestDist = dist.Value;
if (proj2.Min < proj1.Min && dist > 0)
{
bestAxis = -norm;
}
else
{
bestAxis = norm;
}
}
}
if (!bestAxis.HasValue || Math2.Approximately(bestDist, 0))
{
return(null); // they intersect
}
return(Tuple.Create(bestAxis.Value, bestDist));
}
/// <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>
/// Determines if the circle whose bounding boxs top left is at the first postion intersects the line
/// at the second position who is rotated the specified amount about the specified point.
/// </summary>
/// <param name="circle">The circle</param>
/// <param name="line">The line</param>
/// <param name="pos1">The top-left of the circles bounding box</param>
/// <param name="pos2">The origin of the line</param>
/// <param name="rot2">What rotation the line is under</param>
/// <param name="about2">What the line is rotated about</param>
/// <param name="strict">If overlap is required for intersection</param>
/// <returns>If the circle at pos1 intersects the line at pos2 rotated rot2 about about2</returns>
protected static bool CircleIntersectsLine(Circle2 circle, Line2 line, Vector2 pos1, Vector2 pos2, Rotation2 rot2, Vector2 about2, bool strict)
{
// Make more math friendly
var actualLine = new Line2(Math2.Rotate(line.Start, about2, rot2) + pos2, Math2.Rotate(line.End, about2, rot2) + pos2);
var circleCenter = new Vector2(pos1.X + circle.Radius, pos1.Y + circle.Radius);
// Check weird situations
if (actualLine.Horizontal)
{
return(CircleIntersectsHorizontalLine(circle, actualLine, circleCenter, strict));
}
if (actualLine.Vertical)
{
return(CircleIntersectsVerticalLine(circle, actualLine, circleCenter, strict));
}
// Goal:
// 1. Find closest distance, closestDistance, on the line to the circle (assuming the line was infinite)
// 1a Determine if closestPoint is intersects the circle according to strict
// - If it does not, we've shown there is no intersection.
// 2. Find closest point, closestPoint, on the line to the circle (assuming the line was infinite)
// 3. Determine if closestPoint is on the line (including edges)
// - If it is, we've shown there is intersection.
// 4. Determine which edge, edgeClosest, is closest to closestPoint
// 5. Determine if edgeClosest intersects the circle according to strict
// - If it does, we've shown there is intersection
// - If it does not, we've shown there is no intersection
// Step 1
// We're trying to find closestDistance
// Recall that the shortest line from a line to a point will be normal to the line
// Thus, the shortest distance from a line to a point can be found by projecting
// the line onto it's own normal vector and projecting the point onto the lines
// normal vector; the distance between those points is the shortest distance from
// the two points.
// The projection of a line onto its normal will be a single point, and will be same
// for any point on that line. So we pick a point that's convienent (the start or end).
var lineProjectedOntoItsNormal = Vector2.Dot(actualLine.Start, actualLine.Normal);
var centerOfCircleProjectedOntoNormalOfLine = Vector2.Dot(circleCenter, actualLine.Normal);
var closestDistance = Math.Abs(centerOfCircleProjectedOntoNormalOfLine - lineProjectedOntoItsNormal);
// Step 1a
if (strict)
{
if (closestDistance >= circle.Radius)
{
return(false);
}
}
else
{
if (closestDistance > circle.Radius)
{
return(false);
}
}
// Step 2
// We're trying to find closestPoint
// We can just walk the vector from the center to the closest point, which we know is on
// the normal axis and the distance closestDistance. However it's helpful to get the signed
// version End - Start to walk.
var signedDistanceCircleCenterToLine = lineProjectedOntoItsNormal - centerOfCircleProjectedOntoNormalOfLine;
var closestPoint = circleCenter - actualLine.Normal * signedDistanceCircleCenterToLine;
// Step 3
// Determine if closestPoint is on the line (including edges)
// We're going to accomplish this by projecting the line onto it's own axis and the closestPoint onto the lines
// axis. Then we have a 1D comparison.
var lineStartProjectedOntoLineAxis = Vector2.Dot(actualLine.Start, actualLine.Axis);
var lineEndProjectedOntoLineAxis = Vector2.Dot(actualLine.End, actualLine.Axis);
var closestPointProjectedOntoLineAxis = Vector2.Dot(closestPoint, actualLine.Axis);
if (AxisAlignedLine2.Contains(lineStartProjectedOntoLineAxis, lineEndProjectedOntoLineAxis, closestPointProjectedOntoLineAxis, false, true))
{
return(true);
}
// Step 4
// We're trying to find edgeClosest.
//
// We're going to reuse those projections from step 3.
//
// (for each "point" in the next paragraph I mean "point projected on the lines axis" but that's wordy)
//
// We know that the start is closest iff EITHER the start is less than the end and the
// closest point is less than the start, OR the start is greater than the end and
// closest point is greater than the end.
var closestEdge = Vector2.Zero;
if (lineStartProjectedOntoLineAxis < lineEndProjectedOntoLineAxis)
{
closestEdge = (closestPointProjectedOntoLineAxis <= lineStartProjectedOntoLineAxis) ? actualLine.Start : actualLine.End;
}
else
{
closestEdge = (closestPointProjectedOntoLineAxis >= lineEndProjectedOntoLineAxis) ? actualLine.Start : actualLine.End;
}
// Step 5
// Circle->Point intersection for closestEdge
var distToCircleFromClosestEdgeSq = (circleCenter - closestEdge).LengthSquared();
if (strict)
{
return(distToCircleFromClosestEdgeSq < (circle.Radius * circle.Radius));
}
else
{
return(distToCircleFromClosestEdgeSq <= (circle.Radius * circle.Radius));
}
// If you had trouble following, see the horizontal and vertical cases which are the same process but the projections
// are simpler
}
/// <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>
/// Determines if the specified line contains the specified point.
/// </summary>
/// <param name="line">The line</param>
/// <param name="point">The point</param>
/// <param name="strict">If the edges of the line are excluded</param>
/// <returns>if line contains point</returns>
public static bool Contains(AxisAlignedLine2 line, float point, bool strict)
{
return(Contains(line.Min, line.Max, point, strict, false));
}
/// <summary>
/// Determines the shortest distance for line1 to go to touch line2. Returns
/// null if line1 and line 2 intersect (not strictly)
/// </summary>
/// <returns>The distance.</returns>
/// <param name="line1">Line1.</param>
/// <param name="line2">Line2.</param>
public static float?MinDistance(AxisAlignedLine2 line1, AxisAlignedLine2 line2)
{
return(MinDistance(line1.Min, line1.Max, line2.Min, line2.Max, false));
}
/// <summary>
/// Detrmines the shortest distance from the line to get to point. Returns
/// null if the point is on the line (not strict). Always returns a positive value.
/// </summary>
/// <returns>The distance.</returns>
/// <param name="line">Line.</param>
/// <param name="point">Point.</param>
public static float?MinDistance(AxisAlignedLine2 line, float point)
{
return(MinDistance(line.Min, line.Max, point, false));
}
/// <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 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));
}
/// <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));
}